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.     

Idealization of a decomposition theorem

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A _I-sets and A _I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A _I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date.     

On α-I-continuous and α-I-open functions

Montgomery and Vaughan improved a theorem of Erd?s and Fuchs for an arbitrary sequence. Sárközy extended this theorem of Erd?s and Fuchs for two arbitrary sequences which are "near" in a certain sense. Using the idea of Jurkat (differentiation of the generating function), we will extend similarly the result of Montgomery and Vaughan for "sufficiently near" sequences.     

Decompositions of some weaker forms of continuity

The aim of this paper is to give decompositions of some weaker forms of continuity using the concepts of classes B ₁, B ₂, B ₃, αA and αC introduced by ourselves.     

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.     

Crystal and molecular structures of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine.

The crystal structure of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine (C15H19NO3) (I) has been determined by X-ray analysis. It crystallizes orthorhombic space group Pbca with a = 24.295(3), b = 15.086(3), c = 7.552(3)A, V = 2768(1)A3, Z = 8, Dcalc = 1.254 g/cm3, mu = (Mo K(alpha)) = 0.87 cm(-1). The title compound has analgesic activity of cycloaliphatic amine part. The molecule is deviated from planar configuration.