Effect of the Parameters of Three-Mirror Resonators on the Spectral Characteristics of Single-Pulse Laser Generation with Self-Injection of Priming Radiation

Based on a semiclassical theory, investigations were made of the dynamics and spectral composition of pulsed generation with self-injection of priming radiation from the active part of a three-mirror linear resonator, the passive part of which contains an active loss modulator and serves as the output reflector of the laser. It is shown that there exists a range of resonator parameters at which pulsed lasing has virtually a single frequency irrespective of the detuning of the frequencies of the priming radiation and of the nearest eigenmode of the composite resonator. Considering graphically the phase conditions of generation, it is established that among pulsed lasers with self-injection of priming radiation which are constructed on the basis of three-mirror linear and branched resonators, the most efficient for creating single-frequency generation are those in which the length of the main resonator, where generation of the pulse occurs, is larger than the length of the additional one intended for forming the priming radiation. With an inverse ratio of the lengths of the resonators, the conditions of single-frequency pulsed generation becomes dependent on the priming radiation frequency.     

Remote stereocontrol by the sulfinyl group: Mukaiyama aldol reactions of (S)-2-[2-(p-tolylsulfinyl)phenyl]acetaldehyde in the asymmetric synthesis of β-hydroxyacids and 1,3-diols

(S)-2-[2-(p-Tolylsulfinyl)phenyl]acetaldehyde reacts with different O-silylated ketenethioacetals in the presence of Yb(OTf)₃ yielding β-hydroxythioesters in high yields and diastereoselectivities. The obtained compounds were readily transformed into β-hydroxyacids and their corresponding diols. These Mukaiyama aldol reactions are a direct evidence of the ability of the sulfinyl group to control 1,5- and 1,6-asymmetric induction processes.     

Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

Investigations of Solid State Dynamics at the NRSSR Beamline at PETRA II. An Overview

The present status of the new nuclear resonance beamline PETRA 1 at HASYLAB, DESY, Hamburg is described. Besides an overview of the experimental setup some examples of recent experiments are given. Those cover the main applications, i.e., inelastic scattering from iron alloys and quasielastic scattering from glass-forming liquids. This revised version was published online in August 2006 with corrections to the Cover Date.     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

On Quantum Team Games

Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

Some formulae for the q-Bernoulli and Euler polynomials of higher order

The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570).     

Coupled intervals in the discrete calculus of variations: necessity and sufficiency

In this work we study nonnegativity and positivity of a discrete quadratic functional with separately varying endpoints. We introduce a notion of an interval coupled with 0, and hence, extend the notion of conjugate interval to 0 from the case of fixed to variable endpoint(s). We show that the nonnegativity of the discrete quadratic functional is equivalent to each of the following conditions: The nonexistence of intervals coupled with 0, the existence of a solution to Riccati matrix equation and its boundary conditions. Natural strengthening of each of these conditions yields a characterization of the positivity of the discrete quadratic functional. Since the quadratic functional under consideration could be a second variation of a discrete calculus of variations problem with varying endpoints, we apply our results to obtain necessary and sufficient optimality conditions for such problems. This paper generalizes our recent work in [R. Hilscher, V. Zeidan, Comput. Math. Appl., to appear], where the right endpoint is fixed.