Gradient flows of the entropy for finite Markov chains

Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wasserstein gradient flow interpretation of the heat flow in Rn by Jordan, Kinderlehrer and Otto (1998). The metric W is similar to, but different from, the L²-Wasserstein metric, and is defined via a discrete variant of the Benamou-Brenier formula.     

Convergence of multi-level iterative aggregation-disaggregation methods

This paper introduces an error propagation formula of a certain class of multi-level iterative aggregation-disaggregation (IAD) methods for numerical solutions of stationary probability vectors of discrete finite Markov chains. The formula can be used to investigate convergence by computing the spectral radius of the error propagation matrix for specific Markov chains. Numerical experiments indicate that the same type of the formula could be used for a wider class of the multi-level IAD methods. Using the formula we show that for given data there is no relation between convergence of two-level and of multi-level IAD methods.     

Discrete element method-based studies on dynamic interactions of a lugged wheel with granular media

Terramechanics plays an important role in determining the design and control of autonomous robots and other vehicles that move on granular surfaces. Traction capabilities, slippage, and sinkage of a robot are governed by the interaction of a robot’s appendage with the operating terrain. It is important to understand how the terrain flows under this appendage during such an interaction. In this work, dynamics of soil performance and locomotion performance of a lugged wheel travelling on soft soil are numerically investigated. Studies are conducted with a two-dimensional model by using the discrete element method to analyze the interactions between a lugged wheel and the soil. The soil performance is studied by examining the force distribution and evolution of force networks during the course of the wheel travel. For two different control modes, namely, slip-based wheel control and angular velocity-based wheel control, the performance parameters such as, sinkage, traction, traction efficiency, and power consumption of the wheel are compared for various wheel configurations. The findings of this work are expected to be useful for optimal design and control of the lugged wheel travelling on deformable surfaces.     

Topological Loewner theory on Riemann surfaces

We prove that topological evolution families on a Riemann surface S are rather trivial unless S is conformally equivalent to the unit disc or the punctuated unit disc. We also prove that, except for the torus where there is no non-trivial continuous Loewner chain, there is a topological evolution family associated to any topological Loewner chain and, conversely, any topological evolution family comes from a topological Loewner chain on the same Riemann surface.     

Enhanced Electron Transfer Properties of Carbon Spheres Chains via Electrochemical Functionalization

Electrochemical functionalization via electrochemical oxidation in nitric acid of various concentrations (0.1 M, 0.2 M and 2 M) was employed to enrich the surface of carbon sphere chains (CSCs) with some useful physico‐chemical properties such as hydrophilicity, oxygen functionalities and electron transfer properties. The functionalization process in 2 M HNO₃ solution led to the creation of an original hybrid material made of carbon sphere chains‐carbon nanobuds. This material displayed a prominent response towards the electrocatalytic oxidation of ferrocyanide with a peak current three times and twice superior to those delivered by pristine CSC and multiwalled carbon nanotubes (MWCNTs) electrodes, respectively.     

Preparations,IR spectra and crystal structures of cyano-bridged bimetallic complexes of zinc(II) and cadmium(II) with tetracyanopalladate(II)

The novel heteronuclear compounds [Zn(hydet-en)₂Pd(CN)₄] (1) and [Cd(hydet-en)₂Pd(CN)₄] (2) {hydet-en: N-(2-hydroxyethyl-ethylenediamine)} have been synthesized and characterized by elemental analyses and IR spectra. The crystal structures of 1 and 2 have been determined by X-ray diffraction. Structural analysis shows that both compounds have shown a polymeric chain, in which the Zn(II)/Pd(II) and Cd(II)/Pd(II) centres are linked by two CN groups. Both zinc and cadmium atoms are six coordinate with two trans cyanide–nitrogen and four hydet-en N atoms in a distorted octahedron arrangement; the palladium atoms in 1 and 2 are four coordinate with four cyanide-C atoms in a square planar arrangement. The chains in both compounds are connected through weak interchain hydrogen bonds, N–H?···?O, N–H?···?N and O–H?···?N, thereby forming a three-dimensional network.     

Synthesis of some alkoxy based bisthiadiazolines

The bisthiadiazolines 3a–3h built around the alkyl chains of varying lengths have been synthesized in good yields by refluxing bisthiosemicarbazones 2a–2h in acetic anhydride. The reactions of bisaldehydes 1a–1h with thiosemicarbazide in alcoholic medium provided 2a–2h and the former were obtained by using the reported methods. The formation and stereochemical features of the bisthiadiazolines 3a–3h are found to be independent of the internal spacer length. The intermediates 2a–2h and bisheterocyclic compounds 3a–3h have been characterized by means of IR, ¹H NMR, ¹³C NMR, Mass (ESI) and elemental analysis.     

Spectroscopy of Molecualr Crystals: A Bibliography for 1975

Abstract

Our previous thermodynamical approach was reexamined to study phase transition of anion radical salts, [(C₆H₅)₃PCH₃]⁺ _{1 ? x}[(C₆H₅)₃AsCH₃]⁺ _x(TCNQ)^? ₂,(0≤x≤1). The mechanism of the phase transition of the solid solution at 1 atm pressure was confirmed to be αy [(C₆H₅)₃PCH₃]⁺ _{1 ? x}[(C₆H₅)₃AsCH₃]⁺ _x(TCNQ)^? ₂,(0≤x≤1) βy, and the volume change assoiated with the phase transition was estimated to be ΔV =-1.3 (1-x) cm³/mol.     

M/M/c休假排队系统稳态分布的数值计算

从数值计算角度研究M/M/c休假排队系统稳定状态的概率分布.采用GMRES方法求解概率分布向量所满足的大型线性方程,构造了一个循环预处理算子加速GMRES方法的收敛.数值实例验证了该算法的优越性.