Monochromatic k-edge-connection colorings of graphs

A path in an edge-colored graph $G$ is called monochromatic if any two edges on the path have the same color. For $k\ge 2$, an edge-colored graph $G$ is said to be monochromatic $k$-edge-connected if every two distinct vertices of $G$ are connected by at least $k$ edge-disjoint monochromatic paths, and $G$ is said to be uniformly monochromatic $k$-edge-connected if every two distinct vertices are connected by at least $k$ edge-disjoint monochromatic paths such that all edges of these $k$ paths are colored with a same color. We use $m{c}_k\left(G\right)$ and $um{c}_k\left(G\right)$ to denote the maximum number of colors that ensures $G$ to be monochromatic $k$-edge-connected and, respectively, $G$ to be uniformly monochromatic $k$-edge-connected. In this paper, we first conjecture that for any $k$-edge-connected graph $G$, $m{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+\lfloor \frac{k}{2}\rfloor$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$. We verify the conjecture for $k=2$. We also prove the conjecture for $G=K_{k+1}$ and $G=K_{k,n}$ with $n\ge k\ge 3$. When $G$ is a minimal $k$-edge-connected graph, we give an upper bound of $m{c}_k\left(G\right)$, i.e., $m{c}_k\left(G\right)\le k-1$. For the uniformly monochromatic $k$-edge-connectivity, we prove that for all $k$, $um{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+1$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$.     

The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

Adsorption effects and NMR properties: Continuous chain approach

The NMR properties of nuclei linked to long linear polymer molecules are sensitive to the influence of hard walls. In this context, the residual energy of tensorial spin-spin interactions is calculated using a path integral approach. Several thermodynamic quantities of the polymer system (free energy, equation of state,...) are also expressed, taking chain stiffness effects and the presence of two repulsive walls into consideration.     

迈克尔逊干涉仪中补偿板与干涉条纹

通过分析缺失补偿板的迈克尔逊干涉仪中的附加光程差,推出干涉条纹满足的方程式,并用计算机模拟了动镜移动过程中变化的干涉条纹,与实验结果相一致.     

Large set of P3‐decompositions

Let G=(V(G),E(G)) be a graph. A (n,G, λ)‐GD is a partition of the edges of λK_n into subgraphs (G‐blocks), each of which is isomorphic to G. The (n,G,λ)‐GD is named as graph design for G or G‐decomposition. The large set of (n,G,λ)‐GD is denoted by (n,G,λ)‐LGD. In this work, we obtain the existence spectrum of (n,P₃,λ)‐LGD. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 151–159, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10008     

Stability Properties of Feynman's Operational Calculus for Exponential Functions of Noncommuting Operators

Stability properties of Feynman's operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.     

拆边法求最短路径

本文利用局部比较法 ,在图中定义子图、无效路径、以及可去边 .利用推导的有关定理 ,拆去可去边 ,利用最短路径相同的等价性 ,达到化简图 ,从而求出最短路径     

Field Theory Methods in Classical Dynamics

A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger–Feynman–Dyson perturbation expansion and detailed rules are derived for computations. Complexification formalisms are given for the time evolution operator suitable for phase space analyses, and then extended to a two-dimensional setting for a study of the geometrical Berry phase as an example. Finally a direct integration of Hamilton's equations is shown to lead naturally to a path integral expression, as a resolution of the identity, as applied to arbitrary functions of generalized coordinates and momenta.     

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*.     

光纤白光干涉仪等臂长技术研究

介绍了几种光纤干涉仪等臂长技术,比较了各自的优缺点和适用范围,对光纤干涉仪的平衡有较大的参考价值。