A variant of Nim

We discuss a version of Nim in which players are allowed to use a move from the traditional form of Nim or to split a pile after adding some predetermined number $q$ of coins to the pile. When $q$ is odd or negative, the play proceeds as in regular Nim. For $q$ even and non-negative, we find three patterns: $q=0$, $q=2$ and $q?4$.     

Degree Ramsey numbers for even cycles

Let $H\stackrel{s}{?}G$ denote that any $s$-coloring of $E\left(H\right)$ contains a monochromatic $G$. The degree Ramsey number of a graph $G$, denoted by $R_{\Delta }(G,s)$, is $min\{\Delta \left(H\right):H\stackrel{s}{?}G\}$. We consider degree Ramsey numbers where $G$ is a fixed even cycle. Kinnersley, Milans, and West showed that $R_{\Delta }(C_{2k},s)\ge 2s$, and Kang and Perarnau showed that $R_{\Delta }(C_4,s)=\Theta \left(s^2\right)$. Our main result is that $R_{\Delta }(C_6,s)=\Theta \left(s^{3∕2}\right)$ and $R_{\Delta }(C_{10},s)=\Theta \left(s^{5∕4}\right)$. Additionally, we substantially improve the lower bound for $R_{\Delta }(C_{2k},s)$ for general $k$.     

反转岛附近原子核奇特性质研究进展

反转岛附近原子核奇特性质的研究是当前核物理研究的热点。 首先简要回顾和介绍了反转岛附近原子核奇特性质的实验进展, 然后介绍了对这些奇特核性质的理论研究进展。 主要包括相对论平均场模型、 壳模型、 Hartree Fock模型和宏观 微观模型在该区域的发展和研究结果。 重点介绍了宏观 微观模型在反转岛附近原子核奇特性质研究中的进展。 此外, 还分析和比较了各种理论模型在描述反转岛附近原子核性质上取得的成功和模型之间的差异。     

金纳米薄膜导电和导热性质的实验研究

由于尺寸效应和晶界效应的影响,纳米薄膜在导电和导热方面呈现出与体材料不同的性质.本文实验研究了不同厚度(20～54 nm)金薄膜在不同温度(100～340 K)的导电、导热性质.测量结果显示,薄膜的电导率和热导率比体材料小,洛伦兹数比体材料大,Wiedemann-Franz定律不再成立.随着厚度增加,薄膜的电导率,热导率和电阻温度系数都增加.薄膜热导率随温度变化趋势与体材料相反,随着温度升高而升高.电导率随温度变化趋势与体材料相同,随着温度升高而降低;但薄膜没有体材料对温度变化敏感,导致电阻温度系数下降.     

磁场微重力效应的研究

将导电的液体置于磁场中,使导电液体中浮力驱动的自然对流减弱甚至消失,在导电液体中制造出了二级微重力效应,将这种情况称为磁场微重力效应.通过研究导电液体自然对流驱动力的无量纲Grashof数的变化,发现微重力效应的水平可以用公式g_m＝（β₀/β_m）（ν₀ /ν_m）²g₀ 计算,如果略去一次项,则可用g_m＝（ν₀ /ν_m）²g₀来估算.测量研究了不同磁场条件下硅熔体的磁黏度,估算不同磁场强度对应的磁场微重力水平后,发现估算结果与实验结果基本符合. 关键词： 磁场 二级微重力效应 Grashof数 微重力水平     

二维可压缩流体Kelvin-Helmholtz不稳定性

利用高精度数值格式,研究了二维可压缩流体中的Kelvin-Helmholtz不稳定性,主要研究了可压缩性对Kelvin-Helmholtz稳定性增长率的影响.模拟定量的给出低Mach和高Mach数两种情况下,初始静压和对流Mach数以及Kelvin-Helmholtz不稳定性线性增长率的关系.模拟结果和自由剪切层以及混合层的实验结果以及理论分析一致.模拟表明,对流Mach数是描述流体可压缩性的合适参数,对流Mach数越小流体越不可压,Kelvin-Helmholtz不稳定性的线性增长率随对流Mach数的增加而减小. 关键词： Kelvin-Helmholtz不稳定性 可压缩流体 Mach数 超音速流体     

Analysis of steady state polydisperse counterflow spray diffusion flames in the large Stokes number limit

A new mathematical analysis is presented of certain aspects of the behavior of opposed flow polydisperse spray diffusion flames within the framework of a model in which large slip is permitted between the droplets and their host surroundings. The sectional approach is used to model the polydisperse spray. Operating conditions are identified under which the inverses of sectional Stokes numbers are small spray-related parameters to be used in a perturbation analysis of the liquid phase governing equations. The steady state equations and their solutions are similar in form to the equivalent equations considered in previous work of the authors in which dynamical equilibrium of the droplets with the carrier phase was assumed. However, here there is much more mathematical complexity involved in the spray equations solution. A hybrid Eulerian–Lagrangian approach is also suggested to get an insight into the phenomenon of reversal in the motion of the droplets that has been reported in independent experimental and computational research. Computed results based on the analytical solutions up to the 1st order of approximation reveal the influence of large droplet slip on the droplets velocity field and on the spray diffusion flame’s thermal field, for which appreciable heterogeneous combustion can occur under the operating conditions considered.     

The feature study on the <Emphasis Type="Italic">π</Emphasis> and proton rapidity distributions at AGS,SPS and RHIC

The features of nuclear stopping power and multi-hadron production systematically are studied by making an analysis of rapidity distributions of pion and proton at AGS, SPS and RHIC in this work. It is found that nuclear stopping power increases linearly with project rapidity y _p at AGS and SPS, but that is not liner at RHIC. It is argued that the average rapidity loss is saturated at central rapidity region at RHIC. For pion distribution, it is found that the phase space of pion distribution distributes uniformly in the longitudinal direction, and a linear relationship of 〈βγ〉_L with log√s is given at AGS and SPS. Non-uniform flow model may explain the features of the distribution at AGS and SPS, but may not explain those of at RHIC. Supported by the Excellent Youth Foundation of Hubei Scientific Committee (Grant No. 2006ABB036), the Educational Commission of Hubei Province of China (Grant No. Z20081302), and the Natural Science Foundation of China Three Gorges University (Grant No. 2003C02)     

Particle number scale invariant feature of the states around the critical point of the first order nuclear shape phase transition

We study systematically the evolutive behaviors of some energy ratios,E2 transition rate ratios and isomer shift in the nuclear shape phase transitions.We find that the quantities sensitive to the phase transition and independent of free parameter(s) are approximately particle number N scale invariant around the critical point of the first order phase transition,similar to that in the second order phase transition.