q-positive definiteness and related operators

We are in progress of extending the family of ‘q-deformed operators’ considered in the previous papers by joining to them q-subnormal as well as q-formally subnormal ones. It turns out that q-positive definiteness, a notion generalizing Halmos' standard positive definiteness of bounded subnormal operators, is likewise central for our new scheme.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

应变Si1-xGex层中p型杂质电离常温和低温特性

本文采用解析的方法计算了应变Si1-xGex层中p型杂质电离度与Ge组分x、温度T以及掺杂浓度N的关系.发现常温时,在同一Ge组分下,随着掺杂浓度的升高,杂质的电离度的先变小,而后又迅速上升到1.在同一掺杂浓度下,轻掺杂时,杂质的电离度随Ge组分的增加先变大,而后几乎不变;重掺杂时,杂质电离能变为0后,杂质电离度为1.低温下,轻掺杂时,载流子低温冻析效应较为明显,杂质的电离度普遍较小,当掺杂浓度大于Mott转换点时,载流子冻析效应不再明显,电离率迅速上升到1.在同一Ge组分下,随着掺杂浓度的升高,杂质的电离度先变小,后变大,而后又迅速上升到1.在同一掺杂浓度下,轻掺杂时,杂质的电离度随Ge组分的增加变大;重掺杂时,杂质电离能变为0后,杂质电离度为1.     

基于爆轰波原理声源定位方法初探

基于弹丸发射时所发出的爆轰波,利用传感器接收时差信息,从而确定声源位置。本文建立了该声源定位反问题的物理和数学模型,并依据该模型寻求适当的数值解法,最后针对延拓-广义逆法声源定位问题进行了演算和简要分析。     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

A Modified Szilard Engine: Measurement, Information, and Maxwell's Demon

Using an isolated measurement process, we calculate the effect measurement has on entropy for the multi-cylinder Szilard engine. We find that the system of cylinders possesses an entropy associated with cylinder total energy states, and that it records information transferred at measurement. Contrary to other's results, we find that the apparatus loses entropy due to measurement. The Second Law of Thermodynamics may be preserved if Maxwell's demon gains entropy moving the engine partition.     

Thermal Effects of Microwave Energy in Agricultural Soil Radiation

The thermal treatment by millimeter waves for the soil disinfection can be one possible alternative to chemical treatments. This physical method is based on incrementing the soil temperature and its pathogens irradiating with high frequency electromagnetic waves. So the previous knowledge of the temperature distribution in the irradiated soil is essential for achieving an effective bad microorganism and weed seeds elimination. This report analyse the heating kinetic and spatial distribution of the maximum temperatures reached by the soil. It is presented a mathematic model about how are distributed the reached temperatures in the depth of the irradiated soil. This model concludes that when an orchard soil is irradiated superficially by microwaves, the microwaves have a big attenuation due to the soil dielectric properties and the water located in the pores of the most superficial layer. This fact causes a shield effect blocking the waves penetration in few centimetres. The heating by radiation is reduced to the superficial layer. The heating propagation in the depth is occurred by conduction following the Fourier equations.     

A web-based workforce management system for Sainsburys Supermarkets Ltd

Labour scheduling plays an important and critical role in Sainsburys day to day operations and profitability. The integrated workforce management solution for Sainsburys is an intelligent solution for the operational deployment of human resources, integrated business forecasting, generation and calculation of workload and staff scheduling. The workforce management technology has provided Sainsburys with a fully web-based and centralised system that produces optimised schedules for all employees satisfying the forecasted demand of work with granularity of fifteen minutes. The system is configured to respect all operational and business requirements as well as employee contractual constraints. This paper introduces the workforce management solution system designed, developed and implemented for Sainsburys. We concentrate on two modelling structures, namely the work pattern model and optimisation model, and briefly discuss the optimisation process.     

Low sintering temperature MnZn-ferrites for power applications in the frequency region of 400 kHz

In this paper, the effect of cubic zinc metaborate Zn₄O(BO₂)₆ on the sintering of MnZn-ferrites for medium frequency power applications is investigated. Zinc metaborate is synthesized in the laboratory using zinc oxide and boric acid as metal precursors. As observed, when zinc metaborate is added to the MnZn-ferrites at an optimum amount of 0.02 wt%, it significantly enhances densification and therefore allows, for a given density, reduction of the firing temperature by almost 200 °C. MnZn-ferrites exhibiting power losses of 70 mW/cm³ (measured at a frequency of 400 kHz, magnetic field 50 mT and temperature of 90 °C) are synthesized from conventionally milled powders with average particle diameter 0.6 μm, compacted and fired at 1100 °C. Identical experiments conducted under the same conditions on specimens without zinc metaborate additions revealed power losses greater than 300 mW/cm³, because of insufficient densification.