On Riemann's theory of algebraic functions and their integrals : a supplement to the usual treatises /

Photocopy. [Ithaca, N.Y. : Cornell University Libraries, 1977]--xii, 76 p. on [44] leaves ; 26 x 38 cm. fold. to 25 x 19 cm.

Contributions to a theory of summability of trigonometric integrals.

Bibliography: p. 227.

Applications of elliptic functions to problems of closure.

Mode of access: Internet.

Neue theorie der ultraelliptischen functionen.

Available on demand as hard copy or computer file from Cornell University Library.

Introduction to the theory of Fourier's series and integrals.

Vol. 2 has title: Introduction to the mathematical theory of the conduction of heat in solids. First published in 1906 in 1 vol. with title: Fourier's series and conduction of heat.--cf. Pref.

Elements of the integral calculus, with a key to the solution of differential equations, and a short table of integrals.

Mode of access: Internet.

The differential and integral calculus : containing differentiation, integration, development, series, differential equations, differences, summation, equations of differences, calculus of variations, definite integrals,--with applications to algebra, plane geometry, solid geometry, and mechanics. Also, Elementary illustrations of the differential and integral calculus /

First issued in 25 parts, July 15, 1836, to June 1, 1842.

Introduction to the theory of Fourier's series and integrals and the mathematical theory of the conduction of heat,

Bibliography: Fournier's series: p. [411]-418; The conduction of heat: p.[419]-429.

Computational aspects of modular parametrizations of elliptic curves

Thesis (Ph.D.)--University of Washington, 2016-06

Existence and multiplicity results for quasilinear elliptic equations

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f (x, s), we show the following problem: -Delta(p)u = lambda f(x,u) in Omega, u/(partial derivative Omega) = 0, where Omega is a bounded open subset of R-N, N >= 2, with smooth boundary, lambda is a positive parameter and Delta(p) is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large lambda.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.