Rigidity and flexibility analysis of a kind of surfaces of revolution and visualization

In this paper we consider a class of toroids generated by a meridian in a shape of quadrangle in an arbitrary position to the axis of revolution.We give geometrical meaning of the non-rigidity condition based on the position of the diagonals of meridian. Special classes of quadrangular meridians (trapezium, parallelogram, deltoid, … ) are discussed. The number of flexible toroids is considered. A tool SurfBend is developed for the rigidity and visualization.     

Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind

In this paper we define generalized Kählerian spaces of the first kind (\(G_1^K N\)) given by (2.1)–(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces (\(G_1^K N\) and \(G_1^{\bar K} N\)) and for them we find invariant geometric objects.     

Positive Solutions of Fourth Order Thomas-Fermi Type Differential Equations in the Framework of Regular Variation

The fourth order nonlinear differential equations A with regularly varying coefficient q(t) are studied in the framework of regular variation. It is shown that thorough and complete information can be acquired about the existence of all possible regularly varying solutions of (A) and their accurate asymptotic behavior at infinity.     

A novel bifunctional N-acetylglutamate synthase-kinase from <Emphasis Type="Italic">Xanthomonas campestris</Emphasis> that is closely related to mammalian N-acetylglutamate synthase

Background  

In microorganisms and plants, the first two reactions of arginine biosynthesis are catalyzed by N-acetylglutamate synthase (NAGS) and N-acetylglutamate kinase (NAGK). In mammals, NAGS produces an essential activator of carbamylphosphate synthetase I, the first enzyme of the urea cycle, and no functional NAGK homolog has been found. Unlike the other urea cycle enzymes, whose bacterial counterparts could be readily identified by their sequence conservation with arginine biosynthetic enzymes, mammalian NAGS gene was very divergent, making it the last urea cycle gene to be discovered. Limited sequence similarity between E. coli NAGS and fungal NAGK suggests that bacterial and eukaryotic NAGS, and fungal NAGK arose from the fusion of genes encoding an ancestral NAGK (argB) and an acetyltransferase. However, mammalian NAGS no longer retains any NAGK catalytic activity.     

A dinuclear hydride complex of platinum(I) containing both bidentate and monodentate bis(diphenylphosphino)methane ligands: the crystal structure of [Pt2H(Ph2PCH2PPh2)(μ-Ph2PCH2PPh2)2][PF6]

The crystal structure of the title compound has been determined from 6049 X-ray diffractometric intensities with I > 3σ(I), and refined by a least-squares procedure to R = 0.050. The crystals are monoclinic, space group P2₁/n, a = 13.702(2) b = 14.255(2), c = 39.556(6) Å, β = 94.75(1)°, Z = 4. The structure of the cation displays two different coordination modes of the Ph₂PCH₂PPh₂ ligands. Two of these are bidentate, bridging the Pt-Pt bond [2.769(1)Å] to form a Pt₂(μ-Ph₂PCH₂PPh₂)₂ nucleus, while the third acts as a monodentate two-electron donor. The hydrido ligand was not located, but its position is inferred from the coordination geometry of the platinum atom to which it is bonded. The metalligand distances are: Pt-P(trans to P) 2.248(3)–2.289(4) and Pt—P(trans to Pt) 2.347(4) Å.     

Green chemistry approach to the synthesis of 3-substituted-quinazolin-4(3H)-ones and 2-methyl-3-substituted-quinazolin-4(3H)-ones and biological evaluation

ABSTRACT

A synthesis of two series of 3-substituted quinazolinones was performed utilizing a green chemistry approach, deep eutectic solvents and microwaves, namely. 2-Methyl-3-substituted-quinazolin-4(3H)-one derivatives were synthesized in a two-step reaction, using choline chloride:urea deep eutectic solvent (DES). 3-Substituted-quinazolin-4(3H)-ones were synthesized in one-pot one-step reaction of anthranilic acid, amines and orthoester in a microwave reactor. For the synthesis of 2-methyl-3-substituted-quinazolin-4(3H)-ones, first conventional synthesis of benzoxazinone, as an intermediate, was performed. Further, benzoxazinone in reaction with corresponding amines, in choline choline:urea deep eutectic solvent, furnished desired compounds. These procedures are based on green principles with the aim of developing synthetic routes for the potential antitumor agents. All compounds were characterized by LC/MS, ¹H NMR and ¹³C NMR spectral techniques. Compound 1 bearing trifluoromethoxyphenyl group showed promising activity against HuT-78 cell line with IC₅₀ of 51.4?±?5.1?µM.