Analysis of Collectivism and Egoism Phenomena within the Context of Social Welfare

Comparative benefits provided by the basic social strategies including collectivism and egoism are investigated within the framework of democratic decision-making. In particular, we study the mechanism of growing "snowball" of cooperation.Comment: 12 pages, 5 figures. Translated from Russian. Original Russian Text published in Problemy Upravleniya, 2008, No. 4, pp. 30-3

S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

A topological interpretation of the walk distances

The walk distances in graphs have no direct interpretation in terms of walk weights, since they are introduced via the \emph{logarithms} of walk weights. Only in the limiting cases where the logarithms vanish such representations follow straightforwardly. The interpretation proposed in this paper rests on the identity \ln\det B=\tr\ln B applied to the cofactors of the matrix $I-tA,$ where $A$ is the weighted adjacency matrix of a weighted multigraph and $t$ is a sufficiently small positive parameter. In addition, this interpretation is based on the power series expansion of the logarithm of a matrix. Kasteleyn (1967) was probably the first to apply the foregoing approach to expanding the determinant of $I-A$. We show that using a certain linear transformation the same approach can be extended to the cofactors of $I-tA,$ which provides a topological interpretation of the walk distances.Comment: 13 pages, 1 figure. Version #

FUNCTIONAL FOOD COMPOSITIONS BASED ON WHEY PROTEIN ISOLATE, FISH OIL AND SOY PHOSPHOLIPIDS

The aim of the research was to study the impact of whey protein isolate on the solubility and oxidative stability of the lipid composition based on soy phosphatidylcholine and fish oil. The relationship between the molecular parameters (density; ζ-potential) of the formed complex particles and their functional properties was found using laser light scattering (static, dynamic, electrophoretic) and spectrophotometry. The studied compositions could be used as the basis for the development of multifunctional food additives with an objective of the enrichment of foods and beverages with omega-3 polyunsaturated fatty acids (PUFAs). The main advantages of such composition are a high level of protection of the lipids against oxidation and degradation, a high solubility in an aqueous medium and the clean label.The aim of the research was to study the impact of whey protein isolate on the solubility and oxidative stability of the lipid composition based on soy phosphatidylcholine and fish oil. The relationship between the molecular parameters (density; ζ-potential) of the formed complex particles and their functional properties was found using laser light scattering (static, dynamic, electrophoretic) and spectrophotometry. The studied compositions could be used as the basis for the development of multifunctional food additives with an objective of the enrichment of foods and beverages with omega-3 polyunsaturated fatty acids (PUFAs). The main advantages of such composition are a high level of protection of the lipids against oxidation and degradation, a high solubility in an aqueous medium and the clean label

Covariant Quantum Dynamical Semigroups: Unbounded generators

A survey of the probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. The relations with the classical Levy-Khinchin formula are elucidated. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equations. Important topics for future investigation are outlined.Comment: 14 pages,Latex, no figures, submitted to the Semigroup Volume, Group 21, Goslar 199