Time evolution of infinitely many particles: An existence theorem

In this paper we deal with systems of infinitely many particles in ³, given by a two-body, short-range potential and an external potential, depending on the position of the particles. We show the existence of dynamics for a set of initial configurations, which has measure one with respect to the Gibbs measure induced by a suitable family of Hamiltonians.     

AuCu3熔体快速冷却过程中的键对与多面体

Based on the FS(Finnis-Sinclair) many-body potential model, the rapid cooling process of a system, which consists of 375 Cu atoms and 125 Au atoms, controlled by period boundary condition was simulated. The dependence of pair distribution function of melten compound AuCu3 on the temperature under these conditions was researched. It can be concluded that the noncrystal exists under 700 K, and the liquid-glass transition temperature is approximately 680 K according to the Abraham′s method. Furthermore, the feature of version of cluster in melten AuCu3 was investigated by Honeycutt pair analysis technique. It is demonstrated that the structural configuration in melten AuCu3 has remarkable variation during the formation of noncrystal according to the relationship between the bonded pairs and polyhedron and temperatures. The defective polyhedra in liquid AuCu3 have greatest changes accompanying the changing temperatures.     

带凹凸项的分数阶Laplace方程解的存在性

<正>该文研究带凹凸项的分数阶Laplace方程{(-△)su=λa(x)|u|p-2u在Ω上,u=0在R2\Ω上解的存在性,其中Ω是R~n中的有界区域,s∈(0,1),q∈(1,2),p∈(2,2_s~*],2_s~*=(2n)/(n-2s)n2s,λ0,a(x)和b(x)都是有界连续函数,且b(x)非负、a(x)变号.应用山路引理,证明了方程在临界和次临界情形下,至少有一个非负非平凡解;而且,利用喷泉定理,证明了方程在次临界情形下有无穷多个解.     

Existence and Mann iterative approximations of nonoscillatory solutions of nth-order neutral delay differential equations

In this paper we consider the following nth-order neutral delay differential equation:

     

A note on the stability of the many-queue head-of-the-line processor-sharing system with permanent customers

We consider a single server system consisting of n queues with different types of customers and k permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). By means of Loynes’ monotonicity method a stationary work load process is constructed and using sample path analysis general stability conditions are derived. They allow to decide which queues are stable and, moreover, to compute the fraction of processor capacity devoted to the permanent customers. In case of a stable system the constructed stationary state process is the only one and for any initial state the system converges pathwise to the steady state. This revised version was published online in June 2006 with corrections to the Cover Date.     

Infinitely many solutions for perturbed difference equations

Using variational methods and critical point theory, the existence of infinitely many solutions for perturbed nonlinear difference equations with discrete Dirichlet boundary conditions is ensured.     

Quantum search of many vertices on the joined complete graph

The quantum search on the graph is a very important topic. In this work, we develop a theoretic method on searching of single vertex on the graph [$Phys. Rev. Lett$. 114 110503 (2015)], and systematically study the search of many vertices on one low-connectivity graph, the joined complete graph. Our results reveal that, with the optimal jumping rate obtained from the theoretical method, we can find such target vertices at the time $Oleft({sqrt N } right)$, where $N$ is the number of total vertices. Therefore, the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.