Related papers: Generalization of the Borel-Cantelli Lemma
We establish some cohomological bounds in D-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the b-function lemma for non-holonomic D-modules.
In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
The aim of this paper is to give a proof of improving of Zalcman's lemma.
We prove several generalisations of the ping-pong lemma for negatively curved groups.
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
In this paper we give the Bohr-Sommerfeld-Heisenberg quantization of the mathematical pendulum.
In this paper, we generalize the Bohr-Rogosinski sum for the Ma-Minda classes of starlike and convex functions. Also the phenomenon is studied for the classes of starlike functions with respect to symmetric points and conjugate points along…
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We prove an infinitary version of the Brauer-Schur theorem.
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
In this paper we prove a generalization of Montel's theorem for a class of first order elliptic equations with measurable coefficients involving Hodge-Dirac operators. We then apply this result to sequences of solutions of second order…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.
In this paper we use probabilistic methods to derive some results on the generalized Bernoulli and generalized Euler polynomials. Our approach is based on the properties of Appell polynomials associated with uniformly distributed and…
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici \`a…