Starlikeness and Certain Class of Rational Functions

A new criterion for starlikeness in the unit disc and an application to a certain class of rational functions are given.     

Tamm oscillations in semi-infinite nonlinear waveguide arrays

We demonstrate the existence of nonlinear Tamm oscillations at the interface between a substrate and a one-dimensional waveguide array with either cubic or saturable, self-focusing or self-defocusing nonlinearity. Light is trapped in the vicinity of the array boundary due to the interplay between the repulsive edge potential and Bragg reflection inside the array. In the special case when this potential is linear these oscillations reduce themselves to surface Bloch oscillations.     

A synthesis of N-alkyl and N,N-dialkyl O-ethyl thiocarbamates from diethyl dixanthogenate using different oxidants

Abstract  

A novel synthesis of N-alkyl and N,N-dialkyl O-ethyl thiocarbamates from diethyl dixanthogenate and primary and secondary amines, using three oxidizing systems, has been developed on the laboratory scale, and the method using sodium hypochlorite has been applied on a semi-industrial scale. The effect of the oxidizing agents, sodium hypochlorite, in-situ-generated peracetic acid, and the manganese(II) acetate/oxygen system on product purity and yield was studied. The results obtained by use of these three methods were compared with those obtained by reaction of sodium ethyl xanthogenacetate and amines, and of sodium ethyl xanthate with amines in the presence of sulfated nickel zeolite catalyst. The reaction mechanism of sodium hypochlorite oxidation has been established on the basis of isolation of reaction intermediates and determination of their structure by use of Fourier-transform infrared, ¹H and ¹³C NMR, and mass spectrometric methods. The suggested sodium hypochlorite and manganese(II) acetate/oxygen systems have many advantages in comparison with commercial and catalytically promoted synthetic methods, because they are new ecologically friendly syntheses.     

Estimates for the norm of powers of Volterra's operator through its singular values

We prove that for every Volterra operator T the inequality holds, where b is an absolute constant and are its singular values. Received January 26, 2000 / Published online February 5, 2001     

Syntheses of N-alkyl, N,N-dialkyl, and N-(4-substituted phenyl) O-ethyl thioncarbamates: a kinetic study

Abstract  

The kinetics of the syntheses of N-alkyl, N,N-dialkyl, and N-(4-substituted phenyl) O-ethyl thioncarbamates from sodium ethyl xanthogenacetate, ten alkylamines, and eight substituted anilines were studied at 25, 30, 35, and 40 °C. The reactions were found to follow second-order kinetics. The kinetic (Arrhenius) parameters, such as the activation energy and the frequency factor, as well as the Eyring parameters, such as the standard entropy, the standard Gibbs energy, and the standard enthalpy of activation, were calculated from the second-order rate constants. The mechanism of the reaction was postulated based on the kinetic studies presented and the optimization of the reaction mechanism using the MOPAC PM6 semi-empirical method.     

Mobility of high-power solitons in saturable nonlinear photonic lattices

We theoretically study the properties of one-dimensional nonlinear saturable photonic lattices exhibiting multiple mobility windows for stationary solutions. The effective energy barrier decreases to a minimum in those power regions where a new intermediate stationary solution appears. As an application, we investigate the dynamics of high-power Gaussian-like beams finding several regions where the light transport is enhanced.