Points entiers et modèles des courbes algébriques

LetC: F(X, Y)=0 be an algebraic curve of genus 1, over a number fieldK. In this work we construct a modelG(Z,W)=0 of the curveC, over a fixed number fieldL with , having the following property: ifx, y are algebraic integers ofK withF(x, y)=0, thenz=Z(x, y), w=W(x, y) are algebraic integers ofL withG(z, w)=0. Also, the total degree and the height of the polynomialG are bounded. As an application of this result, we give a reduction of the problem to determine effectively the integer points on a curve of genus 2, over a number field, to the problem to determine effectively the integer solutions of an equation of degree 4, over a number field. Also we consider a family of curvesF(X, Y)=0, defined over a number fieldK, which are cyclic coverings ofP ¹ and we calculate, using our previous results, an explicit upper bound for the height of the integer points ofF(X, Y)=0 overK.

     

Isolation,purification, and enzymatic activity of cellulase components of the fungus <Emphasis Type="Italic">Aspergillus terreus</Emphasis>

The accumulation dynamics of cellulolytic enzymes in culture media of the basidiomycete fungi Panus tigrinus, Pleurotus ostreatus, Fomes fomentarus, and the micromycete Aspergillus terreus were studied during a long incubation period. It was found that A. terreus was the most active producer of cellulolytic enzymes among the studied fungi. Two protein fractions with cellulase activity were isolated using gel filtration and ion-exchange chromatography. PAAG electrophoresis showed that fraction-I consisted of four components; fraction-II, an electrophoretically homogeneous protein. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 489–491, September–October, 2007.     

Compatibilisation effect of PP-g-MA copolymer on iPP/SiO2 nanocomposites prepared by melt mixing

In the present study, a series of iPP/SiO₂ nanocomposites, containing 1, 2.5, 5, 7.5, 10 and 15 wt% SiO₂ nanoparticles, were prepared by melt mixing in a twin screw co-rotating extruder. Poly(propylene-g-maleic anhydride) copolymer (PP-g-MA) containing 0.6 wt% maleic anhydride content was added to all nanocomposites at three different concentrations, 1, 2.5 and 5 wt%, based on silica content. Mechanical properties such as tensile strength at break and Young’s modulus were found to increase and to be mainly affected by the content of silica nanoparticles as well as by the copolymer content. For the tensile strength at break as well as for yield point, a maximum was observed, corresponding to the samples containing 2.5-5 wt% SiO₂. At higher concentrations, large nanosilica agglomerates are formed that have as a result a decrease in tensile strength. Young’s modulus increases almost linearly on the addition of SiO₂, and takes values up to 60% higher than that of neat iPP. Higher concentrations of PP-g-MA resulted in a further enhancement of mechanical properties due to silica agglomerate reduction. This finding was verified from SEM and TEM micrographs. Evidently the surface silica hydroxyl groups of SiO₂ nanoparticles react with maleic anhydride groups of PP-g-MA and lead to a finer dispersion of individual SiO₂ nanoparticles in the iPP matrix. The enhanced adhesion in the interface of the two materials, as a result of the mentioned reaction, has been studied and proved by using several equations. The increased Vicat point of all nanocomposites, by increasing the PP-g-MA content, can also be mentioned as a positive effect.     

Clays as a host matrix in the synthesis of organic macrocycles

A new approach for the synthesis of amide macrocycles, based on the use of organo-clay derivatives as controlling template, is proposed as an alternative to the rotaxane method. Dications of p-xylylene diamine inserted in the clay interlayer space act as molding pillars around which neutral diamine molecules are erected via hydrogen bonding and pi-pi interactions to form supramolecular arrays. Condensation of diamines in the supramolecular arrays with diacetyl dichlorides yields various tetramide macrocycles in good yields. Shape, aromaticity and dimensions of the reactants are factors affecting the condensation reaction.     

High-performance capillary electrophoretic analysis of hyaluronan and galactosaminoglycan-disaccharides in gastrointestinal carcinomas. Differential disaccharide composition as a possible tool-indicator for malignancies

The glycosaminoglycans (GAGs) have documented implications for the growth and progression of malignant tumors. Gastrointestinal carcinomas (gastric, colon, rectum and pancreatic) are the most frequent malignancies occurring in human. GAGs, isolated from the tissues after digestion with papain, were analyzed by high-performance capillary electrophoresis (HPCE) following treatment with chondroitinase ABC. The composition of GAGs in disaccharides derived from the various gastrointestinal carcinomas was compared with those of normal tissues. We report that human gastrointestinal carcinomas are characterized by increased concentrations of GAGs, which have quite different disaccharide composition which, in turn, is associated with marked increase of non-sulfated (Delta(di)-nonS) and 6-sulfated (Delta(di)-mono6S) Delta-disaccharides. Particularly, a 12-51-fold increase in Delta(di)-nonS and a 3-42-fold increase in Delta(di)-mono6S content characterize these carcinomas, while the 4-sulfated units (Delta(di)-mono4S) showed a lower increase, about 0.5-1.5-fold. Moreover, the quantitation of hyaluronan (HA)-derived Delta-disaccharides (Delta(di)-nonS(HA)) also revealed a marked increase (1-12-fold) in the malignant tissues. On the other hand, the content of the chondroitinase ABC-resistant GAGs showed a low decrease, about 0.2-0.7-fold. The high amounts of hyaluronan (HA) produced by these carcinomas and the ectopic production of chondroitin sulphate (CS) proteoglycans, in which (Delta(di)-nonS) and (Delta(di)-mono6S) predominated, suggest a close relation between the content of these GAGs and the malignant phenotype, the metastatic ability and the survival time.     

A Scalable Bayesian Sampling Method Based on Stochastic Gradient Descent Isotropization

Stochastic gradient sg-based algorithms for Markov chain Monte Carlo sampling (sgmcmc) tackle large-scale Bayesian modeling problems by operating on mini-batches and injecting noise on sgsteps. The sampling properties of these algorithms are determined by user choices, such as the covariance of the injected noise and the learning rate, and by problem-specific factors, such as assumptions on the loss landscape and the covariance of sg noise. However, current sgmcmc algorithms applied to popular complex models such as Deep Nets cannot simultaneously satisfy the assumptions on loss landscapes and on the behavior of the covariance of the sg noise, while operating with the practical requirement of non-vanishing learning rates. In this work we propose a novel practical method, which makes the sg noise isotropic, using a fixed learning rate that we determine analytically. Extensive experimental validations indicate that our proposal is competitive with the state of the art on sgmcmc.     

Nonlinear constitutive force model selection,update and uncertainty quantification for periodically sequential impact applications

Nonlinear Dynamics - Contact–impact events frequently occur between solid contact interfaces in complex dynamic mechanical systems and engineering applications. Impact force models are used...     

Monitoring of Polycyclic Aromatic Hydrocarbon Levels in Mussels (Mytilus galloprovincialis) from Aquaculture Farms in Central Macedonia Region,Greece, Using Gas Chromatography–Tandem Mass Spectrometry Method

A new sensitive and selective gas chromatography tandem mass spectrometry (GC-MS/MS) method was developed for the analysis of 26 polycyclic aromatic hydrocarbons (PAHs), including 16 Environmental Protection Agency (EPA) and 15 + 1 European Union (EU) PAHs, in mussel samples from aquaculture farms in Thermaikos and Strymonian Gulf, Central Macedonia Region, in three sampling periods. Concentrations were found at moderate to low values at all sampling sites, without exceeding maximum levels set by EU. Low molecular weight PAHs were predominant in all samples. Seasonal variation of the concentrations was observed; values were slightly higher in the winter period. Use of diagnostic ratios for potential sources of PAHs showed both petrogenic and pyrolitic origin. In comparison to other related studies of mussels from the Mediterranean Sea, Greek mussels cultivated in the studied gulfs are low in contaminants due to minimal environmental pollution effects. Low concentrations of PAHs are in compliance with the low values of other POPs which were found in the mussels.     

Prediction Helps Analytical Experimental Work for Environmental Purposes

 Analytical work, especially for environmental purposes, involves in the typical case determination of organic compounds in compartments, where their presence is very small. Identification of the appropriate experimental technique, whose range of applicability covers the concentration value involved, requires an estimate of this value. To this purpose, we present in this study a methodology for the prediction of the concentration of organic pollutants in the various environmental compartments (aquatic biota, air, sediment and soil) from the knowledge of the concentration in one of them. In case where the pollutant’s concentration is not available for any of the compartments, the proposed methodology can be used to estimate the maximum expected concentration in each one of them assuming that the water phase is saturated with the pollutant. The latter value can be obtained from a simple correlation presented here. The methodology is based on the correlation of the partition coefficients of pollutants among the various environmental compartments with two important thermodynamic quantities of pollutants: the octanol/water partition coefficient and the Henry’s law coefficient, which can be easily predicted by simple models presented here. Application of the methodology to field experimental data gives very satisfactory results at least for identifying the appropriate experimental technique.