A Note on Classification of Cylindrically Symmetric Non-static Space–Times According to Their Teleparallel Killing Vector Fields in the Teleparallel Theory of Gravitation

In this paper, we explored the conservation laws of cylindrically symmetric non-static space–times by using direct integration technique. This classification also covers non-static plane symmetric space–times, static cylindrically symmetric space–times and plane symmetric static space–times. In this paper, we will only present the results of non-static cylindrically symmetric and non-static plane symmetric space–times. The results of static cylindrically symmetric space–times and plane static space–times can be found in Shabbir and Khan (Mod Phys Lett A 25:525, 2010). It turns out that the non-static cylindrically symmetric space–times admit four, five, or seven conservation laws. It is important to note that the above space–times admit at least one or at the most four extra conservation laws.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

Urease inhibition and anti-leishmanial assay of substituted benzoylguanidines and their copper(II) complexes

A series of N,N',N'-trisubstituted guanidines (1-6) and their copper(II) complexes, [κ(2)(O,N)-C(6)H(5)CONHC(NHC(6)H(4)Cl)NR](2)Cu(ii) (R = iso-propyl (1a), n-butyl (2a), sec-butyl (3a), tert-butyl (4a), benzyl (5a), and para-tolyl (6a)) were synthesized and characterized using elemental analysis, FTIR and NMR spectroscopy. DFT studies were used to assess the location of the protons in the free ligands. However, calculations have shown that, in all cases, hydrogen bonding from either N-H group gives conformations that are very similar in energy. Single crystal XRD studies were used to characterize ligands 1 and 4 and the related complexes 1a and 4a. The structures reveal that these complexes are mononuclear in the solid state and that copper adopts a regular square planar geometry. In both metallic species, the N, N', N'-trisubstituted guanidine ligands chelate the Cu(II) atom using the oxygen and one nitrogen. The synthesized compounds were investigated for urease inhibition using thiourea as a standard drug. Most complexes exhibit a better activity than the respective guanidines and compound 1a was found to be the most active with IC(50) = 9.83 ± 0.07 μM (the IC(50) for thiourea is 21.0 ± 0.1 μM). The species were also screened for their anti-leishmanial activity. However, all of the compounds were devoid of any significant activity.     

The formation of novel 1,3-dioxolanes: atypical Baylis-Hillman reaction of a sesquiterpene lactone parthenin

The Baylis-Hillman reaction of a sesquiterpene lactone parthenin with various aldehydes gave unexpected products containing a 1,3-dioxolane moiety. Both small aliphatic and aromatic aldehydes produced 1,3-dioxolanes, whereas higher aliphatic aldehydes produced normal Baylis-Hillman products.     

Microbial transformation of mestranol by Cunninghamella elegans

The microbial transformation of an oral contraceptive, mestranol (1) by Cunninghamella elegans yielded two hydroxylated metabolites, 6beta-hydroxymestranol (2) and 6beta,12beta-dihydroxymestranol (3). Metabolite 3 was found to be a new compound. These metabolites were structurally characterized on the basis of spectroscopic techniques.     

体模型的一种细分格式

In this paper, a subdivision scheme which generalizes a surface scheme in previous papers to volume meshes is designed. The scheme exhibits significant control over shrink-age/size of volumetric models. It also has the ability to conveniently incorporate boundaries and creases into a smooth limit shape of models. The method presented here is much simpler and easier as compared to MacCracken and Joy‘s. This method makes no restrictions on the local topology of meshes. Particularly, it can be applied without any change to meshes of nonmanifold topology.     

Classification of Teleparallel Homothetic Vector Fields in Cylindrically Symmetric Static Space-Times in Teleparallel Theory of Gravitation

In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times.