微分对策中的联盟解

提出时间区间[t_0,∞)上的n人微分对策两阶段联盟解. 在第一阶段不能形成大联盟的假设是自然的,即源于这一思想. 在第一阶段以联盟作为局中人的对策中计算得到其纳什均衡,之后对每个联盟的收益按Shapley值进行分配. 一个n人微分减排模型的例子阐明了上述结果.     

含裂纹体的单位分解扩展无网格方法

不连续体的数值模拟尤其是动态裂纹的追踪问题一直是工程界研究的热点和难点问题。无网格方法仅仅需要结点信息,非常适合于求解这类问题。基于单位分解思想,在移动最小二乘近似函数(MLS)中根据裂纹面的不连续位移增加一个Heaviside函数,在裂尖则增加四个扩展函数描述渐进裂纹位移场;应用Galerkin方法推导了平衡方程的离散线性方程,并给出了求解裂纹问题应力强度因子的计算公式。与其他类型的扩展无网格相比,在裂尖处近似函数不需要使用可视准则,很容易生成r1/2奇异;另一个优势是影响域并没有因为裂纹的存在而改变,不会降低方程的稀疏性,求解效率较高。数值算例表明,该方法能方便有效地模拟不连续问题,具有十分广阔的应用空间。     

一类六边形网格上拉普拉斯4点差分格式及其预条件子

本文提出平面上拉普拉斯算子在一类平行六边形网格上的成对4点差分格式.这种差分格式虽然只有一阶的局部截断误差,但实际具有二阶的收敛性.基于平行六边形网格可以被分解为两套三向三角形网格,我们给出成对4点格式的二阶收敛性的证明,并且提出相应的预条件子快速解法.文末给出的数值算例符合我们的结论.     

完全配分及其算法

本文讨论了在物理和其他科学研究中极有应用价值的完全配分问题,并给出了计算完全配分的FORTRAN-77程序。     

求解高维路径积分的快速递推方法

推导出一种计算N重路径积分表述的量子配分函数的递推蒙特卡罗方法.通过对一个具体算例的研究,讨论了数值结果对轨道折点数和轨道的稳定性情况.     

A Family of Partition Identities Proved Combinatorially

We present three infinite families of partitions that, for corresponding parameters, are equinumerous. This generalizes an identity proved by the first author (Pacific Journal of Mathematics, 77(1) (1978)) and two identities proved by the second and third authors (Relatório Técnico 08/99 IMECC-UNICAMP, 1999).     

Low‐frequency ESR studies on permeable and impermeable deuterated nitroxyl radicals in corn oil solution

Low‐frequency electron spin resonance studies were performed for 2 mM concentration of deuterated permeable and impermeable nitroxyl spin probes, 3‐methoxycarbonyl‐2,2,5,5‐tetramethyl‐pyrrolidine‐1‐oxyl and 3‐carboxy‐2,2,5,5,‐tetramethyl‐1‐pyrrolidinyloxy in pure water and various concentrations of corn oil solution. The electron spin resonance parameters such as the line width, hyperfine coupling constant, g factor, rotational correlation time, permeability, and partition parameter were estimated. The broadening of line width was observed for nitroxyl radicals in corn oil mixture. The rotational correlation time increases with increasing concentration of corn oil, which indicates the less mobile nature of spin probe in corn oil mixture. The membrane permeability and partition parameter values were estimated as a function of corn oil concentration, which reveals that the nitroxyl radicals permeate equally into the aqueous phase and oil phase at the corn oil concentration of 50%. The electron spin resonance spectra demonstrate the permeable and impermeable nature of nitroxyl spin probes. From these results, the corn oil concentration was optimized as 50% for phantom studies. In this work, the corn oil and pure water mixture phantom models with various viscosities correspond to plasma membrane, and whole blood membrane with different hematocrit levels was studied for monitoring the biological characteristics and their interactions with permeable nitroxyl spin probe. These results will be useful for the development of electron spin resonance and Overhauser‐enhanced magnetic resonance imaging modalities in biomedical applications.     

Equitable 2-partitions of the Hamming graphs with the second eigenvalue

The eigenvalues of the Hamming graph $H(n,q)$ are known to be ${\lambda }_i(n,q)=(q-1)n-qi$, $0\le i\le n$. The characterization of equitable 2-partitions of the Hamming graphs $H(n,q)$ with eigenvalue ${\lambda }_1(n,q)$ was obtained by Meyerowitz (2003). We study the equitable 2-partitions of $H(n,q)$ with eigenvalue ${\lambda }_2(n,q)$. We show that these partitions are reduced to equitable 2-partitions of $H(3,q)$ with eigenvalue ${\lambda }_2(3,q)$ with the exception of two constructions.     

Partition functions and thermodynamic properties of paraboson and parafermion systems

New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for such systems. We analyze and discuss the average number of particles on an orbital, and the average number of particles in the system. For some special cases (identical orbital energies, or equidistant orbital energies) we can simplify the grand partition functions and describe thermodynamic properties in more detail. Some specific properties are also illustrated in plots of thermodynamic functions.     

Superstatistics of Modified Rosen-Morse Potential with Dirac Delta and Uniform Distributions

We discuss the thermodynamic properties of a modified Rosen-Morse potential using the $q$-deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.