Related papers: Fourier Analysis: A New Result
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
In this paper we prove the existence and uniqueness theorem, comparison theorem of a class of anticipated mean-field backward stochastic differential equations with jumps.
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
We study the presence of a non-trivial revival effect in the solution of linear dispersive boundary value problems for two benchmark models which arise in applications: the Airy equation and the dislocated Laplacian Schr{\"o}dinger…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this paper, we will prove several new inequalities of Hardy's types with explicit constants. The main results will be proved by making use of some generalizations of Opial's type inequalities and H\"older's inequality. To the best of the…
The aim of this paper is to establish new inequalities for the Euler-Mascheroni by the continued fraction method.
This paper provides a novel metametaphysical approach to quantum indeterminacy. More specifically, it argues that bivalent quantum logic can successfully account for this kind of indeterminacy, given the non-truth-functional character of…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
This is a review article on the development of the probe and enclosure methods from past to present, focused on their central ideas together with various applications.
Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for…
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…
We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when the position of an isolated discontinuity in the function and…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.
The main goal of this paper is to prove several new results about frieze patterns and their equivalents, the quiddity (or $\eta$-)sequences and to obtain a formula giving the number of non-similar frieze patterns of given finite width.