Le Système d'Euler de Kato en Famillie(Ⅱ)

This article is the second article on the generalization of Kato's Euler system. The main subject of this article is to construct a family of Kato's Euler systems over the cuspidal eigencurve, which interpolate the Kato's Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato's Euler system to construct a family of distributions on Z_p over the cuspidal eigencurve; this distribution gives us a two-variable p-adic L function which interpolate the p-adic L function of modular forms.     

Application of h-adaptive,high order finite element method to solve radial Schrödinger equation

The h-adaptive, high order finite element method is applied to solve a second order one dimension eigenvalue problem. The finite element formulation for the Lobatto basis is given, for which basis functions of arbitrary order can be constructed. The adaptive algorithm is simple, yet very efficient and straightforward to implement. The algorithm is based on the observation that the expansion coefficients of Lobatto basis functions decay rapidly. It allows evaluating the smallest eigenvalues simultaneously with the comparable accuracy for all eigenvalues. The presented algorithm is applied to solve the radial Schrödinger equation with the Coulomb and the Woods–Saxon potentials. For both potentials the convergence rate is presented. After seven adaptive iterations nine-digit accuracy was obtained.     

Fortran codes for the correlation functions of hard sphere fluids

Our Fortran codes for hard sphere fluids and their mixtures for the correlation functions that arise from the Percus–Yevick theory and the Verlet–Weis semi-empirical correction have proven useful during a period of nearly four decades and continue to be useful. In order to make these codes even more widely available, a brief summary is presented here and listings of these codes are given in the electronically accessible Supplementary Material to this paper.     

Thermodynamics of substituted coumarin VII: Potentiometric and spectrophotometric studies of 1-acetyl-2-(coumarin-iminecarboxamide-3-yl) hydrazine transition metal complexes

The dissociation constant of l-acetyl-2-(coumariniminecarboxamide-3-yl) hydrazine (ACCH) has been determined potentiometrically in 0.1 M KC1 and 40% (v/v) ethanol-water mixture. The stepwise stability constants of the formed complexes of Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺ and UO₂ ²⁺ with ACCH have been determined. The stability constants were found to UO₂ ²⁺ > Cu²⁺> Zn²⁺ > Ni²⁺ < CO²⁺ < Mn²⁺. The effect of temperature on the dissociation of ACCH and the stability of its formed complexes were studied. The corresponding thermodynamic functions were also determined and discussed. The spectral data of ACCH were investigated in pure organic solvents as well as in Britton Robinson buffer solutions of varying pH values. The dissociation constant pK^H ₁ of ACCH and the overall stability constants logβ of their complexes were determined in 20% (v/v) ethanol-water mixture at 298K.     

The thermodynamic functions and the regions of (P,T)-states of dense carbon and boron nitride modifications

Abstract

For the first time the thermodynamic functions for boron nitride and carbon were defined in the temperature range 300 to 4000K by a computational procedure which was impossible in the previous empirical approach. This involved the application of the theoretical functions from Refs. 1, 2, and 3. There the temperature dependence of the heat capacity is characterized by a sum of two Debye functions that reflect the contribution of vibration modes of different characteristic temperature to the heat capacity. The above-mentioned theoretical functions make it possible to calculate the thermodynamic function without allowing for the anharmonic effect in the temperature range rather wider th-an the one wherein the initial experiments were conducted. It is sufficient for their computation to define Debye characteristic temperatures. One of the procedures of their calculation using experimental enthalpy data is described in Ref. 4. Besides, this work contains the majority of known experimental and theoretical data which enable various methods of the thermodynamic function characterizations for carbon and boron nitride to be compared.     

Control of multi-node mobile communications networks with time-varying channels via stability methods

Consider a communications network consisting of mobiles and random external data processes, each destined to a particular destination. Each mobile can serve as a node in the multi-hop path from source to destination. At each mobile the data is queued according to the source destination pair. The quality of the connecting channels are randomly varying. Time is divided into small scheduling intervals. At the beginning of each interval, the channels are estimated and this information is used for the decisions concerning allocation of transmission power and/or time, bandwidth, and perhaps antennas, in a queue and channel-state dependent way. Under a natural (and “almost” necessary) “average flow” condition, stochastic stability methods are used to develop scheduling policies that assure stability. The policies are readily implementable and allow a range of tradeoffs between current rates and queue lengths, under very weak conditions. Because of the non-Markovian nature of the problem, we use the perturbed Stochastic Liapunov function method. The choice of Liapunov function allows a choice of the effective performance criteria. All essential factors are incorporated into a “mean rate” function, so that the results cover many different systems. Extensions concerning acknowledgments, multicasting, non-unique routes, and others are given to illustrate the versatility of the method, and a useful method for getting the a priori routes is discussed.     

Distribution functions for random walk processes on networks: An analytic method

A novel analytic method for deriving and analyzing probability distribution functions of variables arising in random walk problems is presented. Applications of the method to quasi-one-dimensional systems show that the generating functions of interest possess simple poles, and no branch cuts outside the unit complex disk. This fact makes it possible to derive closed formulas for the full probability distribution functions and to analyze their properties. We find that transverse structures attached to a one-dimensional backbone can be responsible for the appearance of power laws in observables such as the distribution of first arrival times or the total current moving through a (model) photoexcited dirty semiconductor (our results compare well with experiment). We conclude that in some cases a geometrical effect, e.g., that of a transverse structure, may be indistinguishable from a dynamical effect (long waiting time); we also find universal shapes of distribution functions (humped structures) which are not characterized by power laws. The role of bias in determining properties of quasi-one-dimensional structures is examined. A master equation for generating functions is derived and applied to the computation of currents. Our method is also applied to a fractal structure, yielding nontrivial power laws. In all finite networks considered, all probability distributions decay exponentially for asymptotically long times.For a relatively recent review with some historical background see Ref. 2.     

高维分形函数与插值

1 预备知识 1986年,Barnsley[1]采用某种特殊的迭代函数系统(IFS)构造了分形插值函数(FIF), 在计算机图形学等领域得到了广泛的应用(参见[1,2,5,6])．Massopust[4],J．S．Geronimo和 D．P．Hardin[3]等构造了三角形域上的自仿射分形函数,其图像称为分形曲面。文献[7]发现了矩形区域上分形函数的特征定理,并由此解决了矩形区域的分形插值问题．本文中     

新超复结构和Clifford分析

本文在Ｈ．Ｍａｌｏｎｅｋ［１］新的超复结构的意义下，研究Ｃｌｉｆｆｏｒｄ分析中Ａ值函数超复可微性及其一种新的锁链规则和微分法则．