Analysis of mode-locked internally frequency doubled broad-band continuous wave lasers

Closed-form analysis of pulse evolution in the transient regime in an actively modelocked internally frequency doubled broad-band continuous wave laser is presented. The analysis enables investigation of the effect of nonlinear crystal inside the laser cavity on mode-locked pulse parameters at the fundamental frequency. It is shown that the presence of internal second harmonic crystal broadens the fundamental mode-locked pulse while accelerating the approach of the system to steady-state. The dependence of pulse parameters on the bandwidth of the tuning element, modulation depth of the active mode-locker and conversion efficiency of the frequency doubler is presented in detailed graphical form.     

More results on Schur complements in Euclidean Jordan algebras

In a recent article Gowda and Sznajder (Linear Algebra Appl 432:1553–1559, 2010) studied the concept of Schur complement in Euclidean Jordan algebras and described Schur determinantal and Haynsworth inertia formulas. In this article, we establish some more results on the Schur complement. Specifically, we prove, in the setting of Euclidean Jordan algebras, an analogue of the Crabtree-Haynsworth quotient formula and show that any Schur complement of a strictly diagonally dominant element is strictly diagonally dominant. We also introduce the concept of Schur product of a real symmetric matrix and an element of a Euclidean Jordan algebra when its Peirce decomposition with respect to a Jordan frame is given. An Oppenheim type inequality is proved in this setting.     

Complementarity forms of theorems of Lyapunov and Stein, and related results

The well-known Lyapunov's theorem in matrix theory / continuous dynamical systems asserts that a (complex) square matrix A is positive stable (i.e., all eigenvalues lie in the open right-half plane) if and only if there exists a positive definite matrix X such that AX+XA^* is positive definite. In this paper, we prove a complementarity form of this theorem: A is positive stable if and only if for any Hermitian matrix Q, there exists a positive semidefinite matrix X such that AX+XA^*+Q is positive semidefinite and X[AX+XA^*+Q]=0. By considering cone complementarity problems corresponding to linear transformations of the form I−S, we show that a (complex) matrix A has all eigenvalues in the open unit disk of the complex plane if and only if for every Hermitian matrix Q, there exists a positive semidefinite matrix X such that X−AXA^*+Q is positive semidefinite and X[X−AXA^*+Q]=0. By specializing Q (to −I), we deduce the well known Stein's theorem in discrete linear dynamical systems: A has all eigenvalues in the open unit disk if and only if there exists a positive definite matrix X such that X−AXA^* is positive definite.     

Spectrophotometric determination of certain vicinal dihydroxybenzene derivatives in pharmaceutical preparations.

A simple, rapid and sensitive spectrophotometric method for the assay of certain adrenergic drugs, [pyrocatechol (PC), levodopa (LD), methyldopa (MD) and dopamine (DP)] is described. The method involves the oxidation of o-dihydroxybenzene derivatives by K2CrO4 followed by oxidative coupling with sulfanilic acid (SPA), leading to the formation of a red or violet colored product having maximum absorbance at 490-495 nm for LD, MD and DP or at 560 nm for PC. This method has been successfully applied to the determination of LD, MD and DP in tablets and injections of pharmaceutical preparation. The common excipients do not interfere with the proposed method. A statistical comparison of these results with those of a reported method shows good agreement and indicates no significant difference in precision.     

Organo-rhodium(I) complexes containing mono and bidentate N-heterocycles

Complexes of the type [Rh(diolefin)(μ-X)]₂ [X = Cl or Br; diolefin = cod (cycloocta-1,5-diene) or nbd (norbornadiene)] undergo dihalobridge cleavage with 2-substituted benzimidazoles to produce mononuclear complexes, RhX(diolefin)(R-BzlH) (R = α-Py or Ph), and N-heterocycle bridged dimers, [RhX(diolefin)]₂(μ-N–N) (N–N = β-PyBzlH or γ-PyBzlH). Facile replacement ofone or both diolefins by CO occurs in the products to yield the corresponding di/tetracarbonyl complexes. Probable structures have been proposed for the complexes on the basis of physical, i.r., far-i.r. and ¹H- and ¹³C-n.m.r. spectral techniques and FAB-MS. This revised version was published online in June 2006 with corrections to the Cover Date.     

Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras

In this article, we study the concept of Schur complement in the setting of Euclidean Jordan algebras and describe Schur determinantal and Haynsworth inertia formulas.     

Kinetic and mechanistic studies of oxidation of alanine and phenylalanine by sodium N-chlorobenzene sulfonamide (chloramine-B) in hydrochloric acid medium

The kinetics of oxidation of alanine and phenylalanine by sodium N-chlorobenzene sulfonamide (CAB) has been investigated at 30°C in two ranges of acid concentrations. The reactions follow identical kinetics for both amino acids. At low acid concentration (0.03–0.10M), simultaneous catalysis by H⁺ and Cl^? ions is noted. The rate shows a first-order dependence on [CAB], but is independent of [substrate]. A variation of the ionic strength or the dielectric constant of the medium or the presence of the added reaction product benzene sulfonamide (BSA) has no pronounced effect on the rate. At [HCl] > 0.2M, the rate is independent of [H⁺], but shows a first-order dependence on [CAB] and a fractional-order dependence on [amino acid]. The addition of BSA or Cl^? ions, or a change in the ionic strength of the medium has no influence on the rate. Upon decreasing the dielectric constant of the medium, the rate increased, indicating positive ion–dipole interaction in the rate-determining step. The reaction was studied at different temperatures, and activation parameters have been computed. Rate laws in agreement with experimental results have been derived. Suitable mechanisms to account for the observed kinetics are proposed. The rate constants obtained from the derived rate laws as [H⁺], [Cl^?], and [substrate] vary are in excellent agreement with the observed rate constants, thus justifying the proposed rate laws and hence the suggested mechanistic schemes.     

Oxidation of L-aspartic acid and L-glutamic acid by manganese(III) ions in aqueous sulphuric acid,acetic acid,and pyrophosphate media: A kinetic study

Kinetics of oxidation of L-aspartic acid and L-glutamic acid by manganese(III) ions have been studied in aqueous sulphuric acid, acetic acid, and pyrophosphate media. Manganese(III) solutions were prepared by known electrolytic/chemical methods in the three media. The nature of the oxidizing species present in manganese(III) solutions was determined by spectrophotometric and redox potential measurements. The reaction shows a variable order in [manganese(III)]_o: the order changes from two to one as the reactive oxidizing species changes from an aquo ionic form to a complex form. There is a first-order dependence of the rate on [amino acid]_o in all the three media while the other common features include an inverse dependence each on [H⁺] and on [manganese(II)]. Effects of varying ionic strength and solvent composition were studied. Added anions such as pyrophosphate, fluoride, or chloride alter the reaction rate and mechanism by changing the formal redox potential of Mn(III)-Mn(II) couple. Activation parameters have been evaluated using the Arrhenius and Eyring plots. Mechanisms consistent with the kinetic data have been proposed and discussed. © 1995 John Wiley & Sons, Inc.