The Regge Calculus approximates a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge model employed in this work limits the choice of the link lengths to a finite number. This makes the computational evaluation of the path integral much faster. A main concern in lattice fie...

It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...

We study integral operators related to a regularized version of the classical Poincaré path integral and the adjoint class generalizing Bogovskiı̆’s integral operator, acting on differential forms in R. We prove that these operators are pseudodifferential operators of order −1. The Poincaré-type operators map polynomials to polynomials and can have applications in finite element analysis. For a ...

A new conservative discrete ordinate method for nonlinear model kinetic equations is proposed. The conservation property with respect to the collision integral is achieved by satisfying at the discrete level approximation conditions used in deriving the model collision integrals. Additionally to the conservation property, the method ensures the correct approximation of the heat uxes. Numerical ...

A path integral representation appropriate for further Monte Carlo simulations is derived for the electron-phonon Holstein model in three spatial dimensions. The model is studied within mean-field theory. Charge density wave and superconducting phase transitions are discussed.

In this paper we consider integrals of the form / e-xK(x,y)f(x)dx, Jo with / 6 C[0, oo) n C«(0, oo), q > p > 0, and x¡f^'\x) 6 C[0, oo), / = I, ... , q -p , when q > p . They appear for instance in certain WienerHopf integral equations and are of interest if one wants to solve these by a Nyström method. To discretize the integral above, we propose to use a product rule of interpolatory type bas...

We are concerned with the existence of smooth time functions on connected time–oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just defined a field of tangent convex cones (Cx)x∈M enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on ...

This article introduces a numerical method based on an M(n+ 1) set of general, hybrid orthonormal Bernstein functions coupled with Block-Pulse Functions(HOBB) on the interval [0,1] for approximating solutions of a Coupled System of linear and non linear Volterra integral and Integro-Differential equations. This method reduces a Coupled System of Volterra integral and IntegroDifferential equatio...