Planar graph colorings without short monochromatic cycles

It is well known that every planar graph G is 2‐colorable in such a way that no 3‐cycle of G is monochromatic. In this paper, we prove that G has a 2‐coloring such that no cycle of length 3 or 4 is monochromatic. The complete graph K₅ does not admit such a coloring. On the other hand, we extend the result to K₅‐minor‐free graphs. There are planar graphs with the property that each of their 2‐colorings has a monochromatic cycle of length 3, 4, or 5. In this sense, our result is best possible. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 25–38, 2004     

匀强磁场对刚性载流线圈磁力矩公式的一般推导

利用矢量代数和矢量场论的有关结果严谨地推证了匀强磁场中载流线圈所受合磁力矩表达式。     

外平面图的全染色与列表全染色

本文证明了,如果G是满足条件Δ(G)≥4的外平面图,则x_T~L(G)=Δ(G) 1,同时对Δ(G)=3给出了XT(G)=Δ(G) 1的简短的新证明,从而蕴含Δ(G)≥3时,XT(G)=Δ(G) 1,其中XT(G)是G的点边全色数,x_T~L(G)是G的点边列表全色数。     

Choosability of K5-minor-free graphs

Thomassen, 1994 showed that all planar graphs are 5-choosable. In this paper we extend this result, by showing that all K₅-minor-free graphs are 5-choosable.     

Laser Raman spectroscopic study of ferroelastic LiCsSO4

Lithium caesium sulphate has been reported to undergo a phase transition from the room temperature orthorhombic phase with space groupP cmn to a final phase with space groupP 2₂/n. Though a sharp anomaly in its physical properties has been found at 202.0;K, it was found that there was a need for careful investigations in the vicinity of 240 and 210.0;K. Since the changes in the crystal structure involve primarily a rotation of the SO₄ tetrahedron about thec-axis and as this may be reflected both in the intensity and polarisation of the internal as well as external phonon modes, the laser Raman spectra of oriented single crystals of LiCsSO₄ at different temperatures were investigated. For correlation and definite identification of the spectral features, its infrared absorption spectrum was also studied. An analysis of the intensities and polarizations of the internal modes of the sulphate ions reveals the change in symmetry of the crystal. The integrated intensity and peak height of thev ₁ line, plotted against temperature show anomalous peaks in the region of the phase transition. Differential scanning calorimetric study gives the enthalpy change ΔH across the phase transition to be 0.213 kJ/mol.     

Constrained Markov decision processes with total cost criteria: Occupation measures and primal LP

This paper is the third in a series on constrained Markov decision processes (CMDPs) with a countable state space and unbounded cost. In the previous papers we studied the expected average and the discounted cost. We analyze in this paper the total cost criterion. We study the properties of the set of occupation measures achieved by different classes of policies; we then focus on stationary policies and on mixed deterministic policies and present conditions under which optimal policies exist within these classes. We conclude by introducing an equivalent infinite Linear Program.     

光子晶体光纤模式特征的研究

从基空间填充模出发，将光子晶体光纤的包层等效成均匀介质，从而将光子晶体光纤等效为阶跃折射率光纤。利用等效折射率模型，对光子晶体光纤的模式特征进行了详尽的研究，主要包括模式特性、传输常量、模场分布、功率限制特性、瑞利散射损牦特性、色散特性，等等。并通过功率限制因子这一参量将它与单模光纤进行比较。结果表明，光子晶体光纤单模工作波长范围比较宽，功率限制因子比较高，可用于制作更高抽运效率的光纤放大器。     

Positivity‐preserving,flux‐limited finite‐difference and finite‐element methods for reactive transport

A new class of positivity‐preserving, flux‐limited finite‐difference and Petrov–Galerkin (PG) finite‐element methods are devised for reactive transport problems.The methods are similar to classical TVD flux‐limited schemes with the main difference being that the flux‐limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite‐element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity‐preserving property. Analysis of the latter scheme shows that positivity‐preserving solutions of the resulting difference equations can only be guaranteed if the flux‐limited scheme is both implicit and satisfies an additional lower‐bound condition on time‐step size. We show that this condition also applies to standard Galerkin linear finite‐element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time‐step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction. Copyright © 2003 John Wiley & Sons, Ltd.