A Characterization of Graphs without Even Factors

In this paper, we first reduce the problem of finding a minimum parity (g,f)-factor of a graph G into the problem of finding a minimum perfect matching in a weighted simple graph G*. Using the structure of G*, a necessary and sufficient condition for the existence of an even factor is derived. This paper was accomplished while the second author was visiting the Center for Combinatorics, Nankai University. The research is supported by NSFC     

具有平整表面的定向纳米碳管膜的制备

为了获得表面平整的定向纳米碳管，通过化学及物理的方法将纳米碳管膜进行反转，使其原来的AAO模板底面成为新的表面，用溶液逐步去除表面的铝和氧化铝后，获得了平整的定向纳米碳管膜表面，从而可将其作为工作面使用. 还比较了5％NaOH和6%H₃PO₄＋1.8%H₂CrO₄溶液去除氧化铝的效果.     

含IIIA或VA族杂原子的碳原子簇负离子的研究

在自制的仪器上，以脉冲激光束在高真空中溅射适当的样品，产生了一系列合有1个VA族原子（N、P、As）或ⅢA族原子（B、Al）及13个以下碳原子的原子簇负离子。在实验记录的飞行时间质谱中，这些簇离子的信号强度均因其碳原子数的奇偶而发生交替变化．对实验结果的分析研究显示：这些簇离子均为直链构型．VA或ⅢA族原子位于链的一端，所有成簇原子的价键均得到满足．     

Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. D. S. Watkins partly supported by Deutsche Forschungsgemeinschaft through Matheon, the DFG Research Center Mathematics for key technologies in Berlin.     

Classicalization times of parametrically amplified “Schrödinger cat” states coupled to phase-sensitive reservoirs

The exact Wigner function of a parametrically excited quantum oscillator in a phase-sensitive amplifying/attenuating reservoir is found for initial even/odd coherent states. Studying the evolution of negativity of the Wigner function we show the difference between the “initial positivization time” (IPT), which is inversely proportional to the square of the initial size of the superposition, and the “final positivization time” (FPT), which does not depend on this size. Both these times can be made arbitrarily long in maximally squeezed high-temperature reservoirs. Besides, we find the conditions when some (small) squeezing can exist even after the Wigner function becomes totally positive.     

态|ψ3(3)〉q中广义磁场分量的N次方Y压缩效应

构造了由多模复共轭相干态|{Z_j^*}〉_q、多模复共轭虚相干态|{iZ_j^*}〉_q和多模真空态|{Q_j} 〉_q这三态的线性叠加所组成的第Ⅲ类三态叠加多模叠加态光场|ψ₃⁽³⁾〉_q.利用多模压缩态理论研究了态|ψ₃⁽³⁾〉_q中广义磁场分量的任意偶数次广义非线性等幂次N次方Y压缩特性.结果发现:在压缩次数N取偶数,只要各模的初始相位φ_j(j=1,2,3,…,…,q),态间的初始相位差(θ_i-θ₂)(i=1,3)和各单模相干态光场平均光子数R_j²之和 分别满足各自的取值条件,态|ψ₃⁽³⁾〉_q的广义磁场分量(即第一正交相位分量)就可呈现出周期性变化的、任意偶数次的广义非线性等幂次N次方Y压缩效应.     

Gauss整环上不可分解的Hermite型

本文给出了构作虚二次域Ｑ（－ｍ）的整数环上不可分解的正定整Ｈｅｒ ｍｉｔｅ型的方法．     

Equicontinuity and Sensitivity of Group Actions*

Let(X, G) be a dynamical system(G-system for short), that is, X is a topological space and G is an infinite topological group continuously acting on X. In the paper,the authors introduce the concepts of Hausdorff sensitivity, Hausdorff equicontinuity and topological equicontinuity for G-systems and prove that a minimal G-system(X, G) is either topologically equicontinuous or Hausdorff sensitive under the assumption that X is a T₃-space and they provide a classification of transitive d...     

Odd length for even hyperoctahedral groups and signed generating functions

We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types $A$ and $B$. We compute the signed (by length) generating function of this statistic over the whole group and over its maximal and some other quotients and show that it always factors nicely. We also present some conjectures.     

Even subgraphs of bridgeless graphs and 2-factors of line graphs

By Petersen's theorem, a bridgeless cubic multigraph has a 2-factor. Fleischner generalised this result to bridgeless multigraphs of minimum degree at least three by showing that every such multigraph has a spanning even subgraph. Our main result is that every bridgeless simple graph with minimum degree at least three has a spanning even subgraph in which every component has at least four vertices. We deduce that if G is a simple bridgeless graph with n vertices and minimum degree at least three, then its line graph has a 2-factor with at most max{1,(3n-4)/10} components. This upper bound is best possible.