Factorization in Weighted Wiener Matrix Algebras on Linearly Ordered Abelian Groups

Factorizations of Wiener-Hopf type of elements of weighted Wiener algebras of continuous matrix-valued functions on a compact abelian group are studied. The factorizations are with respect to a fixed linear order in the character group (considered with the discrete topology). Among other results, it is proved that if a matrix function has a canonical factorization in one such matrix Wiener algebra then it belongs to the connected component of the identity of the group of invertible elements in the algebra, and moreover, the factors of the canonical factorization depend continuously on the matrix function. In the scalar case, complete characterizations of canonical and noncanonical factorability are given in terms of abstract winding numbers. Wiener-Hopf equivalence of matrix functions with elements in weighted Wiener algebras is also discussed. The second author is supported by COFIN grant 2004015437 and by INdAM; the third and the fourth authors are partially supported by NSF grant DMS-0456625; the third author is also partially supported by the Faculty Research Assignment from the College of William and Mary.     

Numerical investigations of flow and energy fields near a thermoacoustic couple

The flow field and the energy transport near thermoacoustic couples are simulated using a 2D full Navier-Stokes solver. The thermoacoustic couple plate is maintained at a constant temperature; plate lengths, which are "short" and "long" compared with the particle displacement lengths of the acoustic standing waves, are tested. Also investigated are the effects of plate spacing and the amplitude of the standing wave. Results are examined in the form of energy vectors, particle paths, and overall entropy generation rates. These show that a net heat-pumping effect appears only near the edges of thermoacoustic couple plates, within about a particle displacement distance from the ends. A heat-pumping effect can be seen even on the shortest plates tested when the plate spacing exceeds the thermal penetration depth. It is observed that energy dissipation near the plate increases quadratically as the plate spacing is reduced. The results also indicate that there may be a larger scale vortical motion outside the plates which disappears as the plate spacing is reduced.     

Aspartate modulates the ethanol-induced oxidative stress and glutathione utilizing enzymes in rat testes

In order to develop a preventive strategy against ethanol-induced oxidative damages on various tissues and organs, we have examined the protective effect of aspartate on the pathogenesis of testes in the ethanol treated animals. Adult male Sprague-Dawley rats were given ethanol in an amount of 36% of total calories via Lieber-DeCarli liquid diet for 6 weeks without or with aspartate (2 mM in the diet). The control group was pair-fed the diet containing isocaloric dextrin-maltose instead of ethanol. The pathogenesis of testes at post- 6 weeks of experiments were carried out by histochemistry and biochemical parameters for oxidative stress such as the level of thiobarbituric acid reactive substances (TBARS) and the activities of glutathione utilizing enzymes were also examined. Chronic ethanol administration resulted in the increased amount of thiobarbituric acid reactive substances (TBARS) in the testes, which was significantly lessened by concurrent aspartate treatment (p < 0.05). In addition to this, liver function test indicated by alkaline phosphatase activity in serum showed that the ethanol-induced hepatotoxicity was significantly ameliorated by aspartate administration. And the activities of glucose-6-phosphate dehydrogenase and glutathione transferase in testis cytosol were decreased in the ethanol treated rats (p < 0.01 and < 0.005, respectively). These data suggest that aspartate may attenuate the ethanol-induced oxidative tissue damage in rat testes possibly through a redox-related protective effect on peroxidation.     

Drag measurements at Mach 5 using a stress wave force balance

The stress wave force balance, which has been used for measurements of drag on short models in hypersonic impulse facilities, is investigated here for its suitability for drag measurements on a longer, axisymmetric model. The sensitivity of the balance to loading distribution is investigated and results are reported for experiments on a 5° semi-angle cone, 425 mm in length and of 1.71 kg mass. Experimental drag measurements are shown to be in good agreement with theoretical levels. An investigation into the period over which the stress wave force balance can be used is addressed and, for the present model, the balance is shown to be suitable for measurements in flows of durations of one to several milliseconds with an estimated accuracy of ±10%.     

Synthesis and Properties of Pentafluorosulfanyl Group (SF5)-Containing Meta-Diamide Insecticides

Herein, we describe novel pentafluorosulfanyl (SF₅) group-containing meta-diamide insecticides. For the facile preparation of the SF₅-based compounds 4a–d, practical synthetic methods were applied. Among newly synthesized compounds, 3-benzamido-N-(2,6-dimethyl-4-(pentafluoro-λ⁶-sulfanyl)phenyl)-2-fluorobenzamide 4d showed (i) a high insecticidal activity, (ii) an excellent selectivity to insects, and (iii) good levels of water solubility and log P values. In this study, we demonstrated that the pentafluorosulfanyl moiety could serve as an attractive functionality for the discovery of a new scope of crop-protecting agents.     

A Facile One-Step Synthesis of Ethyl 2-(L,L-Dialkyl and Arylmethyl) Malonates

Diethyl ethoxymethylenemalonate (EMME) is unexpectedly converted into diethyl 2-(1,1 -dialkyl and diarylmethyl) malonate derivatives by a classical Grignard reaction. Addition of organocuprates to EMME gave diethyl 2-(l-ethoxyalkyl) malonate derivatives. The yields range from 42-63%.     

Drag measurements in a hypervelocity expansion tube

A technique is described for the measurement of aerodynamic drag in a hypervelocity expansion tube in which the test flow period may be as short as 50 s. The technique is an application of the stress wave force balance first proposed by Sanderson and Simmons (1991). The experiments were conducted in a test flow of partially dissociated Carbon Dioxide where the flow speed was in excess of 7 kms. The validity of the technique is first demonstrated by comparing the forces measured on a range of sharp cones with those expected theoretically. Agreement to within 10% is achieved. Two re-entry type heat shield geometries were then tested with the experimental drag forces being compared with a Modified-Newtonian prediction. In both cases agreement to within 11% was obtained. Received 12 December 1995 / Accepted 29 April 1996     

Fast computation of two-level circulant preconditioners

In this paper we present an algorithm for the construction of the superoptimal circulant preconditioner for a two-level Toeplitz linear system. The algorithm is fast, in the sense that it operates in FFT time. Numerical results are given to assess its performance when applied to the solution of two-level Toeplitz systems by the conjugate gradient method, compared with the Strang and optimal circulant preconditioners.     

Perturbation results for exponentially dichotomous operators on general Banach spaces

Some perturbation results for exponentially dichotomous operators are applied to prove the existence of stable and anti-stable solutions of Riccati equations associated to block operators on general Banach spaces, both for compact perturbations and for bisemigroups made up of immediately norm continuous semigroups.