New Solutions for (1+1)-Dimensional and (2+1)-Dimensional Kaup–Kupershmidt Equations

In this paper, using the exp-function method we obtain some new exact solutions for (1+1)-dimensional and (2+1)-dimensional Kaup–Kupershmidt (KK) equations. We show figures of some of the new solutions obtained here. We conclude that the exp-function method presents a wider applicability for handling nonlinear partial differential equations.     

Optical solitons with time-dependent dispersion,nonlinearity and attenuation in a power-law media

This paper studies optical solitons in a power-law media with time-dependent coefficients of dispersion, nonlinearity and attenuation. The 1-soliton solution is obtained for the nonlinear Schrödinger’s equation with power-law nonlinearity. In addition, a relation between these coefficients is obtained for the solitons to exist. Finally, the velocity of the soliton is also obtained in terms of these coefficients.     

Relaxation of the rigid backbone of an oligoamide-foldamer-based α-helix mimetic: identification of potent Bcl-xL inhibitors

By conducting a structure-activity relationship study of the backbone of a series of oligoamide-foldamer-based α-helix mimetics of the Bak BH3 helix, we have identified especially potent inhibitors of Bcl-x(L). The most potent compound has a K(i) value of 94 nM in vitro, and single-digit micromolar IC(50) values against the proliferation of several Bcl-x(L)-overexpressing cancer cell lines.     

TRANSITION METAL,NON-METAL CARBONYL CLUSTRS AS SUPPORTS FOR UNUSUAL ACETYLIDE REACTIVITY

Group 16 elements serve as useful bridging and stabilising single atom ligands in mixed-metal carbonyl complexes and impart unusual reactivity on coordinated acetylenic moieties. Reactions of [Fe ₃ (CO) ₉ (μ ₃ -E) ₂ ] (E = S, or Se) with mononuclear acetylide complexes, [CpM(CO)_3-x(CCR)] (M = Mo or W, x = 0, R = Ph; M = Fe, x = 1, R = Ph or ferrocenyl) under facile conditions yield complexes featuring acetylide coupling, acetylide-flip and formation of oxo and acetylide-bridged complexes. In presence of free acetylenes, unusual ligand systems arising from C─S bond formation are observed and under certain conditions, formation of quinones by coupling of acetylenes with carbon monoxide is facilitated.     

Thermal hysteresis of some important physical properties of nanoparticles

Gold nanoparticles show thermal hysteresis with properties such as surface plasmon absorption, conductivity, and zeta potential. The direction of the incremental change in plasmon peak position and its extinction depend on the nature of surface conjugation. The thermal profile of a surface plasmon resonance spectrum for nanoparticles may serve as a signature for the associated small molecule or macromolecule on which it is seeded. The thermal responses of zeta potential and conductivity profile are found to be independent of the surface conjugation with the later being subjected to a phase transition phenomenon as revealed by a temperature criticality.     

Singular Value Decomposition Solution of the Schrödinger Equation in the Presence of Exchange Terms

A new numerical method of solving integro-differential equations appearing in the theory of atomic and nuclear scattering systems has been devised. It is termed Singular Value Decomposition Method (SVD). It consists in expanding the exchange kernel into a number of separable terms by means of the Singular Value Decomposition and then iterating over the remainder. In this paper, we extend our SVD method to the scattering of low energy electron-helium which has been the subject of interest, both theoretically and experimentally. We compare our results with the Moments Method which is widely used. The Moments Method consists of making an expansion of the solution into an especially favorable basis that takes care of the non-exchange part of the Hamiltonian.     

Tree-level breaking of SU(2)×U(1) in general SUGRA theories

It is shown that SU(2)×U(1) can be broken at the tree level, without the occurrence of global potential minima that break U(1)_e.m., in supergravity models that are more general than those proposed by Nilles, Srednicki and Wyler. The study comprises an analysis of models with a general soft supersymmetry-breaking structure as well as those of the Hall-Lykken-Weinberg type.