957 resultados para Riemann-Liouville and Caputo Fractional Derivatives
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L’application des métaux de transition à la fonctionnalisation directe a ouvert la voie à une nouvelle classe de réactions pour la formation de liens carbone-carbone. De par l'omniprésence des liaisons C–H, l’introduction de nouvelles fonctionnalités chimiques par voie directe et pré-activation minimale s’impose comme une stratégie de synthèse très attrayante. Ainsi, il est envisageable de préparer de manière rapide et efficace des supports complexes menant à des molécules complexes, qui pourraient être utiles dans divers domaines de la chimie. L'objectif principal de la présente thèse vise la fonctionnalisation directe des arènes hétérocycliques et non hétérocycliques et, plus précisément, les techniques d’arylation. Dans un premier temps, nous allons aborder le thème de l’arylation directe tout en mettant l’accent sur les pyridines (Chapitre 1). Ces molécules sont à la base d'une multitude de composés biologiquement actifs et jouent un rôle important dans le domaine des sciences des matériaux, de l’agrochimie et de la synthèse des produits naturels. Dans un deuxième temps, nous discuterons de nos travaux sur l’arylation directe catalysé par un complex de palladium sur des ylures de N-iminopyridinium en soulignant la dérivatisation du sel de pyridinium après une phénylation sp2 (Chapitre 2). L’étude de ce procédé nous a permis de mettre en lumière plusieurs découvertes importantes, que nous expliquerons en détails une à une : l’arylation benzylique directe lorsque des ylures N-iminopyridinium substituées avec un groupement alkyl à la position 2 sont utilisés comme partenaires dans la réaction; les allylations Tsuji-Trost catalysée par un complex de palladium; et l’alkylation directe et sans métal via une catalyse par transfert de phase. Plusieurs défis restent à relever pour le développement de procédés directs utilisant des métaux de transition peu coûteux, d’autant plus que la synthèse par transformation directe des pyridines 2-alcényles, lesquelles sont pertinentes sur le plan pharmacologique, n’a pas encore été rapportée à ce jour. Avec cette problématique en tête, nous avons réussi à mettre au point une alcénylation directe catalysé par un complex de cuivre sur des ylures de N-iminopyridinium. Nous discuterons également d’une nouvelle méthode pour la préparation des iodures de vinyle utilisés dans les couplages. Ces réactions sont non seulement remarquablement chimiosélectives, mais sont aussi applicables à plusieurs substrats (Chapitre 3). En optimisant ce procédé direct, nous avons découvert une façon unique de synthétiser les pyrazolo[1,5-a]pyridines 2-substituées (Chapitre 4). Le mécanisme global met en jeu une séquence tandem de fonctionnalisation-cyclisation directe et un procédé direct en cascade, qui n’avais jamais été rapporté. Cela simplifie ansi la synthèse autrement compliquée de ces substrats en y apportant une solution à un problème de longue date. Dans les deux derniers chapitres, nous examinerons en détail les techniques d’arylation directe qui n'impliquent pas les partenaires de couplage hétérocycliques. Entre autres, au Chapitre 5, nous soulignerons notre découverte d’un umpolung dirigé et catalysé par un complexe de palladium du benzène et de quelques autres dérivés arènes. Il s’agit là du premier cas de fonctionnalisation directe dans laquelle le groupe directeur se trouve sur le partenaire halogène et il s’ajoute à la courte liste d’exemples connus dans la littérature rapportant une arylation directe du benzène. Finalement, au Chapitre 6, nous passerons en revue une nouvelle arylation directe catalysée au fer, qui se veut un procédé peu coûteux, durable et présentant une économie d’atomes. Nous discutons des substrats possibles ainsi des études mécanistiques réalisés.
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In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.
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Exam questions and solutions in PDF
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Exercises and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files
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Exam questions and solutions in LaTex
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Exam questions and solutions in PDF
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Exam questions and solutions in LaTex
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Exercises and solutions in LaTex
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In the present PhD thesis we studied the solid-phase peptide synthesis of antimicrobial peptides derived from the lead peptides BP100 and BPC194. First, peptides derived from BP100 containing D-amino acids at different positions of the sequences were prepared. Moreover, peptidotriazoles derived from BP100 were also synthesized containing the triazole ring at the side-chain of different amino acids. Then, we proceeded to perform studies for the synthesis of multivalent peptides derived from BPC194. To achieve this objective, the synthesis of cyclic peptides containig a triazole ring at amino acids side-chain with different elongations was carried out. Finally, we prepared various carbopeptides containing 2 and 4 units of BP100 and/or its derivatives. The evaluation of the biological activity allowed the identification of active sequences against the economically important phytopathogenic bacteria and fungi and not toxic against eukaryotic cells.
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This paper contains an outline of study for hearing impaired children to learn language through the study of Latin and Greek roots, derivatives and prefixes.
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Four European Pulicaria species, P. odora, P. paludosa, P. sicula and P. vulgare, were analysed for their surface and vacuolar constituents for comparison with previous data obtained for P. dysenterica. Each species had a distinct flavonoid pattern with notable differences between leaf and inflorescence. 6-Hydroxyflavonols were the major lipophilic components in all of the species and tissues except in the leaves of P. paludosa and P. vulgare, where scutellarein 6-methyl ether was the main constituent. In the leaves of P. sicula a more unusual flavone, 6-hydroxyluteolin 5,6,7,3′,4′-pentamethyl ether, was a major component. Pulicaria odora was distinguished by the presence of a series of methylated 6-hydroxykaempferol derivatives including a 3,5,6,7,4′-pentamethyl ether. Quercetagetin hexamethyl ether occurred in both tissues of P. sicula together with the 3,7,3,4′-tetra methyl ether and other quercetagetin derivatives, which were 5-methylated. Quercetagetin 3,7,3′-methyl ether was present in all species except P. odora. Flavonol glucuronides were characteristic vacuolar constituents of all the taxa studied. Two rare glycosides, patuletin and 6-hydroxykaempferol 6-methyl ether 7-glucuronides were identified in the inflorescence of P. odora. Pulicaria vulgaris, a rare plant of southern England, had the vacuolar flavonoid profile most similar to the other more abundant British plant, P. dysenterica.
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The kinetics of the photodimerisation reactions of the 2- and 4-β-halogeno-derivatives of trans-cinnamic acid (where the halogen is fluorine, chlorine or bromine) have been investigated by infrared microspectroscopy. It is found that none of the reactions proceed to 100% yield. This is in line with a reaction mechanism developed by Wernick and his co-workers that postulates the formation of isolated monomers within the solid, which cannot react. β-4-Bromo and β-4-chloro-trans-cinnamic acids show approximately first order kinetics, although in both cases the reaction accelerates somewhat as it proceeds. First order kinetics is explained in terms of a reaction between one excited- and one ground-state monomer molecule, while the acceleration of the reaction implies that it is promoted as defects are formed within the crystal. By contrast β-2-chloro-trans-cinnamic acid shows a strongly accelerating reaction which models closely to the contracting cube equation. β-2-Fluoro- and β-4-fluoro-trans-cinnamic acids show a close match to first order kinetics. The 4-fluoro-derivative, however, shows a reaction that proceeds via a structural intermediate. The difference in behaviour between the 2-fluoro- and 4-fluoro-derivative may be due to different C–HF hydrogen bonds observed within these single-crystalline starting materials.
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The concentration of hydroxytyrosol (3,4-DHPEA) and its secoiridoid derivatives (3,4-DHPEA-EDA and 3,4-DHPEA-EA) in virgin olive oil decreased rapidly when the oil was repeatedly used for preparing french fries in deep-fat frying operations. At the end of the first frying process (10 min at 180 degreesC), the concentration of the dihydroxyphenol components was reduced to 50-60% of the original value, and after six frying operations only about 10% of the initial components remained. However, tyrosol (p-HPEA) and its derivatives (p-HPEA-EDA and p-HPEA-EA) in the oil were much more stable during 12 frying operations. The reduction in their original concentration was much smaller than that for hydroxytyrosol and its derivatives and showed a roughly linear relationship with the number of frying operations. The antioxidant activity of the phenolic extract measured using the DPPH test rapidly diminished during the first six frying processes, from a total antioxidant activity higher than 740,mumol of Trolox/kg down to less than 250 mumol/kg. On the other hand, the concentration of polar compounds, oxidized triacylglycerol monomers (oxTGs), dimeric TGs, and polymerized TGs rapidly increased from the sixth frying operation onward, when the antioxidant activity of the phenolic extract was very low, and as a consequence the oil was much more susceptible to oxidation. The loss of antioxidant activity in the phenolic fraction due to deep-fat frying was confirmed by the storage oil and oil-in-water emulsions containing added extracts from olive oil used for 12 frying operations.
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In this work libraries of morpholines and oxazepanes have been prepared via the reductive amination reaction between dialdehydes, derived from carbohydrates, and a range of amines. In this way, functionalised morpholines and oxazepanes have been prepared that include N-alkylated derivatives, disaccharide analogues, and ester containing derivatives. The abilities of these functionalised morpholines and oxazepanes to inhibit a broad panel of glycosidase enzymes, that are associated with a range of diseases, have been probed and in this way new inhibitors of a range of glycosidases, but particularly β-d-galactosidase derived from Bovine kidney, have been discovered. N-Alkyl morpholines demonstrated the best inhibition profiles for this enzyme and derivatives (15a)–(15d) acted as non-competitive inhibitors with IC50 values of 55.1–88.6 μM. Within this study, some preliminary structure–activity relationships are proposed, and it is demonstrated that N-substituted morpholines display better inhibitory profiles for the enzymes analysed than any of the N-substituted oxazepanes.
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Naphthalene and anthracene transition metalates are potent reagents, but their electronic structures have remained poorly explored. A study of four Cp*-substituted iron complexes (Cp* = pentamethylcyclopentadienyl) now gives rare insight into the bonding features of such species. The highly oxygen- and water-sensitive compounds [K(18-crown- 6){Cp*Fe(η4-C10H8)}] (K1), [K(18-crown-6){Cp*Fe(η4-C14H10)}] (K2), [Cp*Fe(η4-C10H8)] (1), and [Cp*Fe(η4-C14H10)] (2) were synthesized and characterized by NMR, UV−vis, and 57Fe Mössbauer spectroscopy. The paramagnetic complexes 1 and 2 were additionally characterized by electron paramagnetic resonance (EPR) spectroscopy and magnetic susceptibility measurements. The molecular structures of complexes K1, K2, and 2 were determined by single-crystal X-ray crystallography. Cyclic voltammetry of 1 and 2 and spectroelectrochemical experiments revealed the redox properties of these complexes, which are reversibly reduced to the monoanions [Cp*Fe(η4-C10H8)]− (1−) and [Cp*Fe(η4-C14H10)]− (2−) and reversibly oxidized to the cations [Cp*Fe(η6-C10H8)]+ (1+) and [Cp*Fe(η6-C14H10)]+ (2+). Reduced orbital charges and spin densities of the naphthalene complexes 1−/0/+ and the anthracene derivatives 2−/0/+ were obtained by density functional theory (DFT) methods. Analysis of these data suggests that the electronic structures of the anions 1− and 2− are best represented by low-spin FeII ions coordinated by anionic Cp* and dianionic naphthalene and anthracene ligands. The electronic structures of the neutral complexes 1 and 2 may be described by a superposition of two resonance configurations which, on the one hand, involve a low-spin FeI ion coordinated by the neutral naphthalene or anthracene ligand L, and, on the other hand, a low-spin FeII ion coordinated to a ligand radical L•−. Our study thus reveals the redox noninnocent character of the naphthalene and anthracene ligands, which effectively stabilize the iron atoms in a low formal, but significantly higher spectroscopic oxidation state.