Related papers: Generalization of the Borel-Cantelli Lemma
The purpose of this paper is to generalize the classical Mazur's lemma from the classical convex analysis to the framework of locally $L^0$-convex modules. In this version an extra condition of countable concatenation is included. We…
We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formulas in their proof of the positivity results about these…
The paper contains an interesting generalization of the classical Taylor expansion formula and four applications
In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J.…
In this paper we give a generalization of a result of Wei.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.
With a view to establishing measure theoretic approximation properties of Delone sets, we study a setup which arises naturally in the problem of averaging almost periodic functions along exponential sequences. In this setting, we establish…
We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.
A description of the generalized Gerasimov-Drell-Hearn sum rule for neutron is suggested, using its relation to the Burkhardt-Cottingham sum rule.
We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function.…
Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].
We improve constants in the Rademacher-Menchov inequality.
We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the…
In this article we generalize Borel's classical approximation results for the regular continued fraction expansion to the alpha-Rosen fraction expansion, using a geometric method. We give a Haas-Series-type result about all possible good…
We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is…
We discuss a generalisation of the Herbert formula for double points, when the normal bundle of an immersion admits an additional structure, and an application.
This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).