Application of a separating transformation to estimates of inner radii of open sets

We obtain solutions of new extremal problems of the geometric theory of functions of a complex variable related to estimates for the inner radii of nonoverlapping domains. Some known results are generalized to the case of open sets. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1313–1321, October, 2007.     

AI and OR in management of operations: history and trends

The last decade has seen a considerable growth in the use of Artificial Intelligence (AI) for operations management with the aim of finding solutions to problems that are increasing in complexity and scale. This paper begins by setting the context for the survey through a historical perspective of OR and AI. An extensive survey of applications of AI techniques for operations management, covering a total of over 1200 papers published from 1995 to 2004 is then presented. The survey utilizes Elsevier's ScienceDirect database as a source. Hence, the survey may not cover all the relevant journals but includes a sufficiently wide range of publications to make it representative of the research in the field. The papers are categorized into four areas of operations management: (a) design, (b) scheduling, (c) process planning and control and (d) quality, maintenance and fault diagnosis. Each of the four areas is categorized in terms of the AI techniques used: genetic algorithms, case-based reasoning, knowledge-based systems, fuzzy logic and hybrid techniques. The trends over the last decade are identified, discussed with respect to expected trends and directions for future work suggested.     

Clustering of spectra and fractals of regular graphs

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labeled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind.     

The σ<Emphasis Type="Italic">g</Emphasis>-Drazin Inverse and the Generalized Mbekhta Decomposition

In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended Mbekhta decomposition gives a characterization of circularly isolated spectral sets.     

The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.     

Photothermal techniques applied to the determination of the water vapor diffusion coefficient and thermal diffusivity of edible films.

Water vapor diffusion coefficient (WVDC) and thermal diffusivity (alpha) were determined in gelatin-starch films through photothermal techniques. The effect of different variables in the elaboration of these films, such as starch and glycerol concentrations and pH, were evaluated through the response surface methodology. The results indicated that an increase in the glycerol concentration and pH favored the WVDC of the films. On the other hand, alpha was influenced principally by the starch content and pH of the film-forming solution. The minimum alpha value was 4.5 x 10(-4) cm2/s, which is compared with alpha values reported for commercial synthetic polymers.     

Optimal block length for Basic mode data transmission control procedure

This paper considers two models of BASIC mode data transmission: When we transmit data with length l

1. (1) data are divided into N blocks and each block is transmitted individually

2. (2) data are divided into N sub-blocks and all sub-blocks are transmitted together.

We derive total average transmission data lengths of each model and discuss optimal numbers N* and block length B* which minimize them. In model 1, the length of one block is approximately determined independently of l. It is shown in a numerical example that when l is large, model 2 is better than model 1.     

High-Throughput Screening of Ten Microcystins and Nodularins, Cyanobacterial Peptide Hepatotoxins, by Reversed-Phase Liquid Chromatography-Electrospray Ionisation Mass Spectrometry

Liquid chromatography-electrospray ionisation mass spectrometry was evaluated in the high-throughput analysis of microcystins and nodularins, cyanobacterial peptide hepatotoxins. Extracts originating from cyanobacterial strains and field material were separated on a 30 mm × 4 mm I.D. Merck Purospher STAR RP-18e column using a rapid gradient of aqueous formic acid and acetonitrile, ionised by electrospray technique and analysed on a Micromass Quattro II triple-quadrupole mass spectrometer operated in the selected ion recording (SIR) mode. The total analysis time per sample was 2.8 min corresponding to 514 samples a day. The system showed good robustness during a series of 320 repetitive injections of a field sample containing three major microcystins.