Optimal allocation of amplifiers in a dispersion-managed line for a wavelength-division-multiplexed soliton transmission system

Optimal allocation of amplifiers in a dispersion-managed line is theoretically derived by means of minimizing the collision-induced frequency shift in a two-channel wavelength-division-multiplexed soliton transmission system. Almost complete cancellation of the frequency shift can be obtained for such a system with any strength of dispersion management.     

Along the Lines of Nonadditive Entropies: q-Prime Numbers and q-Zeta Functions

The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n−s=∏pprime11−p−s, Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended ζ(s) to the complex plane z and conjectured that all nontrivial zeros are in the R(z)=1/2 axis. The nonadditive entropy Sq=k∑ipilnq(1/pi)(q∈R;S1=SBG≡−k∑ipilnpi, where BG stands for Boltzmann-Gibbs) on which nonextensive statistical mechanics is based, involves the function lnqz≡z1−q−11−q(ln1z=lnz). It is already known that this function paves the way for the emergence of a q-generalized algebra, using q-numbers defined as 〈x〉q≡elnqx, which recover the number x for q=1. The q-prime numbers are then defined as the q-natural numbers 〈n〉q≡elnqn(n=1,2,3,⋯), where n is a prime number p=2,3,5,7,⋯ We show that, for any value of q, infinitely many q-prime numbers exist; for q≤1 they diverge for increasing prime number, whereas they converge for q>1; the standard prime numbers are recovered for q=1. For q≤1, we generalize the ζ(s) function as follows: ζq(s)≡〈ζ(s)〉q (s∈R). We show that this function appears to diverge at s=1+0, ∀q. Also, we alternatively define, for q≤1, ζq∑(s)≡∑n=1∞1〈n〉qs=1+1〈2〉qs+⋯ and ζq∏(s)≡∏pprime11−〈p〉q−s=11−〈2〉q−s11−〈3〉q−s11−〈5〉q−s⋯, which, for q<1, generically satisfy ζq∑(s)<ζq∏(s), in variance with the q=1 case, where of course ζ1∑(s)=ζ1∏(s).     

Analysis of Gordon-Haus jitter in a dispersion-compensated optical transmission system

We theoretically analyzed the Gordon-Haus timing jitter in a periodically dispersion-compensated optical transmission system as a result of upgrading a preinstalled uniform-dispersion system. We show that the enhanced peak power for a large dispersion difference in the period reduces the frequency shift induced by noise, and a proper setting of the receiver position further reduces the timing jitter.     

Overtone intensities in resonance Raman scattering

A model calculation of resonance Raman scattering tensors has been carried out for a diatomic molecule with a harmonic potential for the ground state and a linear repulsive potential for the excited state. Expressions for scattering tensors have been obtained by using a series of recurrence formulas induced from the Green function of the nuclear hamiltonian of the repulsive potential of the excited state and nuclear wavefunctions for the harmonic potential. The relative scattering intensities of overtones depend on the gradient of the repulsive potential curve and are interpreted in terms of the overlap integrals between nuclear wavefunctions of upper and lower states.     

Residuenfreie Differentiale und der Cartier-Operator algebraischer Funktionenkörper

Ohne ZusammenfassungThe author acknowledges support received from the National Research Council of Canada, Grant A-7210.Herrn. Prof. E.Lamprecht und Herrn Dr. H.Mathieu dankt Verfasser für ihre Anmerkungen, die zu Verbesserungen der ursprünglichen Fassung führten.     

Structure of an anti-plasmin inhibitor, eckol, isolated from the brown alga Ecklonia kurome Okamura and inhibitory activities of its derivatives on plasma plasmin inhibitors

Eckol (1), a novel phlorotannin with a dibenzo-1,4-dioxin skeleton, has been isolated from the brown alga Ecklonia kurome Okamura as a potent and specific anti-plasmin inhibitor. Its structure has been elucidated based on the spectral data, in particular, by means of negative nuclear Overhauser effect (NOE), and finally established as 1-(3,5-dihydroxyphenoxy)-2,4,7,9-tetrahydroxydibenzo-1,4-dio xin by X-ray analysis. Some partially methoxylated derivatives of eckol were prepared by methylation with diazomethane and also by selective dimethylation of eckol permethylate (1b) to establish the structural requirements for inhibitory activities on alpha 2-macroglobulin and alpha 2-plasmin inhibitor, the main plasmin inhibitors in plasma.     

Simple Synthesis of a Heterocyclophane Exhibiting Anti-c-Met Activity by Acting as a Hatch Blocking Access to the Active Site**

A simple approach to the synthesis of heterocyclophane consisting of two 4,4’-bithiazoles has been developed in mild conditions. The heterocyclophane with two short chains was conveniently prepared by Hantzsch thiazoles synthesis using the reaction of 3-tert-butoxycarbonyl-3-azapentanethiocarboxamide with 1,4-dibromobutane-2,3-dione in methanol under reflux for only 15 min. Amino groups at the linkers of this heterocyclophane can be functionalized to give acylated and carbamate derivatives. Their properties as protein kinase inhibitors were investigated, and one of the heterocyclophanes exhibited specific anti-activity for c-mesenchymal epithelial transition factor (IC₅₀=603 nm ), among seven types of protein kinases investigated. The computational site identification by ligand competitive saturation method was used to determine why the one heterocyclophane exhibited strong anti-activity for c-mesenchymal epithelial transition factor.     

Subincanadines A-C,novel quaternary indole alkaloids from Aspidosperma subincanum

Three novel quaternary indole alkaloids with an unprecedented 1-azoniatricyclo[4.3.3.0(1,5)]undecane moiety, subincanadines A-C (1-3), as well as two new indole alkaloids with a 1-azabicyclo[5.2.2]undecane moiety, subincanadines D (4) and E (5), and a new indole alkaloid with a 1-azabicyclo[4.3.1]decane moiety, subincanadine F (6), have been isolated from the barks of Aspidosperma subincanum Mart, and the structures of 1-6 and the stereochemistry of 1-3 were elucidated by spectroscopic data and chemical means.     

Dielectrically controlled resolution (DCR) of 3-aminopiperidine via diastereomeric salt formation with N-tosyl-(S)-phenylalanine

A useful key intermediate for the dipeptidyl peptidase-4 (DPP-4) inhibitor, 3-aminopiperidine 1, was successfully resolved with an enantiomerically pure resolving agent, N-tosyl-(S)-phenylalanine 2, to give both stereoisomers (R)-1 and (S)-1 as a less-soluble diastereomeric salt with (S)-2, via a dielectrically controlled resolution (DCR) phenomenon.