Annals of Mathematics and Physics
https://www.mathematicsgroup.us/journals/annals-of-mathematics-and-physics
A Peertechz Open Access Journalen-usWhat is Light, Really? A Quantum Dialectical View19 Oct, 2024
https://www.mathematicsgroup.us/articles/AMP-7-235.php
Radiant energy in the form of visible light has been and still remains the most mysterious and venerated object in human history. Gradual understanding of the nature of light now in its very wide range of energy, both above and below the visible range; has led to the proliferation of technologies, especially after the recognition of its quantum nature. Although impressive knowledge about the nature of light, its properties, its source, and its interaction with other existing matter, etc., have been gained and profitably utilized in technologies; its fundamental unit as a discrete point particle or an extended continuous wavelet, as well as its mass, still remains a subject of intense debate among the physicists.
Understanding the enigmatic properties and the nature of light as difficult as it proved to be; understanding the velocity of its propagation proved to be the most misunderstood aspect of light. As has been shown through some recent publications by this author, the false axiomatic notion of Albert Einstein at the turn of the 20th century, about the universal and absolute constancy (in vacuum) of the velocity c of light; caused the century-long confusion, paradoxes, myths and ironically, the darkest period of modern physics and cosmology! Another wrong centuries-old axiomatic notion of Isaac Newton about the one-sided universal gravitational attraction of matter, acted in a synergistic way with Einstein’s false axiomatic notion about light; to create the modern and sophisticated ruling mythology of the “Big Bang” creation of the universe, undermining scientific progress both in theoretical physics and in cosmology, since Copernicus and Johannes Kepler.
It can now be demonstrated that this new mythology has absolutely no basis in objective reality and is the product of brain-cooked and abstract mathematical fabrications based on an axiomatic truth and apparently willful deceptions by official science. A quantum dialectical approach reveals that light is composed of point particles (photons) with a wide range of energy, velocity, and mass; over the whole electromagnetic spectrum, from the microwave to the highest energy gamma-ray photons. The only difference from other matter particles is that photons exist only in their free elementary state and are created instantly (until absorbed) from their virtual existence in matter atoms or in the quantum vacuum; in this infinite, eternal, and ever-changing universe; thereby resolving all mysteries about light. Simpson Type Estimations for Convex Functions via Quantum Calculus15 Oct, 2024
https://www.mathematicsgroup.us/articles/AMP-7-234.php
We first establish a new identity including quantum integrals and quantum numbers via q -differentiable functions. After that, with the help of this equality, a Simpson-type inequality for functions whose quantum derivatives in modulus are convex is derived, and some new inequalities for powers of quantum derivatives in absolute value are provided. It is also discussed how results come out in the case when q approaches 1.
Mathematics Subject Classification: 26D15, 26D10, 26A51, 34A08.Dynamics of Destruction of Two-dimensional Analog Models Discrete Environments with Different Organization of their Structural Compositions01 Oct, 2024
https://www.mathematicsgroup.us/articles/AMP-7-233.php
Based on the main phenomenological features of the Coulomb-Navier rheological body, several most characteristic simulated models of discrete environments with different structural compositions have been proposed. Mechanical testing of the specified simulator models allows for investigating the dynamics of deformation (restructuring of composition) of discrete (including loose) environments with varying organization (within a wide range) of their structural compositions. The main thermodynamic peculiarities of the deformation and destruction processes of discrete environment structures under different variations of external loading application schemes have been identified.Rayleigh Quotient and Surjectivity of Nonlinear Operators in Hilbert space28 Sep, 2024
https://www.mathematicsgroup.us/articles/AMP-7-232.php
We consider continuous operators acting in a real Hilbert space and indicate conditions ensuring their continuous invertibility and/or surjectivity. In the case of bounded linear operators, these facts are well-known from basic Functional Analysis. The objective of this work is to indicate how similar properties can be proved also when the operators are not necessarily linear, using as a main tool their Rayleigh quotient and especially its lower and upper bound. In particular, we focus our attention on gradient operators and show a quantitative criterion that ensures their surjectivity through the positivity of an additional constant related to the measure of noncompactness. Stepwise Alternating Direction Implicit Method of the Three Dimensional Convective-Diffusion Equation19 Sep, 2024
https://www.mathematicsgroup.us/articles/AMP-7-231.php
A stepwise alternating direction implicit method of the three dimensional convective-diffusion equation is considered in this paper. We constructed an implicit difference scheme and analyzes it's truncation error, convergence and stabilities. The theoretical and numerical analysis shows that the implicit difference scheme is unconditional stable. Then the Greedy Algorithm is proposed to solve the numerical solution on x,y and z axis separately by using implicit difference scheme and the numerical solution is convergent theoretically, however with no physical meaning.
The Stepwise Alternating Direction Implicit Method (SADIM) is proposed, which uses the implicit difference scheme in this paper. Using Sauls scheme to pretreat the initial-boundary condition before iterating, thus eliminate the numerical oscillation caused by discontinuous initial boundary conditions. This SADIM is at least six ordered convergent, and is one of high ordered numerical methods for three dimensional problem. Our implicit difference scheme is more ideal than the standard Galerkin centered on finite difference scheme, quicker than SOR iteration method. The convergence of our implicit scheme is better than finite element method, characteristic line method, and mesh-less method. Our method eliminates the numerical oscillation caused by the convection dominant, resists the dispersion effectively and addresses dissipation caused by diffusion dominant.The implicit difference scheme has good theoretical and practical value. Algebraic Cubic Equation <em>vs</em>. Freedman Equations for the Geometry of our Universe10 Sep, 2024
https://www.mathematicsgroup.us/articles/AMP-7-230.php
In 1921 the famous Russian mathematician Alexander Freedman proved by analyzing Einstein’s general relativity that the geometry of our Universe has three possibilities namely Euclidean, Hyperbolic, and Spherical. Various cosmological experimental and observational probes of BOOMERanG, NASA’s WMAP, and ESA’s PLANCK mission revealed that the shape of our universe is flat. But to this day, there is no mathematical formulation for the geometry of our universe. In this short work, the author attempts to show that the geometry of our universe is Euclidean.The Riemann's Hypothesis, the Prime Numbers Theorem (PNT), and the Error31 Aug, 2024
https://www.mathematicsgroup.us/articles/AMP-7-229.php
In this simple paper, a small refinement to the Prime Number Theorem (PNT) is proposed, which allows us to limit the error with which said theorem predicts the value of the Prime-counting function π(x); and, in this way, endorse the veracity of the Riemann Hypothesis.
Many people know that the Riemann Hypothesis is a difficult mathematical problem - even to understand - without a certain background in mathematics. Many techniques have been used, for more than 150 years, to try to solve it. Among them is the one that establishes that, if the Riemann hypothesis is true, then the error term that appears in the prime number theorem can be bounded in the best possible way. Specifically, Helge von Koch demonstrated in 1901 that it should be:Kinetic Modeling of Mass Loss during Carbonization of Sodium Carboxymethyl Cellulose (CMC) Aerogels17 Aug, 2024
https://www.mathematicsgroup.us/articles/AMP-7-228.php
The carbonization of sodium carboxymethyl cellulose (CMC) aerogels involves complex thermal decomposition processes leading to the formation of carbonaceous residues. Understanding the kinetics of mass loss during carbonization is vital for optimizing the production of CMC carbon aerogels with desired properties. In this study, a mathematical model is presented that describes the kinetics of mass loss during the carbonization process of CMC aerogels. This model considers the temperature and concentration dependence of CMC decomposition reactions and is validated against experimental data obtained at various conditions. The proposed kinetic model elucidates the underlying mechanisms governing mass loss during carbonization, offering valuable insights for the design and optimization of CMC carbon aerogels across diverse applications. Furthermore, the analysis of the experimental data reveals variations in both the reaction order and the rate constant for different concentrations of CMC aerogels, indicating distinct kinetic behavior. These findings contribute to a deeper understanding of the carbonization process and pave the way for tailored synthesis approaches to meet specific application requirements.Beam Dynamic Equations for Predictive Modeling of Semicircular Canal Pathologies13 Aug, 2024
https://www.mathematicsgroup.us/articles/AMP-7-227.php
This short paper presents a general strategy devoted to an original analytical approach of looped 1.5D equations. It considers particular properties of rod/beam equations for wave and structural modal representation. Specific boundary conditions introduce local singularities representing discontinuities and inversions. The process presented in the paper links this kind of original analysis with possible models of the physiological and pathological dynamic behavior of solid-fluid interaction in inner-ear elements such as the anterior and superior semicircular canals. Thus, these models propose a robust representation of these elements, offering observation/control perspectives for diagnostics and cure.New Quantum Estimates for Midpoint and Trapezoid Type Inequalities Through (α,m)-Convex Functions with Applications06 Aug, 2024
https://www.mathematicsgroup.us/articles/AMP-7-226.php
The main goal of current investigation is to present two new q-integral identities for midpoint and trapezoid type inequalities. Then using these identities, we develop several new quantum estimates for midpoint and trapezoid type inequalities via (α, m)-convexity. Some special cases of these new inequalities can be turned into quantum midpoint and quantum trapezoid type inequalities for convex functions, classical midpoint and trapezoid type inequalities for convex functions without having to prove each one separately. Finally, we discuss how the special means can be used to address newly discovered inequalities.
2010 Mathematics Subject Classification. 26D10, 26D15, 26B25.The Nature of the Physics of Matter with Negative Mass16 Jul, 2024
https://www.mathematicsgroup.us/articles/AMP-7-225.php
The formation of a substance with negative mass (negamatter) at very high temperatures or body speeds above 235696.8871 km/s is theoretically justified. The reason for this is the reversal of the direction of time inside the substance. The law of dependence of body weight on the rate of time passing in the physical body has been derived. Based on the weakness of gravitational forces, the stability of negamatter is justified, under appropriate conditions.Optimizing Dijkstra's Algorithm for Managing Urban Traffic Using Simulation of Urban Mobility (Sumo) Software16 Jul, 2024
https://www.mathematicsgroup.us/articles/AMP-7-224.php
Among the challenges of urbanization is traffic management as a measure of growth and progress. Recent population growth has resulted in a significant increase in vehicles, causing traffic jams that are challenging for the existing transportation networks. This congestion affects other services, including public transit, airports, road maintenance, and pollution caused by emissions of CO2 and other gases. Furthermore, it doubles the amount of fuel used. This has negative consequences for society as well as economic losses. This paper focuses on an improved Dijkstra algorithm based on traffic congestion levels to address the above problems. Improved Dijkstra algorithm can provide (a) real data collected from the map via OpenStreetMap, (b) Add four features to SUMO(Simulation of Urban Mobility) simulator software (time period, rush-hour, number of vehicles, and routing algorithm), (c) it could know congestion level for roads (d) rerouting vehicles to avoid traffic congestion. Based on the simulation results and analysis presented in the paper, it was found that the proposed improved Dijkstra algorithm increased the performance of the road traffic flow by reducing the number of related vehicles in traffic congestion and average delay time for experiment scenarios.Refinement of Jensen Mercer and Hermite–Hadamard-Mercer type inequalities for generalized convex functions on co-ordinates with their computational analysis28 Jun, 2024
https://www.mathematicsgroup.us/articles/AMP-7-223.php
In the current study, the Jensen-Mercer inequality is extended to co-ordinated h-convex functions. Additionally, a novel inequality is employed to derive Hermite–Hadamard-Mercer type inequalities for h-convex functions defined on the co-ordinates of a rectangle in the plane. These developments not only reinforce the core tenets of convex analysis but also expand the applicability of Hermite-Hadamard-Mercer type inequalities to generalized convex functions on co-ordinates. This provides valuable tools for data analysis and optimization problem-solving. The practical utility and efficacy of this generalized inequality in real-world scenarios involving co-ordinates are demonstrated through a computational study.
Mathematics Subject Classification: 26D10, 26D15, 26A51, 34A08.The dark side of screens: Exploring impairment with the iRAT framework26 Jun, 2024
https://www.mathematicsgroup.us/articles/AMP-7-222.php
This paper introduces the iRAT model, an extension of the existing RAT framework, to comprehensively evaluate the integration of digital media in educational settings. While the traditional RAT framework focuses on Replacement, Amplification, and Transformation, the iRAT model includes a fourth category: Impairment. This new category addresses the potential negative impacts of digital media use, such as unnecessary app usage, distractions from learning objectives, lack of pedagogical integration, and resource wastage. The study employs a mixed-methods approach, including participatory observation, lesson plan evaluation, expert think-aloud protocols, and AI-driven scenario identification, to validate the iRAT model. Findings highlight the importance of considering both positive and negative aspects of digital media integration, suggesting that future research should adopt the iRAT framework for a balanced evaluation. This study closes a significant research gap and challenges the overly optimistic view of digital media in education, advocating for a more critical perspective.Pseudo-algebraically commutative fields of quasi-fourier–smale curves and hyperbolic topological spaces25 Jun, 2024
https://www.mathematicsgroup.us/articles/AMP-7-221.php
Let us suppose we are given a category Σ. Is it possible to construct commutative vectors? We show that I < ∞. It is essential to consider that C may be geometric. A useful survey of the subject can be found in [1]. Mathematical analysis of a predator-prey system with shared resource, climatic effects, and neural network insight11 Jun, 2024
https://www.mathematicsgroup.us/articles/AMP-7-220.php
This research paper introduces a predator-prey system in which both organisms depend on a common sustenance source. In order to establish environmental dynamics that are more plausible, we integrated climatic effects on the predator population by implementing a sigmoidal function. The objective is to study the impact of climate on the population dynamics of interacting species by employing mathematical tools like stability analysis and Artificial Neural Networks. By employing meticulous mathematical analysis, we were able to ascertain the equilibrium points of the system and examine their stability on a global scale. Our investigation covered both diffusive and non-diffusive models, providing insight into the unique dynamical characteristics of each. Moreover, in order to leverage the capabilities of modern computational methods, a neural network strategy was implemented to analyses the system's complexities in greater detail. In conclusion, exhaustive diagrams were used to meticulously illustrate the effect of varying parameters, thereby providing invaluable insights into the behavior of the system under various conditions.New prime number theory11 Jun, 2024
https://www.mathematicsgroup.us/articles/AMP-7-219.php
This paper introduces a novel approach to estimating the sum of prime numbers by leveraging insights from partition theory, prime number gaps, and the angles of triangles. The methodology is applied to infinite sums and the nth sum, and several ways of defining the nth sum of a prime number are proposed. By using the Ramanujan infinite series of natural numbers, it is possible to derive an infinite series of prime numbers.Understanding Lorentz Utilizing Galilei: The Emergence of a Friendly Extended Special Relativity Theory that Admits Relativistic Multi-Particle Entanglement03 Jun, 2024
https://www.mathematicsgroup.us/articles/AMP-7-218.php
Special relativity theory stems from the Lorentz transformation of signature (1,3). The incorporation into special relativity of the Lorentz transformations of signature (m,n) for all m,n∈ℕ (n = 3 in physical applications) enriches the theory. The resulting enriched special relativity is a friendly extended special relativity that admits multi-particle entanglement, as demanded by relativistic quantum mechanics. The Lorentz transformation of signature (m,n) admits a novel physical interpretation induced by the intuitively clear interpretation of the Galilei transformation of signature (m,n) for all m,n > 1. In this sense we understand Lorentz utilizing Galilei in m temporal and n spatial dimensions, resulting in the emergence of multi-particle entanglement that the enriched special theory of relativity admits. Remarkably, it turns out that, for any m,n∈ℕ, the group of Lorentz transformations of signature (m,n) is the symmetry group that underlies any multi-particle system that consists of m n - dimensional entangled particles.Comment: Paper on the progress of pure mathematics "proof of 3x + 1 conjecture"21 May, 2024
https://www.mathematicsgroup.us/articles/AMP-7-217.php
The unresolved problem in number theory: the 3x+1 problem, deeply loved by math enthusiasts. I saw a paper titled "Proof of 3x+1 Conjecture" in the Journal of Pure Mathematical Progress (ISSN Print: 2160-0368), and its proof was incorrect.Vibration eigenfrequencies of an elastic sphere with large radius07 May, 2024
https://www.mathematicsgroup.us/articles/AMP-7-216.php
An estimation is given for the free vibration eigenfrequencies (normal modes) of a homogeneous solid sphere with a large radius, with application to Earth's free vibrations. The free vibration eigenfrequencies of a fluid sphere are also derived as a particular case. Various corrections arising from static and dynamic gravitation, rotation, and inhomegeneities are estimated, and a tentative notion of an earthquake temperature is introduced.High temperature negative mass plasma29 Apr, 2024
https://www.mathematicsgroup.us/articles/AMP-7-215.php
A review of studies of matter with negative mass - negamatter, consisting of negaparticles - is given. Based on the assumption that Newton's laws are valid for negaparticles, their behavior in relation to other particles is described. It has been discovered that high-temperature plasma is a negasubstance, but only such a plasma whose temperature is above a certain critical temperature, depending on the chemical composition of the original substance, can be calculated using the appropriate formula. In addition, if anybody is in a state of motion with a speed above 235696.8871 km/s, then its substance undergoes a phase transition and becomes negamatter.On Λ-Fractional fluid mechanics26 Apr, 2024
https://www.mathematicsgroup.us/articles/AMP-7-214.php
Λ-fractional analysis has already been presented as the only fractional analysis conforming with the Differential Topology prerequisites. That is, the Leibniz rule and chain rule do not apply to other fractional derivatives; This, according to Differential Topology, makes the definition of a differential impossible for these derivatives. Therefore, this leaves Λ-fractional analysis the only analysis generating differential geometry necessary to establish the governing laws in physics and mechanics. Hence, it is most necessary to use Λ-fractional derivative and Λ-fractional transformation to describe fractional mathematical models. Other fractional “derivatives” are not proper derivatives, according to Differential Topology; they are just operators. This fact makes their application to mathematical problems questionable while Λ-derivative faces no such problems. Basic Fluid Mechanics equations are studied and revised under the prism of Λ-Fractional Continuum Mechanics (Λ-FCM). Extending the already presented principles of Continuum Mechanics in the area of solids into the area of fluids, the basic Λ-fractional fluid equations concerning the Navier-Stokes, Euler, and Bernoulli flows are derived, and the Λ-fractional Darcy’s flow in porous media is studied. Since global minimization of the various fields is accepted only in the Λ-fractional analysis, shocks in the Λ-fractional motion of fluids are exhibited. Mathematical modeling of velocity field induced by the vortex16 Apr, 2024
https://www.peertechzpublications.org/articles/AMP-7-213.pdf
In new technological applications, it is important to use vortex distributions in the area for obtaining large velocity fields. This paper, it was calculated the distribution of the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of the finite number of vortex threads: 1) circular vortex lines in a finite cylinder, positioned on its inner, 2) spiral vortex threads, positioned on the inner surface of the finite cylinder or cone, and 3) linear vortex lines in the plane channel, positioned on its boundary.
An original method was used to calculate the components of the velocity vectors. Such kind of procedure allows calculating the velocity fields inside the domain depending on the arrangement, the intensity, and the radii of vortex lines. In this paper, we have developed a mathematical model for the process in the element of Hurricane Energy Transformer. This element is a central figure in the so-called RKA (ReaktionsKraftAnlage) used on the cars’ roofs.Coefficient estimates for a subclass of bi-univalent functions associated with the Salagean differential operator05 Apr, 2024
https://www.mathematicsgroup.us/articles/AMP-7-212.php
In this paper, we present and examine a novel subset of the function class ∑, which consists of analytic and bi-univalent functions defined in the open unit disk U and connected to the Salagean differential operator. Additionally, we determine estimates for the Taylor-Maclaurin coefficients |a2| and |a3| functions within this new subclass and enhance some recent findings.
2010 Mathematics Subject Classification. 30C45; 30C50.Abundant dynamical solitary waves solutions of M -fractional Oskolkov model02 Apr, 2024
https://www.mathematicsgroup.us/articles/AMP-7-211.php
This work uses a truncated M-fractional derivative variant of the Oskolkov model to investigate the dynamic behavior of solitary wavefronts. The methods used in this framework produce a variety of solitary waveforms, such as bright and dark solitons. A suitable choice of the free parameters is used to investigate the geometrical structures for the wave solutions, which are further characterized by stable bright periodic and soliton waves. The coefficient of the highest-order derivative and the effects of fractionality are shown in the figures. Moreover, the graphics are arranged to highlight the characteristics of novel soliton wave propagation. The findings of this research demonstrate that the fractional Oskolkov model may accommodate fundamental and higher-order soliton behaviors, each of which has unique characteristics. The fractional form of the several dynamical solitary waves seen in the study represents their practical ramifications. These waves can be seen as transmission waves via a Kelvin-Voigt fluid. Analyzing twin primes, Goldbach's strong conjecture and Polignac's conjecture21 Mar, 2024
https://www.mathematicsgroup.us/articles/AMP-7-210.php
Here we analyze three well-known conjectures: (i) the existence of infinitely many twin primes, (ii) Goldbach's strong conjecture, and (iii) Polignac's conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of Goldbach's strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac's conjecture. Our first step is an analysis of the existence of infinitely many twin prime numbers. For this, using the formula 4((n−1)!+1) ≡−n (mod n(n + 2)) – satisfied if and only if (n, n + 2) are twin primes –, together with Wilson's theorem, we obtain conditions that must be met for two numbers to be twin primes. Our results, obtained from an analytic and functional study, lead us to conclude that there may exist infinitely many twin primes. Next, we consider the validity of Goldbach's strong conjecture. After showing that the conjecture is true for the first even numbers, we notice a pattern that we analyze for any even number, reducing it to three cases: (i) when the even number 2n is two times a prime number n; (ii) when the even number 2n is such that n=2m, with 2m-1 and 2m+1 twin primes; (iii) all other cases, i.e., for any 2n even number ∀n∈N with n > 1, n prime or not, with independence of n=2m being 2m-1 and 2m+1 twin primes or not. In this last case, we show that one can always find a certain r∈N such that 1 < r < n satisfying that n − r and n + r are primes, so that their sum is 2n. In this case, we use the reduction to absurd method, and our results lead us to conclude that Goldbach's strong conjecture is true to the best of our calculations, and Polignac's conjecture as well. Study of vibration shock processes of non-linear mechanical systems with distributed parameters12 Mar, 2024
https://www.mathematicsgroup.us/articles/AMP-7-209.php
In practice, under the conditions of perfection and constructive development of modern equipment and machines, nonlinear mechanical systems with distributed parameters are often encountered, which, depending on the principles of operation, are affected by vibration shock. Therefore, the study of vibration shock processes of the mentioned systems has great theoretical and practical importance and as a result to determine the optimal parameters of vibration protection devices to ensure their safe operation. In our case, the displacement field of two interacting non-linear mechanical systems with distributed parameters is considered, when their interaction is of vibration shock nature. Obviously, the mentioned events are more pronounced when the self-oscillation frequency of one or both systems momentarily approaches the frequency of forced vibration shock processes. In addition, critical moments are fixed during the phase shifts of forced oscillations of oscillatory systems, in this case, the frequencies of forced oscillations approach mutually opposing phase moments. By choosing the optimal parameters of hysteresis losses, it is possible to almost exclude sub-harmonic modes superimposed on the main resonance modes in vibration shock processes.
During hysteresis losses of the parabolic type, the value of µ changes automatically in connection with impulsive loads, which will allow us to transfer the vibration shock processes to automatic modes and, accordingly, the practically safe operation of the mentioned systems.Generation of a substance with negative mass12 Mar, 2024
https://www.mathematicsgroup.us/articles/AMP-7-208.php
An analysis of known experiments was carried out to determine the dependence of the mass of electrons on their speed. Errors were discovered in determining the sign of the electron mass. It is shown that at electron velocities above the critical ω = 235696.8871 km/s their masses are negative. The results obtained are explained on the basis of the Principle of Nonequivalence of inertial and gravitational masses since inertial mass can only be positive, and gravitational mass can only be positive or negative The purpose of this work is to show that since radioactive substances can emit electrons with negative mass at velocities above ω, they can be a source of their production.A note on Cardano’s formula29 Feb, 2024
https://www.mathematicsgroup.us/articles/AMP-7-207.php
In this paper, we show that Cardano’s formula for the solution of cubic equations can be reduced to expressions involving only square roots of rational numbers if the real root itself is rational.
MSC: 01A40Mathematical analysis of the new α - difference operator with an application to prey-predator model with harvesting. Quadratic invariant20 Feb, 2024
https://www.mathematicsgroup.us/articles/AMP-7-206.php
In this research paper, we introduce a novel mathematical operator known as the alpha-difference operator (α-DO) and its corresponding integral. We establish the foundational theorems related to this operator and demonstrate its applications in both linear and nonlinear dynamical equations. A key focus of our study is the application of α-DO in the context of the prey-predator model with harvesting. In the linear scenario, we derive exact solutions for the model. For the nonlinear case, we develop an iterative scheme to obtain approximate solutions. We also prove a theorem that guarantees the convergence of this scheme. We conduct a thorough investigation of the dynamical behavior of the system as the parameter varies. This is visualized through graphical representations. Our findings reveal that the system exhibits local memory, which significantly influences the evolution of the system. We observe that the α-DO is particularly effective in describing dynamical systems that undergo a change in behavior at a specific characteristic time. This is especially relevant to the system under consideration. A prime example of such a system is the Exposed-Infected-Recovery System (EIRS). Lastly, we construct the Hamiltonian function using a quadratic invariant. This provides further insights into the energy conservation and stability properties of the system. Our research opens up new insight for the application of the α-DO in various fields of science and engineering.Energy metrics and their Ricci flows06 Feb, 2024
https://www.mathematicsgroup.us/articles/AMP-7-205.pdf
The framework of the Deformed Space-Time theory has been extended in the past from four to five dimensions, where the fifth coordinate is the energy exchanged by the interaction. In this theory, each fundamental interaction is described by an energy-dependent metric.
This picture has been exploited in order to take care of the interaction behaviour both when Lorentz invariance holds and the spacetime is Minkowskian and when Lorentz is violated and must be recovered in a non-minkowskian spacetime.
It has been successfully attempted to complete the pentadimensional metric of the four fundamental interactions calculating the fifth element of the metric corresponding to the fifth coordinate energy.
The mathematical tool exploited is the method of the Ricci flow which gave the complete explicit form of the fifth element of the metric, answering in this way the question of "how the energy measure the energy" for each interaction, setting the electromagnetic interaction as the reference for the energy measure. In this sense it has been given meaning to the problem of the energy gauge for interaction, identifying the gauge with the fifth metric element.
The consequences of the nuclear metamorphosis have been also examined for reaching the technological goal of a device stably producing this metamorphosis under the hadronic metric. The most valuable consequence is that in this pentadimensional picture, the old Einsteinian dream of a complete geometrization of the interactions is reached.
The results achieved in the present work have allowed to design, build, and test of devices capable of exploiting the behavior of the fifth element of the metrics to obtain the production of electric charges directly from the nuclear metamorphosis of the matter.Lorentz Transformation and time dilatation10 Jan, 2024
https://www.mathematicsgroup.us/articles/AMP-7-204.php
We consider two inertial frames S and and suppose that frame moves, for simplicity, in a single direction: the X -direction of frame S with a constant velocity v as measured in frame S.
Using homogeneity of space and time we derive a modified Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT.
Roughly speaking we suppose: (H) Any clock which is at rest in its frame measures a small increment of time by some factor s=s(v). As a corollary of relativity theory (H) holds with Lorentz factor 1/γ. For s=1 we get the Galilean transformation of Newtonian physics, which assumes an absolute space and time. We also consider the relation between absolute space and Special Relativity Theory, thereafter STR.
It seems here that we need a physical explanation for (H).
We introduce Postulate 3. The two-way speed of light in and -directions are c and outline derivation of (LT) in this setting. Note that Postulate 3 is a weaker assumption than Einstein's second postulate. A new reduced quantile function for generating families of distributions09 Jan, 2024
https://www.mathematicsgroup.us/articles/AMP-7-203.php
In this paper, a variant of the T-X(Y) generator was developed by suppressing the scale parameter of the classical Lomax distribution in the quantile function. Uniquely, the reduction of the number of parameters essentially accounts for the parsimony of the attendant model. The study considered the Exponential distribution as the transformer and consequently obtained the New Reduced Quantile Exponential-G (NRQE-G) family. The Type-II Gumbel distribution was deployed as the baseline to obtain a special sub-model known as the New Reduced Quantile Exponential Type-II Gumbel (NRQE-T2G) model. Some functional properties of the distribution namely, moment and its related measures such as the mean, variance, second, third, and fourth moments were obtained. The Mode, skewness, Kurtosis, index of dispersion, coefficient of variation, order statistics, survival, hazard, and quantile function were also derived. The maximum likelihood estimation method was used to estimate its parameters. The model's credibility, applicability, and flexibility were proven using two real-life datasets. Coincidence and common fixed points for F-Contractive mappings28 Dec, 2023
http://www.mathematicsgroup.us/articles/AMP-6-202.pdf
The purpose of this article is to establish the existence and uniqueness of coincidence and common fixed point of discontinuous non-compatible faintly compatible pair of self maps in non-complete metric space without using containment requirement of range space of involved maps satisfying Ciric type F-contraction and Hardy-Roger type F-contraction. Some illustrative examples associated with pictographic validations are provided to demonstrate the main results and to show the genuineness of our results. We consider the application of our results to the study of a two-point boundary value problem related to second order differential equation, solve the two-point boundary value problem of the second-order differential equation arising in electric circuit equation, and also apply our results to Volterra type integral equation using Ciric type F-contraction as well as Hardy Roger type F-contraction.
Mathematics subject classification: 47H10; 54H25; 54E50Numerical simulations in a generalized Liénard's type system26 Dec, 2023
https://www.mathematicsgroup.us/articles/AMP-6-201.php
In this note we present some numerical simulations of the asymptotic behavior of a Generalized Liénard Equation, taking into account a recently defined differential operator. We must point out that these numerical variations have not been obtained as usual: by varying the functions of the right member of the system considered, but, on the contrary, by varying the kernels and the order of the generalized operator used. The above provides breadth and generality to the results obtained, which complement some known in the literature. Successive differentiation of some mathematical functions using hypergeometric mechanism08 Dec, 2023
https://www.mathematicsgroup.us/articles/AMP-6-200.php
In this article, we obtain successive differentiation of some composite mathematical functions:Calculation of the influence of the entropy of stars on the Earth's exosphere and the theory of entropic gravity05 Dec, 2023
https://www.mathematicsgroup.us/articles/AMP-6-199.php
In the first part of this study, the entropic contribution of star objects, observable during the night between November 13 and 14, 2021, in the sky above Belgrade (Lat. 44o 49' 04'' N, Long. 20o 27' 25'' E, mean Elev. 117 m), Serbia, to the thermodynamic equilibrium of the Earth's exosphere, was determined. In the second part of the study, the force of gravitational attraction between the considered star objects and the Earth was calculated, by applying entropic gravity theory. The obtained results shed new light on the importance of star objects for sustaining the Earth's thermodynamic system.Study of the effect of multiple phase transformations and relaxation annealing on the microstructure of a martensitic TiNi alloy in different structural states09 Nov, 2023
https://www.mathematicsgroup.us/articles/AMP-6-198.php
The work was devoted to studying the effect of multiple phase transformations in the temperature range of phase transformations of a TiNi alloy with a martensitic structure in various initial states - coarse-grained, ultrafine-grained, nanostructured. The conducted studies have shown that in the process of thermal cycling, the accumulation of defects in the crystalline structure occurs - dislocations, which contribute to a decrease in the size of structural elements. Subsequent relaxation annealing, slightly reducing the dislocation density, made it possible to obtain a stable and more equilibrium microstructure, including the nanostructural state.All physical information is discretely connected from the beginning and all geometrical appearance is a delayed statistical consequence09 Nov, 2023
https://www.mathematicsgroup.us/articles/AMP-6-197.php
Information is physically measurable as a selection from a set of possibilities, the domain of information. This defines the term "information". The domain of the information must be known together reproducibly beforehand. As a practical consequence, digital information exchange can be made globally efficient, interoperable, and searchable to a large extent by online definition of application-optimized domains of information. There are even more far-reaching consequences for physics. The purpose of this article is to present prerequisites and possibilities for a physical approach that is consistent with the precise definition of information. This concerns not only the discretization of the sets of possible experimental results but also the order of their definition over time. The access to or comparison with the domain of information is more frequent, the earlier it was defined. The geometrical appearance of our space is apparently a delayed statistical consequence of a very frequent connection with the common primary domain of information. Revisiting the holstein-primakov transformations31 Oct, 2023
https://www.mathematicsgroup.us/articles/AMP-6-196.php
It is shown that in addition to the Holstein-Primakov transformations in the theory of magnetism, a number of other transformations can be proposed which also lead to very interesting and consistent results. In particular, with the help of the transformation proposed in the paper for spin operators, it turns out to be possible to strictly analytically calculate the temperature dependence of the ferromagnet magnetization in a wide temperature range from zero and up to the Curie temperature. It is shown that for these transformations in the Curie temperature area, the magnetization tends to zero exponentially.
Thus, the aim of this study is to describe magnetization over a wide range of temperatures using a new transformation for electron spin operators. Sequential method conformal mappings04 Oct, 2023
https://www.mathematicsgroup.us/articles/AMP-6-195.php
The well-known, very important Schwarz–Christoffel integral does not yet completely solve the problem of mapping a half-plane onto a predetermined polygon. This integral includes parameters (inverse images of the polygon), the relationship of which with the lengths of the edges of the polygon is not known in advance. The main difficulty in using the Schwarz–Christoffel formula lies in determining these parameters. If this difficulty can be overcome in some effective way, then the Schwarz–Christoffel formula expands the range of conformally mapped regions so much that it can be considered “universal”, given that the curvilinear boundary of the mapped region can be approximated by a broken line. Thus, together with the Schwarz–Christoffel formula, a new direction in the theory of functions arises - numerical methods of conformal mapping. However, these approximate numerical methods were developed independently of the Schwarz–Christoffel formula.Unique factorization theorem for pure quantum states15 Sep, 2023
https://www.mathematicsgroup.us/articles/AMP-6-194.php
In this paper we establish a unique factorization theorem for pure quantum states expressed in computational basis. We show that there always exists unique factorization for any given N-qubit pure quantum state in terms of the tensor product of non-factorable or ``prime'' pure quantum states. This result is based on a simple criterion: Given N-qubit pure quantum state in computational basis can be factorized as the tensor product of an m-qubit pure quantum state and an n-qubit pure quantum state, where (m + n) = N, if and only if the rank of the certain associated matrix is equal to one. This simple criterion leads to a factorization algorithm which when applied to an N-qubit pure quantum state factorizes that state into the tensor product of non-factorable or ``prime'' pure quantum states. This paper shows that for any given N-qubit pure quantum state the said factorization always ``exists'' and is ``unique''. We demonstrated our work here on a computational basis.
PACS Number: 03.67.Mn, 03.65.Ca, 03.65.UdOpen path theory: Pattern and structure in prime numbers25 Aug, 2023
https://www.mathematicsgroup.us/articles/AMP-6-193.php
The Open Path theory, supported by experimental data, is presented. The main hypothesis proposes that Prime Numbers's positions are determined by previous Prime Numbers as well as their spacing, in a complex, but deterministic way. The concepts of Open Path, Perfect Space, and Primorial Perfect Space are introduced. The Open Path theory can predict prime gaps of any minimum predetermined size. Two rudimentary algorithms based on this theory are presented. The first algorithm returns a sample (a few hundredth of numbers) containing 25 % of Prime Numbers at distances above 1011. The mirrored sample gives a similar percentage of Prime Numbers. The algorithm execution time is of a few milliseconds. The second algorithm presented determines if a number belonging to a Perfect Space is a composite number or a Prime Number. The behavior of population dispersion employing various numerical techniques18 Aug, 2023
https://www.mathematicsgroup.us/articles/AMP-6-192.php
The exploration of population diversity motivated us to present this paper. A mathematical model for the ecological process of population dispersion is finally considered by us to figure out the dispersion of population along the area. The dispersal from one's home site to the next is considered the most important phenomenon in the demographic and evolutionary dynamics of the population. The most important factor regarding dispersal is the spatial distribution of individuals. This dispersal may result in enhanced clamping, huge randomness, or even more spacing. The Adomian Decomposition method has opted to work out the problem analytically. Numerical schemes brought an approximate solution by incorporating the Forward-in-Time and Central-In-Space (FTCS) scheme, the Crank Nicolson (CN) scheme, and Numerov’s method. The validity and efficiency of schemes employed for the proposed model are supported by core properties like stability, consistency, and convergence. A comparison is made between the results calculated via schemes and the one analytically. A substance with negative mass16 Aug, 2023
https://www.mathematicsgroup.us/articles/AMP-6-191.php
The conditions for the formation of a substance with a negative mass are investigated. The critical velocity of a body ω = 235696.8871 km/s, necessary for its transition to a massless state, was determined by two independent methods. Zeroing of the mass of matter also occurs at a temperature T =2.17 . 1036 mo (mo is the rest mass of the particle in grams). At higher temperatures or speeds of movement, the mass of bodies becomes negative. The resulting formulas made it possible to calculate the masses of X,Y-bosons equal to 4.606 . 10-9 g. The temperature of the Superunification of the four fundamental interactions, including gravity, is estimated to be 4.72 . 1031 K. The speed of the body at the moment of transition to a massless state is a new world constant04 Aug, 2023
https://www.mathematicsgroup.us/articles/AMP-6-190.php
Based on the kinetic theory of gases, the minimum temperature and critical velocity of a body necessary for its transition to a massless state are estimated. The value of this speed ω = 235696.8871 km⁄s is a new world constant, since it is the same for a body, regardless of its size, mass, density, and chemical composition. For the first time, the masses of X, and Y - bosons, as well as the zeroing temperatures of the mass of elementary particles have been calculated.Some fixed point results in rectangular metric spaces19 Jul, 2023
https://www.mathematicsgroup.us/articles/AMP-6-189.php
After motivation from Geraghty-type contractions and of Farhan, et al. we define α-admissible mappings and demonstrate the fixed point theorems for the above-mentioned contractions in rectangular metric space in this study. In the end, we discuss some consequences of our results as corollaries.
2010 MSC: 47H10, 54H25.Covariance edges matrix of geometric elements01 Jul, 2023
https://www.mathematicsgroup.us/articles/AMP-6-188.php
In this paper, we introduce a new matrix associated with polygons and polyhedrons, namely the covariance edges matrix. We show that, for a regular polygon or polyhedron the corresponding matrix is proportional to the identity of size two or three. Based on this fact, we propose, as an application, several algebraic shape quality measures for convex polygons or polyhedrons. Furthermore, this matrix may be related to the metric of a simplex. Future studies will be devoted to the definition of the covariance edges matrix for higher elements and real applications to mesh optimisation.The conclusion of the limitless hotel problem19 Jun, 2023
https://www.mathematicsgroup.us/articles/AMP-6-186.php
Mathematician Cantor's Set theory appeared paradox and mathematical theory crisis. The famous German mathematician Hilbert used "Hilbert Hotel" to describe Cantor's Set theory paradox. At that time, people could not find a strict mathematical theory to refute Cantor's Set theory, but let everyone get used to and accept Cantor's Set theory, and thought that it was not a paradox. After the proposal of the limitless Hotel question, it caused controversy between the two parties.
I quoted the definition of mathematical logic and got the correct answer.
Proved that there is no paradox in limitless hotels (Reason: limitless hotels cannot increase the number of new guests staying.).
A deep analysis of Cantor's limitless elements and the infeasibility of one-to-one correspondence was conducted.
2020 Mathematics Subject Classification: 03G27, 03F07, 03D45, 03F55Comparison of the performances between the gray and non-gray media approaches of thermal transport in silicon-tin17 Jun, 2023
https://www.mathematicsgroup.us/articles/AMP-6-185.php
We have compared the performances of the gray and non–gray media approaches of thermal transport in Silicon – Tin using Monte Carlo Simulation. The Boltzmann Transport Equation (BTE) for phonons was used to describe the heat flow and ballistic conduction in semiconducting alloy systems. In this work, we have attempted solving the BTE using Monte Carlo (MC) simulation Computational domains for both gray and non-gray media approaches are modeled and the geometry and dimensions of unit cell and sub-cells in the domain are determined. In addition, the computational performances of the gray and non-gray media approaches are compared. The results revealed that when compared to non- gray approach, the gray media approach has more errors in the sub-cells. The maximum relative error is about 3.5%. The results also show that the non–gray media approach of thermal transport in Silicon – Tin exhibited numerical predictions with a very close match to experimental data.An innovative method and a medical screening device for cancer detection in real-time17 Jun, 2023
https://www.mathematicsgroup.us/articles/AMP-6-184.php
Histopathology is the main technique to assess the presence of cancer cells in biopsy material and for the evaluation of positive resection margins, but it is not real-time. Older methods to assess resection margin intraoperatively are either time-consuming or exhibit a low accuracy. More recent imaging techniques have various drawbacks, like the need for exogenous contrast agents or excessive time to assess the entire resection surface or a low diagnostic performance in detecting certain types of cancer. The purpose of the current research work is the development of a medical screening device for cancer cells detection with very high accuracy and selectivity, based on a newly developed method in order to experimentally measure in real-time the excitation response of the charged elements of the biological tissue under study to the applied alternative electrical field, over a wide range of frequency spectra.
The aim of this study is to present an innovative method and results from a prototype medical screening device, which allows the selective and “real-time” detection of cancer cells of any type among normal cells in any tissue type.
The innovation of the proposed method lies in the view of the cell membrane emulation as an electrical circuit and also in the ability to experimentally measure in real-time the excitation response of the charged elements of the biological tissue under studies like ions, interfaces or dipoles to the applied alternative electrical field, over a wide range of frequency spectra according to the dielectric spectroscopy method. The ions can very easily follow the variations of the applied alternating electric field moving along the dynamic lines of the field. In contrast, the incapability of the abnormal neoplastic cellular formations to follow the frequency changes causes them to perform dipole oscillation instead of moving along the dynamic lines of the field. This experimentally appears as a significant increase of the capacitive component contribution to the total impedance of the tissue, relative to the purely electrical resistance contribution of the ions. A model, backed by the relevant mathematical equations, has been developed to integrate the unknown impedance of both the tissue under assessment and the interdigital micro-sensor with the known complex impedance of the data acquisition system. The ability to selectively detect cancer cells has an obvious interest and various applications in cancer diagnosis and therapy. Analyzing Riemann's hypothesis16 Jun, 2023
https://www.mathematicsgroup.us/articles/AMP-6-183.php
In this paper we perform a detailed analysis of Riemann's hypothesis, dealing with the zeros of the analytically-extended zeta function. We use the functional equation for complex numbers s such that 0<Re(s)<1, and the reduction to the absurd method, where we use an analytical study based on a complex function and its modulus as a real function of two real variables, in combination with a deep numerical analysis, to show that the real part of the non-trivial zeros of the Riemann zeta function is equal to ½, to the best of our resources. This is done in two steps. First, we show what would happen if we assumed that the real part of s has a value between 0 and 1 but different from 1/2, arriving at a possible contradiction for the zeros. Second, assuming that there is no real value y such that ζ(1/2+yi)=0, by applying the rules of logic to negate a quantifier and the corresponding Morgan's law we also arrive at a plausible contradiction. Finally, we analyze what conditions should be satisfied by y∈ℝ such that ζ(1/2+yi)=0. While these results are valid to the best of our numerical calculations, we do not observe and foresee any tendency for a change. Our findings open the way towards assessing the validity of Riemman's hypothesis from a fresh and new mathematical perspective.Confirm that the imaginary number i is a closed field13 Jun, 2023
https://www.mathematicsgroup.us/articles/AMP-6-182.php
In the History of mathematics of mankind, some strange symbols appeared when dealing with some mathematical problems, which were defined as imaginary numbers by mankind. The imaginary number has been idle for a long time since it was discovered. Later, mathematicians such as Gauss moved the imaginary number to the mathematical plane (Complex plane).
Humans have also learned the difference between imaginary and real numbers, and have obtained the difference between the two types of numbers on the square root.
My contribution is to discover the inconsistency between real and imaginary numbers.
I have discovered a new method of calculating imaginary number logic that is deeply hidden.
2020 Mathematics Subject Classification: 03G27, 03F07, 03D45, 11U09, 08A05, 08A40. Quō Vādis theoretical physics and cosmology? from Newton’s Metaphysics to Einstein’s Theology02 Jun, 2023
https://www.mathematicsgroup.us/articles/AMP-6-181.php
The crisis in modern theoretical physics and cosmology has its root in its use, along with theology as a ruling-class tool, since medieval Europe. The Copernican revolution overthrowing the geocentric cosmology of theology led to unprecedented social and scientific developments in history. But Isaac Newton’s mathematical idealism-based and on-sided theory of universal gravitational attraction, in essence, restored the idealist geocentric cosmology; undermining the Copernican revolution. Albert Einstein’s theories of relativity proposed since the turn of the 20th century reinforced Newtonian mathematical idealism in modern theoretical physics and cosmology, exacerbating the crisis and hampering further progress. Moreover, the recognition of the quantum world - a fundamentally unintuitive new realm of objective reality, which is in conflict with the prevailing causality-based epistemology, requires a rethink of the philosophical foundation of theoretical physics and cosmology in particular and of natural science in general. J/Ψ (1S) and Ψ (2S) Production in p-p Collisions at E=5.44 TeV20 May, 2023
https://www.mathematicsgroup.us/articles/AMP-6-180.php
I estimate the differential rapidity cross sections for J/Ψ and Ψ (2S) via pp (proton-proton) collisions at E=510 GeV. The J/Ψ is a standard charm quark and anti-charm quark, c and while Ψ (2S) is a mixed hybrid c meson. For the Ψ (2S) I use the mixed heavy quark hybrid theory, with states approximately 50% standard and 50% hybrid charmonium. The fractal analysis - Powerful tool for geodynamic investigations12 May, 2023
https://www.mathematicsgroup.us/articles/AMP-6-179.php
This is a short review of fractal analysis applications in Bulgaria to investigate the geodynamics at the local, regional, and global levels.
Certain results of Aleph-Function based on natural transform of fractional order25 Apr, 2023
https://www.mathematicsgroup.us/articles/AMP-6-178.php
In this research article, a new type of fractional integral transform namely the N-transform of fractional order is proposed, and derived a number of useful results of a more generalized function (Aleph-function) of fractional calculus by making use of the N-transform of fractional order. Further, the relation between it and other fractional transforms is given and some special cases have also been discussed.The link between <em>s</em> and <em>d</em> components of electron boson coupling constants in one band d wave Eliashberg theory for high <em>T<sub>c</sub></em> superconductors07 Apr, 2023
https://www.mathematicsgroup.us/articles/AMP-6-177.php
The phenomenology of overdoped high Tc uperconductors can be described by a one band d wave Eliashberg theory where the mechanism of superconducting coupling is mediated by antiferromagnetic spin fluctuations and whose characteristic energy Ω0 scales with Tc according to the empirical law Ω0 = 5.8 kBTc. This model presents universal characteristics that are independent of the critical temperature such as the link between the s and d components of electron boson coupling constants and the invariance of the ratio 2∆/kBTc. This situation arises from the particular structure of Eliashberg's equations which, despite being non-linear equations, present solutions with these simple properties. Fractal space-time and variations of the hubble constant30 Mar, 2023
https://www.mathematicsgroup.us/articles/AMP-6-176.php
Spatial variations of the Hubble constant are considered according to Riess, et al. (2018). It is noted that the values of the Hubble constant form an almost fractal manifold. This fact suggests that the variations may be associated with local gravitational perturbations in the neighborhoods of galaxies, in which there are Cepheids and supernovae selected for measurement. The aim and purpose of the study is to show that the spatial variations of the Hubble constant may be due to the fact that the galaxies belong to outskirts of the Local Supercluster.Determinism and chaos – a story about Big Bang, singularity and the future of mankind17 Mar, 2023
https://www.mathematicsgroup.us/articles/AMP-6-175.php
People have always tried to understand and tame the nature around them. It is a well-known fact that the sanest and safe approach from a psychological point of view is to focus on the present moment, the here and now. Nevertheless, we keep looking and living in the past or daydreaming and making predictions about what the future will bring. This paper is looking at this topic trying to unify several perspectives, stemming from a very diverse set of disciplines: biology, genetics, economics and cryptography, which are apparently working in parallel to solve the same problem. They all aim to find a theory of everything, one that can make sense out of chaos, light out of darkness and that can accurately predict the future based on present and past events. The current paper is supposed to inspire researchers to ask themselves tough questions, sometimes completely outside of their comfort zone, that can lead to discoveries with a huge positive impact on us all.On Λ-fractional variational calculus01 Mar, 2023
https://www.mathematicsgroup.us/articles/AMP-6-174.php
Pointing out that Λ-fractional analysis is the unique fractional calculus theory including mathematically acceptable fractional derivatives, variational calculus for Λ-fractional analysis is established. Since Λ-fractional analysis is a non-local procedure, global extremals are only accepted. That means the extremals should satisfy not only the Euler–Lagrange equation but also the additional Weierstrass-Erdmann corner conditions. Hence non-local stability criteria are introduced. The proposed variational procedure is applied to any branch of physics, mechanics, biomechanics, etc. The present analysis is applied to the Λ-fractional refraction of light. Experimental and theoretical studies of the influence of the bench elements on the transient operation of the turbine22 Feb, 2023
https://www.mathematicsgroup.us/articles/AMP-6-173.php
The energy parameters obtained during the tests of turbines of power units on the stand differ from those in the product. The research data, which results are presented in the materials of the paper, are aimed at analyzing the discrepancies between the parametric indicators of power units and bench tests of the turbines. The novelty of the obtained results reveals the direct and inverse relationship of changes in the amplitude-frequency characteristics of the elements of the stand (depending on the realized turbine power) with the obtained results of measuring the turbine power on the stand. We developed and described an algorithm for constructing dynamic analysis during the formation of the wave field of the test bench for turbines both in transient modes and in stationary modes corresponding to a constant number of turbine revolutions. It is shown that, by using the algorithm of modal deduction and conditions of dynamic excitation of vibrations from the tested turbine with elements of studying its power, it is possible to construct transients with certain reliability when the number of revolutions of the turbine changes, i.e. its power. The diagnostic model has a novelty since it allows not only to assess of the influence of the elements of the stand on the nature of the transient process when measuring turbine power in transient modes, taking into account the frequency adjustment when changing the revolutions of the turbine and the elements of the stand but also to form requirements for the frequency tuning of the stand. To clarify the transfer function of the "stand–turbine" system, a modal analysis was applied, which made it possible to clarify the structure of the transfer function in the frequency range of the natural (partial) frequencies of the elements of the stand when the restructuring of the wave field during the transient operation of the turbine, but also when the turbine reaches the specified power.Calculation of the magnetic field of the asteroid 4 Vesta parent body (Application of SK theory)18 Feb, 2023
https://www.mathematicsgroup.us/articles/AMP-6-172.php
The SK theory provides a deeper insight into the magnetic properties of celestial bodies. In this study, the magnetic field calculated of the parent body of asteroid 4 Vesta, could facilitate deeper insight into the formation of planets or the Universe. A remark on a perturbed Benjamin-Bona-Mahony type equation and its complete integrability14 Feb, 2023
https://mathematicsgroup.us/articles/AMP-6-171.pdf
In the Letter, we study a perturbed Benjamin-Bona-Mahony nonlinear equation, which was derived for describing shallow water waves and possessing a rich Lie symmetry structure. Based on the gradient-holonomic integrability checking scheme applied to this equation, we have analytically constructed its infinite hierarchy of conservation laws, derived two compatible Poisson structure and stated its complete integrability.Spectral analysis of the Sturm-Liouville operator given on a system of segments07 Feb, 2023
https://mathematicsgroup.us/articles/AMP-6-170.pdf
The spectral analysis of the Sturm-Liouville operator defined on a finite segment is the subject of an extensive literature [1,2]. Sturm-Liouville operators on a finite segment are well studied and have numerous applications [1-6]. The study of such operators already given on the system segments (graphs) was received in the works [7,8]. This work is devoted to the study of operators
Two methods for determining combinatorial identities10 Jan, 2023
https://www.mathematicsgroup.us/articles/AMP-6-169.php
Two methods are presented for determining advanced combinatorial identities. The first is based on extending the original identity so that it can be expressed in terms of hypergeometric functions whereupon tabulated values of the functions can be used to reduce the identity to a simpler form. The second is a computer method based on Koepf's version of the Wilf-Zeilberger approach that has been implemented in a suite of intrinsic routines in Maple. As a consequence, some new identities are presented. About the connection of the electron binding energy of a single carbon anion with binding energies of an electron attached to carbon molecules09 Jan, 2023
https://www.mathematicsgroup.us/articles/AMP-6-168.php
We demonstrate that the model of zero-range potentials can be successfully employed for the description of attached electrons in atomic and molecular anions, for example, negatively charged carbon clusters. To illustrate the capability of the model we calculate the energies of the attached electron for the family of carbon cluster anions consisting of two-, three- (equilateral triangle) and four (tetrahedron) carbon atoms equidistant from each other as well as for a C3 molecule having a chain structure. The considered approach can be easily extended to carbon clusters containing an arbitrary number of atoms arranged in an arbitrary configuration.Boundary value problem for the third-order equation with multiple characteristics06 Jan, 2023
https://www.mathematicsgroup.us/articles/AMP-6-167.php
The article constructs a unique solution to a tertiary-order equation with multiple characteristics with boundary conditions that include all possible local boundary conditions. The uniqueness of the solution of boundary value problems is proved by the method of integral equations using the sign-definiteness of quadratic forms. When proving the existence of a solution to the problem, Green's function method, the theory of integral equations and potentials are used.Common sense and quantum mechanics29 Dec, 2022
https://www.mathematicsgroup.us/articles/AMP-5-166.php
It is shown how changing only one word in the usual interpretation of quantum mechanics makes it possible to turn its puzzles and miracles into obvious trivialitiesA simple algorithm for GCD of polynomials23 Dec, 2022
https://www.mathematicsgroup.us/articles/AMP-5-165.php
Based on the Bezout approach we propose a simple algorithm to determine the gcd of two polynomials that don't need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only n steps for polynomials of degree n. Formal manipulations give the discriminant or the resultant for any degree without needing division or determinant calculation. Importance of atomic physics in verification of experimental results and diagnostics of solar and astrophysical observations16 Dec, 2022
https://www.mathematicsgroup.us/articles/AMP-5-164.php
Accurate results are needed to confirm the experimental results of various atomic processes and analyze the solar and astrophysical observations of intensities of emission lines to infer plasma parameters like electron density, electron temperature and element abundance. A number of theories have been developed over the years to calculate phase shifts when electrons and positrons are scattered from targets. We discuss in this article the recent hybrid theory which has been applied to scattering processes, resonances and photoabsorption process, which is a bound-free transition.Convolutional modelling of epidemics03 Dec, 2022
https://www.mathematicsgroup.us/articles/AMP-5-163.php
Traditional deterministic modeling of epidemics is usually based on a linear system of differential equations in which compartment transitions are proportional to their population, implicitly assuming an exponential process for leaving a compartment as happens in radioactive decay. Nonetheless, this assumption is quite unrealistic since it permits a class transition such as the passage from illness to recovery that does not depend on the time an individual got infected. This trouble significantly affects the time evolution of epidemy computed by these models. This paper describes a new deterministic epidemic model in which transitions among different population classes are described by a convolutional law connecting the input and output fluxes of each class. The new model guarantees that class changes always take place according to a realistic timing, which is defined by the impulse response function of that transition, avoiding model output fluxes by the exponential decay typical of previous models. The model contains five population compartments and can take into consideration healthy carriers and recovered-to-susceptible transition. The paper provides a complete mathematical description of the convolutional model and presents three sets of simulations that show its performance. A comparison with predictions of the SIR model is given. Outcomes of simulation of the COVID-19 pandemic are discussed which predicts the truly observed time changes of the dynamic case-fatality rate. The new model foresees the possibility of successive epidemic waves as well as the asymptotic instauration of a quasi-stationary regime of lower infection circulation that prevents a definite stopping of the epidemy. We show the existence of a quadrature function that formally solves the system of equations of the convolutive and the SIR models and whose asymptotic limit roughly matches the epidemic basic reproduction number.The continuity of prime numbers can lead to even continuity <br> (Relationship with Gold Bach’s conjecture)02 Dec, 2022
https://www.mathematicsgroup.us/articles/AMP-5-162.php
N continuous prime numbers can combine a group of continuous even numbers. If an adjacent prime number is followed, the even number will continue. For example, if we take the prime number 3, we can get an even number 6. If we follow an adjacent prime number 5, we can get even numbers by using 3 and 5: 6, 8 and 10. If a group of continuous prime numbers 3, 5, 7, 11, ..., P, we can get a group of continuous even numbers 6, 8, 10, 12,..., 2n. Then if an adjacent prime number q is followed, the Original group of even numbers 6, 8, 10, 12,..., 2n will be finitely extended to 2(n + 1) or more adjacent even numbers. My purpose is to prove that the continuity of prime numbers will lead to even continuity as long as 2(n + 1) can be extended. If the continuity of even numbers is Discontinuous, it violates the Bertrand Chebyshev theorem of prime Numbers.
Because there are infinitely many prime numbers: 3, 5, 7, 11,...
We can get infinitely many continuous even numbers: 6, 8, 10, 12,...
Get: Gold Bach conjecture holds.
2020 Mathématiques Subjectif Classification: 11P32, 11U05, 11N05, 11P70.
Research ideas:
If the prime number is continuous and any pairwise addition can obtain even number continuity, then Gold Bach’s conjecture is true.
Human even number experiments all get (prime number + prime number).
I propose a new topic: the continuity of prime numbers can lead to even continuity.
I designed a continuous combination of prime numbers and got even continuity.
If the prime numbers are combined continuously and the even numbers are forced to be discontinuous, a breakpoint occurs.
It violates Bertrand Chebyshev's theorem.
It is proved that prime numbers are continuous and even numbers are continuous.
The logic is: if Gold Bach's conjecture holds, it must be that the continuity of prime numbers can lead to the continuity of even numbers.
Image interpretation: turn Gold Bach’s conjecture into a ball, and I kick the ball into Gold Bach’s conjecture channel.
There are several paths in this channel and the ball is not allowed to meet Gold Bach’s conjecture conclusion in each path.
This makes the ball crazy, and the crazy ball must violate Bertrand Chebyshev's theorem.Critical behavior and stability problem in a scalar field model29 Nov, 2022
https://www.mathematicsgroup.us/articles/AMP-5-161.php
As shown in the works [1-3], the asymptotic behavior of the propagator in the Euclidean region of momenta for the model of a complex scalar field φ and a real scalar field χ with the interaction drastically changes depending on the value of the coupling constant. For small values of the coupling, the propagator of the field φ behaves asymptotically as free, while in the strong-coupling region the propagator in the deep Euclidean region tends to be a constant.
In this paper, the influence of the vacuum stability problem of this model on this critical behavior is investigated. It is shown that within the framework of the approximations used, the addition of a stabilizing term of type to the Lagrangian leads to a renormalization of the mass and does not change the main effect of changing the ultraviolet behavior of the propagator.
PACS number: 11.10.Jj.A new form of discrete real Fourier transform and its potential applications24 Nov, 2022
https://www.mathematicsgroup.us/articles/AMP-5-160.php
The paper will present a new version of a real discrete Fourier transform, based on a symmetric frequencies combination of sine and cosine functions. Basic aspects of the construction as well as the potential applications will be discussed. This will include elements of the standard Fourier analysis as well as applications to the class of differential equations in string theory.Different approaches to system science24 Nov, 2022
https://www.mathematicsgroup.us/articles/AMP-5-159.php
The goal of the paper is to present a new definition of a holistic approach to the description of complex systems including features such as emergent behavior, exaptation, contingency, self-organization, etc. The presented approach is based on concepts such as singularity (internal behavior of a partial system component without any links), duality (analyses of links between pairs of system components) and a plurality (links between clusters of system components). Energetics is presented as a new science (third-order cybernetics) using the results of the theory of complex systems connected with the algorithms of artificial intelligence so that a better coexistence between humans and machines occurs.Solving train scheduling problems as a job shop: A brief review15 Nov, 2022
https://www.mathematicsgroup.us/articles/AMP-5-158.php
An interesting practical problem is the single-track train scheduling problem which can be considered a job shop scheduling problem, namely since the sequence of sections is fixed for a train route, it corresponds to fixed machine routes (technological orders) in a job shop scheduling problem. However, for a train scheduling problem, typically some additional constraints such as blocking, sidings, stations with parallel tracks, deadlocks, train length, or headways, etc. have to be considered. The job shop problem has been well investigated in the literature and belongs to the hardest problems in scheduling theory. In this mini-review, some results in this area are discussed, where the main focus is on results that the author has obtained with his collaborators and Ph.D. students during the last decade.
MSC classification: 90 B 35Physical contradictions ruling out photonic quantum nonlocality29 Oct, 2022
https://www.mathematicsgroup.us/articles/AMP-5-157.php
A series of physical contradictions can be identified in an opinion article published in December 2015 (A. Aspect, “Closing the Door on Einstein and Bohr’s Quantum Debate,” Physics 8, 123, 2015) claiming definitive proof of quantum nonlocality based on entangled pairs of photons. For example, experimental results published simultaneously in Physical Review Letters (250401 and 250402, 2015) were theoretically fitted with distributions containing a dominant unentangled component, contradicting the need for maximally entangled states underpinning quantum nonlocality. Such contradictions were ignored by the 2022 Nobel Prize Committee raising doubts about the validity of their decision.Sound Energy Harvesting and Converting Electricity (SEHCE)04 Oct, 2022
https://www.mathematicsgroup.us/articles/AMP-5-156.php
The research study “Sound Energy Harvesting and Converting Electricity (SEHCE)” aims to create a better and easier way of producing another source of clean and renewable energy through sound. The study did not aim to be compared to other proven sources of electricity such as heat, wind, solar and hydroelectric, instead, it was created to find and explore new ways of producing an alternative source of energy. The project will undergo several processes such as designing, construction, testing, and evaluation. Through this, the researcher will be able to find out that sound energy can be converted to electricity.Complex network reveals the spatiotemporal pattern of summer extreme precipitation in Eastern China04 Oct, 2022
https://www.mathematicsgroup.us/articles/AMP-5-155.php
In this study, complex networks were constructed based on the synchronization of summer extreme precipitation events (SEPEs) in eastern China. Then, a detailed analysis of spatiotemporal patterns of SEPEs and the relationship between SEPEs in eastern China with the eastern Asian monsoon was presented. The results showed that (1) the event synchronization is low in the coastal region but high in the inland region; (2) the intensity of the monsoon varies at different phases of summer and the area and intensity of the monsoon's influence on the summer extreme rainfall events were different. In conclusion, this study provides valuable insights to reveal the influence of monsoon strength on SEPEs in different regions of China. Lissajous curves with a finite sum of prime number frequencies26 Sep, 2022
https://www.mathematicsgroup.us/articles/AMP-5-154.php
The Ulam spiral inspired us to calculate and present Lissajous curves where the orthogonally added functions are a finite sum of sinus and cosines functions with consecutive prime number frequencies.Simple way to calculate neutrino masses24 Sep, 2022
https://www.mathematicsgroup.us/articles/AMP-5-153.php
Thermodynamic-induced geometry of self-gravitating systems16 Sep, 2022
https://www.mathematicsgroup.us/articles/AMP-5-152.php
A new approach based on the nonequilibrium statistical operator is presented that makes it possible to take into account the inhomogeneous particle distribution and provides obtaining all thermodynamic relations of self-gravitating systems. The equations corresponding to the extremum of the partition function completely reproduce the well-known equations of the general theory of relativity. Guided by the principle of Mach's "economing of thinking" quantitatively and qualitatively, is shown that the classical statistical description and the associated thermodynamic relations reproduce Einstein's gravitational equation. The article answers the question of how is it possible to substantiate the general relativistic equations in terms of the statistical methods for the description of the behavior of the system in the classical case.From Engle & Granger model to Johansen model for a more accurate photovoltaic power output forecast13 Sep, 2022
https://www.mathematicsgroup.us/articles/AMP-5-151.php
The French government has recently decided to increase the Photovoltaic (PV) capacities to reach 35GW by 2028 in all french territories, the European territory, and overseas territories such as Reunion Island in the Indian Ocean. However, integrating growing numbers of PV power installations and microgrids onto the grid can result in larger-than-expected fluctuations in grid frequency. This is due to PV power output that is not only a function of the operating temperature and solar irradiation but also of other environmental parameters. In this paper, only two environmental parameters are considered in the European zone and when the Engle & Granger statistical method is used, a relationship between variables such as photovoltaic power output and solar irradiation at a different level is obtained. The final relationship without suspicious heteroscedasticity is determined. The model is formulated on the basis of photovoltaic real conditions statistical approach and is more realistic than steady approach models. The Engle & Granger method does not distinguish several cointegration relationships when more variables are considered. For the overseas zone, we added other measured environmental variables and applied a more robust statistical method known as the Johansen vector error correction model (VECM) cointegration approach. In the VECM model, for N explanatory variables and for N > 2, we established a long-run equilibrium relationship that has been tested and the outcome is more than reliable when comparing the model to measured data.Cooperative investment problem with an authoritative risk determined by Central Bank30 Aug, 2022
https://www.mathematicsgroup.us/articles/AMP-8-150.pdf
In this paper, we are interested to provide an analytic solution for cooperative investment risk with an authoritative risk determined by the central Bank. This problem plays an important role in solving cooperative investment problems in an investment sector such as insurance companies or banks etc and keeping in our mind the effect of a risk determined by the central Bank which has not been done before. We reformulate cooperative investment risk by writing dual representation for each risk preference (Coherent risk measure) for each agent (investor). Finding an analytic solution for this problem for both cases individual and cooperative investment problem by using dual representation for each risk preference has a strong effect on the financial market. Moreover, we find the equilibrium allocation in terms of an equilibrium price by formulating the optimization problem in the case of equilibrium with an initial endowment for each agent’s ’investor’. In addition, formulate a problem that covers the risk minimization problem with an expected return constraint and expected return maximization problem with risk constraint, in both individual and cooperative investment cases, for the general case of an arbitrary joint distribution for the asset return under certain conditions and assuming that all coherent risk measure is continuous from below. Thus, the optimal portfolio is written as the optimal Lagrange multiplier associated with an equality-constrained dual problem. Furthermore, a unique equilibrium allocation as a fair optimal allocation solution in terms of equilibrium price density function for each agent (investor) is also shown.
AMS Subject Classification: [2022].Development online models for automatic speech recognition systems with a low data level23 Aug, 2022
https://www.mathematicsgroup.us/articles/AMP-5-149.php
Speech recognition is a rapidly growing field in machine learning. Conventional automatic speech recognition systems were built based on independent components, that is an acoustic model, a language model and a vocabulary, which were tuned and trained separately. The acoustic model is used to predict the context-dependent states of phonemes, and the language model and lexicon determine the most possible sequences of spoken phrases. The development of deep learning technologies has contributed to the improvement of other scientific areas, which includes speech recognition. Today, the most popular speech recognition systems are systems based on an end-to-end (E2E) structure, which trains the components of a traditional model simultaneously without isolating individual elements, representing the system as a single neural network. The E2E structure represents the system as one whole element, in contrast to the traditional one, which has several independent elements. The E2E system provides a direct mapping of acoustic signals in a sequence of labels without intermediate states, without the need for post-processing at the output, which makes it easy to implement. Today, the popular models are those that directly output the sequence of words based on the input sound in real-time, which are online end-to-end models. This article provides a detailed overview of popular online-based models for E2E systems such as RNN-T, Neural Transducer (NT) and Monotonic Chunkwise Attention (MoChA). It should be emphasized that online models for Kazakh speech recognition have not been developed at the moment. For low-resource languages, like the Kazakh language, the above models have not been studied. Thus, systems based on these models have been trained to recognize Kazakh speech. The results obtained showed that all three models work well for recognizing Kazakh speech without the use of external additions.Graphene oxide-based waveguides for enhanced self-phase modulation09 Aug, 2022
https://www.mathematicsgroup.us/articles/AMP-5-148.php
The enhanced self-phase modulation (SPM) in silicon nitride (Si3N4) and silicon (Si) waveguides integrated with graphene oxide (GO) films is experimentally demonstrated. By using both picosecond and femtosecond optical pulses, we observe significant spectral broadening in the waveguides due to the high Kerr nonlinearity of GO films. The maximum broadening factors of up to ~3.4 and ~4.3 are achieved in GO-coated Si3N4 waveguides and GO-coated Si waveguides, respectively. The spectral broadening for femtosecond pulses is more significant than the picosecond pulses, which can be attributed to their relatively high peak power. These results show the strong potential of GO films for improving the Kerr nonlinearity of photonic devices. Weyl conformal symmetry for gravitation and cosmology02 Aug, 2022
https://www.mathematicsgroup.us/articles/AMP-5-147.php
The novel paradigm of universal conformal symmetry has been found to explain accelerating Hubble expansion, centripetal lensing by dark galactic halos, and observed excessive galactic rotational velocities, without dark matter. A tractroid realization of a 2d black hole vacuum01 Aug, 2022
https://www.mathematicsgroup.us/articles/AMP-5-146.php
The two-dimensional black hole vacuum obtained from a spatial slice of the BTZ black hole is mapped explicitly to a tractroid surface minus a bounding circle.The amazing systemic structure of Mathematics19 Jul, 2022
https://www.mathematicsgroup.us/articles/AMP-5-145.php
Starting with the works of Ludwig von Bertalanffy, the general systems theory went from being applied to biological systems to identifying systemic structures in different natural, technological and social phenomena, even systemic structures are appreciated in different branches of science.
Precontinuity and applications13 Jul, 2022
https://www.mathematicsgroup.us/articles/AMP-5-144.pdf
In this note, a map f acting between metric (or topological) spaces is referred to be pre-continuous at a point x if, for some sequence of points different from x and converging to x, the sequence converges to (section 2, Definition 1).Surface energy for nanowire08 Jul, 2022
https://www.mathematicsgroup.us/articles/AMP-5-143.php
The theory of surface phenomena in the production of micro-and nanocylinder for important cases is considered. Analytical solution to Gibbs–Tolman–Koenig–Buff equation for nanowire surface is given. Analytical solutions to equations for case the cylindrical surface for the linear and nonlinear Van der Waals theory are analyzed. But for a nonlinear theory, this correspondence is absent.Changchun SLR data analysis using different techniques07 Jul, 2022
https://www.mathematicsgroup.us/articles/AMP-5-142.php
The aim of the present study is to investigate three different techniques for fitting the SLR data observed from the Changchun observatory in China which is characterized by its huge amount of data points and to examine which of the three techniques is more proper for fitting such kind of data. The first technique is the interpolation using the Chebyshev polynomial for fitting the total number of satellite laser ranging (SLR) data points. The second technique is the spline technique which is used for matching continuous intervals for fitting the SLR data. The third technique is the method, which is used at Changchun observatory, known as the Iterative 4th order polynomial fit. The three techniques are applied to 100 samples; 50 samples for the satellite LAGEOS I and the other 50 samples for the satellite Starlette that were observed during the first quarter of 2018. From the obtained results, it is found that the first two techniques, namely the Chebyshev polynomial and Spline techniques provide better standard deviation in comparison to the Iterative 4th order polynomial fit technique that is used at Changchun observatory, with merit to Spline technique over the Chebyshev polynomial. A Poisson “Half-Summation” Formula25 Jun, 2022
https://www.mathematicsgroup.us/articles/AMP-5-141.pdf
A generalization of Poisson’s summation formula is derived – in a non-rigorous way – allowing evaluation of sums from 1 (or any finite integer) ∞ instead of the usual range -∞+∞. This is achieved in two ways, either by introducing a converging factor in a geometric series of exponential functions and letting it approach zero in a controlled way or by applying a Hilbert transform to the series. Several examples illustrate its usefulness in the evaluation of series and specific applications. Dualistic relativity: Unification of Einstein’s Special Relativity and de Broglie’s Matter–Wave Theory18 Jun, 2022
https://www.mathematicsgroup.us/articles/AMP-5-140.php
In Hawking’s view physics has been broken up into many partial theories, while the ultimate goal of physicists is to unify them. The two basic theories of 20th-century physics, relativity theory and quantum theory, are based on completely different logical prerequisites and exactly separate: matter is described as particles in relativity theory and as waves in quantum mechanics. Here, based on the identical logical prerequisites, we unify Einstein’s special relativity (SR) and de Broglie’s matter-wave theory (MWT) into the theory of dualistic relativity (DR), taking a significant step toward the unification of relativity and quantum mechanics. From the definition of time, we derive the Lorentz transformation in differential form and establish the theory of DR, which generalizes the wave-particle duality of matter motion, and uniformly derives Einstein’s formula E=mc2, Planck’s equation E=hf, and de Broglie’s relation λ=h/p. From the logical prerequisite completely different from Einstein’s hypothesis of the invariance of light speed and along the logical path completely different from Einstein’s SR, we have deduced the whole theoretical system of Einstein’s SR and de Broglie’s MWT. In the theory of DR, the two great formulae originally separated, Einstein’s formula E=mc2 and Planck’s equation E=hf, become a pair of twin formulae unified in an identical theoretical system.Modeling and analysis of the Haldane genetic model under Brownian motion using stochastic differential equation30 May, 2022
https://www.mathematicsgroup.us/articles/AMP-5-139.php
Heterozygote advantage as a natural consequence of adaptation in diploid organisms is an attractive mechanism by which two alleles are maintained in natural populations. It has significant effects on biodiversity conservation and plant and animal breeding programs. The mathematical modeling of this biological mechanism is important for eco-evolutionary dynamics studies and genetics investigations. In this paper, I aimed to formalize the changes of gene frequency in time v(t), and in time and space v(t,x) with additive effects in a birth and death process of the Haldane genetic model using Brownian motion under fluctuations of habitat. In addition, the gene-environment interactions were evaluated under the mechanism. The mathematical model was investigated in both deterministic and white noise forms. It was shown that if the environmental random processes in the Haldane genetic model changed quickly and smoothly, then the diffusion approximation of the allele frequencies could be modeled and analyzed by a stochastic partial differential equation. It was revealed that the mathematical model used in this paper belonged to a more general model. The mathematical model was analyzed and since the modeling by the Cauchy problem had not had a usual global solution, the qualitative behavior of the solutions was considered. Besides, the generalizations of ItÔ integral were defined as the integrals of Wick products of random parameters and noise components. It was found that if v(t,x) behaved like a super-Brownian motion and the fatal mutations took place, as a consequence a tiny group of alleles was quickly disappeared. The v(t,x) was unstable when it was close to one. The stationary phase appeared and v(t,x) tended to the stationary situation in the intermediate region under the stabilizing selection. This was a condition under additive gene effect, but with the presence of dominance gene effect, it might be ambidirectional without considering the epistatic effects. The emergence of the dominance and epistatic effects was due to the directional selection. Since Falconer and MacKay had already introduced a deterministic model to study the frequency of genes with no spatial spreading of the population and no stochastic processes, another model was explained to study their equation in the case of heterozygote intermediate for diffusion approximation of frequency of genes, including white noise. It was shown that if the rates of mutation and selection became very small, then the model would be more deterministic and predictable. On the other hand, if the rates of mutation and selection became large, then the model would be more stochastic, and more fluctuations occurred because of the strong effective noise strength. In this case, the stationary situation did not take place. The outlook can help to model the similar biological mechanisms in eco-evolutionary community genetics for studying the indirect genetic effects via the systems of stochastic partial differential equations, and white noise calculus.
2020 mathematics subject classification: Primary 92-XX; Secondary 92Dxx, 92D25.Research of superluminal phenomena revealed the essence and limitation of the relativity20 May, 2022
https://www.mathematicsgroup.us/articles/AMP-5-138.php
Superluminal phenomena have been viewed as a contradiction to the Special Relativity, the in-variance principle of light velocity. This paper proposed the theory of the two kinds of epistemology and world, to explain the contradiction between the Special Relativity (SR) and Superluminal phenomena. It also discussed the influence of superluminal research on other science and technology, such as information science and superluminal communications.The spiral wave trajectory motion of particles is the only reason for the establishment of the Poincare regression theorem (Background radiation is not evidence of the big bang of the cosmic singularity)12 May, 2022
https://www.mathematicsgroup.us/articles/AMP-5-137.php
In short, an isolated and limited system will return to a state very close to the initial state in the long-term evolution process. For example, in a container, gas particles rotate in chaos and return to their initial position after a period of time. I have proved that everything is a spiral wave track (path) and has the property of wave: v = Fλ ; λ= uT. It is proved that any finite object (particle) has a common period: the nearest distance and the farthest distance. Such as the earth and the moon; Earth and the sun; The three bodies of the earth, the moon and the sun, and the comet and the earth all meet periodically. Particles also have this property. The principle is due to the periodicity of the spiral of an object.
The Poincare regression theorem is proved by the spiral periodic wave pattern of the object.
Mathematical classification code: 70F20;70F45;03D55;76Y99; 81V25; 37A55 Children explore to understand the physical world Research and practice in Early Childhood Education12 May, 2022
https://www.peertechzpublications.org/articles/AMP-5-136.pdf
All children are inquisitive and begin to make sense of the physical and natural world around them from the time they are born. Children use their senses to explore the surrounding environment. Early Childhood Centres (ECE) in New Zealand provide care and learning opportunities for children under the age of 5-years. Te Whāriki, our mandated curriculum guides teachers. In an exploratory case study, we investigated the science learning experiences provided by an ECE teacher and the children’s learning that ensued. The data were collected through case study teacher interviews, mentor notes, and 160 learning stories written by the teacher during the research over two years. We found that a teacher with little background in science was able to provide rich science learning experiences for the children. The teacher’s willingness to provide everyday science exploration opportunities and ask questions helped children to develop basic physics concepts. Current research suggests that science is often not taught due to the lack of teacher confidence to teach science because they are generalists and believe they do not have the requisite knowledge or training. Our findings have implications for science teaching and learning in early childhood and primary schools.Proof of Einstein’s postulates28 Apr, 2022
https://www.mathematicsgroup.us/articles/AMP-5-135.php
Based on the assumption that the experiment confirms the STR, it is shown that the value of the speed of light is a very slowly decreasing function of its frequency, so that at a frequency of 2.2989.10-18 S-1, the speed of light becomes zero. Such light represents resting particles – photonics that could serve as the Absolute Reference System, but due to their negligible mass, do not have a noticeable effect on the processes taking place. This explains Einstein’s principle of relativity. The formulas for the change in the speed and frequency of light during the transition from one IRS to another, within the measurement error, remain unchanged, which proves the postulate of the constancy of the speed of light in any IRS. It is shown that all STR formulas include not the speed of light, but the fundamental constant C, equal to the speed of light with a frequency ν = ∞. The proposed explanation of the correctness of Einstein’s postulates is logically, apparently, the only possible one.On the shape and fate of our Universe25 Mar, 2022
https://www.mathematicsgroup.us/articles/AMP-5-134.php
Einstein’s special and general theories of relativity revolutionized physics and cosmology. Newton assumed four identities namely mass, energy, space, and time. He told that space is absolute. Einstein modified and refined Newtonian concepts s by postulating that mass-energy and space-time. This enabled Einstein to find special relativity theory which predicted the variance of mass with velocity, the equivalent of mass and energy, time dilation, and length contraction. The extension and generalization of special relativity theory is the outcome of general relativity theory which is the geometrical interpretation of gravity. Almost all the predictions of Einstein’s general relativity theory have been experimentally verified. By delving into the equations of general relativity, the famous Russian mathematician Alexander Freedman found that the geometry of our Universe has only three possibilities, namely, open, closed, and flat. Freedman’s publication in the 1920s paved the way to study the geometry and fate of our Universe. Recently, NASA’s WMAP spacecraft and ESA’s Planck probes and observations revealed that the geometry of our Universe is flat with a marginal error of 0.04%. But to this day, there is no mathematical proof for these observations. In this short work, by applying the multiplication and division laws of number theory to cosmic triangles the author attempts to show that the shape/geometry of our Universe is FLAT.On Algebra, Cosmic Triangles and the shape of our Universe25 Mar, 2022
https://www.mathematicsgroup.us/articles/AMP-5-133.php
The curvature parameter k and the density parameter omega play the dominant phenomena determining the fate of our universe. According to these two scales, the geometry of the universe has three possibilities namely, flat, open, or closed. The flat and open universe will have continual expansion. But the closed universe will turn around and collapse. If k is zero, the universe is flat, if it is greater than zero, it is closed and if k is less than zero the universe will be open. And if the density parameter Omega is one (1), the universe is flat, if it is greater than one, the universe will be closed and if it is less than one, the universe is open. The main thing is that if the sum of the interior angles of the cosmic triangles is equal to 180 degrees, the geometry of our universe is flat /Euclidean If it is less than 180 degrees, the shape of our universe is open/ hyperbolic and if it is greater than 180 degrees it is closed/elliptic. In this short work, by applying the fundamental operations of classical algebra to the cosmic triangles, the author attempts to prove that the shape of our universe is flat.Logic proves that time does not get faster or slower (the universe is not produced by the singularity big bang)16 Mar, 2022
https://www.mathematicsgroup.us/articles/AMP-5-132.php
I use the axiom that equal conditions must have the same result.
Axiom proves that no matter how the velocity of an object changes, the time of all objects remains unchanged and unified.
Time can be expressed as an eternal constant.
Time belongs to the abstract concept of material attributes, and time is not a material concept.
There is an abstract concept of uniform velocity in the universe (For example, the velocity of light wave in vacuum is constant “C”).
According to the constant and uniform velocity of time, an important physical theory is proved: the universe is not produced by the singularity big bang.
Mathematical classification code: 00A79;83F05;00A30;03A05;70A05;70F20;03A10;03F03. Drag force through gases and plasma25 Jan, 2022
https://www.mathematicsgroup.us/articles/AMP-5-131.php
The drag force in a gas (previously derived by Stokes and Rayleigh) is derived by means of the molecular kinetics (transport equation of the momentum). Two regimes of resistance to motion are identified, governed by the relation of the velocity to the thermal (molecular) velocity. They correspond to the molecular movement, for small velocities, or to the hydrodynamic motion for high velocities. In the former case sound waves are not excited, and energy is dissipated by viscosity (friction), while in the latter case the energy is dissipated by the excitation of the sound waves. Also, the treatment is applied to the plasma. It is shown that in usual plasmas it is unlikely that the body motion excites plasmons. On the special spherical triangles for physical and cosmological applications25 Nov, 2021
https://www.mathematicsgroup.us/articles/AMP-4-130.php
It is well known that a spherical triangle of 270 degree triangle is constructible on the surface of a sphere; a globe is a good example. Take a point (A) on the equator, draw a line 1/4 the way around (90 degrees of longitude) on the equator to a new point (B). ... The angle at each of the vertices (A, B, C) will be ninety degrees, for a total of 270 degrees as shown in Figure 1. It is also possible to draw a spherical triangle whose interior angle sum is equal to 360 degrees. Also, it is possible to construct a special spherical triangle whose interior angle sum up to 540 degrees.
An introduction to the superunified theory of quantum fields & fundamental interactions (Discoveries in pure mathematics)19 Nov, 2021
https://www.mathematicsgroup.us/articles/AMP-4-129.php
This is intended to describe the physical Universe as self-excited and self-organized mathematical continuum. There does exist the universal pure (not applied) mathematical machine perceived by the intelligent observers in a capacity of certain material world. In this short article we are able to indicate only some key points of the theory which suggests practically infinite amount of combinatorics.Paintings crack initiation time caused by microclimate17 Nov, 2021
https://www.mathematicsgroup.us/articles/AMP-4-128.php
The current paper aims to use an irreversible cohesive zone model to investigate the effects of temperature and relative humidity cycles on multilayer thin-film paintings. The homogenous one-dimensional paint layers composed of alkyd and acrylic gesso over a canvas foundation (support) with known constant thicknesses are considered as the mechanical model of painting. Experimental data was used for mathematical modeling of canvas as a linear elastic material and paint as a viscoelastic material with the Prony series. Growth of crack through the length of the paint layers under the low amplitude cyclic stresses are modeled by cyclic mechanical loadings. The three-dimensional system is modeled using a finite element method. Fatigue damage parameters such as crack initiation time and maximum loads are calculated by an irreversible cohesive zone model used to control the interface separation. In addition, the effects of initial crack length and layers thickness are studied. With the increase of the painting thickness and/or the initial crack length, the value of the maximum force increases. Moreover, by increasing the Relative Humidity (RH) and the temperature difference at loading by one cycle per day, the values of initiation time of delamination decrease. It is shown that the thickness of painting layers is the most important parameter in crack initiation times and crack growth rate in historical paintings in museums and conservation settings. Random oscillations of nonlinear systems with distributed Parameter16 Nov, 2021
https://www.mathematicsgroup.us/articles/AMP-4-127.php
The article analyzes random vibrations of nonlinear mechanical systems with distributed parameters. The motion of such systems is described by nonlinear partial differential equations with corresponding initial and boundary conditions. In our case, the system as a whole is limited, so any motion can be considered as the sum of the natural oscillations of the system, i.e. in the form of an expansion of the boundary value problem in terms of own functions. The use of the theory of random processes in the calculation of mechanical systems is a prerequisite for the creation of sound design methods and the creation of effective vibration protection devices, these methods allow us to investigate dynamic processes, to determine the probabilistic characteristics of displacements of points of the system and their first two derivatives. In the work established these conditions are met, they provide effective vibration protection of the system under study with wide changes in the pass band of the frequencies of the random vibration effect, and the frequency of the disturbing force is much greater than the natural frequency of the system as a whole, in addition, with an increase in the damping capacity of the elastic-damping link of the system, the intensity of the random process significantly decreases, which in turn leads to a sharp decrease in the dynamic coefficient of the system.On the Bogolubov’s chain of kinetic equations, the invariant subspaces and the corresponding Dirac type reduction14 Oct, 2021
https://www.mathematicsgroup.us/articles/AMP-4-126.php
We study a special class of dynamical systems of Boltzmann-Bogolubov and Boltzmann-Vlasov type on infinite dimensional functional manifolds modeling kinetic processes in manyparticle media. Based on geometric properties of the manyparticle phase space we succeded in dual analysing of the infinite Bogolubov hierarchy of manyparticle distribution functions and their Hamiltonian structure. Moreover, we proposed a new approach to invariant reducing the Bogolubov hierarchy on a suitably chosen correlation function constraint and deducing the related modified Boltzmann-Bogolubov kinetic equations on a finite set of multiparticle distribution functions. Research on rolling bearing fault feature extraction based on entropy feature16 Aug, 2021
https://www.mathematicsgroup.us/articles/AMP-4-125.php
In large machinery, the most common element we can use is rolling bearing. When the rolling bearing fails, it is very likely to affect the normal operation of the equipment, or even cause danger. Therefore, it is necessary to monitor and diagnose the bearing fault in advance. The most important step in fault diagnosis is feature extraction. This is the research content of this paper. In this paper, the approximate entropy, the sample entropy and the information entropy are analyzed, and the feature is extracted to diagnose the rolling bearing fault. The specific research contents are as follows: (1) Firstly, the concepts of approximate entropy, sample entropy and information entropy are introduced briefly, and the approximate entropy, sample entropy and information entropy of rolling bearing vibration signals under different fault modes are calculated. The feasibility and shortcomings of the features extracted from these three entropy in the fault characteristics of rolling bearing are analyzed. (2) In order to make up for their defects, a method of fault feature extraction based on approximate entropy, sample entropy and information entropy is proposed, and its feasibility is verified. (3) Simulation experiments are carried out to calculate the accuracy of fault feature extraction based on the joint analysis of approximate entropy, sample entropy and information entropy.Waves of the dynamics of the rate of increase in the parameters of Covid-19 in Russia for 03/25/2020-12/31/2020 and the forecast of all cases until 08/31/202127 Jul, 2021
https://www.mathematicsgroup.us/articles/AMP-4-124.php
In applied mathematics and statistics, only linear equations are still used. The article proposes the sum of asymmetric wavelets with variable amplitudes and periods of oscillation. As a result, the behavior of any object or subject is given by the sum of vibrations. Using the identification method based on statistical daily data on four indicators of the dynamics of the rate of Covid-19, quanta of the pandemic behavior in the territory of the Russian Federation from March 25 to December 31, 2020 were identified. It is shown that the rates are infected, cured, died, and “all cases = infected + cured + died” in Russia got two superimposed bulges. Based on the computational capabilities of CurveExpert-1.40, 4-5 components were jointly identified with an overall correlation coefficient above 0.86 for infected and over 0.99 for all cases. It has been proven that the spread of the virus has the form of a set of finite-dimensional wavelets with variable amplitudes and, as a rule, with a decreasing oscillation period. By modeling the standard deviation by the serial numbers of the wavelets, it was proved that the parameters of the Covid-19 pandemic have fractal distributions. For the velocity parameter “died”, the main bulge does not reach its maximum. And the second member of the trend peaked at 164 deaths on 06/18/2020, and it will leave the scene from 03/23/2021. The third member of the model, aimed at countering mortality, at the beginning of the time series on 03/25/2020 received a fluctuation period of 355 days. By the date of December 31, 2020, the fluctuation period became equal to 278 days. More often with constant half-periods of 3.5 and 16.1 days, fluctuations occurred. In this case, the 70th term gives a constant oscillation period, even 1.88 days. The average relative modeling error in modulus is equal for speeds: 1) died - 2.09; all cases - 3.22; cured - 17.17 and infected 29.91%. In this case, the range of error values changes in the following intervals: 1) died from -18.93 to 11.95%; all cases from -31.37 to 20.20%; cured from -248.8 to 396.0%; infected from -1934.0 to 779.7%. According to the distributions of the relative error after 1%, the following rating was obtained: 1) the correlation coefficient of 0.9807 for the speed died; 2) at 0.9768 the rate of all cases; 3) 0.8640 has been cured; 4) 0.8174 - infected. The fractality coefficient is equal to the ratio of the standard deviations of the linear model to the last component: for infected 3572.76 / 310.97 = 11.5; cured 5.8; died 24.3 and all cases 9.6. Further, due to the high range of relative error, the rates of cured and infected are excluded from forecasting. The forecast for the rate of deaths was carried out until 02/14/2021. The right border at the forecast horizon was adopted due to the fact that negative values appear from 15.02.2021. For a longer time interval from 01.01.2021 to 31.08.2021 the model allows predicting the rate of change of all cases. To reduce the relative modeling error, it is recommended to re-identify the model of the dynamics of the parameters died and all cases every three weeks. The identification method is applicable to any statistical series, and not only to dynamic ones.From linear algebra to quantum information20 Jul, 2021
https://www.peertechzpublications.org/articles/AMP-4-123.pdf
Anticipating the realization of quantum computers, we propose the most reader-friendly exposition of quantum information and qubits theory. Although the latter lies within framework of linear algebra, it has some flavor of quantum mechanics and it would be easier to get used to special symbols and terminologies. Quantum mechanics is described in the language of functional analysis: the state space (the totality of all states) of a quantum system is a Hilbert space over the complex numbers and all mechanical quantities are taken as Hermite operators. Hence some basics of functional analysis is necessary. We make a smooth transition from linear algebra to functional analysis by comparing the elements in these theories: Hilbert space vs. finite dimensional vector space, Hermite operator vs. linear map given by a Hermite matrix. Then from Newtonian mechanics to quantum mechanics and then to the theory of qubits. We elucidate qubits theory a bit by accommodating it into linear algebra framework under these precursors.Dirac spinor’s transformation under Lorentz mappings15 Jul, 2021
https://www.mathematicsgroup.us/articles/AMP-4-122.php
For a given Lorentz matrix, we deduce the Dirac spinor’s transformation in terms of four complex quantities.Numerical investigations for flow past two square rods in staggered arrangement through Lattice Boltzmann method03 Jul, 2021
https://www.mathematicsgroup.us/articles/AMP-4-121.php
A numerical study for two dimensional (2-D) incompressible flow past over two square rods in staggered arrangement detached with a rectangular control rod is conducted by applying single-relaxation-time lattice Boltzmann method (SRT-LBM). This study is conducted basically to reduce the fluid forces and to suppress the vortex shedding through passive control method under the effect of gap spacing between the rods and Reynolds number. The gap spacing (g = s/D) between the rods is taken as g = 1, 3 and 6 whereas, Reynolds number Re= u∞ D/γ is selected within the range of Re = 80 – 200. First validity of code and effect of computational domain along with effect of uniform inflow velocity is checked by considering upstream, downstream and height of computational domain respectively, at Lu = 7.5d, Ld = 30d and H = 14d. After that the effect of gap spacing and Reynolds number on flow structure mechanism is studied. The acquired results are obtained in terms of vorticity contour visualization, power spectrum analysis of lift coefficients and force statistics. Here, three different types of flow regimes, named as i) Irregular Single Bluff Body (ISBB), ii) Flip Flopping (FF) and iii) Anti Phase Synchronized (APS) flow regimes are observed at different values of gap spacing and Reynolds number. In study of force statistics, the values of mean drag coefficients (Cdmean), root mean square of drag coefficients (Cdrms), root mean square of lift coefficients (Clrms) and strouhal number (St) of two square rods are calculated. The values of mean drag coefficients for rod R1 is greater than that of rod R2. The Cdmean for R2 increases with increment in the values of Reynolds, while as Cdmean for R1 having mixed trend. The maximum value of Cdmean is attained at (g, Re) = (1,80) that is 1.8971 for R1 as compared to R2, where existing flow regime is the Irregular single bluff body (ISBB) flow regime. The largest value of Strouhal number is obtained for R2 at (g, Re) = (6, 150) that is 0.1608 along with Anti phase synchronized (APS) flow regime.Application of algebra to trisect an angle of 60 degree19 Apr, 2021
https://www.mathematicsgroup.us/articles/AMP-4-120.php
Trisection of an angle, doubling the cube, squaring the circle, to draw a regular septagon and to deduce Euclid V from Euclid I to IV are the famous classical impossibilities. Recently, Sivasubramanian and Kalimuthu jointly and independently found several solutions for the parallel postulate problem. Their findings have been published in various peer reviewed international journals. In this work, by applying linear algebraic equations the authors have attempted and trisected 60 degree without using a protractor.Theoretical calculation of self-propagating high-temperature synthesis (SHS) preparation of AlB1223 Mar, 2021
https://www.mathematicsgroup.us/articles/AMP-4-119.php
Although experimental results of preparing AlB12 by self-propagating high-temperature synthesis using Mg-B2O3-Al2O3 as raw material has been studied, the theoretical calculations for the preparation of AlB12 have not been examined as thoroughly. In this article, for the first time, we report on the study of theoretical calculation and the adiabatic temperature, calculated, and compared with the actual reaction temperature. The Gibbs free energy for each level of reaction is also calculated. The calculation results show that the adiabatic temperature is 2789.5 K, the standard Gibbs free energy of each reaction is less than 0, and the reaction can proceed spontaneously, which is consistent with the results of the experiment.Energy and exergy analyses of combustion process in a DI diesel engine fuelled with diesel-biodiesel blends15 Mar, 2021
https://www.mathematicsgroup.us/articles/AMP-4-118.php
Exergy analysis is achieved by assessing exergies related to the inlet fuel and air, output power, heat loss, gas exhaust loss and destruction or system irreversibility. The exergy fraction of each component is considered for all mixtures by dividing the individual exergy quantity into the exergy of the fuel. In the present investigation, the combustion process has been simulated in a DI diesel engine (OM314) with biodiesel fuel different Blends (B20, B40, B100) of soybean at full load and 1200 rpm by a thermodynamic model using both thermodynamics first and second laws of thermodynamics. The results showed good agreement with the experimental pressure. The results of the analysis of energy and availability balance show that the first and second laws efficiency for pure biodiesel fuel is more than the other two fuel and total availability. indicated work availability, the heat loss availability, burned fuel availability and irreversibility for 20% biodiesel fuel are more than two other fuels.An astrobiological theorem17 Oct, 2020
https://www.mathematicsgroup.us/articles/AMP-3-117.php
The structure of the human brain reflects multifarious random influences of terrestrial and phylogenetic history, yet the higher mental functions correlated with this unique cerebral neurophysiology are generally assumed to embody universals common to intelligences independent of biological substrate. This assumption is deeply embedded in scientific and popular cultures. However, this idea has not been explicitly investigated. The present study proves that any sufficiently advanced organism of non-zero, finite volume (with boundary) must have a ‘natural’ logic equivalent to Sentential (propositional) Calculus (SC). This commonalty arises from the essential transduction from external to internal milieu that must occur at any organism’s boundary surface. This transduction encodes SC in sensory data and the proof demonstrates that any internal inductive construct—including mathematics and physics—inherits this logical bias. The topological origin of deductive logic not only demonstrates a universal commonality subject to very weak constraints, but also demonstrates a surprising biological origin of foundational principles in mathematics and physics.Application of logistic regression equation analysis using derivatives for optimal cutoff discriminative criterion estimation19 Aug, 2020
https://www.mathematicsgroup.us/articles/AMP-3-116.php
Background: Sigmoid curve function is frequently applied for modeling in clinical studies. The main task of scientific research relevant to medicine is to find rational cutoff criterion for decision making rather than finding just equation for probability calculation.
The objective of this study is to analyze the specific features of logistic regression curves in order to evaluate critical points and to assess their implication for continuous predictor variable dichotomization in order to provide optimal cutoff criterion for decision making.
Methods: Second order and third order derivatives were used to analyze estimated logistic regression function, critical values of independent continuous variable that correspond to zero points of second and third derivative were calculated for each logistic regression equation. Using those values continuous predictors of each logistic regression equations were converted into dichotomized scales using 1 value that correspond to second order derivative and 2 values that correspond to zero points of third derivative then receiver operating characteristics of estimated equations with dichotomized predictor were assessed.
Results: Sigmoid curve of logistic regression has the same structure with inflection point corresponding probability 0.5 (zero value of second derivative) and maximal torsion (zero values of third derivative) corresponding 0.2113 and 0.7886 probability values. Thresholds accounting for predictor values that correspond to zero values of second and third derivative provide estimation of logistic regression applying dichotomized predictor with optimal ratio of sensitivity, specificity and overall accuracy with maximal area under curve.
Conclusion: Analysis of logistic regression equation with continuous predictor applying derivatives help to choose optimal thresholds that provide maximally effective discriminative functions with priority sensitivity or specificity. Using this dichotomization discriminative function can be adjusted to the needs of particular task or study depending which characteristic is in priority – sensitivity or specificity.On freedman equation and the shape of our universe17 Jul, 2020
https://www.mathematicsgroup.us/articles/AMP-3-115.php
In the nineteen twenties, the famous Russian mathematician Alexander Freedman formulated an equation which determines the shape and fate of our universe. Freedman derived his equation in general relativity. The equation reveals that the geometry of the universe may be flat, closed or open. The Euclidean, hyperbolic and spherical geometries describe the flat, open and closed universes respectively. Both NASA’s WMAP and ESA’s PLANCK mission show the cosmological curvature parameter, ΩK, to be 0.000±0.005, consistent with a flat universe. Many observational cosmological probes revealed that the universe is flat obeying the classical Euclidean geometry. But till this day, there is no mathematical formulation/proof for the geometry of our universe. In this work, the attempts to establish that the shape of our universe is flat.Time series analysis of Holt model and the ARIMA Model facing Covid-1903 Jul, 2020
https://www.mathematicsgroup.us/articles/AMP-3-114.php
Background: Since the first appearance of the novel coronavirus in Wuhan in December 2019, it has quickly swept the world and become a major security incident facing humanity today. While the novel coronavirus threatens people’s lives and safety, the economies of various countries have also been severely damaged. Due to the epidemic, a large number of enterprises have faced closures, employment has become more difficult, and people’s lives have been greatly affected. Therefore, to establish a time series model for Hubei Province, where the novel coronavirus first broke out, and the United States, where the epidemic is most severe, to analyze the spreading trend and short-term forecast of the new coronavirus, which will help countries better understand the development trend of the epidemic and make more adequate preparation and timely intervention and treatment to prevent the further spread of the virus.
Dynamic model of infectious diseases on the coronavirus disease 201912 Jun, 2020
https://www.mathematicsgroup.us/articles/AMP-3-113.php
Under the general trend of globalization, historically and newly discovered infectious diseases are seriously threatening people’s health and lives, including: Avian influenza H7N9, AIDS HIV, Influenza A H1N1, etc., a new type of corona that is currently spreading in many countries around the world Viral pneumonia (C0VID-19), there is currently no good therapeutic drug, which seriously affects human survival and development. The rapid spread of the new coronavirus in Hong Kong, while starting the epidemic prevention work, uses mathematical modeling methods to construct the propagation model, and then calculates the inflection point for better prevention and control of the spread of epidemic work. The spread of Hong Kong was analyzed, and the quantitative relationship between the growth rate of the number of new coronavirus infections and time was explored.Analysis of the axial stability for an assembly of optical modes with stochastic fluctuations type Markov chain12 May, 2020
https://www.peertechzpublications.org/articles/AMP-3-112.pdf
We describe the engineering of optical modes whose axial structure follows fluctuations of Markov-chain-type.Standard model in a Nutshell07 Mar, 2020
https://www.peertechzpublications.org/articles/AMP-3-111.pdf
Understanding the complexity of the Standard Model (SM) of particle physics is crucial for young students aiming to pursue their future higher studies in physics. Poisson structures on (non)associative noncommutative algebras and integrable Kontsevich type Hamiltonian systems30 Jan, 2020
https://www.mathematicsgroup.us/articles/AMP-3-110.php
We have revisited the classical Poisson manifold approach, closely related to construction of Hamiltonian operators, generated by nonassociative and noncommutative algebras. In particular, we presented its natural and simple generalization allowing effectively to describe a wide class of Lax type integrable nonlinear Kontsevich type Hamiltonian systems on associative noncommutative algebras.Modeling of active thermography through uncertainty quantifi cation of parameters of the heat transfer equation19 Nov, 2019
https://www.mathematicsgroup.us/articles/AMP-2-109.php
Active thermography is an experimental technique used to analyze samples of materials or entire structures without destroying them, by means of a heat source, such as a laser beam of a given power.An analysis of ammonia synthesis by the model of Selective Energy Transfer (SET)26 Sep, 2019
https://www.mathematicsgroup.us/articles/AMP-2-108.php
The SET theory implies that energy is transferred from the catalyst system via infrared radiation to the molecules that are supposed to react. In previous investigations it has been demonstrated that the activation of the reacting species-as long as the molecules are infrared active-can occur at low adsorption strength. However, for molecules that are IR inactive, e.g. dinitrogen, this is not possible.The quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras16 Sep, 2019
https://www.mathematicsgroup.us/articles/AMP-2-107.pdf
There are studied algebraic properties of the quadratic Poisson brackets on nonassociative noncommutive algebras, compatible with their multiplicative structure. Their relations both with differentiations of the symmetric tensor algebras and Yang-Baxter structures on the adjacent Lie algebras are demonstrated.The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure28 Aug, 2019
https://www.mathematicsgroup.us/articles/AMP-2-106.pdf
There are reviewed modern investigations devoted to studying nonlinear dispersiveless heavenly type integrable evolutions systems on functional spaces within the modern differential-geometric and algebraic tools. Main accent is done on the loop diffeomorphism group vector fields on the complexified torus and the related Lie-algebraic structures, generating dispersionless heavenly type integrable systems.Mid-point technique for calculating divergent integrals10 Jul, 2019
https://www.mathematicsgroup.us/articles/AMP-2-105.php
A mid-point technique is introduced to overcome the diffi culties in other techniques. The modied
e⁄ective interaction quark potential which uses to calculate different properties of the NJL model such
as the constituent quark mass, pressure, and energy density is solved using the present technique. The
present method gives good accuracy for the mathematical problem and avoids the physical di¢ culty in
the previous works.Black quanta. On the thermodynamics of the black holes02 Jul, 2019
https://www.mathematicsgroup.us/articles/AMP-2-104.php
It is shown that the quantized internal motion of the black holes consists of Planck quanta (Planck
mass, length, time, etc), which may be called black quanta. The mass of the black hole is a integral
multiple of the Planck mass, and the radius of the black hole (Schwarzschild radius) is an integral multiple
of the Planck length. This circumstance arises from the proportionality of the black hole radius and mass.
The statistical physics and the thermodynamics of the black holes are derived herein from the statistical
motion of the black quanta.Space Equations04 Mar, 2019
https://www.mathematicsgroup.us/articles/AMP-2-103.php
Trying to observe the reason behind the differences in the nature of space that exists on earth and on the outer space led to the path were space and gravity meets. This paper presents a theory which comprises of an already existing effect that has helped to determine the following;
• Space constant.
• The Relationship between Space and Gravity.
• Formulation of Space Equations.
• Verification of the value of acceleration due to gravity, mass, radius of most planetary bodies.
• The Fate of the existence of parallel universes.Integral formulations for 1-D Biharmonic and Second Order Coupled Linear and Nonlinear Boundary Value Problems29 Oct, 2018
https://www.mathematicsgroup.us/articles/AMP-1-101.php
Integral formulations based on a boundary-domain interpretation of the boundary element method
(BEM) are applied to develop the numerical solutions of biharmonic and second order coupled linear and
nonlinear boundary value problems.