Relaxation of ideal classical particles in a one‐dimensional box

We study the deterministic dynamics of non‐interacting classical gas particles confined to a one‐dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone induce a uniform distribution of the gas particles at large times. For the relaxation of the velocity distribution we model the dynamical walls by independent scatterers. The Markov property guarantees a stationary but not necessarily thermal velocity distribution for the gas particles at large times. We identify the conditions for physical walls where the stationary velocity distribution is the Maxwell distribution. For our numerical simulation we represent the wall particles by independent harmonic oscillators. The corresponding dynamical map for oscillators with a fixed phase (Fermi–Ulam accelerator) is chaotic for mesoscopic box dimensions.     

空气密度与气体普适常量测量实验的改进

对测量空气密度和气体普适常量实验装置进行改进,用圆柱形有机玻璃密度瓶代替玻璃密度瓶,用高精度指针式真空表代替热偶真空规式真空计,利用橡胶管和密度瓶接口处的缓慢增气特性来改变空气压强,用电子物理天平称量气体质量,改进后的装置较适合学生实验.     

平面泛复数中代数方程根的规律

利用素理想和环的零因子技巧，讨论泛复系数代数方程根的规律，得到了抛物复系数代数方程f(x)=(an bnk)x^n (an-1 bn-1k)x^n-1 …(a1 b1k)x (a0 b0k)=0（这里虚单位k满足k^2=0)的准确解；而对于双曲复系数代数方程f(x)=(an bnj)x^n (an-1 bn-1j)x^n-1＋…＋（a1 b1j)x (a0 b0j)=0（这里虚单位j满足j^2-1=0），我们将方程转换成方程组，给出了方程的具体解法，并估计了在双曲复数域H中的根的个数。     

格的TL-模糊理想

本文研究了格的TL-模糊理想. 利用生成TL-模糊理想, 证明了一个模格的全体T_M-模糊理想形成一个完备的模格. 此外, 利用L-模糊集的投影和截影, 获得了将直积格的TL-模糊理想表示成分量格的TL-模糊理想的L-直积的一个充分必要条件. 所得结果进一步推广和发展了格的模糊理想的理论.     

Pointwise products of some Banach function spaces and factorization

The well-known factorization theorem of Lozanovski? may be written in the form L¹≡E⊙E^′$L^1\equiv E\odot E^{\prime }$, where ⊙ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the question when one can factorize F through E  , i.e., when F≡E⊙M(E,F)$F\equiv E\odot M(E,F)$, where M(E,F)$M(E,F)$ is the space of pointwise multipliers from E to F  . Properties of M(E,F)$M(E,F)$ were investigated in our earlier paper [41] and here we collect and prove some properties of the construction E⊙F$E\odot F$. The formulas for pointwise product of Calderón–Lozanovski? _Eφ$E_{\phi }$-spaces, Lorentz spaces and Marcinkiewicz spaces are proved. These results are then used to prove factorization theorems for such spaces. Finally, it is proved in Theorem 11 that under some natural assumptions, a rearrangement invariant Banach function space may be factorized through a Marcinkiewicz space.     

Higher moments of certain <Emphasis Type="Italic">L</Emphasis>-functions on the critical line

We study the sixth-power moments of certain L-functions belonging to a sub-class of the Selberg’s class on the critical line and, using this, we conclude an upper bound for the fourth-power moments of certain L-functions related to GL ₃ on the critical line. This is an analogue of the upper bound for the twelfth-power moment of the Riemann zeta-function on the critical line. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 341–380, July–September, 2007.     

Taking the particle interaction into account in a new concept of nucleation theory

Taking the interaction of particles into account in a new theory of nucleation leads to the occurrence of a phase transition in the Van der Waals theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 303–304, August, 2008.     

Extensions of TOPSIS for large scale multi-objective non-linear programming problems with block angular structure

This paper focuses on multi-objective large-scale non-linear programming (MOLSNLP) problems with block angular structure. We extend the technique for order preference by similarity ideal solution (TOPSIS) to solve them. Compromise (TOPSIS) control minimizes the measure of distance, provided that the closest solution should have the shortest distance from the positive ideal solution (PIS) as well as the longest distance from the negative ideal solution (NIS). As the measure of “closeness” L_P-metric is used. Thus, we reduce a q-dimensional objective space to a two-dimensional space by a first-order compromise procedure. The concept of a membership function of fuzzy set theory is used to represent the satisfaction level for both criteria. Moreover, we derive a single objective large-scale non-linear programming (LSNLP) problem using the max–min operator for the second-order compromise operation. Finally, a numerical illustrative example is given to clarify the main results developed in this paper.     

H~2(S)上Toeplitz算子本质谱的局部分解

本文利用Ｂａｎａｃｈ代数中局部化原理给出了多复变Ｈａｒｄｙ空间上Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的一个充分必要条件；同时给出了Ｔｏｅｐｌｉｔｚ算子本质谱的局部分解．     

Examples of Infinitely Generated Function Algebras

Examples of non-finitely generated function algebras on planar sets with small maximal ideal spaces are given.