Metastable decay rates,asymptotic expansions,and analytic continuation of thermodynamic functions

The grand potentialP(z)/kT of the cluster model at fugacityz, neglecting interactions between clusters, is defined by a power series _n Q _n z ⁿ , whereQ _n , which depends on the temperatureT, is the partition function of a cluster of sizen. At low temperatures this series has a finite radius of convergencez _s . Some theorems are proved showing that ifQ _n , considered as a function ofn, is the Laplace transform of a function with suitable properties, thenP(z) can be analytically continued into the complexz plane cut along the real axis fromz _s to + and that (a) the imaginary part ofP(z) on the cut is (apart from a relatively unimportant prefactor) equal to the rate of nucleation of the corresponding metastable state, as given by Becker-Döring theory, and (b) the real part ofP(z) on the cut is approximately equal to the metastable grand potential as calculated by truncating the divergent power series at its smallest term.     

Characterization of measures by potentials

Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f _E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l _∞ ⁿ and wheref(t)=|t| ^p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ _∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ _∞) is positive definite only iff is a constant function.     

Approximating the zeros of analytic functions by the exclusion algorithm

We give a practical version of the exclusion algorithm for localizing the zeros of an analytic function and in particular of a polynomial in a compact of . We extend the real exclusion algorithm to a Jordan curve and give a method which excludes discs without any zero. The result of this algorithm is a set of discs arbitrarily small which contains the zeros of the analytic function.     

An Arithmetic Reduction of Finite Rank 3 Geometries with Linear Spaces as Plane Residues and with Dual Linear Spaces as Point Residues

Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons.     

Interior-point algorithm for quadratically constrained entropy minimization problems

In this paper, we develop an interior point algorithm for quadratically constrained entropy problems. The algorithm uses a variation of Newton's method to follow a central path trajectory in the interior of the feasible set. The primal-dual gap is made less than a given in at most steps, wheren is the dimension of the problem andm is the number of quadratic inequality constraints.     

A global Newton method II: Analytic centers

This paper modifies the convergence conditions of a back-tracking global Newton method announced in Goldstein (1991), making them sharper and easier to apply. A new version of the Kantorovich inequalities is presented that is simple to state and prove. An application is made to the centering problem for polytopes. Based on an idea of Ye (1989), an algorithm is given for the feasibility problem of linear inequalities.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Synthesis of nanostructures based on 1,4- and 1,3,5-phenylethynyl units with π-extended conjugation. Carbon networks dendrimer base units

A convenient and efficient synthesis of 3,5-di(silylethynyl)phenylacetylene and p-[3,5-di(silylethynyl)phenylethynyl]phenylacetylene has been carried out. These compounds serve to prepare nanometer-sized conjugated 1,4- and 1,3,5-phenylethynyl oligomers, by means of cross-coupling with a convenient haloaryl derivative, catalysed by palladium(II), in excellent yields. The phenylethynyl homologues show fluorescence emission, the wavelength of which is displaced by approximately 20 nm by each phenylethynyl unit increasing the conjugate chain.     

用ab initio方法研究NaN_3的几何构型、电子结构和热力学、动力学性质

用ａｂｉｎｉｔｉｏＭＯ方法，在ＭＰ２（ｆｕｌ）／６３１１Ｇ水平下，全优化计算了叠氮化钠（ＮａＮ３）分子的线状和环状两种稳定构型及其转化过渡态的几何参数、电荷分布、分子总能量和振动频率，并研究了它们的热力学性质及转化速率常数和平衡常数．结果表明，线状比环状构型稍稳定（能量低６．０４ｋＪ／ｍｏｌ）；两者相互转化的能垒分别为１３．１５ｋＪ／ｍｏｌ（线型→环状）和７．１１ｋＪ／ｍｏｌ（环状→线型）．热力学和动力学计算均表明：ＮａＮ３通常主要以线型结构存在（占８５％以上），且随温度升高而增多（在１０００Ｋ大于９１％）．     

Synthesis and Crystal Structure of a Vanadium(Ⅴ) Complex with 2-Hydroxy-1-naphthaldehyde Isonicotinoyl Hydrazone

The mononuclear vanadium(Ⅴ) complex with 2-hydroxyl-1-naphthaldehyde isoncotinoyl hydrazone was synthesized and characterized by single-crystal X-ray diffraction.The crystal is of monoclinic,space group P2 1/n with a = 10.3153(15),b = 7.4024(11 ),c = 24.413(4) (A),β= 101.911(2)°,V= 1824.0(5) (A)3,Z = 4,Mr = 427.28,Dc = 1.556 g/cm3,F(000) = 880,μ(MoKα) =0.591,the final R = 0.0372 and wR = 0.0926.The vanadium(Ⅴ) atom adopts a distorted square-pyramidal geometry coordinated by the tridentate ligand and two oxygen atoms.The hydrogen bonds and strong π…π stacking interactions link the complex molecules into a 3-D network structure.