On Oscillation Criteria of Fourth Order Linear Differential Equations

The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.     

Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20     

WEIGHTED APPROXIMATION ON SZASZ—TYPE OPERATORS

In this paper, we use weighted modules ω(?)(f,t)w to study the pointwise approximation on Szasz-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approximation of Jacobi-weighted Szasz-type operators.     

Mechanisms of n‐butanol formation in butyl acrylate latexes

The mechanisms involved in the formation of n‐butanol during the synthesis of butyl acrylate containing latices were investigated. The experimental results showed that neither the hydrolysis of butyl acrylate nor of the ester bond in the butyl acrylate segments of the polymer played a major role in the formation of n‐butanol, which was mainly generated from the polymer backbone, by transfer reactions to polymer chain followed by cyclization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5838–5846, 2007     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

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.