Equivalence and Singularity of Gaussian Measures on the Conic Sigma-Field

The alternative: equivalence-singularity on the conic sigma-field is established for a pair of centered Gaussian distributions and a corresponding criterion is given. The behavior of the logarithmic variation is established for the Radon–Nikodym derivative on the conic sigma-subfield. Bibliography: 6 titles.     

Adaptive server staffing in the presence of time-varying arrivals: a feed-forward control approach

We study the short-term staffing problem of systems that experience random, non-stationary demand. The typical method to accommodate changes in arrival rate is to use historical data to identify peak periods and associated forecasting for upcoming time windows. In this paper, we develop a method that instead detects change as it happens. Motivated by an automatic call distributor system in a call centre with time-varying arrivals, we propose a change detection algorithm based upon non-homogeneous Poisson processes. The proposed method is general and may be thought of as a feed-forward strategy, in which we detect a change in the arrival process, estimate the new magnitude of the arrival rate, and assign an appropriate number of servers to the tasks. The generalized likelihood ratio statistic is used and a recommendation for its decision limit is developed. Simulation results are used to evaluate the performance of the detector in the context of a telephone call centre.     

Receiver set partitioning and sequencing for multicasting traffic in a WDM lightwave single-hop network

This paper considers a receiver set partitioning and sequencing problem in a wavelength division multiplexing single-hop lightwave network for multicasting traffic. The problem is analysed in the approach of uncapacitated single batch-processing machine scheduling. In the analysis, several solution properties are characterized with respect to a mean flow time measure, based upon which two heuristic algorithms are developed, along with a dynamic programming algorithm. Several numerical experiments show that the heuristic algorithms generate good schedules. The problem is extended to consider two measures simultaneously including the mean flow time and the number of transmissions, for which the proposed algorithms also perform well.     

A differential scanning calorimetry method to determine the isothermal crystallization kinetics of cocoa butter

This research aimed to reduce the variability on the data obtained from differential scanning calorimetric (DSC) analysis of the isothermal crystallization kinetics of cocoa butter.

To enable transformation of the DSC crystallization peak to a sigmoid crystallization curve, the DSC peak area has to be integrated. Usually, the start and end points of the crystallization peak are determined visually. The result of this visual determination appeared to be very much dependent on the operator, but also differed considerably when the same operator performed the integration several times. By proposing an objective calculation algorithm to determine the start and end points of integration, the variability caused by the operator during the integration procedure could be eliminated. Furthermore, sample preparation and the DSC heating protocol to melt the sample prior to crystallization were studied. Three heating protocols (65 °C for 15 min, 65 °C for 30 min and 80 °C for 15 min) were compared and it was shown that holding at 65 °C for 15 min was sufficient to eliminate any influence of sample history. Two different sample preparation procedures were compared and it appeared that a change in sample preparation procedure had a significant influence on the measured crystallization process. It is thus important to keep this method constant to eliminate the variability caused by it.     

PERIODIC ENVIRONMENTS AND PERIODIC HARVESTING

ABSTRACT. We consider autonomous population models under periodic harvesting and population models in periodic environments and seek conditions under which there is an asymptotically stable periodic solution.     

On Coercive Estimates for Solutions of Linear Systems of Hydrodynamic Type

Local and nonlocal coercive estimates in Lebesgue, Hölder, and Morrey–Campanato spaces are proved for solutions of linear stationary systems of hydrodynamic type. For this purpose, the technique proposed by Italian mathematicians for the study of solutions to equations and systems of elliptic and parabolic types is developed. Bibliography: 14 titles.     

Absorption and propagation of light in quaterthiophene crystals

We examine absorption of light in quaterthiophene crystals for different directions of the ray and wave-normal vector after refraction on the vacuum/crystal interface. Experimental non-normal incidence spectra are reported where different absorption bands show different behaviour as a function of the angle of incidence. This allows to identify those originating from the b_u Frenkel exciton state.     

Enhancement of measurement sensitivity in determination of changes in the shape of a wavefront by holographic lateral-shearing interferometry

A method for increasing measurement sensitivity in the visualization of dynamics of changes in wavefront shape with the use of holographic lateral-shearing interferometry is considered. At the first stage of this method, a photograph of a reference shear interferogram obtained with tuning to closely spaced fringes is recorded under linear conditions. After chemical treatment, the photograph of the reference shear interferogram is installed in exactly its initial position. At the second stage, a series of photographs of lateral-shear interferograms of the wavefront under study is recorded under nonlinear conditions using the photograph of the reference interferogram. The photographs of the lateral-shear interferograms are optically processed by two coherent beams with selection of the highest diffraction orders, which makes it possible to visualize the dynamic component of the wavefront deformation with an increase in the measurement sensitivity (the static component is excluded in this case). The effect of the degree of nonlinearity of photograph recording on the range in which the measurement sensitivity can be controlled during the optical processing of a pair of matched photographs or one double-exposure photograph of interferograms recorded at different values of a lateral shift is analyzed.     

Condensate formation and vortex generation in Bose gas upon cooling

The mechanism of transition of a Bose gas to the superfluid state via thermal fluctuations under the condition of external cooling at a temperature above the transition point is considered. The probability of formation of such critical fluctuations (instantons) is calculated; it is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.