Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

An expeditious protocol for synthesis of Baylis–Hillman derived piperazine derivatives and evaluation of their AChE inhibition

Research on Chemical Intermediates - The highly efficient and eco-economical “on water” method has been developed for the rapid construction of highly functionalized...     

Non-equilibrium pattern selection in particle sedimentation

In this paper, we explain some well known experimental observations in fluid solid interaction from a thermodynamic perspective. In particular we use the extremum of the rate of entropy production to establish the stability of specific patterns observed in single and multiparticle sedimentation in an infinite fluid and the sedimentation of spheres in the presence of walls. While these phenomena have been explained numerically, there is no known rigorous theoretical argument to establish the stability of the observed configurations. We provide a very convincing theoretical basis using entropy based arguments that are considered by several scientists as the underlying theme of nature, life and evolution. In the absence of many rigorous examples for the entropy production principle, our paper advances this argument and lends it much credibility. In addition to looking at the rate of entropy production, we also put forth a very plausible heuristic argument based on the thermal gradients in the systems being studied, which could be the underlying causal principle for many known patterns in nature.     

Lyapunov density for coupled systems

We prove a necessary and sufficient condition for the existence of Lyapunov density for a system of coupled autonomous ordinary differential equations. In particular, we characterize the kinds of couplings that preserve almost everywhere uniform stability of the origin provided the isolated systems have an almost everywhere uniformly stable equilibrium point at the origin.     

Effect of molecular structure on mesomorphism XX. Unsymmetrical dimeric mesogens

Abstract

A series of unsymmetrical dimeric mesogens was prepared, members of which were composed of a 4′-pentyloxybiphenyl-4-carboxyl core and a 4′-substituted-benzylidene-4-oxyaniline core joined via an alklyene spacer. The structural variants were cyano, nitro and trifluoromethyl. Comparison of mesophase behaviour of the unsymmetrical dimers with that of corresponding monomeric ‘halves’ and also with that of corresponding symmetrical dimers indicated a tendency for the unsymmetrical dimers to form smectic phases although not as highly ordered as those of some of the monomers corresponding to a relevant core group.     

Studies on the Intermolecular Cycloaddition of Diphenylacetonitrile Oxide with Substituted Olefins

We present our findings on the regio- and stereo chemical outcome of the cycloadditions of sterically crowded diphenylacetonitrile oxide towards mono and disubstituted electron deficient and electron rich olefins. The resultant Δ²-isoxazolines are further transformed to their corresponding β-hydroxy carbonyl compounds employing Curran's protocol.     

Synthesis of Isoxazole Conjugates of 1,4-Benzodioxane Moiety via Intermolecular 1,3-Dipolar Cycloaddition

1,3-Dipolar cycloaddition was utilized as a tool to conjugate the 1,4-benzodioxane moiety with several biologically active compounds such as steroid, sugar, and other aromatic scaffolds via isoxazole or triazole bridge. The propynyl ether of 2-hydroxymethyl-1,4-benzodioxane underwent 1,3-dipolar cycloadditions smoothly with different in situ generated nitrile oxides in good yields. The triazole conjugate of 1,4-benzodioxane was synthesized via click chemistry.     

Fate of the superconducting ground state on the Moyal plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is smaller compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt.     

ChemInform Abstract: The Ground-State Potential Energy Surface of Diazene

has been studied by using a complete active space MCSCF wave function generated by distributing eight electrons among eight orbitals.