On the variance of the number of occupied boxes

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its variance V_n tends to infinity. In this work, we mainly focus on the opposite case where V_n is bounded, and derive a simple necessary and sufficient condition for convergence of V_n to a finite limit, thus settling a long-standing question raised by Karlin in the seminal paper of 1967. One striking consequence of our result is that the possible limit may only be a positive integer number. Some new conditions for other types of behavior of the variance, like boundedness or convergence to infinity, are also obtained. The proofs are based on the poissonization techniques.Comment: 34 page

Properties of nano encapsulated l-arginine and resveratrol in watersoluble polymers

This article analyzes properties of nano encapsulated L-arginine and resveratrol using a Nanoparticle Tracking Analysis method, and studies their supramolecular properties using a selforganizatio

Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces

We prove a Miyadera-Voigt type perturbation theorem for strong Feller semigroups. Using this result, we prove well-posedness of the semilinear stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW_H(t) on a separable Banach space E, assuming that F is bounded and measurable and that the associated linear equation, i.e. the equation with F = 0, is well-posed and its transition semigroup is strongly Feller and satisfies an appropriate gradient estimate. We also study existence and uniqueness of invariant measures for the associated transition semigroup.Comment: Revision based on the referee's comment

The Appearance of Traditional Journalism Characteristics in the Corporate Media (Using East Siberian Media as an Example)

New phenomena arise in the typology of the media. They appear with the development of trends. Therefore, their nature is unstable and controversial. The media is a very dynamic field, so it is necessary to understand new phenomena and to describe them. This article discusses one of the most striking trends in the development of Russian corporate media. It is a gradual leveling of the typological differences between traditional media and corporate media. The author identifies characteristics of traditional journalism, penetrating into the corporate media headlines, taking East Siberian media as an example. The features of corporate media resulting in socio-political urban and regional newspapers are also considered.В типологии такого динамичного явления, как средства массовой информации, время от времени возникают новые особенности, требующие осмысления и описания. Они появляются в связи с определенными тенденциями развития и, следовательно, имеют неустойчивый и спорный характер. В статье рассматривается одна их ярчайших тенденций в отечественных корпоративных медиа – постепенное нивелирование типологической разницы между традиционными печатными изданиями и корпоративной периодикой. На примере изданий Восточной Сибири автор выделяет особенности традиционной журналистики, проникающие на страницы корпоративных газет, а также черты корпоративных медиа, возникающие в общественно-политических городских и районных изданиях

Differentiability of solutions of stationary Fokker–Planck–Kolmogorov equations with respect to a parameter

We obtain sufficient conditions for the differentiability of solutions to stationary Fokker-Planck-Kolmogorov equations with respect to a parameter. In particular, this gives conditions for the differentiability of stationary distributions of diffusion processes with respect to a parameter