Characterization of the smectic-A-hexatic-B transition in 65OBC by adiabatic scanning calorimetry

We investigated the smectic-A-hexatic-B (SmA-HexB) transition in the liquid-crystal n-hexyl-4-n-pentyloxybiphenyl-4-carboxilate (65OBC) with adiabatic scanning calorimetry. We were able to prove in a direct way that this transition is indeed very weakly first order, as was already suggested in the literature. The latent heat at the transition was determined to be H_L = 0.04±0.02 J/g. Our experiments confirm the high value for the heat capacity critical exponent earlier reported, yielding = 0.64±0.05.     

Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/ poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D_T) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D_T is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D_T^0, = - 1.69×10^-7cm²(sK)^-1. The Soret coefficient S_T of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).     

Evaluation of the protein solvent-accessible surface using reduced representations in terms of critical points of the electron density

The aim of our study is the development of a method for calculating the interface of dimerization of protein-protein complexes based on simplified medium-resolution structures. In particular, we wished to evaluate if the existing concepts for the computation of the Solvent-Accessible Surface Area (SASA) of macromolecules could be applied to medium-resolution models. Therefore, we selected a set of 140 protein chains and computed their reduced representations by topological analysis of their electron density maps at 2.85 A crystallographic resolution. This procedure leads to a limited number of critical points (CPs) that can be identified and associated to backbone and side-chain parts. To evaluate the SASA and interfaces of dimerization of the reduced representations, we chose and modified two existing programs that calculate the SASA of atomic representations, and tested (1) several radii tables of amino acids, (2) the influence of the backbone and side-chain points, and (3) the radius of the solvent molecule, which rolls over the surface. The results are shown in terms of relative error compared to the values calculated on the corresponding atomic representations of the proteins.     

On comparison of jump point detection for an exchange rate series

The main purpose of this paper is to investigate the detection of jump points of a discontinuous function in the presence of a noise by the wavelet approach. A computing algorithm of our method is proposed and then applied to the daily exchange rate of US Dollar against Deutsche Mark. All the points detected by our method reflect very strong economic and political impacts. Other statistical methods to detect jump points have also been applied to the same exchange rate data. Our proposed method has produced more convincing empirical results than others.     

A New Notion of Conjugacy for Isoperimetric Problems

For problems in the calculus of variations with isoperimetric side constraints, we provide in this paper a set of points whose emptiness, independently of nonsingularity assumptions, is equivalent to the nonnegativity of the second variation along admissible variations. The main objective of introducing a characterization of this condition should be, of course, to obtain a simpler way of verifying it. There are two other sets of points available in the literature, introduced by Loewen and Zheng (1994) and Zeidan (1996), for which this necessary condition implies their emptiness. However, we show that verifying membership of these sets may be more difficult than checking directly if that condition holds. Contrary to this behavior, we prove that the desired objective of characterizing that condition is achieved by means of the set introduced in this paper.     

A note on nice operators

In this note, we characterize nice operators in a class of Banach spaces, which includes spaces and L₁(μ), as those operators that preserve extreme points.     

On strong tractability of weighted multivariate integration

We prove that for every dimension and every number of points, there exists a point-set whose -weighted unanchored discrepancy is bounded from above by independently of provided that the sequence has for some (even arbitrarily large) . Here is a positive number that could be chosen arbitrarily close to zero and depends on but not on or . This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals over unbounded domains such as . It also supplements the results that provide an upper bound of the form when .

     

Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies