Construction of the fundamental solution of disturbed parabolic equation

In present paper the parabolic equation solution is built. The construction is reduced to iterative procedure. And convergence of the latter is proven.     

Shape sensitivity of a plane crack front

The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis of β-phenyl-δ,ε-unsaturated amino acids and stereoselective introduction of side chain groups into [4,3,0]-bicyclic β-turn dipeptides

(2S,3S)- and (2R,3R)-2-amino-3-phenyl-5-hexenoic acids have been synthesized in large scale by using Ni(II)-complexes as a template. The amino acids were used in the synthesis of [4,3,0]-bicyclic β-turn mimetics by a convergent methodology. The unique advantage of this strategy is the convenience of introducing side chain groups with predetermined chiralities on both the five- and six-membered heterocyclic rings.     

On covering bridged plane triangulations with balls

We show that every plane graph of diameter 2r in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius r. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 65–80, 2003     

A calorimetric study of the different thermal behaviour of DNA in the isotropic and liquid-crystalline states

A difference between the thermal behaviour of the isotropic and liquid-crystalline state of sonicated DNA in aqueous salt solution containing poly(ethyleneglycol)(PEG) has been demonstrated. On cooling, a different degree of renaturation of thermally denaturated DNA is observed between samples which form the isotropic state and more concentrated samples which on cooling form the cholesteric state.     

Galactose oxidase immobilized on silica in an analytical determination of galactose-containing carbohydrates.

Galactose oxidase from Fusarium graminearum IMV-1060 adsorbed on, and covalently bound to, silica carriers has been used for analytical determinations of D-galactose and galactose-containing sugars. Using a flowing oxygen electrode of the Clark-type, sensor system for enzymatic analysis of water solutions of galactose-containing carbohydrates was made. Measurements were taken both in the pulse and continuous modes of a substrate flowing through a column with an immobilized biocatalyst. The linear measurement ranges for galactose-containing carbohydrates concentrations were determined.     

Squeezed states and uncertainty relations since 1991

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.     

Linear matrix inequality representation of sets

This article concerns the question, Which subsets of ?^m can be represented with linear matrix inequalities (LMIs)? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also, before having much hope of representing engineering problems as LMIs by automatic methods, one needs a good idea of which problems can and cannot be represented by LMIs. Little is currently known about such problems. In this article we give a necessary condition that we call “rigid convexity,” which must hold for a set ?? ? ?^m in order for ?? to have an LMI representation. Rigid convexity is proved to be necessary and sufficient when m = 2. This settles a question formally stated by Pablo Parrilo and Berndt Sturmfels in [15]. As shown by Lewis, Parillo, and Ramana [11], our main result also establishes (in the case of three variables) a 1958 conjecture by Peter Lax on hyperbolic polynomials. © 2006 Wiley Periodicals, Inc.