Slater integrals for screened hydrogenic orbitals /

Prepared for Air Force Weapons Laboratory.

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.

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.

A treatise on the integral calculus : containing the integration of explicit functions of one variable ; together with the theory of definite integrals and of elliptic functions /

Mode of access: Internet.

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.

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.

On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

On a Class of Generalized Elliptic-type Integrals

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized elliptic-type integrals.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.