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.     

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   

Interaction of polyfluoroalkyl-containing aziridinyl ketones with hydrogen halides

Polyfluoroalkyl-containing aziridinyl ketones, unlike their nonfluorinated analogs, react with hydrogen halides to give only -halo- -anvnoketones or their hydrogen halide salts. Thermal decomposition of the latter in the case where Hal = CI affords -chlorovinyl ketones.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 684–686, March, 1996.     

Quantum Berezinian and the classical capelli identity

We study a superanalogue of the Yangian of the Lie algebra gl _m . We apply our constructions to invariant theory.     

Electronic conduction properties of silver particles in cesium oxide

The electronic conductivity of a particular metallic particles/semiconductor system, i.e. Ag particles in cesium-oxide thin film, has been studied. The experimental results show a transition from a polycrystalline semiconductor to metallic behavior as characterized by the conductivity-temperature curve (log bs 1/T), and a five order of magnitude increase in the room temperature value of the conductivity with surface Ag content increasing from an equivalent thickness of 2Å to 20Å. It was observed by TEM that the deposited Ag was mainly in the form of dispersed particles with the particle size varying from 20 to 200Å and their separations varying from hundreds to tens of angstroms over the Ag content range. These results can hardly be explained with the model of direct electron tunneling through the Schottky barrier at the Ag-particle/cesium-oxide interface. A microstructure model with two conduction layers is presented, and an analogy to the hopping conduction mechanism is proposed to explain the electronic conduction behavior. This model predicts that the attenuation length for electronic wavefunctions localized at Ag particles falls in the range 20–50Å.     

A functional inequality for real-analytic functions

Summary Forf ( C ⁿ() and 0 t x letJ _n (f, t, x) = (–1)ⁿ f(–x)f ⁽ⁿ⁾(t) +f(x)f ⁽ⁿ⁾ (–t). We prove that the only real-analytic functions satisfyingJ _n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e ^x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ ₀ (f, x, x) 0 and ₀ ^x (x – t)^{n – 1}J_n(f, t, x)dt 0 (n 1).     

Thermal noise in Hg0.795Cd0.205Te detectors for large biasing fields

Thermal noise in Hg_0.795Cd_0.205Te detectors is estimated for large biasing fields at a lattice temperature of 77 K, by computing the correlation functions of the velocity fluctuations with the Monte Carlo technique. The noise temperature for current components transverse to the field is almost independent of the field, but that corresponding to the parallel component increases by a factor of about 1.3 at 50 V/cm and by a factor of 3.0 at 300V/cm. The thermal noise voltage for a detector of 85 resistance increases from 0.6nV/Hz^1/2 at low biasing fields to about 3nV/Hz^1/2 at a field of 300 V/cm. The noise power is also found to remain constant up to about 75 GHz, and it decreases thereafter by a factor of 0.25 for doubling of the frequency.