We present several new criteria for the oscillation of the second-order linear equation y(t) + q(t)y(t) = 0, in which the coefficient q may or may not change signs. The criteria involve the integral ∫ tq(t) dt for some γ > 0. The special case γ = 2 is then studied in greater details. AMS Subject Classification: 34C10

We present a new computed tomographymethod, the low third derivative (LTD)method, that is particularly suited for reconstructing the spatial distribution of gas concentrations from path-integral data for a small number of optical paths. The method "nds a spatial distribution of gas concentrations that (1) has path integrals that agree with measured path integrals, and (2) has a low third spatia...

ABSTRACT. With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely denned dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation M(s, i)x = x + A((L)[sdgM(-, t)x). An affine version of this equation is also considered. Under the hypothesis that the evolufion...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

We derive for the Bethe-ansatz solvable open XXZ spin chain of arbitrary length a non-linear integral equation describing the ground state. For this case we disclose how to combine the integral representation with the known determinant formula of norms and scalar products. PACS: 02.30.Ik, 75.10.Pq e-mail: [email protected] e-mail: [email protected]