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。     

相位循环设计中的等价性定理和脉冲单元法

本文提出两条等价性定理,用来判别不同排列的相位循环是否等价。又提出一种新的设计相位循环的方法-脉冲单元法,克服了由多线相干转移路径引起的多值性困难。     

The Ramsey number for hypergraph cycles I

Let C_n denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v₁,…,v_n and edges v₁v₂v₃, v₃v₄v₅, v₅v₆v₇,…,v_n-1v_nv₁. We prove that every red-blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of C_n, where N is asymptotically equal to 5n/4. Moreover this result is (asymptotically) best possible.     

AB5型贮氢合金电极的性能

在金属氢化物一镍电池（MH／Ni）负极材料中，ABS型贮氢合金是非常具有吸引力的一种，以AB。型贮氢合金作为负极材料的MH／Ni电池目前已大批量进入市场．其中A代表混合稀土RE（主要成分为La，Ce，Pr，Nd）；B代表Ni和Co，Mll，AI等取代元素．B侧取代元素已被广泛研究D，习，A侧混合稀土的成分也已引起人们的广泛重视＊‘，’］，＊血1c等【阿针对儿一N13。5C00．75Mll。。A10．3，详细研究了L31。CI。BS系列合金，得出在。＝0．2处合金具有较好的综合性能．本文针对B侧Ni。。。Coo，。Mno、。Alo二。（记为民）成分，在研…     

铟—4—（2—噻唑偶氮）—间苯二酚络合物电化学性质研究

在0.06mol·L~(-1)NH_4OAc底液中,铟与4-(2-噻唑偶氮)-间苯二酚(TAR)形成的络合物产生一灵敏还原吸附峰,可用于单扫描示波极谱法测定痕量铟。铟浓度在1×10~(-8)～1×10~(-6)mol·L~(-1)范围内与峰电流呈线性关系。加入少量十二烷基磺酸钠,灵敏度提高,检出下限为5×10~(-9)mol·L~(-1)。该法应用于测定矿石中痕量铟,结果令人满意,用多种电化学手段对络合物的电化学性质进行了研究。     

Relative Length of Longest Paths and Cycles in Graphs

For a graph G, let diff(G) = p(G) − c(G), where p(G) and c(G) denote the orders of a longest path and a longest cycle in G, respectively. Let G be a 3-connected graph of order n. In the paper, we give a best-possible lower bound to σ₄(G) to assure diff(G) ≤ 1. The result settles a conjecture in J. Graph Theory 37 (2001), 137–156.     

可圈的一个充分条件

本文我们证明如下结果:设G=(V,E)是一个n(n≥3)阶k-连通(k≥2)图,记X1,X2,…,Xk为V的子集,X=X1∪X2∪…∪Xk.若对每个I,I=1,2,…,k,满足:对任意的u,v∈Xi,有d(u) d(v)≥n或|N(u)∪N(v)|≥n-δ或|N(u)∩N(v)|≥α,这里δ是G的最小度,α是G的独立数,则G是X-可圈的.     

Novel image encryption algorithm based on cycle shift and chaotic system

In this paper, a novel image encryption algorithm is proposed. The cycle shift in bits of pixels and the chaotic system are employed for the encryption of the proposed scheme. For cycle shift operations, random integers with the same size of the original image are produced to scramble the plaintext image. Moreover, the scrambled image effects the initial values of the chaotic system for the further encryption process, which increases the sensitivity of plaintext images of the scheme. The scrambled image is encrypted into the ciphered image by the keys which are produced by the chaotic system. The simulation experiments and theoretical analyses indicate that the proposed scheme is superior and able to resist exhaustive attack and statistical attack.