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In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).

We give the converse to Dirichlet's theorem on primes in arithmetic progressions by generalizing an old result of Guinand.

In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some…

In this note we elaborate on a recent counter-example to the Nelson-Seiberg theorem and to its generalizations. We provide sufficient conditions for the existence of such counter-examples, finding new ones. We claim that these…

This is a survey of current and recent works on deformation quantization and index theorems.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

Let $\mathfrak{g}$ be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well-behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie…

Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.

In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars.…

It is shown that the previous [1-3] generalization of the final-value theorem to the average (not necessarily limiting) values, can be extended to the higher-order running averages $(<>_{t}), lim_{s\rightarrow0}[sF(s)] =…

The classes of 1MP-inverses and MP1-inverses are recently introduced classes of generalized inverses of complex matrix. Actually, they coincide with the classes of $\{1,2,3\}$ and $\{1,2,4\}$ inverses, respectively. We consider these…

We generalise the Bernoulli numbers to include the case where the index may be a continuous variable.

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

We consider Gomory and Johnson's infinite group model with a single row. Valid inequalities for this model are expressed by valid functions and it has been recently shown that any valid function is dominated by some nonnegative valid…

In this note we associate a sequence of non-negative integers to any convergent series of positive real numbers and study this sequence for the series $\sum_{n \geq 1} n^{-k}$ where $k$ is an integer $\geq 2$.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.