The path integral approach was introduced by Feynman1 in a seminal paper published in 1948. It provides an alternative formulation of time-dependent quantum mechanics, equivalent to that of Schrödinger. Since its inception, the path integral has found innumerable applications in many areas of physics and chemistry. Its main attractions can be summarized as follows: the path integral formulation...

An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger’s enumeration procedure based on the ellipsoid method of Fincke and Pohst. Recently relative Thue equations have gained an important application, e.g., in computing power integral bases in algebraic number fields. The presented method...

Various issues about integral processes with dead time controlled by a PI controller are discussed. First, the region of the control parameters to guarantee the system stability is characterised. Then, the control parameters to achieve the given gain and/or phase margins (GPM) are determined. Furthermore, the constraint on achievable GPM is derived. These results are obtained on the basis of th...

The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.

Old and new results for characterizing volume forms in functional integration. 1 The Wiener measure Defining volume forms on infinite dimensional spaces is a key problem in the theory of functional integration. The first volume form used in functional integration has been the Wiener measure. From the several equivalent definitions of the Wiener measure, we choose one [1] which can easily be ext...

After reducing a system of higher-order regular Lagrangian into first-order singular Lagrangian using constrained auxiliary description, the Hamilton-Jacobi function is constructed. Besides, the quantization of the system is investigated using the canonical path integral approximation.

A B S T R A C T A new type of seismic imaging, based on Feynman path integrals for waveform modelling , is capable of producing accurate subsurface images without any need for a reference velocity model. Instead of the usual optimization for traveltime curves with maximal signal semblance, a weighted summation over all representative curves avoids the need for velocity analysis, with its common...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...

Abstract. The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partially discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain i...

One of the numerical methods for solving linear Volterra integral equations is block-by-block method, which is explained in [L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, 1985; L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, 1974] and [P.K. Kyte, P. Puri, Computational Methods for Linear Integral Eq...