Related papers: On the difference equation of the Poincare type

Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…

I present here the proofs of results, which are obtained in my papers "On the linear forms with algebraic coefficoients of logarithms of algebraic numbers", VINITI, 1996, 1617-B96, pp. 1 - 23 (in Russian), and "On the systems of linear…

In this paper, we will present several new congruences involving binomial coefficients under integer moduli, which are the continuation of the previous two work by Cai \textit{et al.} (2002, 2007).

The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…

In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].

There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.

We observe some higher order Poincare-type inequalities on a closed manifold, which is inspired by Hurwitz's proof of the Wirtinger's inequality using Fourier theory. We then give some geometric implication of these inequalities by applying…

This paper contains no new results. It is intended to be merely a brief introduction to the long paper: N. J. Kalton, Differentials of complex interpolation processes for Kothe function spaces. Trans. Amer. Math. Soc. 333 (1992), no. 2,…

Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)

This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

Some errors contained in the author's previous article "An example of Bautin-type bifurcation in a delay differential equation", JMAA, 329(2007), 777-789, are listed and corrected. Original abstract: In a previous paper we gave sufficient…

A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.

We show the presence of Poincare anomaly in Maxwell-Chern-Simons theory with an explicit mass term, in 2+1-dimensions.

We highlight four points which have been ignored or underestimated before and which allow a better understanding of "Sur la dynamique de l'electron": (i) the use by Poincare of active Lorentz transformations (boosts); (ii) the necessity,…

We extend the results of the authors from [Abstract and Applied Analysis, Volume 2016, Article ID 9712878] to the case conjugate Fourier series.

In this article we consider a method of proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we…

We prove second and fourth order improved Poincar\'e type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as…

This is an English translation of the following paper, published several years ago: Nikonorov Yu.G., Nikonorova Yu.V. Generalized Popoviciu's problem (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 229-232 (2000), Zbl. 0958.51021. All inserted…

In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…