Optimization of Polynomial Fractional Functions

A new approach is proposed for optimizing a polynomial fractional function under polynomial constraints, or more generally, a synomial fractional function under synomial constraints. The approach is based on reformulating the problem as the optimization of an increasing function under monotonic constraints.     

Kernel density estimation for spatial processes: the L1 theory

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L₁ are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for nonmixing processes. Potential applications include testing for spatial interaction, the spatial analysis of causality structures, the definition of leading/lagging sites, the construction of clusters of comoving sites, etc.     

On the design of open resonators for quasi-optical gyrotrons

In the design of a 120 GHz 200 kW quasi-optical gyrotron, we have analyzed the influence of the open resonator geometry (two circular mirrors facing one another) on the electronic efficiency, the ohmic losses, the output coupling and the multimode behavior. The method we have used to optimized the resonator design will be presented. Mode selectivity is improved by using a resonator formed by two mirrors each of which has a central step. Numerical simulations show that single mode operation can also be attained in the more favorable situation of a magnetic field having a positive taper over the interaction region.     

Flow Characteristics of Granular Bulk Materials

The paper discusses the interest in conventional triaxial tests widely used in soil mechanics for a better understanding of both the mechanical behaviour and flow characteristics of granular bulk materials. It proposes a rheological characterization of granular foodstuffs on diverse types of stress path using a conventional triaxial cell. The characteristic state concept, defining the disaggregation threshold of the granular structure, is found to be suitable and even indispensible for examining the mechanical behaviour and the flowability of stored bulk materials. The experimental results readily suggest, as an indicator of the arching effect, a rheological index that characterizes the particle interlocking breakdown and hence the flowability of the stored materials. In addition, this study offers a realistic physical meaning for parameters in use in constitutive models (yield conditions and flow rules) when describing granular flow in various hopper geometries. The case of silos equipped with vibrating hoppers necessitates additionally the study of the rheological behaviour of materials under cyclic and vibratory loadings in order to analyse the processes of densification or disaggregation conditioning the flowability of the stored materials during emptying operations.     

A Generalization of a Theorem of Dehon for Simple t-Designs

A generalization of a theorem of Dehon for simple t-designs is proved. Several new families of 4- and 5-designs having certain additional property regarding their block intersection numbers are obtained by applying this result.The author acknowledges the support of SFB Forschungsschwerpunkt-Geometrie Grant, University of Heidelberg.     

Van der Pol oscillator under parametric and forced excitations

We study a van der Pol oscillator under parametric and forced excitations. The case where a system contains a small parameter and is quasilinear and the general case (without the assumption of the smallness of nonlinear terms and perturbations) are studied. In the first case, equations of the first approximation are obtained by the Krylov-Bogolyubov-Mitropol’skii technique, their averaging is performed, frequency-amplitude and resonance curves are studied, and the stability of the given system is considered. In the second case, the possibility of chaotic behavior in a deterministic system of oscillator type is shown. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 206–216, February, 2007.     

Stereospecific sequential block copolymerizations of styrene and 1,3‐butadiene with a C5Me5TiMe3/B(C6F5)3/Al(oct)3 catalyst

This article reports a new methodology for preparing highly stereoregular styrene (ST)/1,3‐butadiene (BD) block copolymers, composed of syndiotactic polystyrene (syn‐PS) segments chemically bonded with cis‐polybutadiene (cis‐PB) segments, through a stereospecific sequential block copolymerization of ST with BD in the presence of a C₅Me₅TiMe₃/B(C₆F₅)₃/Al(oct)₃ catalyst. The first polymerization step, conducted in toluene at ?25 °C, was attributed to the syndiospecific living polymerization of ST. The second step, conducted at ?40 °C, was attributed to the cis‐specific living polymerization of BD. The livingness of the whole polymerization system was confirmed through a linear increase in the weight‐average molecular weights of the copolymers versus the polymer yields in both steps, whereas the molar mass distributions remained constant. The profound cross reactivity of the styrenic‐end‐group active species with BD toward ST led to the production of syn‐PS‐b‐cis‐PB copolymers with extremely high block efficiencies. Because of the presence of crystallizable syn‐PS segments, this copolymer exhibited high melting temperatures (up to 270 °C), which were remarkably different from those of the corresponding anionic ST–BD copolymers, for which no melting temperatures were observed. Scanning electron microscopy pictures of a binary syn‐PS/cis‐PB blend with or without the addition of the syn‐PS‐b‐cis‐PB copolymers proved that it could be used as an effective compatibilizer for noncompatibilized syn‐PS/cis‐PB binary blends. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1188–1195, 2005