相关论文: A note on higher-order differential operations

The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present…

Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…

Riccati's differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati's differential equation with the Cole-Hopf transform shows a relation between the first order evolution…

In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…

We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…

We study higher-order theories of gravitation; in particular, we will focus our attention on the second-order theory, in which conformal symmetry can be implemented.

Because of the nonlocal properties of fractional operators, higher order schemes play more important role in discretizing fractional derivatives than classical ones. The striking feature is that higher order schemes of fractional…

We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the…

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…

This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator $\hat{H}$ in quantum mechanics. Starting from the Schr\"odinger equation for a free particle, the work derives…

For certain dimensionally-regulated massive two- and three-loop propagator-type diagrams the higher order epsilon-expansion is constructed.

A new mathematical notation is proposed for the iteration of functions. It facilitates the application of the iteration of functions in mathematical and logical expressions, definitions of sets, and formulations of algorithms. Illustrations…

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…

The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…

We investigate the existence of well-ordered sequences of Baire 1 functions on separable metric spaces.

This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…

In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…

This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space'' (Ann. Appl. Probab.…

This work is concerned with the development of quasi-Trefftz methods for first-order differential systems. It focuses on discrete quasi-Trefftz spaces, starting from their definition and including the construction of corresponding bases…