Equitable list coloring of planar graphs without 4- and 6-cycles

A graph G is equitably k-choosable if for any k-uniform list assignment L, there exists an L-colorable of G such that each color appears on at most vertices. Kostochka, Pelsmajer and West introduced this notion and conjectured that G is equitably k-choosable for k>Δ(G). We prove this for planar graphs with Δ(G)≥6 and no 4- or 6-cycles.     

A generalization of Fan’s results: Distribution of cycle lengths in graphs

Fan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187-202] proved that if G is a graph with minimum degree δ(G)≥3k for any positive integer k, then G contains k+1 cycles C₀,C₁,…,C_k such that k+1<|E(C₀)|<|E(C₁)|<?<|E(C_k)|, |E(C_i)−E(C_i−1)|=2, 1≤i≤k−1, and 1≤|E(C_k)|−|E(C_k−1)|≤2, and furthermore, if δ(G)≥3k+1, then |E(C_k)|−|E(C_k−1)|=2. In this paper, we generalize Fan’s result, and show that if we let G be a graph with minimum degree δ(G)≥3, for any positive integer k (if k≥2, then δ(G)≥4), if d_G(u)+d_G(v)≥6k−1 for every pair of adjacent vertices u,v∈V(G), then G contains k+1 cycles C₀,C₁,…,C_k such that k+1<|E(C₀)|<|E(C₁)|<?<|E(C_k)|, |E(C_i)−E(C_i−1)|=2, 1≤i≤k−1, and 1≤|E(C_k)|−|E(C_k−1)|≤2, and furthermore, if d_G(u)+d_G(v)≥6k+1, then |E(C_k)|−|E(C_k−1)|=2.     

Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.     

Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems

We consider an -hard variant (Δ-Max-ATSP) and an -hard relaxation (Max-3-DCC) of the classical traveling salesman problem. We present a -approximation algorithm for Δ-Max-ATSP and a -approximation algorithm for Max-3-DCC with polynomial running time. The results are obtained via a new way of applying techniques for computing undirected cycle covers to directed problems.     

Planar graphs without 5-cycles or without 6-cycles

Let G be a planar graph without 5-cycles or without 6-cycles. In this paper, we prove that if G is connected and δ(G)≥2, then there exists an edge xy∈E(G) such that d(x)+d(y)≤9, or there is a 2-alternating cycle. By using the above result, we obtain that (1) its linear 2-arboricity , (2) its list total chromatic number is Δ(G)+1 if Δ(G)≥8, and (3) its list edge chromatic number is Δ(G) if Δ(G)≥8.     

一类混合Ramsey数

设a(G)表示图G的点荫度,m为正整数,H为连通图,混合Ramsey数v(a;m;H)被定义的为最小的正整数P,使得对任意P阶图G则有a(G)≥m或者H包括于G^-。本文给出了v(a;m;H)的一种计算方法,并对图Cn和轮Wn确定了v(a;n;Cn)和v(a;m;Wn)的值。     

The number of cycle lengths in graphs of given minimum degree and girth

This paper determines lower bounds on the number of different cycle lengths in a graph of given minimum degree k and girth g. The most general result gives a lower bound of ck^g/8.     

新一代核能布雷顿闭式循环热力学分析研究

核能利用是２０世纪最激动人心的科学成就之一。核能和平利用的重点在核能发电,至今核电站反应堆多为低温水冷堆,采用水或重水作为冷却剂和慢化剂,堆出口载热工质温度较低（２８０“Ｃ～３４０“ｑ,因而多应用常规的Ｒａｎｋｉｎｅ蒸汽热力循环,热转功的效率较低（２８％～３３％）。９０年代以来,随着工业和航空燃气轮机技术长足进步和高温核反应堆的进展,核能布雷顿闭式循环（ＮＥＢＣＣ）展现出提高性能的潜力和发展前景,受到普遍关注。近期提出的模块化高温气冷堆氦气轮机（ＭＨＲ－－ＧＴ）［‘－‘］就是应用ＮＥＢＣＣ的典型…     

Influence of cycle time distribution on coating uniformity of particles in a spray fluidized bed by using CFD-DEM simulations

Cycle Time Distribution (CTD) plays a critical role for determining uniformity of particle coating in spray fluidized beds. However, the CTD is influenced by both geometrical structure and operating conditions of fluidized bed. In this study, a spray fluidized bed of coating process is simulated by a comprehensive Computational Fluid Dynamics-Discrete Element Model (CFD-DEM). To achieve different behaviors of CTD, some modifications are designed on a pseudo-2D internally circulating fluidized bed, which traditionally composes of a high-velocity upward bed and low-velocity downward bed. These modifications include making the air distributor slope and/or laying a baffle in the downward bed. First, the CTD and evolution of particle size distribution under different bed structures are compared. The CTD directly influences the coating uniformity. By making the particles flowing along a parallel direction in the downward bed through the geometrical modifications, the CTD becomes narrower and the coating uniformity is significantly improved. Second, under the optimized bed structure, the influence of operating conditions on the coating uniformity is studied. Properly increasing the fluidization gas velocity and the fluidization gas temperature and reducing the liquid spray rate can improve the coating uniformity.     

跨膜浓度梯度对渗透压囊泡循环活性的调控

本文通过分析囊泡在膨胀状态与孔隙状态的动力学行为,揭示调控膨胀拉伸能与孔隙势能的内在物理参量.建立递推微分方程的分析模型,该模型提供了膨胀-破裂循环特征量膨胀系数在各个循环中初始跨膜浓度梯度依赖性的定量信息.研究得出,通过增加初始跨膜浓度梯度,可加快膨胀系数增长速率(循环数为1时,初始跨膜浓度梯度增加3倍,膨胀系数增长速率增加2.65倍);随着循环数的增多,膨胀系数的增长由线性转变为非线性.此外,初始跨膜浓度梯度与循环次数密切相关,我们的模型计算预测增加初始跨膜浓度梯度可实现循环次数的增多.研究结果为靶组织以可编程方式释放活性生物治疗剂的发展提供了具有实际意义的理论依据.