Groups withS 2′-subgroups andS 3′-subgroups

In this paper we formulate criteria for the solvability of groups of typeE _2′ andE _3′     

The maximum amplitude cost functional in linear systems

The maximum amplitude cost of a control function u(t) taken to be ess sup g(t, u(t)), where g(t, u) is a given function. (A particular example is g(t, u) = the norm of u.) We consider linear systems with this cost functional. The existence of optimal control is proved, and it is shown that the ess sup is uniformly essential with respect to the optimal controls. Properties of the extended attainable set are discussed and compared with the case of an integral cost. Finally, we show in what sense a cost functional of the form $\text{(∝ g(t, u(t))}{}^{\mathrm{q}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>q</mtext>}}$ approximates the ess sup cost functional.     

On symmetric basic sequences in Lorentz sequence spaces

We examine the symmetric basic sequences in some classes of Banach spaces with symmetric bases. We show that the Lorentz sequence spaced(a,p) has a unique symmetric basis and every infinite dimensional subspace ofd(a,p) contains a subspace isomorphic tol ^p. The symmetric basic sequences ind(a,p) are identified and a necessary and sufficient condition for a Lorents sequence space with exactly two nonequivalent symmetric basic sequences in given. We conclude by exhibiting an example of a Lorentz sequence space having a subspace with symmetric basis which is not isomorphic either to a Lorentz sequence space or to anl ^p-space. This is part of the first author's Ph. D. thesis, prepared at the Hebrew University of Jerusalem under the supervision of Dr. L. Tzafriri.     

Bounds on the Optimal Location to the Weber Problem under Conditions of Uncertainty

Optimal and Heuristic bounds are given for the optimal location to the Weber problem when the locations of demand points are not deterministic but may be within given circles. Rectilinear, Euclidean and square Euclidean types of distance measure are discussed. The exact shape of all possible optimal points is given in the rectilinear and square Euclidean cases. A heuristic method for the computation of the region of possible optimal points is developed in the case of Euclidean distance problem. The maximal distance between a possible optimal point and the deterministic solution is also computed heuristically.     

Financial Applications of a Tabu Search Variable Selection Model

We illustrate how a comparatively new technique, a Tabu search variable selection model [Drezner, Marcoulides and Salhi (1999)], can be applied efficiently within finance when the researcher must select a subset of variables from among the whole set of explanatory variables under consideration. Several types of problems in finance, including corporate and personal bankruptcy prediction, mortgage and credit scoring, and the selection of variables for the Arbitrage Pricing Model, require the researcher to select a subset of variables from a larger set. In order to demonstrate the usefulness of the Tabu search variable selection model, we: (1) illustrate its efficiency in comparison to the main alternative search procedures, such as stepwise regression and the Maximum R 2 procedure, and (2) show how a version of the Tabu search procedure may be implemented when attempting to predict corporate bankruptcy. We accomplish (2) by indicating that a Tabu Search procedure increases the predictability of corporate bankruptcy by up to 10 percentage points in comparison to Altman's (1968) Z-Score model.     

A clinical study of failure in microchannel cooled diodes used in large laser systems

In this paper we investigate the source of failure in commercial, microchannel cooled CW diode bars placed in 12 bar horizontal arrays. The arrays were used to pump Nd:YAG rods in our 10 kW developmental laser. The laser was operated at low duty factor over a period of over 2 years. Experimental evidence indicated that the sudden, catastrophic failure was because of degraded cooling. We used optical microscopes, an X-ray microfocus imager, and a thermal neutron scattering camera to look inside the microcoolers. Our investigations revealed only one possible failure mechanism: cooling flow reduction because of delamination of the Au coating the walls of the microcoolers and the entrapment of Au flakes within the microchannel structures. We observed blisters in the microcoolers under working bars, and flake-like structures in the microcoolers under burnt-out bars (all taken from the laser). We observed no evidence of either massive blockages because of electrochemical deposits, or of corrosion/erosion in the microchannel walls. Integral operation times of the high flow-rate cooling system and of the diodes themselves were too short by one and two orders of magnitude, respectively, to explain the observed failures. Microchannel immersion times in the deionized water were, however, long enough to allow for corrosion of metals that may have been exposed through defects in the Au coatings. Three-dimensional heat flow simulations showed that blockage of multiple microchannels towards the edge of a bar can easily lead to catastrophic temperature increases.