Minima of Trigonometric Polynomials

Let 0<n₁<n₂<...<n_N be N distinct integers, and leta₁, a₂, ..., a_N be complex numbers. We set [formula] and [formula] There are two well-known problems concerning the case a₁=a₂=...=a_N=1.1991 Mathematics Subject Classification 42A05.     

A Simple Linear-Time Recognition Algorithm for Weakly Quasi-Threshold Graphs

Weakly quasi-threshold graphs form a proper subclass of the well-known class of cographs by restricting the join operation. In this paper we characterize weakly quasi-threshold graphs by a finite set of forbidden subgraphs: the class of weakly quasi-threshold graphs coincides with the class of {P ₄, co-(2P ₃)}-free graphs. Moreover we give the first linear-time algorithm to decide whether a given graph belongs to the class of weakly quasi-threshold graphs, improving the previously known running time. Based on the simplicity of our recognition algorithm, we can provide certificates of membership (a structure that characterizes weakly quasi-threshold graphs) or non-membership (forbidden induced subgraphs) in additional ${{\mathcal O}(n)}$ time. Furthermore we give a linear-time algorithm for finding the largest induced weakly quasi-threshold subgraph in a cograph.     

String Thermalization in Static Spacetimes

We study the evolution, the transverse spreadingand the subsequent thermalization of string states inthe Weyl static axisymmetric spacetime. This possessesa singular event horizon on the symmetry axis and a naked singularity along the otherdirections. The branching diffusion process of stringbits approaching the singular black-hole horizonprovides the notion of the temperature that iscalculated for this process. We find that the solution of theFokker-Planck equation in the phase space of thetransverse variables of the string, can be factored asa product of two thermal distributions, provided that the classical conjugate variables satisfy theuncertainty principle. We comment on the possiblephysical significance of this result.     

The electromagnetic mass difference of pions from asymptotic QCD

We investigate the Dirac-Kähler operator on a triangular lattice in two dimensions and show that the number of degrees of freedom which survive in the continuum limit is the same as in the case of a square lattice.     

Controlled release from a nanocarrier entrapped within a microcarrier

This study illustrates the entrapment of the dye molecule fluorescein sodium salt (FSS) by hydrogel nanoparticles, which are in turn confined inside a water-in-oil-in-water double-emulsion globule, and its subsequent release by the action of the competing agent hydrochloric acid (HCl). Thus, a "double carrier" concept is being introduced in which a nanoscale delivery vehicle is being transported by a microscale delivery vehicle in order to simultaneously take advantage of both systems. This may facilitate storage and handling while protecting the active substance and improving its action upon application.     

Effects of Osmotic Pressure on Water Transport in W(1)/O/W(2) Emulsions

In a W(1)/O/W(2) double-emulsion globule, when the W(1) phase was made of pure water while salt (NaCl) was present only in the W(2) phase, water was transported from W(1) to W(2) at a constant transport rate, -dR/dt. In the case of hydrated-surfactant transport, rates rose linearly with increasing salt concentration in W(2) through acceleration of the dehydration process of the hydrated surfactants at the O/W(2) interface. When the water was transported through spontaneous emulsification and reverse micellization, the water transport rates were independent of the osmotic pressure over a significant range of salt concentration in W(2). When salt was present in both the W(1) and W(2) phases-though at a higher concentration in W(2)-water transport stopped when the salt concentrations in W(1) and W(2) equalized, indicating that only water may transport through the oil phase while salt stays trapped in the W compartments. In visual-contact experiments, where transport was controlled by the hydrated-surfactant mechanism, the water transport rates were initially constant to then decreased asymptotically to zero. This showed that, as salt concentration in W(1) increased with time, the controlling process shifted from surfactant dehydration at the O/W(2) interface to hydration at the W(1)/O interface. For the spontaneous emulsification and reverse-micellar mechanisms at visual noncontact, water transport rates remained constant during a given experiment and decreased with increasing initial salt concentration in W(1), indicating that the formation process of emulsified water droplets and reverse micelles at the W(1)/O interface was the rate-controlling step. Copyright 2001 Academic Press.     

Electronic and vibrational linear and nonlinear polarizabilities of Li@C60 and [Li@C60]+

Electronic and vibrational nuclear relaxation (NR) contributions to the dipole (hyper)polarizabilities of the endohedral fullerene Li@C(60) and its monovalent cation [Li@C(60)](+) are calculated at the (U)B3LYP level. Many results are new, while others differ significantly from those reported previously using more approximate methods. The properties are compared with those of the corresponding hypothetical noninteracting systems with a valence electron transferred from Li to the cage. Whereas the NR contribution to the static linear polarizabilities is small in comparison with the corresponding electronic property, the opposite is true for the static hyperpolarizabilities. A relatively small, but non-negligible, NR contribution to the dc-Pockels effect is obtained in the infinite frequency approximation.     

Significant nonlinear‐optical switching capacity in atomic clusters built from silicon and lithium: A combined ab initio and density functional study

Starting from a hypothetical but fundamental charge/discharge sequence, the topic of nonlinear optical switching in atomic clusters built from silicon and alkali metals is opened up. The outcomes presented in this work, obtained with ab initio methods of exceptional predictive capabilities, offer strong evidences that sizable hyperpolarizability contrasts between neutral and charged alkali metal doped cluster forms might be simultaneously accomplished. The observed switching procedure involves redox polyatomic clusters formed by Si atoms. These centers function as electron acceptors at the ground state and as electron donors at the excited states facilitating low energy charge transfer transitions upon electronic excitation. © 2014 Wiley Periodicals, Inc.     

Sorption thermodynamics of CO2, CH4, and their mixtures in the ITQ-1 zeolite as revealed by molecular simulations

The thermodynamic properties and siting of carbon dioxide and methane sorbed in the siliceous form of zeolite MCM-22, ITQ-1, were studied by means of grand canonical Monte Carlo simulation. ITQ-1 comprises two independent pore systems of different geometry. It was found to be CO(2)-selective toward CO(2)/CH(4) gas mixtures, its equilibrium selectivity being distinctly higher in its sinusoidal channel pore system than in the large cavity system over a wide range of pressures starting from the Henry law regime, at the three temperatures considered. A maximum in selectivity is observed at low temperature, high pressure, and methane-rich gas-phase composition.