Related papers: Discrete L'Hospital's rule

Recently J.Han\v{c}l obtained a result which improves on approximations to real numbers which correspond to the discrete part of Lagrange spectrum. In the present paper we prove a similar result related to the discrete part of Dirichlet…

We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and…

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

We formulate the Lagrange-D'Alembert principle as a pure mathematical theory that meets modern standards of rigor. While we note several new aspects of the principle, the article is primarily methodological.

In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…

In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…

This paper has been withdrawn by the author(s). The material contained in the paper will be published in a subtantially reorganized form, part of it is now included in math.QA/0510174

Differential privacy is the gold standard for statistical data release. Used by governments, companies, and academics, its mathematically rigorous guarantees and worst-case assumptions on the strength and knowledge of attackers make it a…

In this paper, we introduce two distinct discrete forms of Appell function $F_2$. We determine their convergence domains, integral representations as well as difference-differential equations that are satisfied by these discrete analogues…

The notion of a Laplace ladder for a discrete analogue of the Laplace equation is presented. The adjoint of the discrete Moutard equation and a discrete counterpart of the nonlinear form of Goursat equation are introduced.

We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…

This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…

Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…

In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is…

Proietti et al. (arXiv:1902.05080) reported on an experiment designed to settle, or at least to throw light upon, the paradox of Wigner's friend. Without questioning the rigor or ingenuity of the experimental protocol, I argue that its…

For a fixed pair and fixed exponents, we prove the discreteness of log discrepancies over all log canonical triples formed by attaching a product of ideals with given exponents.

In this short note, we present few results on the use of the discrete Laplace transform in solving first and second order initial value problems of discrete differential equations.

A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.

With more and better clinical data being captured outside of clinical studies and greater data sharing of clinical studies, external controls may become a more attractive alternative to randomized clinical trials. Both industry and…

A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…