The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection with the τ-function representation is discussed.     

Targeting glycosylation pathways and the cell cycle: sugar-dependent activity of butyrate-carbohydrate cancer prodrugs

Short-chain fatty acid (SCFA)-carbohydrate hybrid molecules that target both histone deacetylation and glycosylation pathways to achieve sugar-dependent activity against cancer cells are described in this article. Specifically, n-butyrate esters of N-acetyl-D-mannosamine (But4ManNAc, 1) induced apoptosis, whereas corresponding N-acetyl-D-glucosamine (But4GlcNAc, 2), D-mannose (But5Man, 3), or glycerol (tributryin, 4) derivatives only provided transient cell cycle arrest. Western blots, reporter gene assays, and cell cycle analysis established that n-butyrate, when delivered to cells via any carbohydrate scaffold, functioned as a histone deacetylase inhibitor (HDACi), upregulated p21WAF1/Cip1 expression, and inhibited proliferation. However, only 1, a compound that primed sialic acid biosynthesis and modulated the expression of a different set of genes compared to 3, ultimately killed the cells. These results demonstrate that the biological activity of butyrate can be tuned by sugars to improve its anticancer properties.     

Size distribution in quantum-dot heterostructures

The size distribution functions for nanoclusters in quantum-dot heterostructures are calculated within the LSW theory. The most common numerical characteristics are calculated for these distributions. The corresponding size distribution functions are selected by means of comparison of the calculated dispersion and mean square deviation with the experimental values obtained for real quantum-dot heterostructures. The regularities of variations of certain numerical characteristics as a function of growth mechanism are shown for different distributions, from the well-known modified Wagner and Lifshitz-Slezov distributions to the distributions proposed in this work. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 59–66, April, 2006.     

Kinetics of the Late Stage of Disintegration of Supersaturated Solid Solutions with Pronounced Crystalline Structure

The kinetics of disintegration of a supersaturated solid solution is studied in the context of the Lifshits–Slezov–Wagner (LSW) theory for a quasi-coherent interface between the new phase precipitates and the matrix. It is shown that the particle size distribution lies within a very narrow range of relative particle size (r _m/r _c = 6/5) and that the critical or average particle size varies with time as t^1/6 (r _c t ^1/6).     

Determination and estimation of risk aversion coefficients

Computational Management Science - In the paper we consider two types of utility functions often used in portfolio allocation problems, i.e. the exponential utility and the quadratic utility. We...