Parity considerations for drops in cycles on {1,2,…,n}

In 2019, A. Lazar and M. L. Wachs conjectured that the number of cycles on $[2n]$ with only even-odd drops equals the n-th Genocchi number. In this paper, we restrict our attention to a subset of cycles on $[n]$ such that in all drops in the cycle, the latter entry is odd. We deduce two bivariate generating functions for such a subset of cycles with an extra variable introduced to count the number of odd-odd and even-odd drops, respectively. One of the generating function identities confirms Lazar and Wachs' conjecture, while the other identity implies that the number of cycles on $[2n?1]$ with only odd-odd drops equals the $(n?2)$-th Genocchi median.     

A degree condition implying that every matching is contained in a hamiltonian cycle

We give a degree sum condition for three independent vertices under which every matching of a graph lies in a hamiltonian cycle. We also show that the bound for the degree sum is almost the best possible.     

On embedding a cycle in a plane graph

Consider a planar drawing Γ of a planar graph G such that the vertices are drawn as small circles and the edges are drawn as thin stripes. Consider a non-simple cycle c of G. Is it possible to draw c as a non-intersecting closed curve inside Γ, following the circles that correspond in Γ to the vertices of c and the stripes that connect them? We show that this test can be done in polynomial time and study this problem in the framework of clustered planarity for highly non-connected clustered graphs.     

贮氢电极合金ZrCr_(0.4)Mn_(0.2)V_(0.1)Co_(0.1)Ni_(1.2)高温电化学性能的研究

研究了AB2型Laves相贮氢电极合金ZrCr0.4Mn0.2V0.1Co0.1Ni1.2在不同温度下的放电容量、活化、高倍率和自放电等电化学性能.实验表明:25℃下,合金电极经13次循环后其最大放电容量为336mAh/g,在70℃下,仅需4次循环就达到298mAh/g;该合金在70℃,300mA/g电流下的高倍率放电性能比25℃时提高了约16%,但自放电性能却从3%/d下降到17%/d,虽然温度升高,合金的循环性能有所下降,但还是相当稳定的.这主要是因为循环过程中合金表面形成的氧化膜阻碍了合金元素进一步溶解造成的.     

永磁同步电动机中的混沌现象

讨论永磁同步电动机（PMSM）的动态特性,给出常输入电压、常外部扭转条件下的系统稳态特性表达式,基于Hopf分支条件提出一种调节系统参数的方法,以使其呈现极限环或混沌行为。计算机仿真结果表明在永磁同步电动机中存在混沌现象。     

熔体旋淬合金Zr_(0.9)Ti_(0.1)(Ni,Co,Mn,V)_(2.1)的微结构与电化学性能

对比研究了熔体旋淬和常规熔铸合金Zr0 .9Ti0 .1(Ni,Co ,Mn ,V) 2 .1的微结构和电化学性能 .XRD分析表明 :熔体旋淬合金在退火前后的晶体结构和铸态合金一样 ,均为面心立方结构 ,由LaveC15相组成 ;并且随旋淬速度的增加 ,旋淬合金中的非晶成分越多 .电化学测试表明 :旋淬合金有较好的活化性能 ,但其最大放电容量较低 ,小于 2 80mAh/g ;而退火后的旋淬合金需经 30次循环才能完全活化 ,其最大放电容量皆为 34 0mAh/g左右 ,高于铸态合金和退火前的旋淬合金 ;在电流密度为 30 0mA/g下进行充放电循环 ,发现退火后的旋淬合金循环稳定性明显高于铸态合金电极 ,并且随旋淬速度的增加 ,循环稳定性越好 ,经过 80 0次循环后 ,退火后的 4 0m/s合金容量保持率高达 85 % ,容量衰减率只有 6.9%     

An approximation algorithm for sorting by reversals and transpositions

Genome rearrangement algorithms are powerful tools to analyze gene orders in molecular evolution. Analysis of genomes evolving by reversals and transpositions leads to a combinatorial problem of sorting by reversals and transpositions, the problem of finding a shortest sequence of reversals and transpositions that sorts one genome into the other. In this paper we present a 2k-approximation algorithm for sorting by reversals and transpositions for unsigned permutations where k is the approximation ratio of the algorithm used for cycle decomposition. For the best known value of k our approximation ratio becomes 2.8386+δ for any δ>0. We also derive a lower bound on reversal and transposition distance of an unsigned permutation.     

Edge-bipancyclicity of a hypercube with faulty vertices and edges

A bipartite graph G=(V,E) is said to be bipancyclic if it contains a cycle of every even length from 4 to |V|. Furthermore, a bipancyclic G is said to be edge-bipancyclic if every edge of G lies on a cycle of every even length. Let F_v (respectively, F_e) be the set of faulty vertices (respectively, faulty edges) in an n-dimensional hypercube Q_n. In this paper, we show that every edge of Q_n-F_v-F_e lies on a cycle of every even length from 4 to 2ⁿ-2|F_v| even if |F_v|+|F_e|?n-2, where n?3. Since Q_n is bipartite of equal-size partite sets and is regular of vertex-degree n, both the number of faults tolerated and the length of a longest fault-free cycle obtained are worst-case optimal.     

Note on cycle double covers of graphs

Kriesell [M. Kriesell, Contractions, cycle double covers and cyclic colorings in locally connected graphs, J. Combin. Theory Ser. B 96 (2006) 881-900] proved the cycle double cover conjecture for locally connected graphs. In this note, we give much shorter proofs for two stronger results.