相关论文: Regularisation of functional determinants using bo…

We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a…

We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible we illustrate the general ideas using the Laplacian with…

Regular languages are closed under a wealth of formal language operators. Incorporating such operators in regular expressions leads to concise language specifications, but the transformation of such enhanced regular expressions to finite…

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional…

A general technique is developed for calculating functional determinants of second-order differential operators with Dirichlet, periodic, and antiperiodic boundary conditions. As an example, we give simple formulas for a harmonic oscillator…

In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to…

The multiplicative anomaly related to the functional regularized determinants involving products of elliptic operators is introduced and some of its properties discussed. Its relevance concerning the mathematical consistency is stressed.…

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…

In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…

In this paper we discuss a new approach to the quasinormal-mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex valued…

We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…

We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…

Methods for computing the regularized determinants of fluctuation operators are being developed. The results follow from the fact that these determinants can be expressed by eigenmodes of the fluctuation operator. As an application the…

The Gelfand-Yaglom formula relates the regularized determinant of a differential operator to the solution of an initial value problem. Here we develop a generalized Gelfand-Yaglom formula for a Hamiltonian system with Lagrangian boundary…

This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…

This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact…

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…