Journal of Applied Mathematics and Physics

Journal Information
ISSN / EISSN : 2327-4352 / 2327-4379
Published by: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 1,680
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Latest articles in this journal

Urbain Traoré
Journal of Applied Mathematics and Physics, Volume 09, pp 2414-2429; https://doi.org/10.4236/jamp.2021.910153

Abstract:
In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see [1]). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our theoretical results.
Guoguang Lin, Lujiao Yang
Journal of Applied Mathematics and Physics, Volume 09, pp 2399-2413; https://doi.org/10.4236/jamp.2021.910152

Abstract:
In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.
Faisal Al-Dheleai, Elmetwally Elabbasy
Journal of Applied Mathematics and Physics, Volume 09, pp 2376-2398; https://doi.org/10.4236/jamp.2021.99151

Abstract:
In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscillation of all solutions of this equation. Our results not only unify the oscillation of second order nonlinear differential and difference equations but also can be applied to different types of time scales with sup T = ∞. Our results improve and extend some known results in the literature. Examples which dwell upon the importance of our results are also included.
Bo Qin, Ningxiang Wu, Liyang Xie
Journal of Applied Mathematics and Physics, Volume 09, pp 2345-2354; https://doi.org/10.4236/jamp.2021.99149

Abstract:
Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This paper presents a stochastic simulation method to estimate the Weibull location parameters according to a small size of sample of product life observations and a large amount of statistically simulated life date. Big data technique is applied to find the relationship between the minimal observation in a product life sample of size n (n ≥ 3) and the Weibull location parameter. An example is presented to demonstrate the applicability and the value of the big data based stochastic simulation method. Comparing with other methods, the stochastic simulation method can be applied to very small size of sample such as the sample size of three, and it is easy to apply.
Yujin Liu
Journal of Applied Mathematics and Physics, Volume 09, pp 683-693; https://doi.org/10.4236/jamp.2021.94049

Abstract:
The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementary wave interactions in the phase plane and construct uniquely the solution of this initial value problem. It is found that the combustion wave solution of the corresponding Riemann may be extinguished after perturbation which shows that the unburnt gas is unstable.
Weicheng Xu, Tian Zhou, Di Peng
Journal of Applied Mathematics and Physics, Volume 09, pp 694-706; https://doi.org/10.4236/jamp.2021.94050

Abstract:
In this paper, we characterize the players’ behavior in the stock market by the repeated game model with asymmetric information. We show that the discount price process of stock is a martingale driven by Brownian motion, and give an endogenous explanation for the random fluctuation of stock price: the randomizations in the market is due to the randomizations in the strategy of the informed player which hopes to avoid revealing his private information. On this basis, through studying the corresponding option pricing problem furtherly, we can give the expression of function φ.
Yanan Huang, Junhong Yao, Ting Su
Journal of Applied Mathematics and Physics, Volume 09, pp 2152-2158; https://doi.org/10.4236/jamp.2021.98134

Abstract:
In this paper, a new integrable variable coefficient Toda equation is proposed by utilizing a generalized version of the dressing method. At the same time, we derive the Lax pair of the new integrable variable coefficient Toda equation. The compatibility condition is given, which insures that the new Toda equation is integrable. To further analyze the character of the Toda equation, we derive one soliton solution of the obtained Toda equation by using separation of variables.
Hai Xie
Journal of Applied Mathematics and Physics, Volume 09, pp 2159-2169; https://doi.org/10.4236/jamp.2021.98135

Abstract:
In this paper, we introduce the concepts of additive generators and additive generator pair of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We mainly discuss the conditions under which an n-dimensional overlap function can be expressed in terms of its generator pair.
Güngör Gündüz
Journal of Applied Mathematics and Physics, Volume 09, pp 2004-2037; https://doi.org/10.4236/jamp.2021.98131

Abstract:
The purpose of this research is to characterize shapes in thermodynamic terms, namely, in terms of total energy, dissipative energy, entropy, and temperature. As case studies, polygons and some well-known curves were taken, and they were characterized using physical terms. The relation between entropy and curvature was elucidated, and the black hole surface gravity and temperature were criticized and reinterpreted from this point of view. Particular energy attributions were evaluated by comparing the position of any edge of a polygon (i.e. its angle with the horizontal axis) with a broken crystal surface. Energies of all edges were added up at all positions between 0˚ - 360˚. In regular polygons, the total energy decreases with the increase of the number of edges. Entropy increases in the reverse order, and the increase of the number of edges increases entropy. It implies that the circle has the lowest energy but the highest surface entropy. In curves (circle, sine-curve, spiral, and exponential curve), the total energy, dissipative energy, and entropy all depend on amplitude and also on specific variables. Black hole entropy expressed in terms of the surface area is a configurational entropy and not thermal entropy; therefore, it does not involve a varying temperature term. The surface gravity of a black hole is connected to acceleration and thus to curvature. To relate it with the temperature needs to be reinterpreted, because, surface gravity behaves like an attractive force not exactly like temperature. Hawking radiation is still possible, but the black hole does not get warmer as it evaporates. Material loss from the black hole gets faster as its radius decreases due to the curvature effect, i.e. by a mechanism similar to the Gibbs-Thomson effect.
Pirooz Mohazzabi, Gabrielle Richardson, Gwendolyn Richardson
Journal of Applied Mathematics and Physics, Volume 09, pp 1890-1895; https://doi.org/10.4236/jamp.2021.98122

Abstract:
In this article, the validity of a previously developed model for Coronavirus pandemic is verified by testing it against the global infection cases complied by the World Health Organization. The results further support the validity of the model and its assumptions as was previously verified by the United States data.
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