Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Engel type identities with derivations for right ideals in prime rings

Let R be a prime ring of char R≠2, d a non-zero derivation of R and ρ a non-zero right ideal of R such that [[d(x),d(y)]_n [y,x]_m] = 0 for all x,y ∈ ρ or [[d(x),d(y)]_n d[y,x]_m] = 0 for all x,y ∈ ρ, n, m ≥ 0 are fixed integers. If [ρ,ρ]ρ ≠ 0, then d(ρ)ρ = 0.     

Temperature studies of Fe−Mn nodules

Sea nodules were extensively studied over a wide range of temperature ranging from 77K to 1175K using Mossbauer effect and ESR. The Mossbauer studies of the nodules at 77K and room temperature show a quadrupole doublet whereas at higher temperatures magnetic spectra were obtained starting at around 875K which ultimately gives a hyperfine field of around 390 KOe at 1175 K. The Mossbauer spectra recorded at 30K did not show any significant change in the room temperature spectra. The analysis of the spectra upto 775K showed two positions of Fe^R+, vie., octahedral and tetrahedral which were varified by ESR of the diluted samples.     

Skew-commuting and Commuting Mappings in Rings with Left Identity

Our main object in this paper is to discuss some results on rings with left identity in which certain subsets satisfy some functional identities.     

Excess enthalpies of mixing tetrahydrofuran and tetrahydropyran with some chloroalkanes at 26.9°C

Excess enthalpies of mixing H _m ^E of tetrahydrofuran and tetrahydropyran with trichloromethane, tetrachloromethane, 1,2-dichloroethane, 1,1,2-trichloroethane and 1,1,2,2-tetrachloroethane have been determined at 26.9°C and are found to be negative over the entire composition range for both sets of the ether mixtures. H _m ^E decreases in the sequence; dichloroethane > tetrachloromethane > trichloroethane > trichloromethane > tetrachloroethane. The results are explained on the basis of strong O...H-C and weak Cl...O specific interactions. Flory's theory has been used to correlate the experimental data with good agreement found between the theoretical and experimental values of H _m ^E .     

Effect of pressure on the behavior of nontransition metallic superconductors

An explicit expression has been derived for the volume dependence of electron-phonon coupling strength () by using a recently proposed quadratic form of the screened pseudopotential and by considering the variation of Fermi momentum with volume. Variation of Coulomb pseudopotential ( ^*) has also been explicitly considered by varying the Fermi momentum. Dependence of transition temperatureT _c and the logarithm of the effective interaction strength (N ₀ V) on the volume has been studied for eight nontransition metallic superconductors. A linear drop inT _c for small values of (–/ ₀) as well as the calculated values of= InN ₀ V/ In, exhibits better matching with the experimental data, as compared to the earlier theoretical results.