Identification,synthesis and conformational study of a CN(R,S) synthon by-product: (5R, 10R)-5,10-diphenyl-1,6-diaza-3,8-dioxabicyclo[4.4.1]undecane

The title compound, containing a new heterocyclic skeleton, was identified by X-ray crystallography as the product of condensation of (R)-phenylglycinol with an excess of formaldehyde. The molecule adopts a rigid double twist-chair conformation in both solid and solution states.     

On the vector field problem for O(n)/O(1)xO(1)xO(n-2)

We prove new results about the vector field problem on the real flag manifolds O(n)/O(1) x O(1) x O(n - 2). For some infinite families of these manifolds, we completely solve the vector field problem.     

Investigation of multiwavelength clock recovery based on heterodyne beats of sideband-filtered signal

We investigate a new parallel all-optical clock recovery scheme based on heterodyne beats of an optical sideband-filtered signal. The oscillating clock signal is recovered when the filtered sideband is combined with a stable local oscillator. The filtering is performed with an optical resonator, which by nature provides possibility for multiwavelength operation. The local oscillator could be realized by a multiwavelength laser, whose emission wavelengths are injection seeded with carrier wavelengths of the input data. The output signal of such a configuration benefits from a reduced bit-pattern effect and a stable offset level. The sideband filtering is demonstrated for 23 simultaneous channels at 100 GHz DWDM grid, each hosting a data stream of 10 Gbit/s.     

A new alternating‐direction finite element method for hyperbolic equation

A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one‐dimensional problems. Optimal order H₀¹ and L² error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Lie-group theoretic method for analyzing interaction of discontinuous waves in a relaxing gas

A Lie group of transformations method is used to establish self-similar solutions to the problem of shock wave propagation through a relaxing gas and its interaction with the weak discontinuity wave. The forms of the equilibrium value of the vibrational energy and the relaxation time, varying with the density and pressure are determined for which the system admits self-similar solutions. A particular solution to the problem has been found out and used to study the effects of specific heat ratio and ambient density exponent on the flow parameters. The coefficients of amplitudes of reflected and transmitted waves after the interaction are determined.     

Existence for bounded positive solutions of Schrödinger equations in two-dimensional exterior domains

In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains.