Bounds for pairs in judicious partitioning of graphs

In 2002, Bollobás and Scott posed the following problem: for an integer and a graph G of m edges, what is the smallest f (k, m ) such that V (G ) can be partitioned into V ₁,…,V _k in which for all , where denotes the number of edges with both ends in ? In this paper, we solve this problem asymptotically by showing that . We also show that V (G ) can be partitioned into such that for , where Δ denotes the maximum degree of G . This confirms a conjecture of Bollobás and Scott. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 59–70, 2017     

Almost Automorphic Dynamics of Generalized Li\'enard Equation

In this study, we focus on the solutions of the Li\''enard equation being bounded in the future and characterize the almost automorphic, asymptotically almost automorphic, and weighted pseudo almost automorphic dynamics. An example is presented to illustrate the main findings.     

Regularity Criterion for a Nonhomogeneous Incompressible Ginzburg-Landau-Navier-Stokes System

Applications of Mathematics - We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in ?3. It is proved that if the...     

二阶Volterra系统对平稳正态激励的统计响应的表示定理的数学证明

1974年,Neal根据Kac和Siegert的思想,给出了一个在电子工程、海洋工程、建筑工程、航空工程、自动控制的随机振动中有重要应用的二阶Volterra非线性系统对平稳正态输入的统计响应的表示定理.1984年,Naess对此定理又给出了一个数学证明.经过研究后发现,他们对定理条件的叙述都是模糊的,而且其数学证明都是有问题的.本文重新讨论了这个表示定理,给出了明确的定理条件及严格的数学证明,为它的广泛应用奠定了理论基础.     

正交异性理想塑性材料平面应力问题的裂纹尖端应力场

本文在裂纹尖端场的应力分量仅仅是θ的函数的假设下,利用Hill屈服准则和平衡方程导出了正交异性理想塑性材料平面应力问题中裂纹尖端场的微分方程;在允许应力不连续线存在的情况下,把解析表达和数值计算法结合起来,得到了Ⅰ型和Ⅱ型裂纹尖端的应力场.     

Decomposition of a class of functionals

LetX(t) be a symmetric conservative Hunt process. In this paper, we decompose the functionalu(X(t), t) into a sum of a square integrable martingale and a regular 0-quadratic variation process. This paper is based on the author's dissertation, presented for the degree of Doctor of philosophy in Institute of Applied Mathematics, Academia Sinica under the supervision of Prof. Yan Jia-an.     

The Even Part of Finite-Dimensional Modular Lie Superalgebra Г

Let F be the underlying base field of characteristic p ＞ 3 and denote by Γō the even part of the finite-dimensional Lie superalgebra Γ.We give the generator sets of the Lie algebra Γō.Using certain properties of the canonical tori of Γō,we describe explicitly the derivation algebra of Γō.     

An Improved Upper Bound on the Linear 2-arboricity of 1-planar Graphs

The linear 2-arboricity la_2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests,whose component trees are paths of length at most 2.In this paper,we prove that if G is a 1-planar graph with maximum degree Δ,then la_2(G)≤[(Δ+1)/2]+7.This improves a known result of Liu et al.(2019) that every 1-planar graph G has la_2(G)≤[(Δ+1)/2]+14.We also observe that there exists a 7-regular 1-planar graph G such that la_2(G)=6=[(Δ+1)/2]+2,which implies that our solution is within 6 from optimal.     

Approximation of the Fractional Schrödinger Propagator on Compact Manifolds

Let L be a second order positive, elliptic differential operator that is self-adjoint with respect to some C~∞ density dx on a compact connected manifold M. We proved that if 0 α 1,α/2 s α and f ∈ H~s(M) then the fractional Schr?dinger propagator e~(it Lα/2) on M satisfies e~(it Lα/2) f(x)-f(x) = o(t~(s/α-ε)) almost everywhere as t → 0~+, for any ε 0.     

p-Adic函数空间上Hardy型算子的多线性交换子估计

在p-adic域上研究分数次Hardy型算子与CMO(Qnp)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.