On integral inequalities of the Sobolev type

Summary In this paper some new integral inequalities of the Sobolev type involving many functions of many variables are established. These in turn can be used to serve as generators of other integral inequalities.     

A conflict between sequential rationality and consistency principles

It is shown that no solution concept that selects sequentially rational (perfect, proper, persistent, or members of some stable set of) equilibria satisfies the following consistency property. Suppose that in every solution of the game G, player i's action is a, and denote by G ^a the game in which player i is restricted to choose a. Then some player j≠i has an action c that is used with positive probability in both some solution of G and some solution of G ^a. This result illustrates a conflict between a mild consistency condition and sequential rationality. Received: January 2001/Final version: April 2002     

Fuzzy measures for profit maximization with fuzzy parameters

Profit maximization is an important issue to the firms that pursue the largest economic profit possible. This paper extends the situation from the deterministic to uncertain, where the coefficients are represented by fuzzy numbers. Intuitively, when the problem has fuzzy parameters, the derived profit value should be a fuzzy number as well. The extension principle is utilized to develop a pair of two-level mathematical programs to calculate the upper and lower bounds of the profit value at α-cuts. Following the duality theorem and a variable separation technique, the two-level mathematical programs are transformed into a class of one-level signomial geometric programs to solve. An example is given to illustrate the idea proposed in this paper.     

Fuzzy closure systems on L—ordered sets

In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Generalizations of some results concerning microperiodic mappings

It is well known that a microperiodic function that maps the set of reals into itself and is continuous at a point (Lebesgue measurable, respectively) must be constant (constant almost everywhere, resp.). We generalize those results in several directions. As a consequence we obtain conclusions concerning some systems of functional inequalities.     

The use of a radiation inactivation method for characterization of the structure and catalytic properties of enzymes

The use of a radiation inactivation method for studies of the properties of enzymes of different classes is discussed. The possibilities of characterization of enzymes on the basis of the radiation-chemical parameters concerned are described.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No, 12, pp. 2828–2836, December, 1996.     

An Extended Beam Theory for Smart Materials Applications Part II: Static Formation Problems

In this paper we further develop the theory of the extended Timoshenko beam model, as first introduced in Part I [5] of this work, with particular emphasis on applications of the model in formation theory [11], [12]. We begin with formal development of the equilibrium equations of static formation theory in the context of the extended Timoshenko model, giving a rigorous discussion of existence, uniqueness, and regularity of weak solutions with appropriate assumptions on the coefficients. We continue to obtain the fundamental duality relationship in the context of weak solutions and indicate its usefulness in investigations of approximate formability. Optimal formation problems and corresponding necessary conditions for optimality are discussed. We conclude with a discussion of a particular problem of joint optimization of controls and actuator densities in the context of a prismatic extended Timoshenko beam and we present the results of some computational studies. Accepted 14 November 1996     

Polynomial decay and control of a 1−d hyperbolic-parabolic coupled system

In this paper we consider a linearized model for fluid-structure interaction in one space dimension. The domain where the system evolves consists in two parts in which the wave and heat equations evolve, respectively, with transmission conditions at the interface. First of all we develop a careful spectral asymptotic analysis on high frequencies for the underlying semigroup. It is shown that the semigroup governed by the system can be split into a parabolic and a hyperbolic projection. The dissipative mechanism of the system in the domain where the heat equation holds produces a slow decay of the hyperbolic component of solutions. According to this analysis we obtain sharp polynomial decay rates for the whole energy of smooth solutions. Next, we discuss the problem of null-controllability of the system when the control acts on the boundary of the domain where the heat equation holds. The key observability inequality of the dual system with observation on the heat component is derived though a new Ingham-type inequality, which in turn, thanks to our spectral analysis, is a consequence of a known observability inequality of the same system but with observation on the wave component.     

Coupling constants in the direct configuration interaction method

A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.