Perturbed unstable variational inequalities with unbounded operators on approximately given sets

The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science.     

Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant

Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ^d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship     

Approximation under an arc length constraint

Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p] _b ^a [1 + (p(x)) ²]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755.     

Steroid polyols from the Far-Eastern starfish Henricia sanguinolenta

A new polyhydroxylated steroid (20R,24S)-5-cholestane-3,6,15,24-tetraol and a known glycoside, laeviuscoloside G, was isolated from the Far-Eastern starfish Henricia sanguinolenta, collected in the sea of Okhotsk, and characterized.     

Deoxypegan-1-one derivatives. synthesis and borohydride reduction of 3-[(E)-arylmethylidene]-3,9-dihydropyrrolo[2,1-b]quinazolin-1(2H)-ones

3-[(E)-Arylmethylidene]-3,9-dihydropyrrolo[2,1-b]quinazolin-1(2H)-ones were prepared by reaction of quinazolyl-2-propionic acid hydrochloride with aromatic aldehydes in acetic anhydride in the presence of Et₃N. 3-[(E)-Arylmethylidene]-1,2,3,9-tetrahydropyrrolo[2,1-b]quinazolin-1-ols were formed by reduction of the 3-arylidene derivatives with sodium borohydride in methanol, readily lost water when heated with acids, and were converted into 3-[(E)-arylmethylidene]-3,9-dihydropyrrolo[2,1-b]quinazolines. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 463–467, September–October, 2006.     

Reaction of 1,2-Diamino-4,5-diphenylimidazole with 1,3-Diarylpropenones and Their Dibromo Derivatives

The reaction of 1,2-diamino-4,5-diphenylimidazole with 1,3-diarylpropenones and 1,3-diaryl-2,3-dibromopropenones gives dihydro- and heteroaromatic derivatives of 6-hydroxyimidazopyrimidines and also imidazopyrimidines which do not contain the 6-hydroxy group. It was found that the structure of the products depended on the conditions for carrying it the reaction.     

Stereochemicai study of 7-aryl-1,7,8,8a-tetrahydro-3(2H)indolizinones by1H and13C NMR

Stereochemistry of 7-aryl-1,7,8,8a-tetrahydro-3(2H)-indolizinones was studied by¹H and¹³C NMR. Complete assignment of¹H NMR signals and analysis of¹H-¹H coupling constants were performed using the iterative PANIC program. Values of³ J _6,7,³ J _7,8endo, and⁴ J _5,7 allow one to unambiguously identify the correspondingexo- andendo-stereoisomers. For stereoisomers with exo-orientation of H(7), complete assignment of¹³C NMR signals was performed on the basis of analysis of the¹³C-¹H coupling constants using two dimensional heteronuclear shift-correlating spectroscopy.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 591–593, March, 1996.     

2-[6-Alkyl-3-hetaryl-4-oxo-9,10-dihydro-4H,8H-chromeno-[8,7-<Emphasis Type="Italic">e</Emphasis>][1,3]oxazin-9-yl]acetic acids

The interaction has been studied of a series of substituted 3-hetaryl-7-hydroxychromones with amino acids and formaldehyde (reactants ratio 1: 1: 2 respectively). In the case of glycine and Het = 3-isoxazolyl the product of aminomethylation at position 8 of the chromone was obtained, and with other Het (including Het = 4-phenyl-1,2,4-triazol-3-yl) 2-[6-alkyl-3-hetaryl-4-oxo-9,10-dihydro-4H,8H-chromeno[8,7-e][1,3]-oxazin-9-yl]acetic acids were formed. With β-alanine and Het = 4-phenyl-1,2,4-triazol-3-yl the corresponding β-substituted propionic acid was synthesized, but proline did not participate in the reaction, leading to bis(6-ethyl-3-hetaryl-7-hydroxychromon-8-yl)methane. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 683–689, May, 2007.     

Analysis of NAD(P) and NAD(P)H cofactors by means of imprinted polymers associated with Au surfaces:: A surface plasmon resonance study

Crosslinked films consisting of the acrylamide-acrylamidophenylboronic acid copolymer that are imprinted with recognition sites for β-nicotinamide adenine dinucleotide (NAD⁺), β-nicotinamide adenine dinucleotide phosphate NADP⁺, and their reduced forms (NAD(P)H), are assembled on Au-coated glass supports. The binding of the oxidized cofactors NAD⁺ or NADP⁺ or the reduced cofactors NADH or NADPH to the respective imprinted sites results in the swelling of the polymer films through the uptake of water. Surface plasmon resonance (SPR) spectroscopy is employed to follow the binding of the different cofactors to the respective imprinted sites. The imprinted recognition sites reveal selectivity towards the association of the imprinted cofactors. The method enables the analysis of the NAD(P)⁺ and NAD(P)H cofactors in the concentration range of 1×10⁻⁶ to 1×10⁻³ M. The cofactor-imprinted films associated with the Au-coated glass supports act as active interfaces for the characterization of biocatalyzed transformations that involve the cofactor-dependent enzymes. This is exemplified with the characterization of the biocatalyzed oxidation of lactate to pyruvate in the presence of NAD⁺ and lactate dehydrogenase using the NADH-imprinted polymer film.     

Quantum chemistry study on B32 and B32H2–32

The structures of B32 and B₃₂H^2–₃₂ with I_h symmetry have been investigated by means of ab initio calculations at STO-3G level. The relationship between molecular orbitals of them has been analyzed and their bonding properties have been discussed. Then the possibility of their existence, as well as the similarity and difference between B₃₂ (B₃₂H^2–₃₂) and C₆₀ (C₆₀H₆₀) have been inferred.