Related papers: Formalization of Lerch's Theorem using HOL Light
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical…
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…
Consistent initialization of the Laplace transform has been a fundamental and long-standing issue. The consistency of the L- approach has been questioned, yet it is a popular approach since the L+ approach requires a priori computation of…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…
The Laplace transform approach with convolution theorem is used to find the scattering phase shifts of a Mie-type potential. The normalized scattering wave functions are also studied. The bound state spectrum and the corresponding…
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems.…
Network topology matrices are algebraic representations of graphs that are widely used in modeling and analysis of various applications including electrical circuits, communication networks and transportation systems. In this paper, we…
Discrete fractional order systems have attracted more and more attention in recent years. Nabla Laplace transform is an important tool to deal with the problem of nabla discrete fractional order systems, but there is still much room for its…
This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of linear PDEs which expresses solutions using sums of polynomials…
The dynamic Laplace operator arises from extending problems of isoperimetry from fixed manifolds to manifolds evolved by general nonlinear dynamics. Eigenfunctions of this operator are used to identify and track finite-time coherent sets,…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
Solving for the time evolution of a many particle system whose dynamics is governed by Lindblad equation is hard. We extend the use of the transfer matrix approach to a class of Lindblad equations that admit a closed hierarchy of two point…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
The Laplace transform theory violates a very fundamental requirement of all engineering systems. We show that this theory assumes that all signals must exist over infinite time interval. Since in engineering this infinite time assumption is…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
We study existence, uniqueness and regularity of solutions for linear equations in infinitely many derivatives. We develop a natural framework based on Laplace transform as a correspondence between appropriate $L^p$ and Hardy spaces: this…