Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in \O_n using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of {\L}ojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions $(\mathbb{C}^n,0)\to (\mathbb{C},0)$ for which the {\L}ojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.Comment: 25 pages. Updated with minor change

N-Methylimidazole Promotes The Reaction Of Homophthalic Anhydride With Imines

The addition of N-methylimidazole (NMI) to the reaction of homophthalic anhydride with imines such as pyridine-3-carboxaldehyde-N-trifluoroethylimine (9) reduces the amount of elimination byproduct and improves the yield of the formal cycloadduct, tetrahydroisoquinolonic carboxylate 10. Carboxanilides of such compounds are of interest as potential antimalarial agents. A mechanism that rationalizes the role of NMI is proposed, and a gram-scale procedure for the synthesis and resolution of 10 is also described

Rough Classifiers

this paper a formal definition of a rough classifier is given. We present an e cient algorithm of the rough classifier generation, which can be used for analysis of large information systems thanks to the modification of our earlier method of condition attributes coding. The rough classifiers preserve all positive aspects of the decision algorithms generated in the rough set theory. Roug classi er generatio

Nickel-cobalt separation by solvent extraction method

Separation of cobalt(II), and nickel(II) ions from nitrate solutions using liquid-liqiud extraction process was reported. The measurements were run at 25oC and at fixed ionic strength equal to 0.5 (KNO3,HNO3). Initial concentrations of Co(II) and Ni(II) nitric acid in the aqueous phase were constant (0.01 M and 0.15 M, respectively). Both 1-hexylimidazole (1), and 1-hexyl-2-methylimidazole (2), both in dichloromethane were used as extractants. Their concentrations in organic phase were varied from 0.01 to 0.25 M. Cobalt(II) in an aqueous solution forms both tetrahedral and octahedral complexes. Nickel(II) forms only a six-coordinate complexes. These general differences help to provide the basis for the various separation processes currently used for cobalt-nickel separation. The steric effect for extractant 2 facilitates the extraction of tetrahedral Co(II) complexes. Extraction percent (%E) of cobalt(II) and nickel(II) in the systems studied were calculated. The percentage extraction increases for increasing values of pH of aqueous phase and is the highest for pH = 7.2. In the aqueous phase, of which the pH = 7.2, there remain 75%Ni(II) and 40% Co(II) for extractant 1 and the respective values for extractant 2 are 85% Ni(II) and 20% Co(II). The steric effect increases selectivity coefficients Co(II)/Ni(II). The highest selectivity coefficients for both extractants were obtained at a pH of aqueous phase = 6.2; their values were 5 and 8.9 for extractants 1 and 2, respectively

Support vector machines with example dependent costs

Classical learning algorithms from the fields of artificial neural networks and machine learning, typically, do not take any costs into account or allow only costs depending on the classes of the examples that are used for learning. As an extension of class dependent costs, we consider costs that are example, i.e. feature and class dependent. We present a natural cost-sensitive extension of the support vector machine (SVM) and discuss its relation to the Bayes rule. We also derive an approach for including example dependent costs into an arbitrary cost-insensitive learning algorithm by sampling according to modified probability distributions

Cannabinoid Receptor 1 Gene Polymorphisms and Nonalcoholic Fatty Liver Disease in Women with Polycystic Ovary Syndrome and in Healthy Controls

Context. Polycystic ovary syndrome (PCOS) is frequently associated with nonalcoholic fatty liver disease (NAFLD). The endocannabinoid system may play a crucial role in the pathogenesis of NAFLD. Polymorphism of the cannabinoid receptor 1 gene (CNR1) may be responsible for individual susceptibility to obesity and related conditions. Objective. To determine the role of genetic variants of CNR1 in the etiopathology of NAFLD in women with PCOS. Design and Setting. Our department (a tertiary referral center) conducted a cross-sectional, case-controlled study. Subjects. 173 women with PCOS (aged 20–35) and 125 healthy, age- and weight-matched controls were studied. Methods. Hepatic steatosis was assessed by ultrasound evaluation. Single nucleotide polymorphisms of CNR1 (rs806368, rs12720071, rs1049353, rs806381, rs10485170, rs6454674) were genotyped. Results. Frequency of the G allele of rs806381 (P<0.025) and the GG genotype of rs10485170 (P<0.03) was significantly higher in women with PCOS and NAFLD than in PCOS women without NAFLD. Frequency of the TT genotype of rs6454674 was higher in PCOS women with NAFLD (not significantly, P=0.059). In multivariate stepwise regression, allele G of rs806381 was associated with PCOS + NAFLD phenotype. Conclusion. Our preliminary results suggest the potential role of CNR1 polymorphisms in the etiology of NAFLD, especially in PCOS women