Anionic Halomolybdate(III) Chemistry. Tetrahydrofuran Loss from [MoX(3)Y(THF)(2)](-) (X, Y = Cl, Br, I), Preparation and Properties of [Mo(3)X(12)](3)(-) (X = Br, I), and Crystal Structure of the Edge-Sharing Trioctahedral [PPh(4)](3)[Mo(3)I(12)

By interaction of MoX(3)(THF)(3) with [Cat]X in THF, the salts [Cat][MoX(4)(THF)(2)] have been synthesized [X = I, Cat = PPh(4), NBu(4), NPr(4), (Ph(3)P)(2)N; X = Br, Cat = NBu(4), PPh(4) (Ph(3)P)(2)N]. Mixed-halide species [MoX(3)Y(THF)(2)](-) (X, Y = Cl, Br, I) have also been generated in solution and investigated by (1)H-NMR. When the tetraiodo, tetrabromo, and mixed bromoiodo salts are dissolved in CH(2)Cl(2), clean loss of all coordinated THF is observed by (1)H-NMR. On the other hand, [MoCl(4)(THF)(2)](-) loses only 1.5 THF/Mo. The salts [Cat](3)[Mo(3)X(12)] (X = Br, I) have been isolated from [Cat][MoX(4)(THF)(2)] or by running the reaction between MoX(3)(THF)(3) and [Cat]X directly in CH(2)Cl(2). The crystal structure of [PPh(4)](3)[Mo(3)I(12)] exhibits a linear face-sharing trioctahedron for the trianion: triclinic, space group P&onemacr;; a = 11.385(2), b = 12.697(3), c = 16.849(2) ?; alpha = 76.65(2), beta = 71.967(12), gamma = 84.56(2) degrees; Z = 1; 431 parameters and 3957 data with I > 2sigma(I). The metal-metal distance is 3.258(2) ?. Structural and magnetic data are consistent with the presence of a metal-metal sigma bond order of (1)/(2) and with the remaining 7 electrons being located in 7 substantially nonbonding orbitals. The ground state of the molecule is predicted to be subject to a Jahn-Teller distortion, which is experimentally apparent from the nature of the thermal ellipsoid of the central Mo atom. The [Mo(3)X(12)](3)(-) ions reacts with phosphines (PMe(3), dppe) to form products of lower nuclearity by rupture of the bridging Mo-X bonds.     

Overview on the synthetic routes to nicotine nitriles

The biological and medicinal properties of nicotinonitrile and its analogues have prompted enormous research aimed at developing synthetic routes to these heterocyclic. This review highlights the different synthetic routes to nicotine nitriles.     

An overview on synthetic strategies to coumarins

Coumarins units have recently emerged as a hot topic of research due to their diverse applications. Their synthesis is partly based on classical methodologies such as Pechmann reaction or Knoevenagel condensation, but it also sparked the discovery of completely new pathways. In very recent years so-called vertically expanded coumarins were synthesized, effectively expanding the portfolio of existing architectures. This review serves as a guide through synthesis strategies to coumarins.     

Analysis of 2beta-carbomethoxy-3beta-(4-fluorophenyl)-N-(3-iodo-E-allyl)nortropane in rat plasma. II. Pharmacokinetic profile in male and female Sprague-Dawley rats evaluated by capillary electrophoresis

This paper describes a pharmacokinetic study performed in Sprague-Dawley rats after i.v. administration of a single 6-mg/kg dose of 2beta-carbomethoxy-3beta-(4-fluorophenyl)-N-(3-iodo-E-allyl)nortropane (Altropane). Plasma samples were collected from the retro-orbital sinus at times up to 3 h after drug administration, extracted by solid-phase extraction, and the drug levels determined by capillary electrophoresis (CE). Pharmacokinetic parameters were determined by a standard noncompartmental model using WinNonlin version 1.5. The maximum plasma concentrations, clearances of the drug, and areas under the curve for male and female rats were 5.74 and 7.26 microg/ml, 135.7 and 98.5 ml/kg x min, and 44.23 and 60.92 microg x min/ml, respectively. The drug was cleared very rapidly from the systemic circulation, with a terminal t(1/2) of 7 to 10 min and a mean residence time of about 11 min for both sexes. The volume of distribution was approximately 1 l/kg. No metabolites were detected when the samples were analyzed individually. However, after samples were pooled and concentrated, traces of two unknown peaks that may represent metabolites were detected in concentrates from the last two timepoints. Part I of this work [J. Chromatogr. A, 895 (2000) 87] describes validation of CE methods for the analysis of aqueous and plasma samples of Altropane, including its solid-phase extraction from rat plasma.     

On support properties of functions and their Jacobi transform

The qualitative uncertainty principle proved by Benedicks asserts that f and its Fourier transform \(\hat f\) cannot both concentrated in subsets of finite Lebesgue measure. In this paper we obtain some uncertainty principles concerning sets of finite measure in the Jacobi setting.     

Classification of finite Morse index solutions for Hénon type elliptic equation -\Delta u = |x|^{\alpha } u_{+}^{p}

In this paper we investigate the non-autonomous elliptic equations \(-\Delta u = |x|^{\alpha } u_{+}^{p}\) in \( \mathbb{R }^{N}\) and in \( \mathbb{R }_+^{N}\) with the Dirichlet boundary condition, with \(N \ge 2\) , \(p>1\) and \(\alpha >-2\) . We consider the weak solutions with finite Morse index and obtain some classification results.     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

REPRESENTATION OF GENERALIZED TRANSLATIONS OF THE PRODUCT OF TWO FUNCTIONS ON SIGNED HYPERGROUPS ON THE REAL LINE

In this paper,we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R.Especially,we study the representation of the generalized translations of the product of two functions for these signed hypergroups.     

Study of the contraction flow using grid generation technique

We study a model procedure to solve the incompressible Navier-Stokes equations on the flow inside contraction geometry. The governing equations are expressed in the primitive variable formulation. A rectangular computational plane is arises by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of a curvilinear coordinate system. By transformed the governing equation into computational plane. The time dependent momentum equations are solved explicitly for the velocity field using the explicit marching procedure, the continuity equation is applied at each grid point in the solution of pressure equation, while the successive over relaxation (SOR) method is used for the Neumann problem for pressure. We will apply the technique on several irregular-shape.     

The Webster scalar curvature revisited: the case of the three dimensional CR sphere

In this paper we consider the problem of prescribing the Webster scalar curvature on the three CR sphere of ${\mathbb{C}^{2}}$ . We use techniques related to the theory of critical points at infinity, and obtain existence results for curvature satisfying an assumption of Bahri?CCoron type.