Static Conformally Flat Spherically Symmetric Space-Time in Einstein-Cartan Theory of Gravitation

The exact solution of Einstein-Cartan field equations for static, conformally flat spherically symmetric space-time is derived and it is proved to be Petrov-type D.     

A Recyclable and Highly Effective ZnO-beta Zeolite as a Catalyst for One-pot Three-Component Synthesis of Tetrahydrobenzo[b]pyrans

4H‐Benzo[b]pyrans was synthesized under reflux condition in ethanol via condensation of benzaldehyde, malononitrile and dimedone with ZnO‐beta zeolite as an inexpensive and effective catalyst. The key features of the reported protocols are good to excellent yields, short reaction time and recovery and reusability of catalytic material.     

Structure Equations in the U 4 Theory of Gravitation

Cartan’s equations of structure and Bianchi identities in the U ₄ theory of gravitation are derived. The relativistic language we adopted is that of Newman-Penrose-Jogia and Griffiths (NPJG). A number of important properties which arise in the development of basic equations are also presented in the NPJG formalism. It is hoped that the essence of non-Riemannian geometry can be summarized by exploiting these equations.     

Synthesis and Biological Activities of Some New Annulated Pyrazolopyranopyrimidines and Their Derivatives Containing Indole Nucleus

The key intermediate 6‐amino‐3‐methyl‐4‐aryl‐1‐(5′‐substituted‐3′‐phenyl‐1H‐indol‐2′‐carbonyl)‐1,4‐dihydropyrano[2,3‐c]pyrazol‐5‐carbonitriles 3a , 3b , 3c , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k , 3l , 3m , 3n , 3o were prepared by cyclocondensation of 3‐methyl‐1‐(5′‐substituted‐3′‐phenyl‐1H‐indol‐2′‐carbonyl)‐5‐(4H)‐pyrazolones 1a , 1b , 1c with arylidine derivatives of malononitrile 2a , 2b , 2c , 2d , 2e . The compounds 3a , 3b , 3c , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k , 3l , 3m , 3n , 3o were subjected to cyclocondensation reaction with formamide, formic acid, and carbon disulfide to afford the title compounds 4a , 4b , 4c , 4d , 4e , 4f , 4g , 4h , 4i , 4j , 4k , 4l , 4m , 4n , 4o , 5a , 5b , 5c , 5d , 5e , 5f , 5g , 5h , 5i , 5j , 5k , 5l , 5m , 5n , 5o , and 6a , 6b , 6c , 6d , 6e , 6f , 6g , 6h , 6i , 6j , 6k , 6l , 6m , 6n , 6o , respectively. The structures of all these previously unknown compounds were confirmed by their spectral studies and elemental analysis. These compounds were screened for their antimicrobial and antioxidant activities.     

Scolecite as an efficient heterogeneous catalyst for the synthesis of 2,4,5-triarylimidazoles

Natural scolecite has been found as an effective catalyst for the one-pot synthesis of 2,4,5-triarylimidazole derivatives via a three component reaction using benzil or benzoin, aldehydes and ammonium acetate. This method provides several advantages such as being environmentally benign, reusable, possessing high yields with increased variations of the substituents in the product and preparative simplicity.      

ZnO-beta zeolite mediated simple and efficient method for the one-pot synthesis of quinoxaline derivatives at room temperature

A rapid and an efficient one-pot method for the synthesis of quinoxalines catalysed by ZnO-beta zeolite at room temperature is described. This environmentally benign method provides several advantages over methods that are currently employed such as a simple work-up, mild reaction conditions, good to excellent yields, and a process to recover and reuse the catalyst for several cycles with consistent activity.      

Thin Layer Chromatographic Technique for Detection and Identification of Endosulfan Insecticide with m-Dinitrobenzene Reagent

JPC – Journal of Planar Chromatography – Modern TLC - Endosulfan is commonly encountered in poisoning cases in India. In TLC the compound can be detected by spraying the plate with...     

ZnO-beta zeolite:As an effective and eco-friendly heterogeneous catalyst for the synthesis of benzothiazole derivatives

<正>A cheap and recyclable ZnO-beta zeolite was used as catalyst for the synthesis of benzothiazole derivatives.This method provides several advantages such as environmental friendliness,short reaction times,high yields,simple work-up procedure and catalyst was successfully reused for four cycles without significant loss of activity.     

Third-order geometrical null symmetries of gravitational fields

The first-, the second-, and the third-order null Killing vectors in a gravitational field are explored separately. When an algebraically special Petrov-type free gravitational field isaligned with a source-free (nonnull/null) electromagnetic field, their common propagation vectorl ^a is shown to be a third-order null Killing vector field ( _{l l l} g _ab = 0, _{l l} g _ab 0). When the two fields arenot aligned, the necessary and sufficient conditions for the existence of a third-order null symmetry are obtained in Newman-Penrose formalism.