255 resultados para Functional equations


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The in situ cryo-crystallization study of benzyl derivatives reveals that the molecular packing in these compounds is either through methylene (sp(3)) C-H center dot center dot center dot pi or aromatic (sp(2)) C-H center dot center dot center dot pi interactions depending on the level of acidity of the benzyl proton. These studies of low melting compounds bring out the subtle features of such weak interactions and point to the directional preferences depending on the nature (electron withdrawing, polarizability) of the neighbouring functional group.

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We present a general method for the synthesis of functional nanoporous structures by heat treating a loose compact of nanorods. Partial sintering of such a compact leads to spherodization of the nanorods and their fusion at the contact regions leading to an interconnected porous microstructure. The pore diameter can be controlled by changing the original nanorod diameter. We illustrate the generality of the method using TiO2, ZnO and hydroxyapatite as model systems; the method is applicable for any material that can be grown in the form of nanorods. The kinetics of the sintering process can be significantly enhanced in systems in which additional driving forces for mass transport arise from phase transitions proving an ultrafast pathway for producing biphasic porous structures. The possibility of producing hierarchical porous structures using fugitive sintering aids makes this process ideal for a variety of applications including catalysis, photoanodes for solar cells and scaffolds for biomedical applications.

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SHMT (serine hydoxymethyltransferase), a type I pyridoxal 5'-phosphate-dependent enzyme, catalyses the conversion of L-serine and THF (tetrahydrofolate) into glycine and 5,10 -methylene THE SHMT also catalyses several THF-independent side reactions such as cleavage of P-hydroxy amino acids, trans-amination, racemization and decarboxylation. In the present study, the residues Asn(341), Tyr(60) and Phe(351), which are likely to influence THF binding, were mutated to alanine, alanine and glycine respectively, to elucidate the role of these residues in THF-dependent and -independent reactions catalysed by SHMT. The N341A and Y60A bsSHMT (Bacillus stearothermophilus SHMT) mutants were inactive for the THF-dependent activity, while the mutations had no effect on THF-independent activity. However, mutation of Phe(351) to glycine did not have any effect oil either of the activities. The crystal structures of the glycine binary complexes of the mutants showed that N341A bsSHMT forms an external aldimine as in bsSHMT, whereas Y60A and F351G bsSHMTs exist as a Mixture of internal/external aldimine and gem-diamine forms. Crystal structures of all of the three Mutants obtained in the presence of L-allo-threonine were similar to the respective glycine binary complexes. The structure of the ternary complex of F351G bsSHMT with glycine and FTHF (5-formyl THF) showed that the monoglutamate side chain of FTHF is ordered in both the subunits of the asymmetric unit, unlike in the wild-type bsSHMT. The present studies demonstrate that the residues Asn(341) and Tyr(60) are pivotal for the binding of THF/FTHF, whereas Phe(351) is responsible for the asymmetric binding of FTHF in the two subunits of the dimer.

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The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

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Oxidative stress is caused by an imbalance between the production of reactive oxygen species (ROS) and the biological system's ability to detoxify these reactive intermediates. Mammalian cells have elaborate antioxidant defense mechanisms to control the damaging effects of ROS. Glutathione peroxidase (GPx), a selenoenzyme, plays a key role in protecting the organism from oxidative damage by catalyzing the reduction of harmful hydroperoxides with thiol a ``catalytic triad'' with tryptophan and glutamine, which cofactors. The selenocysteine residue at the active site forms activates the selenium moiety for an efficient reduction of peroxides. After the discovery that ebselen, a synthetic organoselenium compound, mimics the catalytic activity of GPx both in vitro and in vivo, several research groups developed a number of small-molecule selenium compounds as functional mimics of GPx, either by modifying the basic structure of ebselen or by incorporating some structural features of the native enzyme. The synthetic mimics reported in the literature can be classified in three major categories: (i) cyclic selenenyl amides having a Se-N bond, (ii) diaryl diselenides, and (iii) aromatic or aliphatic monoselenides. Recent studies show that ebselen exhibits very poor GPx activity when aryl or benzylic thiols such as PhSH or BnSH are used as cosubstrates. Because the catalytic activity of each GPx mimic largely depends on the thiol cosubstrates used, the difference in the thiols causes the discrepancies observed in different studies. In this Account, we demonstrate the effect of amide and amine substituents on the GPx activity of various organoselenium compounds. The existence of strong Se ... O/N interactions in the selenenyl sulfide intermediates significantly reduces the GPx activity. These interactions facilitate an attack of thiol at selenium rather than at sulfur, leading to thiol exchange reactions that hamper the formation of catalytically active selenol. Therefore, any substituent capable of enhancing the nucleophilic attack of thiol at sulfur in the selenenyl sulfide state would enhance the antioxidant potency of organoselenium compounds. Interestingly, replacement of the sec-amide substituent by a tert-amide group leads to a weakening of Se ... 0 interactions in the selenenyl sulfide intermediates. This modification results in 10- to 20-fold enhancements in the catalytic activities. Another strategy involving the replacement of tert-amide moieties by tert-amino substituents further increases the activity by 3- to 4-fold. The most effective modification so far in benzylamine-based GPx mimics appears to be either the replacement of a tert-amino substituent by a sec-amino group or the introduction of an additional 6-methoxy group in the phenyl ring. These strategies can contribute to a remarkable enhancement in the GPx activity. In addition to enhancing catalytic activity, a change in the substituents near the selenium moiety alters the catalytic mechanisms. The mechanistic investigations of functional mimics are useful not only for understanding the complex chemistry at the active site of GPx but also for designing and synthesizing novel antioxidants and anti-inflammatory agents.

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A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

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In this paper we obtain existence theorems for generalized Hammerstein-type equations K(u)Nu + u = 0, where for each u in the dual X* of a real reflexive Banach space X, K(u): X -- X* is a bounded linear map and N: X* - X is any map (possibly nonlinear). The method we adopt is totally different from the methods adopted so far in solving these equations. Our results in the reflexive spacegeneralize corresponding results of Petry and Schillings.

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This paper introduces CSP-like communication mechanisms into Backus’ Functional Programming (FP) systems extended by nondeterministic constructs. Several new functionals are used to describe nondeterminism and communication in programs. The functionals union and restriction are introduced into FP systems to develop a simple algebra of programs with nondeterminism. The behaviour of other functionals proposed in this paper are characterized by the properties of union and restriction. The axiomatic semantics of communication constructs are presented. Examples show that it is possible to reason about a communicating program by first transforming it into a non-communicating program by using the axioms of communication, and then reasoning about the resulting non-communicating version of the program. It is also shown that communicating programs can be developed from non-communicating programs given as specifications by using a transformational approach.

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An endocellulase (1→4)-β-d-glucan 4-glucanohydrolase was isolated from the culture filtrates of Chaetomium thermophile. The enzyme was homogeneous by PAGE and SDS-PAGE. The molecular weight was 36 000 by SDS-PAGE and 38 000 by gel filtration. It was a glycoprotein. From the amino acid composition, it was found to be rich in glycine, threonine, and aspartic and glutamic acids, but contained only low proportions of histidine and sulfur-containing amino acids. It was optimally active at pH 6 and at 60°. The enzyme did not hydrolyze cellobiose and cellotriose, but hydrolyzed cello-tetraose, -pentaose, and -hexaose at comparable rates. It was specific for molecules containing β-(1→4) linkages. It showed high activity towards amorphous cellulose, and the reaction products contained cellobiose to cellopentaose, showing that it effects random cleavage of cellulose.