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

Nanoparticles as agents for targeted delivery in the treatment of vascular pathologies

The strategy of treatment of cardiovascular diseases with preparations based on nanoparticles. For the visualization of atherosclerotic plaques, nanoparticles conjugated with indium (111In) based on antibodies bound to LOX-1 receptors of low density were used in mic

Supersymmetry and LHC

The motivation for introduction of supersymmetry in high energy physics as well as a possibility for supersymmetry discovery at LHC (Large Hadronic Collider) are discussed. The main notions of the Minimal Supersymmetric Standard Model (MSSM) are introduced. Different regions of parameter space are analyzed and their phenomenological properties are compared. Discovery potential of LHC for the planned luminosity is shown for different channels. The properties of SUSY Higgs bosons are studied and perspectives of their observation at LHC are briefly outlined.Comment: Lectures given at the 9th Moscow International School of Physics (XXXIV ITEP Winter School of Physics

Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States

Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner \cite{Wig} there were no analytical studies on the subject. In this letter we present analytical and numerical results for local spectral density of states (LDOS) for more general case of matrices with a sparsity inside the band. The crossover from the semicircle form of LDOS to that given by the Breit-Wigner formula is studied in detail.Comment: Misprints are corrected and stylistic changes are made. To be published in PR

Bosonization method for second super quantization

A bosonic-fermionic correspondence allows an analytic definition of functional super derivative, in particular, and a bosonic functional calculus, in general, on Bargmann- Gelfand triples for the second super quantization. A Feynman integral for the super transformation matrix elements in terms of bosonic anti-normal Berezin symbols is rigorously constructed.Comment: In memoriam of F. A. Berezin, accepted in Journal of Nonlinear Mathematical Physics, 15 page

Systemic Diagnostics of the Arctic Industry Development Strategy

The article analyzes organizational and economic problems of the industry in the Arctic and discloses methods and tools for researching these problems. An attempt to use the method of system diagnostics is made, which has established itself as a basis for determining the development strategy of industry in the Arctic zone of the Russian Federation (AZRF). This method allows to explore the mechanism of natural resources development in the Arctic, such as hydrocarbons and marine biological resources; as well as the organization of logistics and transport corridors for trade of goods produced in the North and in the central regions of Russia. The role, significance and content of the strategy as an essential element of the system for managing natural wealth development in the Arctic in the context of its growing importance in development of global transport corridor are revealed. Importance of a systematic approach to the development of industry in the Arctic is substantiated, it will ensure development of all investors interested in this region; will allow the state, large corporations, small and medium-sized businesses to work together for the long term. The proposed method for system diagnostics of strategizing the development of industrial potential in the AZRF can be used in the implementation of «Development Strategy for the Arctic Region» as part of roadmap realization for the Arctic region