Exact interior solutions in 2+1-dimensional spacetime

An exact formulation of two-dimensional chiral hydrodynamics with diffeomorphism and conformal anomalies is provided. The constitutive relation involving the stress tensor is computed. It reveals a one parameter class of solutions which is a new result. For a particular value of this parameter, the results found in the gradient expansion scheme are reproduced. Moreover, the constitutive relation is analogous to the corresponding relation for an ideal fluid, appropriately modified to include the chirality property, which has also been derived here.     

Exact Solution of a(2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a(2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function grrproposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum.Grav. 6(1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.     

One-Pot Dual C−C Coupling Reaction via Site Selective Cascade Formation by PdII-Cryptate of an Amino-Ether Heteroditopic Macrobicycle

Selectivity of aryl iodo over ethynyl iodo toward the Suzuki cross coupling reaction is explored by utilizing a palladium complex of amino-ether heteroditopic macrobicycle. Subsequently, unreacted ethynyl iodide undergoes homocoupling reaction in the same catalytic atmosphere, thereby representing a cascade dual C−C coupling reaction. Furthermore, this approach is extended for novel one-pot synthesis of unsymmetrical 1,3-diynes.     

A unique twisted rod-like pattern due to π-π stacking induced host-guest self-assembly

Here, we reported a unique twisted rod-like nano-architecture of as-synthesized 4-fluorocinnmaoyl chloride derived polynorbornene (PNORCNF) on the addition of 1-pyrenemethanol (PM) as a sensing probe. A significant change in the PNORCNF/PM microenvironment's polarity was observed with increasing PM concentration keeping the solvent (THF) unaltered. The change in polarity could be well documented with the morphological changes of the PNORCNF/PM system. We proposed π-π interaction between PM and cinnamoyl moiety of PNORCNF for this type of well-controlled hierarchical self-aggregation.     

Synthesis of Tetraalkenylmethane: Building Blocks for Three-Dimensional Hydrocarbon Networks

In this paper, we show a common strategy to synthesize tetraalkenylmethanes, a cross-linker series for building three-dimensional hydrocarbon networks. To demonstrate the feasibility of this method, we have synthesized tetrapentenylmethane. Attempts to synthesize this cross-linker from pentaerythrityl tetrabromide using substitution reactions resulted in the formation of a spiro compound due to intramolecular cyclization. We also show that the difficulty in reactions at the neopentyl carbon site is due to the neopentyl carbanion stability, not the sterics.     

Wormhole supported by dark energy admitting conformal motion

In this article, we study the possibility of sustaining static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of the detection of wormholes in the outer regions of galactic halos by means of gravitational lensing. Studies of the total gravitational energy for the exotic matter inside a static wormhole configuration are also performed.     

Cosmic No-Hair Theorem for Bianchi Models in Brane-World Scenarios

In this paper we have examined the cosmic no-hair theorem for homogeneous anisotropic Bianchi cosmological models with a scalar field in Randall and Sundrum Brane-world scenarios. It is observed that the form of the potential does not affect the evolution in inflationary era while late time behaviour is controlled by the constant additive factor in the potential for the inflaton field.     

Putralone, a novel 10alpha-hydroxy-25-nor D:A friedo-oleanane triterpenoid from Putranjiva roxburghii

Chemical investigation of the leaves of Putranjiva roxburghii has resulted in the isolation of two new triterpenoids, putralone, a novel 10alpha-hydroxy-25-nor D:A friedo-olean-9(11)-en-3 one and 3beta-acetoxy-cycloart-24-en-23-one, along with a rare hopanoid, adian-5-en-3beta,29-diol. Other known triterpenoids isolated from this plant are 3beta-acetoxy-adian-5-ene, putrol, putrone, putranjivadione, roxburghonic acid, friedelin, friedlan-3alpha-ol, oleanolic acid and erythrodiol. Interestingly, putralone is the first example of a naturally occurring nor friedo-oleanane triterpenoid having a hydroxyl functionality at the C-10 position.     

Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form

Three types of graphs of linear chains, viz. linear chains with unit increment or decrement in weight on one terminal vertex, linear chains with unit increment or decrement in weight on both the terminal vertices and linear chains with unit increment in weight on one terminal vertex and decrement in that on the other terminal vertex, have been considered. The symmetry plane fragmentation and graph squaring techniques have been exploited to express the eigenspectra of such graphs of linear chains in analytical form, and have subsequently been used to express the eigenspectra of graphs of linear chains and cycles with alternant vertex weights. The derived expressions for the eigenspectra have been used to obtain the eigenspectra of linear polyacenes, methylene-substituted linear polyacenes and cylindrical polyacene strips in analytical form.