Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

Kinetics and Mechanism of Oxidation of 1-Phenylsemicarbazide by Peroxydisulphate

Kinetics of oxidation of 1-phenylsemicarbazide (PSC) by peroxydisulphate ion (PDS) have been carried out where by the pseudo first order condition was verified at large excess of PDS concentration. The rate of the reaction was followed spectrophotometrically, The stoichiometry was found to be 1:1 where 1-phenylazoformamide is the oxidation product. The effect of acidity on the rate of oxidation was investigated for different temperatures. The parameters of activation ΔG*, ΔH* and ΔS* were computed for both hydrogen ion depedent and hydrogen ion independent reaction pathes. A free radical mechanism was proposed.     

Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations

In this paper we study autoregressive processes of order 1 with values in a separable Banach space it B. Such ARB(1)-processes are defined by the recursion equation

Effect of constrained donor atom orientations on the stabilities, complexation kinetics, redox potentials, and structures of macrocyclic polythiaether Complexes. Copper(II) complexes with cyclopentanediyl derivatives of [14]aneS4 in 80% methanol

The two ethylene bridges in the macrocyclic tetrathiaether 1,4,8,11-tetrathiacyclotetradecane ([14]aneS(4)) have been systematically replaced by cis- or trans-1,2-cyclopentane to generate a series of new ligands that exhibit differing preferences for the orientation of the sulfur donor atoms while maintaining constant inductive effects. The resulting five dicyclopentanediyl derivatives, along with two previously synthesized monocyclopentanediyl analogues, have been complexed with Cu(II), and their stability constants, formation and dissociation rate constants, and redox potentials have been determined in 80% methanol/20% water (by weight). The crystal structures of the Cu(II) complexes with the five dicyclopentanediyl-[14]aneS(4) diastereomers as well as the structures for a representative Cu(I) complex and one of the free ligands have also been determined. The properties of these complexes are compared to previous data obtained for the corresponding cyclohexanediyl derivatives in an attempt to shed additional light on the influence of sterically constraining substituents upon the properties of macrocyclic ligand complexes.     

Equivalent moduli of continuity, Bloch’s theorem for pluriharmonic mappings in \mathbb{B}{\kern-8pt}\mathbb{B}^{\boldsymbol n}

In this paper, we first establish a Schwarz?CPick type theorem for pluriharmonic mappings and then we apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, we obtain several Landau??s and Bloch??s type theorems for pluriharmonic mappings.     

A green and simple method for the synthesis of 2,4,5-trisubstituted-1H-imidazole derivatives using acidic ionic liquid as an effective and recyclable catalyst under ultrasound

Research on Chemical Intermediates - In the current work, an acidic ionic liquid ([{(IMC)-4-OMBH}BIM][HSO4]3) has been utilized as an effective and recyclable catalyst for the synthesis of...     

〈331〉晶向ZnTe单晶的太赫兹辐射-探测性能理论研究

根据光整流效应辐射太赫兹理论,计算了〈331〉晶向ZnTe单晶的太赫兹辐射性能.通过与〈110〉、〈111〉晶向对比,当晶体方位角为0°或180°时,利用〈331〉晶向ZnTe单晶辐射太赫兹信号可以与〈111〉晶向相当,强于〈110〉晶向.利用电光取样原理,计算了〈331〉晶向ZnTe单晶的太赫兹探测性能,通过理论计算为〈331〉晶向ZnTe 晶体有效辐射太赫兹波提供理论依据.     

Effect of Al mole fraction on structural and electrical properties of AlxGa1−xN/GaN heterostructures grown by plasma-assisted molecular beam epitaxy

The effect of Al mole fractions on the structural and electrical properties of Al_xGa_1−xN/GaN thin films grown by plasma-assisted molecular beam epitaxy (PA-MBE) on Si (1 1 1) substrates has been investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), atomic force microscopy (AFM), and current-voltage (I-V) measurements. X-ray results revealed that the AlGaN/GaN/AlN was epitaxially grown on Si substrate. By applying Vegard's law, the Al mole fractions of Al_xGa_1−xN samples were found to be 0.11, 0.24, 0.30 and 0.43, respectively. The structural and morphology results indicated that there is a relatively larger tensile strain for the sample with the smallest Al mole fraction; while a smaller compressive strain and larger grain size appear with Al mole fraction equal to 0.30. The strain gets relaxed with the highest Al mole fraction sample. Finally, the linear relationship between the barrier height and Al mole fraction was obtained.     

Eigenvalues and eigenfunctions of discontinuous Sturm--Liouville problems with eigenparameter-dependent boundary conditions

We extend some fundamental spectral properties of classic regular Sturm--Liouville problems to discontinuous boundary-value problems with eigenvalue-dependent boundary conditions. We suggest a new approach for investigation of such type discontinuous problems.     

ON ALGEBRAIC VOLUME DENSITY PROPERTY

A smooth affine algebraic variety X equipped with an algebraic volume form ω has the algebraic volume density property (AVDP) if the Lie algebra generated by complete algebraic vector fields of ω-divergence zero coincides with the space of all algebraic vector fields of ω-divergence zero. We develop an effective criterion of verifying whether a given X has AVDP. As an application of this method we establish AVDP for any homogeneous space X = G/R that admits a G-invariant algebraic volume form where G is a linear algebraic group and R is a closed reductive subgroup of G.