Zero sets of bivariate Hermite polynomials

We establish various properties for the zero sets of three families of bivariate Hermite polynomials. Special emphasis is given to those bivariate orthogonal polynomials introduced by Hermite by means of a Rodrigues type formula related to a general positive definite quadratic form. For this family we prove that the zero set of the polynomial of total degree n+m$n+m$ consists of exactly n+m$n+m$ disjoint branches and possesses n+m$n+m$ asymptotes. A natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property. The results show that the properties of the zero sets, considered as affine algebraic curves in R²${\mathbb{R}}^2$, are completely different for the three families analyzed.     

Antitumour tiazofurin analogues embedded with an amide moiety at the C-2′ position

Synthesis of four new tiazofurin analogues has been accomplished starting from d-glucose. The key step of the synthesis was the three-step cascade that enabled an efficient hydrogen sulfide mediated one-pot conversion of 2-azido-3-O-acyl-ribofuranosyl cyanides to the corresponding 2-alkylamido ribofuranosyl thiocarboxamides. The resulting key intermediates were first converted to protected tiazofurin derivatives by cyclocondensation with ethyl bromopyruvate, and finally to target C-nucleosides by treatment with ammonia in methanol. In vitro cytotoxicities of tiazofurin analogues against a number of human tumour cell lines were recorded and compared with those observed for the parent molecule (tiazofurin), as well as the commercial antitumour agent doxorubicin (DOX). Analogues 2b-d have shown a potent in vitro cytotoxic activity against human myelogenous leukaemia K562. Among solid tumour cell lines, HT29 was sensitive only to 2d, while HeLa cells were sensitive to 2a, 2b and 2d. Only analogue 2a was highly cytotoxic against MCF-7 cells. No tiazofurin analogue exhibits any significant cytotoxicity towards normal foetal lung MRC-5 cells. Downregulation of Bcl-2, activation of caspase-3 and presence of cleavage product of PARP suggest that the cytotoxic effects of tiazofurin analogues 2a-d in K562 might be mediated by apoptosis in a caspase-dependent way. On the contrary, tiazofurin did not induce apoptosis of K562 cells, which suggests a different mechanism of action, most probably through the inhibition of IMPDH. Flow cytometry and Western blot analysis data agreed well with the results of MTT assay, and enabled identification of analogue 2c as the most promising antitumour agent that preferentially target cancer cells over normal cells and thus represents a new lead for further optimization.     

Ionisationskonstanten von 5- und 6-substituierten Benzothiazolonen

In the present work the ionization constants of benzothiazolone and its 5- and 6-substituted derivatives in 20 volume % ethanol are determined spectrophotometrically. The influence of the polar effects of the substituents on the ionization of the benzothiazolone is due mainly to the induction effect, confirmed by the correlation between the experimental pK _a values and theTaft ⁰-constants of the substituents.

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Neural networks convergence using physicochemical data

An investigation of the neural network convergence and prediction based on three optimization algorithms, namely, Levenberg-Marquardt, conjugate gradient, and delta rule, is described. Several simulated neural networks built using the above three algorithms indicated that the Levenberg-Marquardt optimizer implemented as a back-propagation neural network converged faster than the other two algorithms and provides in most of the cases better prediction. These conclusions are based on eight physicochemical data sets, each with a significant number of compounds comparable to that usually used in the QSAR/QSPR modeling. The superiority of the Levenberg-Marquardt algorithm is revealed in terms of functional dependence of the change of the neural network weights with respect to the gradient of the error propagation as well as distribution of the weight values. The prediction of the models is assessed by the error of the validation sets not used in the training process.     

Higher Order Turán Inequalities

The celebrated Turán inequalities , where denotes the Legendre polynomial of degree , are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities , which hold for the Maclaurin coefficients of the real entire function in the Laguerre-Pólya class, .

     

In vitro evaluation of cytotoxic and mutagenic activity of avarol

The cytotoxicity of avarol, a main secondary metabolite of the Mediterranean sponge Dysidea avara, was in vitro screened by MTT assay against four human tumour cell lines. The colon HT-29 tumour cells practically showed to be the only sensitive ones towards this organic compound. No toxicity was found against the fetal lung fibroblast MRC-5 cells at the concentrations tested. In comparison with doxorubicin, used as a positive control, avarol actually exhibited at least 588-fold less toxicity towards normal MRC-5 cells. Finally, comet assay indicated that DNA fragmentation was almost fivefold higher upon the treatment with doxorubicin, compared to avarol. The obtained results have actually confirmed that avarol scaffold may contribute to development of new cytostatics inspired by nature.     

Sesquiterpene lactones-based classification of the family asteraceae using neural networks and k-nearest neighbors

In a recent publication we described the application of an unsupervised learning method using self-organizing maps to the separation of three tribes and seven subtribes of the plant family Asteraceae based on a set of sesquiterpene lactones (STLs) isolated from individual species. In the present work, two different structure representations--atom counts (2D) and radial distribution function (RDF) (3D)--and two supervised classification methods--counterpropagation neural networks and k-nearest neighbors (k-NN)--were used to predict the tribe in which a given STL occurs. The data set was extended from 144 to 921 STLs, and the Asteraceae tribes were augmented from three to seven. The k-NN classifier with k = 1 showed the best performance, while the RDF code outperformed the atom counts. The quality of the obtained model was assessed with two test sets, which exemplified two possible applications: (1) finding a plant source for a desired compound and (2) based on a plant species chemical profile (STLs): (a) study the relationship between the current taxonomic classification and plant's chemistry and (b) assign a species to a tribe by majority vote. In addition, the problem of defining the applicability domain of the models was assessed by means of two different approaches-principal component analysis combined with Hotelling T2 statistic and an a posteriori probability-based rule.     

On the spray-drying deposition of TiO2 photocatalytic films

The photocatalytic activity of TiO₂ films deposited on different substrates by the spray-drying method using suspensions of commercially available TiO₂ (Degussa P25 or Tronox) as starting material was studied. The influence of the type of the initial TiO₂, preparation conditions (temperature of the substrate during the film deposition, temperature of the post-deposition annealing), substrate material (glass, fused silica, stainless steel and graphite), the presence of additives in the spraying suspension (polyethylene glycol, ethylene glycol and acetylacetone) and its sonication before spraying on the morphology, size of crystallites and phase composition (rutile/anatase ratio) was studied. Optimal conditions for spray deposition of the films are suggested.     

Monotonicity of zeros of Laguerre polynomials

Denote by x_nk(α), k=1,…,n, the zeros of the Laguerre polynomial . We establish monotonicity with respect to the parameter α of certain functions involving x_nk(α). As a consequence we obtain sharp upper bounds for the largest zero of .