Related papers: On the difference equation of the Poincare type

The recent theory of fractional $h$-difference equations introduced in [N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional variational problems, Signal Process. 91 (2011), no. 3, 513--524], is enriched with useful…

In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

In this article, we show to which extent one can improve a theorem of Bombieri, Friedlander and Iwaniec by using Hooley's variant of the divisor switching technique. We also give an application of the theorem in question, which is a…

We establish formulas for the Poincar\'e polynomial of the type B analogue of the Deligne--Knudsen--Mumford moduli space of rational curves with $n$ marked points, providing type B counterparts to results by Keel, Manin, Getzler and…

Ordinary differential equations of the first order on the torus have been investigated in detail by H. Poincar\'e and A. Denjoy. The long-standing problem of generalising these results for the equations of the order $k>1$ (or for the…

In this note a Fuglede type theorem is proved for Fourier multiplier operators on translation invariant Banach function spaces with order continuous norm over compact abelian groups.

A formula for computation of the bivariate Poincar\'e series $\mathcal{P}_d(z,t)$ for the algebra of covariants of binary $d$-form is found.

This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…

There is the paper by H. Tietze published in 1905 on differential transcendence of solutions of difference Riccati equations. In this paper, we clarify the essence of Tietze's treatment and make it purely algebraic. As an application, the…

In this revised version, we add some expository material and references and make some minor corrections.

We lecture on fundamental Painleve's early Theorems on first order ordinary differential equations with many examples. We end-up with two conjectures about the global analytic continuation of holonomy maps locally defined by Theorem II.

This is a revised version of Sh:430, section 6.

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give sufficient conditions for existence of 2-periodic and…

The results of this paper have been subsumed by those of our new paper arXiv:0910.1858

This is an English (annotated) translation of the German paper by Max Planck (1916) "On the absolute entropy of monatomic bodies" (\"Uber die absolute Entropie einatomiger K\"orper).

The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…

In this short note we give a refinement of Brascamp-Lieb in the style of Houdre-Kagan extension for Poincare inequality in one dimension. This is inspired by works of Helffer and Ledoux.

In this note we show that there exists a new set of operators {Q} (this set is different from the operators which satisfy the Lie algebra of the Poincare group P(1,3) with respect to which the Dirac and Maxwell equations are invariant. We…

In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…