Transition from the Fluctuation Mode of Stimulated Resonant Coherent Raman Scattering to the Energy–Stabilized Mode

The equations of the semiclassical theory for the stimulated resonant coherent Raman scattering (SRS) in an extended medium have been solved numerically. The distribution function of the energy of Stokes pulses at different detunings and energies of a laser has been determined. Just as for the nonresonant coherent SRS, in the situation considered there occurs transition from the large–scale fluctuation mode to the mode of relatively small straggling of the energies of Stokes pulses with increase in the pumping energy. With approach to the resonance, the energy required to stabilize the Stokes radiation decreases.     

一类新型时滞积分不等式及其应用

主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.     

求解非线性规划的原始对偶内点法(英文)

In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.     

Global smoothness and uniform convergence of smooth Gauss–Weierstrass singular operators

In this article we continue with the study of smooth Gauss–Weierstrass singular integral operators over the real line regarding their simultaneous global smoothness preservation property with respect to the L_p norm, 1≤p≤∞, by involving higher order moduli of smoothness. Also we study their simultaneous approximation to the unit operator with rates involving the modulus of continuity with respect to the uniform norm. The produced Jackson type inequalities are almost sharp containing elegant constants, and they reflect the high order of differentiability of the engaged function.     

Global Dynamics of Hopfield Neural Networks with Delay

In this paper,some sufficient estimates of delay are ob-tained by Lyapunov functional method to ensure all thesolutions of Hopfleld neural networks with delay (HNN'D)converge to its equilibrlums as t→∞.     

A switched controller for an underactuated underwater vehicle

We present a switched control law for stabilizing an underactuated underwater vehicle (UUV) moving in a horizontal plane in a neutrally buoyant condition. The control law consists of a sequential series of control actions, each of which achieves a certain objective, finally resulting in the system being moved to the origin. Finite-time controllers are employed at each stage to achieve the desired objective. Simulation results are presented to validate the control law.     

Synthesis of core‐shell structured carboxylated microparticles with a straightforward procedure and their evaluation as a polymer support

Poly(trimethylolpropane trimethacrylate) microspheres with a narrow size distribution were obtained by precipitation polymerization. They were subsequently modified by surface grafting with acrylic acid in a polar ethanol–water reaction medium, without stabilizer, yielding core‐shell particles with diameters in the micrometer range. The resulting polymeric material was characterized by SEM and potentiometric titration, FTIR spectroscopy, and thermal analysis. It was shown that the particle characteristics (size, size distribution, and functionality) obtained by this straightforward procedure can be controlled by modifying the synthesis parameters (monomer concentration, agitation rate, and temperature). The high functionality, the chemical and physico‐mechanical stability, as well as the possibility to control the performances of the resulting polymeric materials by synthesis allow its applications in various areas. Envisaging separation and catalysis domains, Cu(II), Cd(II), and Cr(III) uptake capacity from aqueous solutions was investigated under noncompetitive conditions as a function of synthesized particle functionality, time, and pH range. It was also found that the addition of the carboxylated microparticles to polyethylene stabilized with α‐tocopherol improved the thermo‐oxidative behaviour of the polymeric material. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5889–5898, 2005     

On natural homomorphisms of Witt rings

We prove that the kernel of the ring homomorphism between the Witt ring of any order of a global field and the Witt ring of the field is a nilideal.

     

Reputation and efficiency: A non-parametric assessment of America’s top-rated MBA programs

Widely publicized reports of fresh MBAs getting multiple job offers with six-figure annual salaries leave a long-lasting general impression about the high quality of selected business schools. While such spectacular achievement in job placement rightly deserves recognition, one should not lose sight of the resources expended in order to accomplish this result. In this study, we employ a measure of Pareto-Koopmans global efficiency to evaluate the efficiency levels of the MBA programs in Business Week’s top-rated list. We compute input- and output-oriented radial and non-radial efficiency measures for comparison. Among three tier groups, the schools from a higher tier group on average are more efficient than those from lower tiers, although variations in efficiency levels do occur within the same tier, which exist over different measures of efficiency.     

Efficient interval partitioning for constrained global optimization

A new efficient interval partitioning approach to solve constrained global optimization problems is proposed. This involves a new parallel subdivision direction selection method as well as an adaptive tree search. The latter explores nodes (intervals in variable domains) using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search to identify feasible stationary points. The new tree search management technique results in improved performance across standard solution and computational indicators when compared to previously proposed techniques. On the other hand, the new parallel subdivision direction selection rule detects infeasible and suboptimal boxes earlier than existing rules, and this contributes to performance by enabling earlier reliable deletion of such subintervals from the search space.