937 resultados para Caputo Fractional Derivatives


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In recent years there has been an upsurge of interest in the study of organic reactions in the solid state. It is now realised that the crystalline matrix provides an extra-ordinary spatial control on the initiation and progress of these reactions. Electronic and dipolar effects which are important in solution are replaced by structural and geometric effects in solids. These 'spatial' or 'topochemical' aspects are important in understanding the mechanistic details of the reaction. In our laboratory, the thermally induced acyl migration in salicylamides from 0- to N- position in the solid state has been under study (Scheme 1). The structures of the acetyl and benzoyl derivatives (Ia,IIa, Ib and IIb) have been reported.

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Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

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To study the structure activity relationship (SAR) on the cytotoxic activity and probe the structural requirement for the potent antitumor activity, a series of novel diazaspiro bicyclo hydantoin derivatives were designed and synthesized. Their structures were confirmed by H-1 NMR, LCMS and IR analyses. The antiproliferative effect of these compounds were determined against human leukemia, K562 (chronic myelogenous leukemia) and CEM (T-cell leukemia) cells using trypan blue and MTT assay, and the SAR associated with the position of N-terminal substituents in diazaspiro bicyclo hydantoin have also been discussed. It has been observed that these compounds displayed strong, moderate and weak cytotoxic activities. Interestingly, compounds having electron withdrawing groups at third and fourth position of the phenyl ring displayed selectively cytotoxic activities to both the cell lines tested with IC50 value lower than 50 mu M. In addition, the cytotoxic activities of the compounds 7(a-o) bearing the substituents at N-3 position of diazaspiro bicyclo hydantoin increases in the order alkene > ester > ether and plays an important role in determining their antitumor activities. The position and number of substituents in benzyl group attached to N-8 of diazaspiro bicyclo hydantoin nucleus interacted selectively with specific targets leading to the difference of biochemical and pharmacological effects.

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The application of the CNDO and PPP-CI methods to N,N-dimethyl dithiocarbamate, O-methyl dithiocarbonate (methyl xanthate) and methyl trithiocarbonate ions for the elucidation of electronic structure and electronic spectra is described. The CNDO/2 calculations have been used to obtain the one centre core integrals of the ionic compounds required in calculating the pi electronic spectra of these molecules using the PPP method. The calculated spectra are in good agreement with the experiment. The atomic charge densities determined for alkyl xanthate, dithiocarbamate and trithiocarbonate ions support the earlier qualitative predictions regarding electronic structure from spectroscopic and other studies.

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The dynamics of reactions with low internal barriers are studied both analytically and numerically for two different models. Exact expressions for the average rate,kI, are obtained by solving the associated first passage time problems. Both the average rate constant, kI, and the numerically calculated long-time rate constant, kL, show a fractional power law dependence on the barrier height for very low barriers. The crossover of the reaction dynamics from low to high barrier is investigated.

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The probable modes of binding of Methyl--alpha (and beta)-D-glucopyranosides and some of their derivatives to concanavalin A have been proposed from theoretical studies. Theory predicts that beta-MeGlcP can bind to ConA in three different modes whereas alpha-MeGlcP can bind only in one mode. beta-MeGlcP in its most favourable mode of binding differs from alpha-MeGlcP in its alignment in the active-site of the lectin where it binds in a flipped or inverted orientation. Methyl substitution at the C-2 atom of the alpha-MeGlcP does not significantly affect the possible orientations of the sugar in the active-site of the lectin. Methyl substitution at C-3 or C-4, however, affects the allowed orientations drastically leading to the poor inhibiting power of Methyl-3-O-methyl-alpha-D-glucopyranoside and the inactivity of Methyl-4-O-methyl-alpha-D-glycopyranoside. These studies suggest that the increased activity of the alpha-MeGlcP over beta-MeGlcP may be due to the possibility of formation of better hydrogen bonds and to hydrophobic interactions rather than to steric factors as suggested by earlier workers. These models explain the available NMR and other binding studies.

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New supramolecular organogels based on all-trans-tri(p-phenylenevinylene) (TPV) systems possessing different terminal groups, e.g., oxime, hydrazone, phenylhydrazone, and semicarbazone have been synthesized. The self-assembly properties of the compounds that gelate in specific organic solvents and the aggregation motifs of these molecules in the organogels were investigated using UV−vis, fluorescence, FT-IR, and 1H NMR spectroscopy, electron microscopy, differential scanning calorimetry (DSC), and rheology. The temperature variable UV−vis and fluorescence spectroscopy in different solvents clearly show the aggregation pattern of the self-assemblies promoted by hydrogen bonding, aromatic π-stacking, and van der Waals interactions among the individual TPV units. Gelation could be controlled by variation in the number of hydrogen-bonding donors and acceptors in the terminal functional groups of this class of gelators. Also wherever gelation is observed, the individual fibers in gels change to other types of networks in their aggregates depending on the number of hydrogen-bonding sites in the terminal functions. Comparison of the thermal stability of the gels obtained from DSC data of different gelators demonstrates higher phase transition temperature and enthalpy for the hydrazone-based gelator. Rheological studies indicate that the presence of more hydrogen-bonding donors in the periphery of the gelator molecules makes the gel more viscoelastic solidlike. However, in the presence of more numbers of hydrogen-bonding donor/acceptors at the periphery of TPVs such as with semicarbazone a precipitation as opposed to gelation was observed. Clearly, the choice of the end functional groups and the number of hydrogen-bonding groups in the TPV backbone holds the key and modulates the effective length of the chromophore, resulting in interesting optical properties.

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Hydrazinium acetate, metavanadate, sulfite, sulphamate and thiocyanate have been prepared by the reaction of corresponding ammonium salts with hydrazine hydrate. The compounds were characterised by chemical analysis and infrared spectra. Thermal behaviour of these hydrazinium derivatives have been investigated using thermogravimetry and differential thermal analysis.

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We report here the synthesis and preliminary evaluation of novel 1-(4-methoxyphenethyl)-1H-benzimidazole-5-carboxylic acid derivatives 6(a–k) and their precursors 5(a–k) as potential chemotherapeutic agents. In each case, the structures of the compounds were determined by FTIR, 1H NMR and mass spectroscopy. Among the synthesized molecules, methyl 1-(4-methoxyphenethyl)-2-(4-fluoro-3-nitrophenyl)-1H-benzimidazole-5-carboxylate (5a) induced maximum cell death in leukemic cells with an IC50 value of 3 μM. Using FACS analysis we show that the compound 5a induces S/G2 cell cycle arrest, which was further supported by the observed down regulation of CDK2, Cyclin B1 and PCNA. The observed downregulation of proapoptotic proteins, upregulation of antiapoptotic proteins, cleavage of PARP and elevated levels of DNA strand breaks indicated the activation of apoptosis by 5a. These results suggest that 5a could be a potent anti-leukemic agent.

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Crystal structures of six isopropylidene nucleoside derivatives are described. The results show that, under external cyclic constraints, the ribose assumes a variety of unusual conformations. In those compounds which possess a base-to-sugar cyclization through the C(4′) atom, the furanose pucker is predominantly C(4′)-endo, O(4′)-exo. The possible relevance of the sulphur geometry in two of the compounds to certain structural aspects of the action of the enzyme thymidylate synthetase is also pointed out.

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The reactions of hexachlorocyclotriphosphazatriene, N3P3Cl6, and its geminal bis-t-butylamino- and diphenyl derivatives, with ethylenediamine and ethanolamine are reported. In each case, both chlorine atoms attached to the same phosphorus atoms are replaced, giving rise to spirocyclic derivatives. A small quantity of a bis spirocyclic derivative, N3P3(NHCH2CH2O)2Cl2, is also obtained; this compound occurs in both cis and trans forms. Attempts to prepare fully substituted tris spirocyclic derivatives have been unsuccessful and only resinous materials were obtained. The 1H and 31P n.m.r. spectra of the products are discussed.

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The isolation and characterization of the initial intermediates formed during the irreversible acid denaturation of enzyme Ribonuclease A are described. The products obtained when RNase A is maintained in 0.5 M HCl at 30° for periods up to 20 h have been analyzed by ion-exchange chromatography on Amberlite XE-64. Four distinct components were found to elute earlier to RNase A; these have been designated RNase Aa2, Aa1c, Aa1b, and Aa1a in order of their elution. With the exception of RNase Aa2, the other components are nearly as active as RNase A. Polyacrylamide gel electrophoresis at near-neutral pH indicated that RNase Aa1a, Aa1b, and Aa1c are monodeamidated derivatives of RNase A; RNase Aa2 contains, in addition, a small amount of a dideamidated component. RNase Aa2, which has 75% enzymic activity as compared to RNase A, consists of dideamidated and higher deamidated derivatives of RNase A. Except for differences in the proteolytic susceptibilities at an elevated temperature or acidic pH, the monodeamidated derivatives were found to have very nearly the same enzymic activity and the compact folded structure as the native enzyme. Fingerprint analyses of the tryptic peptides of monodeamidated derivatives have shown that the deamidations are restricted to an amide cluster in the region 67–74 of the polypeptide chain. The initial acid-catalyzed deamidation occurs in and around the 65–72 disulfide loop giving rise to at least three distinct monodeamidated derivatives of RNase A without an appreciable change in the catalytic activity and conformation of the ribonuclease molecule. Significance of this specific deamidation occurring in highly acidic conditions, and the biological implications of the physiological deamidation reactions of proteins are discussed.

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The structure of the novel product obtained from the oxidation of Abel's ketone (1a) and similar spiroketones (1b–d) with 2, 3-dichloro-5, 6-dicyano-1,4-benzoquinone has been determined on basis of spectral data (i.r., n.m.r., and mass)