Hermite expansions on R(N) for radial functions

It is proved that the Riesz means S(R)(delta)f, delta > 0, for the Hermite expansions on R(n), n greater-than-or-equal-to 2, satisfy the uniform estimates \\S(R)(delta)f\\p less-than-or-equal-to C \\f\\p for all radial functions if and only if p lies in the interval 2n/(n + 1 + 2delta) < p < 2n/(n - 1 - 2delta).

Analogues of the Wiener-Tauberian and Schwartz theorems for radial functions on symmetric spaces

We prove a Wiener Tauberian theorem for the L-1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

The Reception of the Maccabean Martyrs : Their Historiographical and Paradigmatic Functions in Antique and Late-antique Jewish and Christian Sources

The study attempts a reception-historical analysis of the Maccabean martyrs. The concept of reception has fundamentally to do with the re-use and interpretation of a text within new texts. In a religious tradition, certain elements become re-circulated and thus their reception may reflect the development of that particular tradition. The Maccabean martyrs first appear in 2 Maccabees. In my study, it is the Maccabean martyr figures who count as the received text; the focus is shifted from the interrelations between texts onto how the figures have been exploited in early Christian and Rabbinic sources. I have divided my sources into two categories and my analysis is in two parts. First, I analyze the reception of the Maccabean martyrs within Jewish and Christian historiographical sources, focusing on the role given to them in the depictions of the Maccabean Revolt (Chapter 3). I conclude that, within Jewish historiography, the martyrs are given roles, which vary between ultimate efficacy and marginal position with regard to making a historical difference. In Christian historiographical sources, the martyrs role grows in importance by time: however, it is not before a Christian cult of the Maccabean martyrs has been established, that the Christian historiographies consider them historically effective. After the first part, I move on to analyze the reception in sources, which make use of the Maccabean martyrs as paradigmatic figures (Chapter 4). I have suggested that the martyrs are paradigmatic in the context of martyrdom, persecution and destruction, on one hand, and in a homiletic context, inspiring religious celebration, on the other. I conclude that, as the figures are considered pre-Christian and biblical martyrs, they function well in terms of Christian martyrdom and have contributed to the development of its ideals. Furthermore, the presentation of the martyr figures in Rabbinic sources demonstrates how the notion of Jewish martyrdom arises from experiences of destruction and despair, not so much from heroic confession of faith in the face of persecution. Before the emergence of a Christian cult of the Maccabean martyrs, their identity is derived namely from their biblical position. Later on, in the homiletic context, their Jewish identity is debated and sometimes reconstructed as fundamentally Christian , despite of their Jewish origins. Similar debate about their identity is not found in the Rabbinic versions of their martyrdom and nothing there indicates a mutual debate between early Christians and Jews. A thematic comparison shows that the Rabbinic and Christian cases of reception are non-reliant on each other but also that they link to one another. Especially the scriptural connections, often made to the Maccabean mother, reveal the similarities. The results of the analyses confirm that the early history of Christianity and Rabbinic Judaism share, at least partly, the same religious environment and intertwining traditions, not only during the first century or two but until Late Antiquity and beyond. More likely, the reception of the Maccabean martyrs demonstrates that these religious traditions never ceased to influence one another.

The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid Mechanics

We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and ID NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of polynomial reproduction whilst deriving the shape functions. Nevertheless, given the higher complexity in forming the knotclouds for tetrahedral elements especially when higher demand is placed on the order of continuity of the shape functions across inter-element boundaries, we presently emphasize an exploration of the triangular prism based formulation in the context of several benchmark problems of interest in linear solid mechanics. In the absence of a more rigorous study on the convergence analyses, the numerical exercise, reported herein, helps establish the method as one of remarkable accuracy and robust performance against numerical ill-conditioning (such as locking of different kinds) vis-a-vis the conventional FEM.

Hybrid Polypeptides: Gabapentin as a Stereochemically Constrained gamma-Amino Acid Residue

The design of folded structures in peptides containing the higher homologues of alpha-amino acid residues requires the restriction of the range of local conformational choices In alpha-amino acids stereochemically constrained residues like alpha,alpha-dialkylated residue, aminoisobutyric acid (Aib), and D-Proline ((D)Pro) have proved extremely useful in the design of helices and hairpins in short peptides Extending this approach, backbone substitution and cyclization are anticipated to bc useful in generating conformationally constrained beta- and gamma-residues This brief review provides a survey of work on hybrid peptide sequences concerning the conformationally constrained gamma-amino acid residue 1-aminomethyl cyclohexane acetic acid, gabapentin (Gpn) This achiral, beta,beta-disubstituted, gamma-residue strongly favors gauche-gauche conformations about the C-alpha-C-beta (0(2)) and C-alpha-C-gamma (0(1)) bonds, facilitating local folding The Gpn residue can adopt both C-7 (NH1 -> CO1) and C-9 (CO1 (I)<- NH1+I) hydrogen bonds which are analogous to the C-5 and C7 (gamma-turn) conformations at alpha-residues In conjunction with adjacent residues, Gpn may be used in ay and gamma alpha segments to generate C-12 hydrogen bonded conformations which may be considered as expanded analogs of conventional beta-turns The structural characterization of C-12 helices, C-12/C-10 helices with mixed hydrogen bond directionalities and beta-hairpins incorporating Gpn residues at the turn segment is illustrated (C) 2010 Wiley Periodicals, Inc Biopolymers (Pept Sci) 94 733-741 2010

Thermodynamics and phase equilibria in the system Ga---In using multi-parameter functions

A four and a five-parameter functions are used to analyse and interpret the high and low temperature thermodynamic data and phase equilibria in the Ga-In system.

Functions Of Cytochrome-C In Regulation Of Electron-Transfer And Protein Folding

Cytochrome c, a "mobile electron carrier" of the mitochondrial respiratory chain, also occurs in detectable amounts in the cytosol, and can receive electrons from cytochromes present in endoplasmic reticulum and plasma membranes as well as from superoxide and ascorbate. The pigment was found to dissociate from mitochondrial membranes in liver and kidney when rats were subjected to heat exposure and starvation, respectively. Treating cytochrome c with hydroxylamine gives a partially deaminated product with altered redox properties; decreased stimulation of respiration by deficient mitochondria, increased reduction by superoxide, and complete loss of reducibility by plasma membranes. Mitochondria isolated from brown adipose tissue of cold-exposed rats are found to be sub-saturated with cytochrome c. The ability of cytochrome c to reactivate reduced ribonuclease is now reinterpreted as a molecular chaperone role for the hemoprotein.

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

Intracellular Pathogen Sensor NOD2 Programs Macrophages to Trigger Notch1 Activation

Intracellular pathogen sensor, NOD2, has been implicated in regulation of wide range of anti-inflammatory responses critical during development of a diverse array of inflammatory diseases; however, underlying molecular details are still imprecisely understood. In this study, we demonstrate that NOD2 programs macrophages to trigger Notch1 signaling. Signaling perturbations or genetic approaches suggest signaling integration through cross-talk between Notch1-PI3K during the NOD2-triggered expression of a multitude of immunological parameters including COX-2/PGE(2) and IL-10. NOD2 stimulation enhanced active recruitment of CSL/RBP-Jk on the COX-2 promoter in vivo. Intriguingly, nitric oxide assumes critical importance in NOD2-mediated activation of Notch1 signaling as iNOS(-/-) macrophages exhibited compromised ability to execute NOD2-triggered Notch1 signaling responses. Correlative evidence demonstrates that this mechanism operates in vivo in brain and splenocytes derived from wild type, but not from iNOS(-/-) mice. Importantly, NOD2-driven activation of the Notch1-PI3K signaling axis contributes to its capacity to impart survival of macrophages against TNF-alpha or IFN-gamma-mediated apoptosis and resolution of inflammation. Current investigation identifies Notch1-PI3K as signaling cohorts involved in the NOD2-triggered expression of a battery of genes associated with anti-inflammatory functions. These findings serve as a paradigm to understand the pathogenesis of NOD2-associated inflammatory diseases and clearly pave a way toward development of novel therapeutics.

A study of cubic bismuth oxides of the type bi(26-X)m(X)O(40-delta) (m=ti, mn, fe, co, ni or pb) related to gamma-bi2O3

A structural investigation of cubic oxides (space group I23) of the formula Bi(26-x)M(x)O(40-delta) (M = Ti, Mn, Fe, Co, Ni and Pb) related to the Y-Bi2O3 phase has been carried out by the Rietveld profile analysis of high-resolution X-ray powder diffraction data in order to establish the cation distributions. Compositional dependence of the cation distribution has been examined in the case of Bi26-xCoxO40-delta (1 < x < 16). The study reveals that in Bi(26-X)M(X)O(40-delta) with M = Ti, Mn, Fe, Co or Pb, the M cations tend to occupy tetrahedral (2a) sites when x < 2 while the octahedral (24f) sites are shared by the excess Co or Ni cations with Bi atoms when x > 2. Also experimental magnetic moments of Mn, Co and Ni derivatives have been used to establish the valence state and distribution of these cations.

Ebselen is a potent non-competitive inhibitor of extracellular nucleoside diphosphokinase

Nucleoside di- and triphosphates and adenosine regulate several components of the mucocilairy clearance process (MCC) that protects the lung against infections, via activation of epithelial purinergic receptors. However, assessing the contribution of individual nucleotides to MCC functions remains difficult due to the complexity of the mechanisms of nucleotide release and metabolism. Enzymatic activities involved in the metabolism of extracellular nucleotides include ecto-ATPases and secreted nucleoside diphosphokinase (NDPK) and adenyl kinase, but potent and selective inhibitors of these activities are sparse. In the present study, we discovered that ebselen markedly reduced NDPK activity while having negligible effect on ecto-ATPase and adenyl kinase activities. Addition of radiotracer gamma P-32]ATP to human bronchial epithelial (HBE) cells resulted in rapid and robust accumulation of P-32]-inorganic phosphate ((32)Pi). Inclusion of UDP in the incubation medium resulted in conversion of gamma P-32]ATP to P-32]UTP, while inclusion of AMP resulted in conversion of gamma P-32]ATP to P-32]ADP. Ebselen markedly reduced P-32]UTP formation but displayed negligible effect on (32)Pi or P-32]ADP accumulations. Incubation of HBE cells with unlabeled UTP and ADP resulted in robust ebselen-sensitive formation of ATP (IC50=6.9 +/- 2 mu M). This NDPK activity was largely recovered in HBE cell secretions and supernatants from lung epithelial A549 cells. Kinetic analysis of NDPK activity indicated that ebselen reduced the V-max of the reaction (K-i=7.6 +/- 3 mu M), having negligible effect on KM values. Our study demonstrates that ebselen is a potent noncompetitive inhibitor of extracellular NDPK.

Waveform synthesis using Walsh functions International Journal of Electronics

A software and a microprocessor based hardware for waveform synthesis using Walsh functions are described. The software is based on Walsh function generation using Hadamard matrices and on the truncated Walsh series expansion for the waveform to be synthesized. The hardware employs six microprocessor controlled programmable Walsh function generators (PWFGs) for generating the first six non-vanishing terms of the truncated Walsh series. Improved approximation to a given waveform may be achieved by employing additional PWFGs.

Molecular Dynamics Simulations of Orientational Relaxation in Dipolar Lattice: Lack of Diffusive Decay for Second and Higher Rank Correlation Functions

Extensive molecular dynamics simulations have been carried out to calculate the orientational correlation functions Cl(t), G(t) = [4n/(21 + l)]Ci=-l (Y*lm(sZ(0)) Ylm(Q(t))) (where Y,,(Q) are the spherical harmonics) of point dipoles in a cubic lattice. The decay of Cl(t) is found to be strikingly different from higher l-correlation functions-the latter do not exhibit diffusive dynamics even in the long time. Both the cumulant expansion expression of Lynden-Bell and the conventional memory function equation provide very good description of the Cl(t) in the short time but fail to reproduce the observed slow, long time decay of c1 (t) .

One protein�many functions

The concept of one enzyme-one activity had influenced biochemistry for over half a century. Over 1000 enzymes are now described. Many of them are highly 'specific'. Some of them are crystallized and their three-dimensional structures determined. They range from 12 to 1000 kDa in molecular weight and possess 124 to several hundreds of amino acids. They occur as single polypeptides or multiple-subunit proteins. The active sites are assembled on these by appropriate tertiary folding of the polypeptide chain, or by interaction of the constituent subunits. The substrate is held by the side-chains of a few amino acids at the active site on the surface, occupying a tiny fraction of the total area. What is the bulk of the protein behind the active site doing? Do all proteins have only one function each? Why not a protein have more than one active site on its large surface? Will we discover more than one activity for some proteins? These newer possibilities are emerging and are finding experimental support. Some proteins purified to homogeneity using assay methods for different activities are now recognized to have the same molecular weight and a high degree of homology of amino acid sequence. Obviously they are identical. They represent the phenomenon of one protein-many functions.