Structure and characterization of tris(4-morpholinedithiocarbamato-S,S′)cobalt(·)acetonitrile solvate complex: [Co(S2CNC4H8O)3]·CH3CN

The crystal and molecular structure of the complex [Co(S₂CNC₄H₈O)₃]·CH₃CN has been determined by X-ray crystallography. The compound crystallizes in the triclinic system, space group P\overline 1 , with lattice parameters a = 10.561(2), b = 11.114(2), c = 13.011(3) Å, = 103.88(3), = 101.58(3), = 114.91(1)°, and Z = 2. X-ray analysis reveals that the cobalt(III) atom is located at the apparent intersection of D ₃ symmetry. Despite the apparent presence of the rotational axes, all of the atoms in the structure were found to be unique; there are no symmetry-related atoms. The central cobalt atom is octahedrally coordinated by an arrangement of six S atoms. The octahedron is distorted as a result of the forced configuration of the four-membered chelate ring. The average Co–S distance is 2.273 Å. The FT-IR spectra clearly show there are acetonitrile molecules in the crystal lattice.     

Hyperbolic orbit and its variation of deep-space probe

While approaching the target body, the deep-space probe is orbiting hyperbolically before the maneuver. We discuss the variation of perturbed hyperbolic orbit using the method similar to that used in elliptic orbit. Ephemeris calculating and orbit control will benefit from the given analytical solution.     

Self-Converse Directed BIBDs with Block Size Four

A directed balanced incomplete block design (or D B(k,;v)) (X,) is called self-converse if there is an isomorphic mapping f from (X,) to (X,^–1), where ^–1={B ^–1:B} and B ^–1=(x _k ,x _{k –1},,x ₂,x ₁) for B=(x ₁,x ₂,,x _{k –1},x _k ). In this paper, we give the existence spectrum for self-converse D B(4,1;v). AMS Classification:05BResearch supported in part by NSFC Grant 10071002 and SRFDP under No. 20010004001     

Stability and Existence of Multidimensional Subsonic Phase Transitions

The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local existence of phase transition solutions.     

Invariant Tori and Boundedness in Asymmetric Oscillations

In this paper,we are concerned with the boundedness of all the solutions of the equation x″ ax^ -bx- Ф(x)=p(t),where p(t) is a smooth 2π-periodic function,a and b are positive constants,and the perturbation Ф(x) is bounded.     

When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

Let _t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when _t is in different states. This new process Z_t is a hidden Markov process. We study the probability distribution of the first passage time for Z_t.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull).     

Hyperbolic Conformal Geometry with Clifford Algebra

In this paper, we study hyperbolic conformal geometry following a Clifford algebraic approach. Similar to embedding an affine space into a one-dimensional higher linear space, we embed the hyperboloid model of the hyperbolic n-space in into . The model is convenient for the study of hyperbolic conformal properties. Besides investigating various properties of the model, we also study conformal transformations using their versor representations.     

A Sharp Inequality of Markov Type for Polynomials Associated with Laguerre Weight

The best possible constant A_n in an inequality of Markov type

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, where ·_[0, ∞) denotes the sup-norm on the half real line [0, ∞) and p_n is an arbitrary polynomial of degree at most n, is determined in terms of the weighted Chebyshev polynomials associated with the Laguerre weight e^−x on [0, ∞).     

Electrochemical studies of the effect of lanthanide ions on the activity of glutamate dehydrogenase

Using the electrochemical method based on the "diffusion" layer concept of the convective system, the effect of lanthanide ions La3+ and Eu3+ on the activity of glutamate dehydrogenase (GLDH) has been determined. In suitable concentrations, the lanthanide ions La3+ and Eu3+ can activate the GLDH in the reductive amination of alpha-Ketoglutarate (alpha-KG). The activation mechanism would be that the lanthanide ions could interrupt the binding of NAD+ to GLDH by combining preferentially to NAD+. This mechanism was proposed by the voltammetric studies.     

Evidence for 2D precursors and interdiffusion in the evolution of self-assembled CdSe quantum dots on ZnSe

The evolution of self-assembled CdSe quantum dots deposited on (and subsequently capped by) ZnSe was investigated on a series of samples grown by molecular beam epitaxy, with CdSe coverages from 0.5 to 2.6 monolayers. The samples were investigated by cross-sectional scanning transmission electron microscopy, as well as macro- and microphotoluminescence. The results clearly indicated a coexistence of 2D ZnCdSe platelets and 3D islands, showing clearly that the platelets act as precursors for the formation of the 3D islands.