Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein-Penner's method

Epstein and Penner give a canonical method of decomposing a cusped hyperbolic manifold into ideal polyhedra. The decomposition depends on arbitrarily specified weights for the cusps. From the construction, it is rather obvious that there appear at most a finite number of decompositions if the given weights are slightly changed. However, since the space of weights is not compact, it is not clear whether the total number of such decompositions is finite. In this paper we prove that the number of polyhedral decompositions of a cusped hyperbolic manifold obtained by the Epstein-Penner's method is finite.

     

On congruences and ideals of partially ordered quasigroups

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

Dynamics of a rotating layer of an ideal electrically conducting incompressible fluid

A system of nonlinear partial differential equations is considered that models perturbations in a layer of an ideal electrically conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces. The system is reduced to a scalar equation. The solvability of initial boundary value problems arising in the theory of waves in conducting rotating fluids can be established by analyzing this equation. Solutions to the scalar equation are constructed that describe small-amplitude wave propagation in an infinite horizontal layer and a long narrow channel.     

关于吸收式碳捕集热力学机制的探索

热再生吸收式碳捕集的传统认识难以揭示其热力学机制,一种新的认识是"热-化学能"转换中存在中间能量形式。本文从热力学碳泵概念出发,对吸收式碳捕集理想系统进行了解耦,其可视为"热机-碳泵"的热力学组合,探索了极限效率的表达,并采用第二定律效率作为评价参数对已有中试试验系统进行了性能水平探索。结果表明,理想循环性能系数仅取决于热源汇温度、碳源汇浓度;中试系统第二定律效率普遍低于20%。本文探索了热驱动的吸收式碳捕集热力学机制,为新型吸收剂设计提供了新思路。     

Thermodynamic coefficients of ideal Fermi gas

We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low-temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg .     

Shocks in local supersonic zones

The results of numerical integration of the Euler equations governing two-dimensional and axisymmetric flows of an ideal (inviscid and non-heat-conducting) gas with local supersonic zones are presented. The subject of the study is the formation of shocks closing local supersonic zones. The flow in the vicinity of the initial point of the closing shock is calculated on embedded, successively refined grids with an accuracy much greater than that previously achieved. The calculations performed, together with the analysis of certain controversial issues, leave no doubt that it is the intersection of C ^?-characteristics proceeding from the sonic line inside the supersonic zone that is responsible for the closing shock formation.     

An alternative approach to calculate the density of states in nonextensive statistical mechanics

A relation between the generalized partition function (Tsallis) and density of states is established by using the method of integral transform which enables reducing some integral equations into the algebraic equations. Inverse Mellin transformation of this equation gives the density of states. Similar relation is also hold the for standard partition function (Boltzmann-Gibbs) and the density of states. Using these relations, we recover the density of states for the classical ideal gas within both statistics.     

N(2,2,0)代数的(∈,∈Vq_(λ,μ))-模糊关联理想若干性质

对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想若干性质进行了详细的研究.首先,运用点态化的方法证明了(∈,∈∨q_((λ,μ)))-模糊关联理想的同态像与同态原像的基本性质;其次,研究了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积;最后,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积的投影子集.     

序半群的阿基米德半群的半格分解

本文通过一个序半群S上的一些二元关系以及它的理想的根集的性质该序半群是阿基米德半群的半格,特别地是阿基米德半群的链的刻划,证明了S是阿基米德链当且仅当S是准素的.通过序半群的m-系的概念,证明了S的任意半素理想是含它的所有素理想的交,并通过该结论,证明了S是阿基米德半群的链当且仅当S是阿基米德半群的半格且S的所有素理想关于集包含关系构成链.作为应用,该结论在一般的半群（没有序）[1]中也成立.