On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n

2000 Mathematics Subject Classification: 26A33, 42B20

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Funkcjonalizacja aglikonu Spiramycyny przez zastosowanie regio- i stereoselektywnych reakcji kaskadowych

Wydział Chemii

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

Synthesis and metal complexes of C2 symmetric ligands obtained from (R)-(+)-Betti and dialdehydes for asymmetric induction reactions

The aim of this master’s research thesis was the employment of an enantiopure 1,3-aminoalcohol, the 1-(α-aminobenzyl)-2-naphthol, known as Betti base, for the synthesis of some novel compounds which show a C2 symmetry. Some of these compounds, after derivatization, were used as ligands in association with transition metals to prepare some catalysts for enantioselective catalytic reactions. Some aminoalcohol (Salan-type) derivatives of these compounds were obtained upon reduction and in some cases it was possible to obtain complexes with transition metals such as Mn, Ni, Co and Cu. Furthermore a novel 6-membered analogue bisoxazoline ligand, 2,6-bis((R)-1-Phenyl-1H-naphtho[1,2-e][1,3]oxazin-3-yl)pyridine, was obtained and from it two Cu-complexes were prepared. The metal complexes were employed in some reactions to test the asymmetric induction, which was in some cases up to discrete values.

Valószínűség, esély, relatív súlyok. Opciók és reálopciók (Probability, chance, relative weights)

There is a long debate (going back to Keynes) how to interpret the concept of probability in economics, in business decisions, in finance. Iván Bélyácz suggested that the Black–Scholes– Merton analysis of fi nancial derivatives has a contribution to this risk vs. uncertainty debate. This article tries to interpret this suggestion, from the viewpoint of traded options, real options, Arrow–Debreu model, Heath–Jarrow–Morton model, insurance business. The article suggests making clear distinction and using different naming ● when the frequents approach and the statistics is relevant, ● when we just use consequent relative weights during the no-arbitrage pricing, and these weight are just interpreted as probabilities, ● when we just lack the necessary information, and there is a basic uncertainty in the business decision making process. The paper suggests making a sharp distinction between fi nancial derivatives used for market risk management and credit risk type derivatives (CDO, CDS, etc) in the reregulation process of the fi nancial markets.

Transformações químicas, caracterizações e estudo de modelagem molecular do clerodano bioativo trans-desidrocrotonina

In this work it were developed synthetic and theoretical studies for clerodane-type diterpenes obtained from Croton cajucara Benth which represents one of the most important medicinal plant of the Brazil amazon region. Specifically, the majoritary biocompound 19-nor-clerodane trans-dehydrocrotonin (t-DCTN) isolated from the bark of this Croton, was used as target molecule. Semi-synthetic derivatives were obtained from t-DCTN by using the followed synthetic procedures: 1) catalytic reduction with H2, 2) reduction using NaBH4 and 3) reduction using NaBH4/CeCl3. The semi-synthetic 19-nor-furan-clerodane alcohol-type derivatives were denominated such as t-CTN, tCTN-OL, t-CTN-OL, t-DCTN-OL, t-DCTN-OL, being all of them characterized by NMR. The furan-clerodane alcohol derivatives t-CTN-OL and tCTN-OL were obtained form the semi-synthetic t-CTN, which can be isolated from the bark of C. cajucara. A theoretical protocol (DFT/B3LYP) involving the prevision of geometric and magnetic properties such as bond length and angles, as well as chemical shifts and coupling constants, were developed for the target t-DCTN in which was correlated NMR theoretical data with structural data, with satisfactory correlation with NMR experimental data (coefficients ranging from 0.97 and 0.99) and X-ray diffraction data. This theoretical methodology was also validated for all semi-synthetic derivatives described in this work. In addition, topological data from the Quantum Theory of Atoms in Molecules (QTAIM) showed the presence of H-H and (C)O--H(C) intramolecular stabilized interactions types for t-DCTN e t-CTN, contributing to the understanding of the different reactivity of this clerodanes in the presence of NaBH4.

Modyfikacja aglikonu Josamycyny z wykorzystaniem regioselektywnej substytucji nukleofilowej typu SN1’ i dipolarnej cykloaddycji Huisgena

Wydział Chemii: Zakład Syntezy i Struktury Związków Organicznych

Quinone studies—Istar, open: Evidence for a new type of substitution reaction of phenanthrene-9,10-quinone derivatives

The para orientation by the carbonyl groups in the bromination of phenanthrenequinone derivatives has been explained on the basis of an excited state resulting from thermal excitation of the quinone and/or from a n→π* transition of the nonbonding electrons of the oxygen atoms. A general preparative method for the syntheses of 3-bromophenanthrenequinone derivatives has been developed. The structure of 2-nitro-6-bromophenanthrenequinone has been established by degradation. Synthesis of 2-nitro-6-bromofluorenone is described. Direct bromination of phenanthrenequinone to 2-bromo and 2,7-dibromo derivatives has also been described.

Three centered hydrogen bonds of the type C=O...H(N)...X-C in diphenyloxamide derivatives involving halogens and a rotating CF3 group: NMR, QTAIM, NCI and NBO studies

The existence of three centered C=O...H(N)...X-C hydrogen bonds (H-bonds) involving organic fluorine and other halogens in diphenyloxamide derivatives has been explored by NMR spectroscopy and quantum theoretical studies. The three centered H-bond with the participation of a rotating CF3 group and the F...H-N intramolecular hydrogen bonds, a rare observation of its kind in organofluorine compounds, has been detected. It is also unambiguously established by a number of one and two dimensional NMR experiments, such as temperature perturbation, solvent titration, N-15-H-1 HSQC, and F-19-H-1 HOESY, and is also confirmed by theoretical calculations, such as quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO) and non-covalent interaction (NCI).

Synthesis and Anti-Human Immunodeficiency Virus Type 1 Activity of (E)-N-Phenylstyryl-N-alkylacetamide Derivatives

A series of (E)-N-phenylstyryl-N-alkylacetamides, 5, were synthesized by direct reduction-acetylation of beta-arylnitroolefins, followed by N-alkylation. The title compounds were characterized by H-1-NMR, EIMS and IR analysis. All the synthesized compound

Solutions de rang k et invariants de Riemann pour les systèmes de type hydrodynamique multidimensionnels

Dans ce travail, nous adaptons la méthode des symétries conditionnelles afin de construire des solutions exprimées en termes des invariants de Riemann. Dans ce contexte, nous considérons des systèmes non elliptiques quasilinéaires homogènes (de type hydrodynamique) du premier ordre d'équations aux dérivées partielles multidimensionnelles. Nous décrivons en détail les conditions nécessaires et suffisantes pour garantir l'existence locale de ce type de solution. Nous étudions les relations entre la structure des éléments intégraux et la possibilité de construire certaines classes de solutions de rang k. Ces classes de solutions incluent les superpositions non linéaires d'ondes de Riemann ainsi que les solutions multisolitoniques. Nous généralisons cette méthode aux systèmes non homogènes quasilinéaires et non elliptiques du premier ordre. Ces méthodes sont appliquées aux équations de la dynamique des fluides en (3+1) dimensions modélisant le flot d'un fluide isentropique. De nouvelles classes de solutions de rang 2 et 3 sont construites et elles incluent des solutions double- et triple-solitoniques. De nouveaux phénomènes non linéaires et linéaires sont établis pour la superposition des ondes de Riemann. Finalement, nous discutons de certains aspects concernant la construction de solutions de rang 2 pour l'équation de Kadomtsev-Petviashvili sans dispersion.

Persistence of a wild type Escherichia coli and its multiple antibiotic-resistant (MAR) derivatives in the abattoir and on chilled pig carcasses

The aim of this study was to evaluate the ability of an Escherichia coli with the multiple antibiotic resistance (MAR) phenotype to withstand the stresses of slaughter compared to an isogenic progenitor strain. A wild type E. coli isolate (345-2RifC) of porcine origin was used to derive 3 isogenic MAR mutants. Escherichia coli 345-2RifC and its MAR derivatives were inoculated into separate groups of pigs. Once colonisation was established, the pigs were slaughtered and persistence of the E. coli strains in the abattoir environment and on the pig carcasses was monitored and compared. No significant difference (P>0.05) was detected between the shedding of the different E. coli strains from the live pigs. Both the parent strain and its MAR derivatives persisted in the abattoir environment, however the parent strain was recovered from 6 of the 13 locations sampled while the MAR derivatives were recovered from 11 of 13 and the number of MAR E. coil recovered was 10-fold higher than the parent strain at half of the locations. The parent strain was not recovered from any of the 6 chilled carcasses whereas the MAR derivatives were recovered from 3 out of 5 (P<0.001). This study demonstrates that the expression of MAR in 345-2RifC increased its ability to survive the stresses of the slaughter and chilling processes. Therefore in E. coli, MAR can give a selective advantage, compared to non-MAR strains, for persistence on chilled carcasses thereby facilitating transit of these strains through the food chain. (C) 2010 Elsevier B.V. All rights reserved.