Canonical factorization of continuous functions on the -torus

In this article we study the canonical factorization of continuous complex-valued functions on the -dimensional torus belonging to a weighted Wiener algebra with respect to a linear order on the -tuples of integers. It is proved that a function has a canonical factorization in this algebra if and only if it has a logarithm belonging to this algebra. A second characterization is given in terms of winding numbers. Moreover, the maximal ideal spaces of the relevant Banach algebras are identified.

     

Nonautonomous Exponential Dichotomy

In this note we generalize the strongly continuous bisemigroups generated by exponentially dichotomous operators to so-called bievolution families. These families are then related to strongly continuous bisemigroups on certain Banach spaces of continuous and measurable vector-valued functions. The research leading to this note was supported by the Italian Ministry of Education and Research (MIUR) under PRIN grant no. 2006017542-003, and by INdAM-GNCS.     

Multidisk file design: An analysis of folding buckets to disks

A technique called folding for mapping file buckets to multiple disks is evaluated. In particular, an upper bound to expected costs given any size partial match query is found. Folding is compared to Disk Modulo allocation.     

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.     

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.     

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%.     

Antibody interference with N-acyl homoserine lactone-mediated bacterial quorum sensing

Many bacterial pathogens coordinate their virulence factor expression in a cell density-dependent manner. This population-dependent coordination of gene expression in bacteria has been termed "quorum sensing" (QS). N-Acyl homoserine lactones (AHLs) are used by over 70 Gram-negative bacterial species as autoinducers. Inhibition of QS signaling might represent a new target for antimicrobial therapy. Here we report the hapten design, synthesis, generation of monoclonal antibodies (mAbs) against AHLs, and the evaluation of these mAbs for their ability to blunt QS signaling and inhibit virulence factor expression in P. aeruginosa. The mAbs can be envisioned as a tool for future investigations into AHL-based QS, which may aid in gaining new insights into the pathogenesis of P. aeruginosa and may ultimately lead to the development of new strategies to combat bacterial diseases.