Mathematical Programming with System of Equilibrium Constraints

In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions.     

时滞格微分方程组的行波解

本文利用Schauder不动点定理的方法和上、下解技巧,研究了时滞格微分方程组的行波解,给出了当系统的非线性项满足“拟单调条件”和“指数拟单调条件”时行波解的存在性.     

On the spectral norms of Cauchy–Toeplitz and Cauchy–Hankel matrices

In this study, we have found upper and lower bounds for the spectral norm of Cauchy–Toeplitz and Cauchy–Hankel matrices in the forms T_n=[1/(a+(i−j)b)]ⁿ_i,j=1, H_n=[1/(a+(i+j)b)]ⁿ_i,j=1.     

Upper domination and upper irredundance perfect graphs

Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. A graph G is called IR-perfect if Γ(H) =IR(H), for every induced subgraph H of G. In this paper, we present a characterization of Γ-perfect graphs in terms of a family of forbidden induced subgraphs, and show that the class of Γ-perfect graphs is a subclass of IR-perfect graphs and that the class of absorbantly perfect graphs is a subclass of Γ-perfect graphs. These results imply a number of known theorems on Γ-perfect graphs and IR-perfect graphs. Moreover, we prove a sufficient condition for a graph to be Γ-perfect and IR-perfect which improves a known analogous result.     

Existence of traveling wave fronts of delayed lattice differential equations

Existence of traveling wave fronts for delayed lattice differential equations is established by Schauder fixed point theorem. The main result is applied to a delayed and discretely diffusive model for the population of Daphnia magna.     

The Upper Semicontinuity of Random Attractor for Stochastic Suspension Bridge Equation

Based on the existence of pullback attractors for stochastic suspension bridge in \cite{Yao1}, in the paper, we further investigate the upper semicontinuity of pullback attractors for the problem.     

Formation of upper rim acylated calix[4]arenes using a sacrificial zinc anode

A straightforward electrosynthetic method is described, which allows upper rim acylation of non-p-halogenated calix[4]arenes. For example, a solution of tetrapropoxycalix[4]arene 4 was electrolysed in the presence of ZnBr₂ in an undivided cell fitted with a sacrificial zinc anode using pure acetonitrile as solvent, yielding an organozinc species, which was then treated with acetyl chloride in the presence of a palladium catalyst to afford 5,11-diacetyl-25,26,27,28-tetrapropoxycalix[4]arene 5 in ca. 35% yield after workup.     

Maximum Waring Ranks of Monomials and Sums of Coprime Monomials

We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.     

Semilinear limit problems for reaction–diffusion equations with variable exponents

In this work we study PDE limit problems for nonlinear reaction–diffusion equations and we study the sensitivity of nonlinear PDEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction–diffusion equations with spatially variable exponents when the exponents go to 2 in $L^{\infty }(\mathrm{\Omega })$.     

Analytical sequences of upper and lower solutions for a class of elliptic equations

Comparison arguments are applied to derive decreasing sequences of upper solutions and increasing sequences of lower solutions for a class of nonlinear elliptic equations. The monotonicity of the two sequences is proven. These polynomial sequences are obtained by applying new algorithms and solving linear differential equations. The obtained upper and lower solutions are analytic and have closed forms. Different examples are presented to explore the effectiveness of the new algorithms. The presented ideas and algorithms can be extended to deal with different classes of equations.