Aleksandr I︠A︡kovlevich Khinchin

Bio: Aleksandr I︠A︡kovlevich Khinchin is an academic researcher. The author has contributed to research in topics: G-network & Probability theory. The author has an hindex of 6, co-authored 13 publications receiving 2403 citations.

Analytic Number Theory

Abstract: Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large sieve Exponential sums The Dirichlet polynomials Zero-density estimates Sums over finite fields Character sums Sums over primes Holomorphic modular forms Spectral theory of automorphic forms Sums of Kloosterman sums Primes in arithmetic progressions The least prime in an arithmetic progression The Goldbach problem The circle method Equidistribution Imaginary quadratic fields Effective bounds for the class number The critical zeros of the Riemann zeta function The spacing of zeros of the Riemann zeta-function Central values of $L$-functions Bibliography Index.

Semantic similarity in a taxonomy: an information-based measure and its application to problems of ambiguity in natural language

Abstract: This article presents a measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edge-counting approach. The article presents algorithms that take advantage of taxonomic similarity in resolving syntactic and semantic ambiguity, along with experimental results demonstrating their effectiveness.

Stirring by chaotic advection

Abstract: In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two-dimensional incompressible flow this system is Hamiltonian and has just one degree of freedom. For unsteady flow the system is non-autonomous and one must in general expect to observe chaotic particle motion. These ideas are developed and subsequently corroborated through the study of a very simple model which provides an idealization of a stirred tank. In the model the fluid is assumed incompressible and inviscid and its motion wholly two-dimensional. The agitator is modelled as a point vortex, which, together with its image(s) in the bounding contour, provides a source of unsteady potential flow. The motion of a particle in this model device is computed numerically. It is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator. With the agitator held at a fixed position, integrable marker motion ensues, and the model device does not stir very efficiently. If, on the other hand, the agitator is moved in such a way that the potential flow is unsteady, chaotic marker motion can be produced. This leads to efficient stirring. A certain case of the general model, for which the differential equations can be integrated for a finite time to produce an explicitly given, invertible, area-preserving mapping, is used for the calculations. The paper contains discussion of several issues that put this regime of chaotic advection in perspective relative to both the subject of turbulent advection and to recent work on critical points in the advection patterns of steady laminar flows. Extensions of the model, and the notion of chaotic advection, to more realistic flow situations are commented upon.

On the Measurement of Niche Breadth and Overlap

Abstract: Measures of niche breadth and overlap that depend on the distribution of individual among resource states (ecological categories) should be independent of the relative abundance of the species and of the number of resource states considered. Such measures should also take into account the degree of distinctness of the resource states from the point of view of the organisms concerned. An ecoassay of the distinctness of resource states may well be easier and more meaningful than measurements of physical and chemical factors. We propose that the species composition of communities utilizing different resource states may be used to develop weighting factors with which each state may be weighted in proportion to its degree of distinctness. The weighting factors are used in the development of indices of niche breadth and overlap that correct for variation in the range and distinctness of resource states and that suffer less from human subjectivity than do the measures used to date. The use of such indices and the relationship of niche overlap to competition are discussed.