Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

Formal and convergent solutions of singular partial differential equations

We consider the problem of the existence of convergent series solutions for partial differential operators of the form . We give first conditions for P such that the linear equation Pu=f has an analytic solution, then we solve nonlinear equations of the form Pu=F(x,u). For applications we treat also cases with parameters and give a proof of a theorem of S. Kaplan [5]. In the last section we consider a case where small denominators occur.     

Ōtsukische Räume mit Einem Zweifach Rekurrenten Metrischen Grundtensor

In this note necessary and sufficient conditions are determined for Weyl—tsukispaces to have a birecurrent metric, i.e., _{m k} g _ij = _km g _ij . It is proved that in this space the metric tensor is an eigen-tensor. The special caseP _j ⁱ = (x) _j ⁱ is examined and we prove that in this case the recurrent metric tensor is likewise birecurrent.

     

On the generation of novel anticancer drugs by recombinant DNA technology: the use of combinatorial biosynthesis to produce novel drugs

Chemotherapeutic drugs for cancer treatment have been traditionally originated by the isolation of natural products from different environmental niches, by chemical synthesis or by a combination of both approaches thus generating semisynthetic drugs. In the last years, a number of gene clusters from several antitumor biosynthetic pathways, mainly produced by actinomycetes and belonging to the polyketides family, are being characterized. Genetic manipulation of these antitumor biosynthetic pathways will offer in the near future an alternative for the generation of novel antitumor derivatives and thus complementing current methods for obtaining novel anticancer drugs. Novel antitumor derivatives have been produced by targetted gene disruption and heterologous expression of single (or a few) gene(s) in another hosts or by combining genes from different, but structurally related, biosynthetic pathways ("combinatorial biosynthesis"). These strategies take advantage from the "relaxed substrate specificity" that characterize secondary metabolism enzymes.     

Thermal investigation of PEG 4000 — oxazepam binary system

A thermal study using DSC and Hot Stage Microscopy (HSM) was carried out to investigate the interaction in solid state of the binary system PEG 4000 — oxazepam, and to establish their phase diagram. The eutectic composition, which melting occurs at lower temperature as compared with the pure components, has been determined. The results obtained by DSC and HSM have indicated that PEG 4000 — oxazepam mixtures displays no obvious incompatibilities, and that the system shows a typical eutectic behaviour. However because of the closeness of the melting of PEG 4000 to the eutectic temperature, it was difficult to determine precisely the eutectic composition and temperature on the basis of DSC measurements alone. The use of heats of fusion corresponding to physical mixtures allowed an estimation of the eutectic composition at 6% w/w oxazepam. Additional information of temperature (57.6C) and composition (5–10% w/w oxazepam) of the eutectic was obtained by HSM using the contact method. This low melting temperature in this range of compositions offers advantages in terms of drug stability and easy manufacture.     

Evaluation of the redox properties and anti/pro-oxidant effects of selected flavonoids by means of a DNA-based electrochemical biosensor

Quercetin and rutin as well as catechin and epigallocatechin gallate were investigated, as widely distributed representatives of flavonols and flavanols, respectively, regarding their anti/pro-oxidant properties. The flavonoids are irreversibly oxidized at a dsDNA-modified screen-printed electrode within 0.368 to 0.449 V vs. SHE without binding to DNA. Using the DNA biosensor the detection scheme of a DNA prevention/degradation exploits the [Co(phen)(3)](3+) complex as an electrochemical DNA marker. Antioxidant activity of flavonoids was tested in a model cleavage mixture composed of 5 x 10(-7) mol L(-1) [Cu(phen)(2)](2+) as the catalyst, 1 x 10(-3) mol L(-1) ascorbic acid as the chemical reductant and atmospheric oxygen as the natural oxidant where reactive oxygen radicals are generated. The antioxidant activity increases with the concentration of flavonoids reaching a maximum where pro-oxidative behaviour becomes of importance. The pro-oxidant potency of flavonoids depends on the presence of atmospheric oxygen and follows the order quercetin>rutin>epigallocatechin gallate>catechin.     

Gas chromatographic analysis of flunixin in equine urine after extractive methylation

A quantitative method for the analysis of flunixin, 2-(2-methyl-3-trifluoromethylanilino) nicotinic acid, in equine urine by gas chromatography with nitrogen-phosphorus detection has been developed. Flunixin and the internal standard, mefenamic acid, N-(2,3-xylyl) anthranilic acid, were analysed after extractive methylation of the carboxylic acid group using methyl iodide. The extraction and alkylation conditions of flunixin and mefenamic acid have been studied. The detection limit of the method was 0.25 mumol/l flunixin in urine (74 ng/ml). Flunixin was found to be conjugated to 96.5% in equine urine, and the conjugate was spontaneously hydrolysed to free flunixin. This approach can also be used to confirm the presence of flunixin or mefenamic acid in horse urine in the doping control of racehorses.     

Direct HPLC resolution of beta-aminoalcohol (tazifylline,ranolazine, sotalol) enantiomers

Summary A routine chiral analysis has been developed to control the optical purity of chiral drugs and to monitor their asymmetric synthesis. The recent advent of new chiral stationary phases for HPLC enabled us to achieve the direct resolution of chiral drugs without any derivatization. The factors affecting chiral resolution on a new alpha₁-acid glycoprotein column (EnantioPac, LKB) were assessed with three beta-aminoalcohols.