Experimental observation of autosoliton propagation in a dispersion-managed system guided by nonlinear optical loop mirrors

Observation of autosoliton propagation in a dispersion-managed optical transmission system controlled by in-line nonlinear fiber loop switches is reported for what is believed to be the first time. The system is based on a strong dispersion map with large amplifier spacing. Operation at transmission rates of 10 and 40 Gbits/s is demonstrated.     

Depressed cladding, buried waveguide laser formed in a YAG:Nd3+ crystal by femtosecond laser writing

Depressed cladding waveguides have been formed in laser crystals by a tightly focused beam of a femtosecond laser. A laser based on a depressed cladding waveguide in a neodymium-doped YAG crystal has been demonstrated for what is believed to be the first time.     

Free interpolation in H∞ A La P. Jones

There is recounted a simplification of the new proof of the Newman-Carleson theorem on interpolation sequences, recently discovered by P. Jones.     

Entropy meaning of summability of the logarithm

We consider the mutual relations between the concepts of sets of uniqueness for analytic functions, the loss of entropy in nondetermined stationary linear filters, Szegö's theorem and the familiar condition of summability of the logarithm. The goal of the paper is to give the physical meaning of these mutual relations. Here we take the concept of linear stationary filter and loss of entropy in it as basic. In the first part of the paper the account is given for the case of discrete time, and in the second part we give the method of passing to continuous time. To this end we introduce the concept of stationary sampling system. This is a sequence of functions from L²(), which transforms any stationary Gaussian process with continuous correlation function into a stationary Gaussian process with discrete time. Such systems can be described in terms of the Fourier transform. Laguerre systems where z is a fixed point in the upper half-plane, play a special role among all sampling systems. If z=i, then is a classical Laguerre function on the line up to a multiplicative constant. Laguerre sampling systems allow one to give the entropy meaning to the values of the harmonic extension to the upper half-plane of the logarithm of the spectral density of the processTranslated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 152–187, 1977.     

Synthesis of planar chiral ferrocene alcohols as potential dendrimer cores

Planar chiral compounds, 1-hydroxymethyl-2-methylferrocene and new 3-(2-hydroxymethylferrocenyl)propanol, were synthesized to be used as dendrimer cores. The ethers of these compounds, namely, 1-(benzyloxymethyl)-2-methylferrocene and 2-(benzyloxymethyl)-1-(benzyloxypropyl)ferrocene, can be regarded as zero-generation Freche type dendrimers. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1116–1119, July, 2006.     

The total synthesis of sevanol,a novel lignan isolated from the thyme plant (Thymus armeniacus)

Recently, a novel lignan sevanol was isolated from the thyme plant Thymus armeniacus. During structure-functional elucidation it showed significant biological activity on ASIC3 acid sensing channels. Herein we describe the first synthesis of sevanol with a 3% overall yield. The construction of a dihydronaphthalene ring by oxidative dimerization of a protected dihydroxycinnamic acid ester in the presence of ferric chloride (III) is a key step in this first total synthesis of sevanol.