The Pontryagin Maximum Principle 50 years later

Proceedings of the Steklov Institute of Mathematics -     

Coagulation in lipid- and protein-containing systems

The behavior of real disperse systems with organic impurities was examined under conditions of destabilization by inorganic coagulants. A number of physicochemical methods of analysis and a simulation method were used to identify the character and type of the complexes formed and to calculate their stability constants.     

Pseudo-Finsleroid standard model analysis of electroweak interactions

A standard model Lagrangian is constructed making the pseudo-Finsleroid generalization of the Yang-Mills field equation by the conformal method. The Higgs field potential is suggested that ensures generation of particle masses caused by the spontaneous symmetry breaking. After transition to the conformal coordinates, the expressions obtained assume the standard form that in many cases allows the results of pseudo-Euclidean theory to be used in calculations of the Feynman diagrams. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 44–51, April, 2006.     

1,1,3-Trimethyl-3-phenylindan as a Luminescent Additive to a Plastic Scintillator Based on Poly(methyl Methacrylate)

The luminescence and scintillation properties of poly(methyl methacrylate) containing 1,1,3-trimethyl-3-phenylindan were studied.     

Solving of second order nonlinear PDE problems by using artificial controls with controlled error

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region inR ². We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error inL ₁ is controlled.     

On p-Extensions of Fields of Characteristic p

It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.     

A Kinematic Formula for Affine Diameters and Affine Medians of a Convex Set

For a planar convex set K with C ²-smooth boundary, the area of the set of the points lying on a given number of affine diameters of K is estimated. As a corollary, it is proved that the area of K is at most pM² /4\pi M^2 /4 , where M is the largest length of a chord of K halving the area of K. Bibliography: 2 titles.