Annals of Mathematics and Physics
https://peertechzpublications.com/journals/annals-of-mathematics-and-physics
A Peertechz Open Access Journalen-usOn Λ-fractional variational calculus01 Mar, 2023
https://www.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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://peertechzpublications.com/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://peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/articles/AMP-5-153.php
Thermodynamic-induced geometry of self-gravitating systems16 Sep, 2022
https://www.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/articles/AMP-5-151.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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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://peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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://peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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://peertechzpublications.com/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://peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/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.peertechzpublications.com/articles/AMP-2-104.pdf
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.peertechzpublications.com/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.peertechzpublications.com/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.