C72,La2@C72几何结构和电子性质的计算研究

采用密度泛涵理论(density functional theory,DFT)中的广义梯度近似(generally gradient approximation,GGA)对富勒烯C72和内掺金属La富勒烯La2@C72三种同分异构体的几何结构和电子结构进行研究.发现在C72的三种同分异构体中,满足独立五边形规则(isolated-pentagon-rule,IPR)的C72(D6d)结构最为稳定;在La2@C72三种同分异构体中,有着两对两两相邻五元环(twofused-pentagon)的La2@C72(#10611)结构最为稳定,而满足IPR的La2@C72(D6d)的结构变成了最不稳定结构.从能级图和态密度图分析得知,笼子稳定性的变化与La原子的原子轨道与C72原子轨道之间的杂化有关.Mulliken电荷分析得知,La2@C72(#10611)的两个La原子共转移了约3个电子给C72,并且,它们几乎分布在整个C笼上,形成的电子结构为La23+@C3-72.净自旋分析得知,La2@C72(#10611)中La原子磁性完全淬灭.     

Arithmetic expressions of Selberg's zeta functions for congruence subgroups

In [P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982) 229-247], it was proved that the Selberg zeta function for SL₂(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL₂(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem and the asymptotic formula of the sum of the class number.     

The communication complexity of private value single-item auctions

This paper is concerned with information revelation in single-item auctions. We compute how much data needs to be transmitted in three strategically equivalent auctions—the Vickrey auction, the English auction and the recently proposed bisection auction—and show that in the truth-telling equilibrium the bisection auction is the best performer.     

First-Principles Study on the Electronic Structures for Y^3＋：PbWO4 Crystals

The possible defect models of Y^3＋：PbWO4 crystals are discussed by defect chemistry and the most possible substituting positions of the impurity Y^3＋ ions are studied by using the general utility lattice program （GULP）. The calculated results indicate that in the lightly doped Y^3＋ ：PWO crystal, the main compensating mechanism is [2Ypb^＋ ＋ VPb^2-], and in the heavily doped Y^3＋ ：PWO crystal, it will bring interstitial oxygen ions to compensate the positive electricity caused by YPb^＋, forming defect clusters of [2Ypb^＋ ＋Oi^2-] in the crystal. The electronic structures of Y3＋ ：PWO with different defect models are calculated using the DV-Xα method. It can be concluded from the electronic structures that, for lightly doped cases, the energy gap of the crystal would be broadened and the 420nm absorption band will be restricted; for heavily doped cases, because of the existence of interstitial oxygen ions, it can bring a new absorption band and reduce the radiation hardness of the crystal.     

Graphical operations on projective spaces

Motivated by the work of Crapo and Rota [6] on the lifting of a projective complex, we introduce a class of invariant operations associated to integral-weighted graphs, which we call graphical operations. Such operations generalize the sixth harmonic of a quadranguler set on a projective line. We determine the expansion of the graphical operations in terms of multi-linear bracket polynomials in a Grassmann-Cayley algebra. Reducibility and compositions of such invariant operations are also investigated with a number of examples.Supported by Courant Instructorship, New York University.     

Dual Homogeneous Forms and Varieties of Power Sums

We review the classical definition of the dual homogeneous form of arbitrary even degree which generalizes the well-known notion of the dual quadratic form. Following the ideas of S. Mukai we apply this construction to the study of the varieties parametrizing representations of a homogeneous polynomial as a sum of powers of linear forms.Research supported in part by NSF Grant DMS 0245203.Lecture held in the Seminario Matematico e Fisico on October 15, 2003Received: April, 2004     

Phase separation of poly(γ-benzyl L-glutamate) to liquid crystal and isotropic solution in various helicogenic solvents

Solvent effects on the phase separation of poly(72/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0">-benzyl L-glutamate) to liquid crystal and isotropic solution have been observed in various helicogenic solvents. The temperature-composition phase diagrams have been determined for each solution. The critical concentrations,72/xxlarge957.gif" alt="ngr" align="BASELINE" BORDER="0"> ₂ ^* , at which the phase separation occours have been compared in various solvents. In dimethylformamide in which the polymer is molecularly dispersed, the observed72/xxlarge957.gif" alt="ngr" align="BASELINE" BORDER="0"> ₂ ^* value has agreed with that calculated by Flory's theory. In some solvents in which the polymer aggregates in a head-to-tail mode such as chloroform, the observed72/xxlarge957.gif" alt="ngr" align="BASELINE" BORDER="0"> ₂ ^* values have been considerably small. It is assumed that the polymer aggregates behave as longer particles than the original particles. In dioxane in which the polymer aggregates highly both in a head-to-tail and a side-by-side modes, the72/xxlarge957.gif" alt="ngr" align="BASELINE" BORDER="0"> ₂ ^* value has been a little larger than that in chloroform. In this case the relationship between the aggregation and the liquid crystal formation is so complicated that further investigation is necessary. In aromatic solvents such asm-cresol that dissolves the polymer almost molecularly, the72/xxlarge957.gif" alt="ngr" align="BASELINE" BORDER="0"> ₂ ^* is smaller than that in dimethylformamide. Therefore, the intermolecular interactions between the phenyl groups in the side groups of the polymer and those in solvent molecules must be considered.The author is grateful to Mr. K. Sano and Mr. M. Watanabe for their observation of the liquid crystal formation.     

Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.

     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces

This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ⁿ equipped with an _p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general -presented polytopes in _p spaces with 1相似文献