Abstract. In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from hi to ∞ to be from −∞ to ∞ by multiplying the integrand by a periodic square wave that approximates the domain of the integral. This square wave is expressed by its Fourier series expansion. Then a Chole...

The need for increasing fidelity and accuracy in mission-critical electromagnetic applications have pushed the problem sizes toward extreme computational scales. Therefore, there is a large premium placed on the investigation of parallel and scalable integral equation simulators, a particularly useful class of computational electromagnetics, to meet this demand. This dissertation will focus on ...

Generally, the Schwarzschild black hole was proved stable through two different methods: the mode-decomposition method and the integral method. In the paper, we show the integral method can only apply to the initial data vanishing at both the horizon and the spatial infinity. It can not treat the initial data only vanishing at the spatial infinity. We give an example to show the misleading info...

We develop a representation of reverse time migration in terms of Fourier integral operators the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation with a boundary source and homogeneous initial conditions using wave packets. On this basis, we develop a numerical procedure for the reverse time continuat...

Reiner and Webb (preprint, 2002) compute the Sn-module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper proves that the simplicial boundary map interacts in a nice fashion with the Eulerian idempotents. The Laplacian acting on the top chain group in the complex of injective words is also shown to eq...

We develop a representation of reverse-time migration (RTM) in terms of Fourier integral operators, the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation with a boundary source and homogeneous initial conditions using wave packets. On this basis, we develop a numerical procedure for the reverse-time co...

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB2(A), where A is a division algebra of d...

In general only vector spaces whose scalar domains are fields have been investigated. In this paper we study vector spaces whose scalar domains are integral domains in which every ideal has a finite basis. It is shown that the theory of the linear subsets of such a vector space can be developed by using exactly the same technique which has always been applied to the ideals of an integral domain...

The paper studies an approximate multiresolution analysis for spaces generated by smooth functions which provide high order cubature formulas for integral operators of mathematical physics. Since these functions satisfy reenement equations with any prescribed accuracy methods of the wavelet theory can be applied. We obtain a decomposition of the nest scale space into almost orthogonal wavelet s...

The numerical evaluation of the transforms in the title, and their inverses, is considered, using a variety of decomposition, truncation, and quadrature methods. Extensive numerical testing is provided and an application given to the numerical evaluation of the kernel of a Fredholm integral equation of interest in mixed boundary value problems on wedge-shaped domains. AMS subject classification...