Empirical torsional potential functions from protein structure data. Phi- and psi-potentials for non-glycyl amino acid residues.

The torsional potential functions Vt(phi) and Vt(psi) around single bonds N--C alpha and C alpha--C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (phi, psi)-plane with the value of Vtot(phi, psi), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in L-configuration, are Vt(phi) = 1.0 cos (phi + 60 degrees); Vt(psi) = 0.5 cos (psi + 60 degrees) - 1.0 cos (2 psi + 30 degrees) - 0.5 cos (3 psi + 30 degrees). The dipeptide energy maps Vtot(phi, psi) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line psi = 0 degrees. These functions derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.

Estimation of variables at ungaged locations by empirical orthogonal functions

A technique based on empirical orthogonal functions is used to estimate hydrologic time-series variables at ungaged locations. The technique is applied to estimate daily and monthly rainfall, temperature and runoff values. The accuracy of the method is tested by application to locations where data are available. The second-order characteristics of the estimated data are compared with those of the observed data. The results indicate that the method is quick and accurate.

Exploring glueball wave functions on the lattice

We calculate the string tension and 0++ and 2++ glueball masses in pure gauge QCD using an improved lattice action. We compare various smearing methods, and find that the best glueball signal is obtained using smeared Wilson loops of a size of about 0.5 fm. Our results for mass ratios m0++/√σ=3.5(3) and m2++/m0++=1.6(2) are consistent with those computed with the simple plaquette action.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

Empirical torsional potential functions from protiesn structure DATA Phi- and Psi-Potentials for Non-glycyl Amino Acid Residues

The torsional potential functions Vt(φ) and Vt(ψ) around single bonds N–Cα and Cα-C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (φ, ψ)-plane with the value of Vtot(φ, ψ), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in l-configuration, are Vt(φ) = – 1.0 cos (φ + 60°); Vt(ψ) = – 0.5 cos (ψ + 60°) – 1.0 cos (2ψ + 30°) – 0.5 cos (3ψ + 30°). The dipeptide energy maps Vtot(φ, ψ) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line ψ = 0°. These functions, derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.

On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

On some results of A. E. Livingston and coefficient problems for concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of a bounded convex set. We call these functions concave univalent functions. In 1994, Livingston presented a characterization for these functions. In this paper, we observe that there is a minor flaw with this characterization. We obtain certain sharp estimates and the exact set of variability involving Laurent and Taylor coefficients for concave functions. We also present the exact set of variability of the linear combination of certain successive Taylor coefficients of concave functions.

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 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.

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.

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) .