966 resultados para Caputo Fractional Derivatives


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Even though cellulose is the most abundant polymer on Earth, its utilisation has some limitations regarding its efficient use in the production of bio-based materials. It is quite clear from statistics that only a relatively small fraction of cellulose is used for the production of commodity materials and chemicals. This fact was the driving force in our research into understanding, designing, synthesising and finding new alternative applications for this well-known but underused biomaterial. This thesis focuses on the developing advanced materials and products from cellulose by using novel approaches. The aim of this study was to investigate and explore the versatility of cellulose as a starting material for the synthesis of cellulose-based materials, to introduce new synthetic methods for cellulose modification, and to widen the already existing synthetic approaches. Due to the insolubility of cellulose in organic solvents and in water, ionic liquids were applied extensively as the reaction media in the modification reactions. Cellulose derivatives were designed and fine-tuned to obtain desired properties. This was done by altering the inherent hydrogen bond network by introducing different substituents. These substituents either prevented spontaneous formation of hydrogen bonding completely or created new interactions between the cellulose chains. This enabled spontaneous self-assembly leading to supramolecular structures. It was also demonstrated that the material properties of cellulose can be modified even those molecules with a low degree of substitution when highly hydrophobic films and aerogels were prepared from fatty acid derivatives of nanocellulose. Development towards advanced cellulose-based materials was demostrated by synthesising chlorophyllcellulose derivatives that showed potential in photocurrent generation systems. In addition, liquid crystalline cellulose derivatives prepared in this study, showed to function as UV-absorbers in paper.

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The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

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The synthesis of 4,4,N,N-tetramethyl-NN-dinitroso-2,2-methylenedianiline (1) by the route p-MeC6H4NH2+ HCHO + OH–(p-MeC6H4NMe)2CH2(7b); (7b)+ acid at 70 °C 4,N-dimethyl-6-(N-methyl-p-toluidinomethyl)aniline (4b); (4b)+ acid at 130 °C 4,4,NN-tetramethyl-2,2-methylenedianiline (3b); (3b)+ HNO2(1), is described. Aspects of the 1H n.m.r. spectra of the above and related compounds are discussed. A crystal-structure analysis of compound (1) shows one of the N-nitroso-groups to be disordered with the endo-form being in preponderance (4 : 1) over the exo-form. The other N-nitroso-group is exclusively exo in the solid state. There is little or no resonance between the benzene ring and the nitroso-group attached to the ring, the two groups being almost perpendicular to each other. In one of the N-nitroso-groups, the nitrogen atom deviates significantly from the plane of the benzene ring to which it is attached. Both amide nitrogen atoms show some pyramidal character.

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α-d-Mannopyranosyl units were attached to an aromatic scaffold through disulfide linkages to obtain mono- to trivalent glycosylated ligands for lectin binding studies. Isothermal titration calorimetric (ITC) measurements indicated that binding affinities of these derivatives to Concanavalin A (Con A) were comparable to or slightly higher than that of methyl α-d-mannopyranoside (Ka values in the range of 104 M−1). The stoichiometries of the lectin-ligand complexes were in agreement with the formal valencies (1–3) of the respective ligands indicating cross-linking in interactions with the di- and trivalent derivatives. Multivalency effects could not, however, be observed with the latter. These ligands were shown to bind to the carbohydrate binding site of Con A using saturation transfer difference (STD) NMR competition experiments.

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Oxidation of spiroketones 3a–f with DDQ in dry benzene gave tropone derivatives 4a–f and DDHQ esters 5a–f (cis -cis isomer 6a–f, (cis -cis isomer 7a–f). While the aryl substituted spirokeone 17a gave a 2:1 mixture of 19a and the corresponding trans -trans isomer, the aryl substituted spiroketones 17b–d gave exclusively trans-trans isomers 19b–d. Heating acid chloride of acid 9c with DDHQ resulted in compounds 4a and 7a, thus confirming the structures assigned. Mechanism of formation of these compounds has been rationalised. A detailed study of 2D 1H-1H COSY, 1H-13C COSY, HMBC and 2D NOESY of compound 7d led to complete assignment of 1H and 13C NMR signals and its solution conformation.

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Design and synthesis of a novel 3-hydroxy-cyclobut-3-ene-1,2-dione derivatives are reported and their in vitro thyroid hormone receptor selectivity has been evaluated in the thyroid luciferase receptor assay. The 3-[3,5-dichloro-4-(4-hydroxy-3-isopropylphenoxy)-phenylamino]-4-hydroxy-cyclobut-3-ene-1,2-dione 21 has shown selectivity towards thyroid hormone receptor β.

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Simple and convenient methods for introducing deuterium label at C-3 and C-6 position of N-acetyl-D-galactosamine and D-galactose, respectively, are described. For the synthesis of 2-acetamido-2-deoxy-D-3-[2H] galactopyranose, benzyl 2-acetamido-2-deoxy-4,6-O-benzylidene-agr-D-galactopyranoside was oxidized with dimethyl sulfoxide- acetic anhydride and the product was reduced with sodium borodeuteride to introduce the deuterium at C-3. After benzylidene reduction, the mixture was subjected to hydrogenolysis and purified by column chromatography. 1,2:3,4-di-O-isopropylidene-agr-D-galactopyranoside was oxidized followed by reduction with sodium borodeuteride and deprotection to yield D-6-[2H] galactose.

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The present work deals with the anticancer effect of benzimidazole derivatives associated with the pyridine framework. By varying the functional group at N-terminal of the benzimidazole by different L-amino acids, several 2-(4-(2,2,2-trifluoroethoxy)-3-methylpyridin-2-ylthio)-1H-benzo[d]imid azole derivatives 9(a-j) were synthesized. Their chemical structures were confirmed by H-1 NMR, IR and mass spectroscopic techniques. The synthesized compounds were examined for their antiproliferative effects against human leukemia cell lines, K562 and CEM. The preliminary results showed most of the derivatives had moderate antitumor activity. Compound 9j containing cysteine residue exhibited good inhibition compared to other amino acid resides. In addition DNA fragmentation results suggest that 9j is more cytotoxic and able to induce apoptosis.

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The 270 MHz 1H n.m.r. spectrum of benzyloxycarbonyl-Pro-N-methylamide in CDCl3 is exchange broadened at 293° K. Spectral lines due to two species are frozen out at 253° K and a dynamically averaged spectrum is obtained at 323° K. A selective broadening of the Cβ and Cγ resonances in the 13C n.m.r. spectrum is observed at 253° K, with a splitting of the Cβ and Cγ resonances into a pair of lines of unequal intensity. A similar broadening of Cβ and Cγ peaks is also detected in pivaloyl-Pro-N-methylamide where cis-trans interconversion about the imide bond is precluded by the bulky t-butyl group. The rate process is thus attributed to rotation about the Cα-CO bond (ψ) and a barrier (ΔG#) of 14kcal mol-1 is estimated. 13C n.m.r. data for pivaloyl-Pro-N-methylamide in a number of solvents is presented and the differences in the Cβ and Cγ chemical shifts are interpreted in terms of rotational isomerism about the Cα-CO bond.

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Two new donor-acceptor type liquid crystalline semiconductors based on benzothiazole have been synthesized. Their structural, photophysical and electronic properties were investigated using X-ray diffraction, atomic force microscopy, cyclic voltammetry, UV-Vis, photoluminescence, and Raman spectroscopy. The liquid crystalline behaviour of the molecules was thoroughly examined by differential scanning calorimetry (DSC) and optical polarizing microscope. The DSC and thermogravimetric analysis (TGA) show that these materials posses excellent thermal stability and have decomposition temperatures in excess of 300 degrees C. Beyond 160 degrees C both molecules show a smectic A liquid crystalline phase that exists till about 240 degrees C. Field-effect transistors were fabricated by vacuum evaporating the semiconductor layer using standard bottom gate/top contact geometry. The devices exhibit p-channel behaviour with hole mobilities of 10(-2) cm(2)/Vs. (C) 2009 Elsevier B.V. All rights reserved.

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PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

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Background: The incidence of all forms of congenital heart defects is 0.75%. For patients with congenital heart defects, life-expectancy has improved with new treatment modalities. Structural heart defects may require surgical or catheter treatment which may be corrective or palliative. Even those with corrective therapy need regular follow-up due to residual lesions, late sequelae, and possible complications after interventions. Aims: The aim of this thesis was to evaluate cardiac function before and after treatment for volume overload of the right ventricle (RV) caused by atrial septal defect (ASD), volume overload of the left ventricle (LV) caused by patent ductus arteriosus (PDA), and pressure overload of the LV caused by coarctation of the aorta (CoA), and to evaluate cardiac function in patients with Mulibrey nanism. Methods: In Study I, of the 24 children with ASD, 7 underwent surgical correction and 17 percutaneous occlusion of ASD. Study II had 33 patients with PDA undergoing percutaneous occlusion. In Study III, 28 patients with CoA underwent either surgical correction or percutaneous balloon dilatation of CoA. Study IV comprised 26 children with Mulibrey nanism. A total of 76 healthy voluntary children were examined as a control group. In each study, controls were matched to patients. All patients and controls underwent clinical cardiovascular examinations, two-dimensional (2D) and three-dimensional (3D) echocardiographic examinations, and blood sampling for measurement of natriuretic peptides prior to the intervention and twice or three times thereafter. Control children were examined once by 2D and 3D echocardiography. M-mode echocardiography was performed from the parasternal long axis view directed by 2D echocardiography. The left atrium-to-aorta (LA/Ao) ratio was calculated as an index of LA size. The end-diastolic and end-systolic dimensions of LV as well as the end-diastolic thicknesses of the interventricular septum and LV posterior wall were measured. LV volumes, and the fractional shortening (FS) and ejection fraction (EF) as indices of contractility were then calculated, and the z scores of LV dimensions determined. Diastolic function of LV was estimated from the mitral inflow signal obtained by Doppler echocardiography. In three-dimensional echocardiography, time-volume curves were used to determine end-diastolic and end-systolic volumes, stroke volume, and EF. Diastolic and systolic function of LV was estimated from the calculated first derivatives of these curves. Results: (I): In all children with ASD, during the one-year follow-up, the z score of the RV end-diastolic diameter decreased and that of LV increased. However, dilatation of RV did not resolve entirely during the follow-up in either treatment group. In addition, the size of LV increased more slowly in the surgical subgroup but reached control levels in both groups. Concentrations of natriuretic peptides in patients treated percutaneously increased during the first month after ASD closure and normalized thereafter, but in patients treated surgically, they remained higher than in controls. (II): In the PDA group, at baseline, the end-diastolic diameter of LV measured over 2SD in 5 of 33 patients. The median N-terminal pro-brain natriuretic peptide (proBNP) concentration before closure measured 72 ng/l in the control group and 141 ng/l in the PDA group (P = 0.001) and 6 months after closure measured 78.5 ng/l (P = NS). Patients differed from control subjects in indices of LV diastolic and systolic function at baseline, but by the end of follow-up, all these differences had disappeared. Even in the subgroup of patients with normal-sized LV at baseline, the LV end-diastolic volume decreased significantly during follow-up. (III): Before repair, the size and wall thickness of LV were higher in patients with CoA than in controls. Systolic blood pressure measured a median 123 mm Hg in patients before repair (P < 0.001) and 103 mm Hg one year thereafter, and 101 mm Hg in controls. The diameter of the coarctation segment measured a median 3.0 mm at baseline, and 7.9 at the 12-month (P = 0.006) follow-up. Thicknesses of the interventricular septum and posterior wall of the LV decreased after repair but increased to the initial level one year thereafter. The velocity time integrals of mitral inflow increased, but no changes were evident in LV dimensions or contractility. During follow-up, serum levels of natriuretic peptides decreased correlating with diastolic and systolic indices of LV function in 2D and 3D echocardiography. (IV): In 2D echocardiography, the interventricular septum and LV posterior wall were thicker, and velocity time integrals of mitral inflow shorter in patients with Mulibrey nanism than in controls. In 3D echocardiography, LV end-diastolic volume measured a median 51.9 (range 33.3 to 73.4) ml/m² in patients and 59.7 (range 37.6 to 87.6) ml/m² in controls (P = 0.040), and serum levels of ANPN and proBNP a median 0.54 (range 0.04 to 4.7) nmol/l and 289 (range 18 to 9170) ng/l, in patients and 0.28 (range 0.09 to 0.72) nmol/l (P < 0.001) and 54 (range 26 to 139) ng/l (P < 0.001) in controls. They correlated with several indices of diastolic LV function. Conclusions (I): During the one-year follow-up after the ASD closure, RV size decreased but did not normalize in all patients. The size of the LV normalized after ASD closure but the increase in LV size was slower in patients treated surgically than in those treated with the percutaneous technique. Serum levels of ANPN and proBNP were elevated prior to ASD closure but decreased thereafter to control levels in patients treated with the percutaneous technique but not in those treated surgically. (II): Changes in LV volume and function caused by PDA disappeared by 6 months after percutaneous closure. Even the children with normal-sized LV benefited from the procedure. (III): After repair of CoA, the RV size and the velocity time integrals of mitral inflow increased, and serum levels of natriuretic peptides decreased. Patients need close follow-up, despite cessation of LV pressure overload, since LV hypertrophy persisted even in normotensive patients with normal growth of the coarctation segment. (IV): In children with Mulibrey nanism, the LV wall was hypertrophied, with myocardial restriction and impairment of LV function. Significant correlations appeared between indices of LV function, size of the left atrium, and levels of natriuretic peptides, indicating that measurement of serum levels of natriuretic peptides can be used in the clinical follow-up of this patient group despite its dependence on loading conditions.

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Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.