一类Hilfer型分数阶微分方程解的存在和唯一性

用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.     

Qualitative analysis of thermal explosion of sodium droplet with variable thermophysical properties and thermal radiations

There are many coolants frequently used in the industry for controlling not only heat transfer, but also temperature distribution in a confined domain. However, little is known on the thermal properties of sodium droplets. The qualitative analysis of differential equations that model the thermal explosion, nonlinear dynamic of sodium droplet with variable thermophysical properties when thermal radiations are considered as suggested by Cogley et al, Sohrab et al, and P‐1 approximation Sazhin et al is deliberated upon in this study. The governing equations, first‐order nonlinear ordinary differential equations, are nondimensionalized using the appropriate similarity variables. The existence and uniqueness of the solutions, concavity, and convexity of the temperature distribution, and positivity nature of the solutions of the dimensionless governing equations are established. It is concluded that there exists a solution for a certain range of the admissible parameters and when the reduced activation energy is negative and temperature distribution fits concavity. More so, the major criteria to obtain a positive solution are outlined in this study.     

High-order approximations of three-phase-lag heat conduction model: Some qualitative results

This article deals with some high-order approximations of the three-phase-lag heat transfer model aiming, at first, to identify the restrictions that make them well-posed consistence. Consequently, a first result about the uniqueness and continuous dependence of the solutions with respect to the given initial data and to the supply term is established for the related initial boundary value problems. Subsequently, to provide a more comprehensive analysis of the model, some further spatial decay results are established, this time conveniently relaxing the hypotheses about the delay times and the thermal conductivities. More precisely, a theorem of influence domain is proved for the wave propagating models and an exponential decaying estimate of Saint-Venant type is established for the diffusive models.     

Cosserat理论的应变能定理及解的唯一性

Cosserat理论已广泛应用于岩土工程，求解Cosserat问题时，解析方法与数值方法都曾被采用，证明了Cosserat问题的能量原理及解的唯一性定理，进一步完善了该理论，并保证了数值及解析求解结果的正确性。     

Potential method in the theory of thermoviscoelastic mixtures

In this article, the linear theory of binary thermoviscoelastic mixtures is considered and the basic boundary value problems (BVPs) of steady vibrations are investigated. Namely, the fundamental solution of the system of equations of steady vibrations is constructed explicitly and its basic properties are established. Green’s second and third identities are obtained and the uniqueness theorems for classical solutions of the internal and external basic BVPs of steady vibrations are proved. The surface and volume potentials are constructed and their basic properties are given. The determinants of symbolic matrices are calculated explicitly. The BVPs are reduced to the always solvable singular integral equations for which Fredholm’s theorems are valid. Finally, the existence theorems for classical solutions of the internal and external BVPs of steady vibrations are proved by the potential method and the theory of singular integral equations.     

A new analytical method for solving systems of Volterra integral equations

In this paper, a new modified homotopy perturbation method (NHPM) is introduced for solving systems of Volterra integral equations of the second kind. Theorems of existence and uniqueness of the solutions to these equations are presented. Comparison of the results of applying the NHPM with those of the homotopy perturbation method and Adomian's decomposition method leads to significant consequences. Several examples, including the system of linear and nonlinear Volterra integral equations, are given to demonstrate the efficiency of the new method.     

摩擦接触系统多极边界元法二次建模与数值优化

讨论了摩擦接触系统的建模与求解问题。将系统方程组的多极边界元法求解归结为变分问题并证明其等价性。在系统最优化数学模型的基础上,通过引入严格凸二次函数建立系统的二次规划模型,证明其最优解存在且唯一,并给出模型求解的最优性条件。     

On the existence,uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems

In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems. Later, we present a set of necessary and sufficient conditions for uniqueness of Filippov solutions for bimodal piecewise affine systems. We also study the so-called Zeno behavior (possibility of infinitely many switchings within a finite time interval) for Filippov solutions.     

How heterogeneous community engage newcomers? The effect of community diversity on newcomers’ perception of inclusion: An empirical study in social media service

Online communities that provide social media services need to engage newcomers so as to not lose them to competitors. This study examines the role of community diversity (in terms of perceived visible dissimilarity, perceived informational dissimilarity and perceived value dissimilarity) in influencing perceived inclusion of newcomers in the online community and the influence of such perception on newcomers’ engagement intention. The theoretical background on perceived inclusion is obtained from the optimal distinctiveness theory, which comprises of two dimensions, namely, social identification and perceived uniqueness. The results support the multiple roles of community diversity on a newcomer’s perceived inclusion. The findings of this study contribute to a better understanding of the effect of community diversity on newcomers’ engagement behavior, and provide recommendations on designing a personalized community diversity environment.     

UNIQUENESS CONDITIONS OF CL-STRUCTURES IN GL-STRUCTURE EQUIVALENCE CLASSES OF SYSTEM RECONSTRUCTABILITY ANALYSIS

This paper first introduces the basic notions of overall systems with logical relations, their subsystems, structure representation graphs, sets of H-structures and G-structures with logical relations S _H ^L and S _G ^L, immediate refinement and aggregate with logical relations, structure-graph mappings r_V ^L, r_G ^L, etc., and the notions of inclusiveness with logical relations, upper bounding and lower bounding with logical relations. Then it proves the sufficient conditions under which representation graphs R ^L form a lattice. By defining the least upper bound and largest lower bound of (R^L, ) and recommending a lemma on distributivity, this paper proves the sufficient conditions under which G-structures with logical relations form Boolean lattices. Finally after defining the M-structures and C-structures with logical relations, i.e. M-structures and C-structures, this paper proposes the sufficient conditions for the uniqueness of C-structures in G-structure equivalence classes, and proves that the C ^L-structure is the least refined GL-structure in equivalence class S _G ^L/r _G ^L.