982 resultados para hyperbolic double-complex Laplace operator
Resumo:
Exam questions and solutions in PDF
Resumo:
The copper(I) complex of L, the 1:2 condensate of benzil dihydrazone and 2-formylpyridine, exists as single, helical [CuL](+) and double helical [Cu2L2](2+) in dichloromethane solution but crystallizes only as the double helicate [Cu2L2](ClO4)(2). In contrast, earlier [New J Chem, 27 (2003) 193] it has been found that with L', the 1:2 condensate of benzil dihydrazone and 2-acetylpyridine, only the single helical monomeric species [CuL'](+) is isolable as solid. This contrasting behaviour of the copper(I) complexes of L and L' are scrutinised here by density functional calculations.
Resumo:
The crystallization kinetics of each constituent of poly(p-dioxanone)-b-poly(epsilon-caprolactone) diblock copolymers (PPDX-b-PCL) has been determined in a wide composition range by differential scanning calorimetry and compared to that of the equivalent homopolymers. Spherulitic growth rates were also measured by polarized optical microscopy while atomic force microscopy was employed to reveal the morphology of one selected diblock copolymer. It was found that crystallization drives structure formation and both components form lamellae within mixed spherulitic superstructures. The overall isothermal crystallization kinetics of the PPDX block at high temperatures, where the PCL is molten, was determined by accelerating the kinetics through a previous self-nucleation procedure. The application of the Lauritzen and Ho. man theory to overall growth rate data yielded successful results for PPDX and the diblock copolymers. The theory was applied to isothermal overall crystallization of previously self-nucleated PPDX ( where growth should be the dominant factor if self-nucleation was effective) and the energetic parameters obtained were perfectly matched with those obtained from spherulitic growth rate data of neat PPDX. A quantitative estimate of the increase in the energy barrier for crystallization of the PPDX block, caused by the covalently bonded molten PCL as compared to homo-PPDX, was thus determined. This energy increase can dramatically reduce the crystallization rate of the PPDX block as compared to homo-PPDX. In the case of the PCL block, both the crystallization kinetics and the self-nucleation results indicate that the PPDX is able to nucleate the PCL within the copolymers and heterogeneous nucleation is always present regardless of composition. Finally, preliminary results on hydrolytic degradation showed that the presence of relatively small amounts of PCL within PPDX-bPCL copolymers substantially retards hydrolytic degradation of the material in comparison to homo-PPDX. This increased resistance to hydrolysis is a complex function of composition and its knowledge may allow future prediction of the lifetime of the material for biomedical applications.
Resumo:
Neuromuscular disorders affect millions of people world-wide. Upper limb tremor is a common symptom, and due to its complex aetiology it is difficult to compensate for except, in particular cases by surgical intervention or drug therapy. Wearable devices that mechanically compensate for limb tremor could benefit a considerable number of patients, but the technology to assist suffers in this way is under-developed. In this paper we propose an innovative orthosis that can dynamically suppress pathological tremor, by applying viscous damping to the affected limb in a controlled manner. The orthosis design utilises a new actuator design based on Magneto-Rheological Fluids that efficiently deliver damping action in response to the instantaneous tremor frequency and amplitude.
Resumo:
Retinal blurring resulting from the human eye's depth of focus has been shown to assist visual perception. Infinite focal depth within stereoscopically displayed virtual environments may cause undesirable effects, for instance, objects positioned at a distance in front of or behind the observer's fixation point will be perceived in sharp focus with large disparities thereby causing diplopia. Although published research on incorporation of synthetically generated Depth of Field (DoF) suggests that this might act as an enhancement to perceived image quality, no quantitative testimonies of perceptional performance gains exist. This may be due to the difficulty of dynamic generation of synthetic DoF where focal distance is actively linked to fixation distance. In this paper, such a system is described. A desktop stereographic display is used to project a virtual scene in which synthetically generated DoF is actively controlled from vergence-derived distance. A performance evaluation experiment on this system which involved subjects carrying out observations in a spatially complex virtual environment was undertaken. The virtual environment consisted of components interconnected by pipes on a distractive background. The subject was tasked with making an observation based on the connectivity of the components. The effects of focal depth variation in static and actively controlled focal distance conditions were investigated. The results and analysis are presented which show that performance gains may be achieved by addition of synthetic DoF. The merits of the application of synthetic DoF are discussed.
Resumo:
We describe a crystal structure, at atomic resolution (1.1 Å, 100 K), of a ruthenium polypyridyl complex bound to duplex DNA, in which one ligand acts as a wedge in the minor groove, resulting in the 51° kinking of the double helix. The complex cation Λ-[Ru(1,4,5,8-tetraazaphenanthrene)2(dipyridophenazine)]2+ crystallizes in a 1∶1 ratio with the oligonucleotide d(TCGGCGCCGA) in the presence of barium ions. Each complex binds to one duplex by intercalation of the dipyridophenazine ligand and also by semiintercalation of one of the orthogonal tetraazaphenanthrene ligands into a second symmetrically equivalent duplex. The result is noncovalent cross-linking and marked kinking of DNA.
Resumo:
The synthesis and X-ray crystal structure of the MnII,11 complex double salt [Mn2(η1η1µ2-oda)(phen)4(H2O)2][Mn2(η1η1µ2-oda(phen)4(η1-oda)2]·4H2O is reported, together with its catalytic activity towards the disproportionation of H2O2.
Resumo:
In this placebo-controlled, double-blind, crossover human feeding study, the effects of polydextrose (PDX; 8 g/d) on the colonic microbial composition, immune parameters, bowel habits and quality of life were investigated. PDX is a complex glucose oligomer used as a sugar replacer. The main goal of the present study was to identify the microbial groups affected by PDX fermentation in the colon. PDX was shown to significantly increase the known butyrate producer Ruminococcus intestinalis and bacteria of the Clostridium clusters I, II and IV. Of the other microbial groups investigated, decreases in the faecal Lactobacillus–Enterococcus group were demonstrated. Denaturing gel gradient electrophoresis analysis showed that bacterial profiles between PDX and placebo treatments were significantly different. PDX was shown to be slowly degraded in the colon, and the fermentation significantly reduced the genotoxicity of the faecal water. PDX also affected bowel habits of the subjects, as less abdominal discomfort was recorded and there was a trend for less hard and more formed stools during PDX consumption. Furthermore, reduced snacking was observed upon PDX consumption. This study demonstrated the impact of PDX on the
Resumo:
A penta-nuclear. star-shaped hetero-metallic compound containing a unique Ni4KO8 core has been synthesized. The X-ray single crystal structure analysis reveals that in the complex, [K(Ni(LH)(2))(4)(OH2)(8)](Br)(ClO4)(8)center dot 11H(2)O (LH=(CH3)(2)HN+(CH2)(3)N=CHC6H4O-) the eight coordinate central K+ ion is encapsulated by four terminal [Ni(LH)(2)](2+) units through the double water bridges between K+ and each Ni(II) ions.
Resumo:
A diphenoxido-bridged dinuclear copper(II) complex, [Cu2L2(ClO4)(2)] (1), has been synthesized using a tridentate reduced Schiff base ligand, 2-[[2-(diethylamino)-ethylamino]methyl]phenol (HL). The addition of triethylamine to the methanolic solution of this complex produced a novel triple bridged (double phenoxido and single hydroxido) dinuclear copper(II) complex, [Cu2L2(OH)]ClO4 (2). Both complexes 1 and 2 were characterized by X-ray structural analyses, variable-temperature magnetic susceptibility measurements, and spectroscopic methods. In 1, the two phenoxido bridges are equatorial-equatorial and the species shows strong antiferromagnetic coupling with J = -615.6(6.1) cm(-1). The inclusion of the equatorial-equatorial hydroxido bridge in 2 changes the Cu center dot center dot center dot Cu distance from 3.018 angstrom (avg.) to 2.798 angstrom (avg.), the positions of the phenoxido bridges to axial-equatorial, and the magnetic coupling to ferromagnetic with J = 50.1(1.4) cm(-1). Using 3,5-di-tert-butylcatechol as the substrate, the catecholase activity of the complexes has been studied in a methanol solution; compound 2 shows higher catecholase activity (k(cat) = 233.4 h(-1)) than compound 1 (k(cat) = 93.6 h(-1)). Both complexes generate identical species in solution, and they are interconvertible simply by changing the pH of their solutions. The higher catecholase activity of 2 seems to be due to the presence of the OH group, which increases the pH of its solution.
Resumo:
Three double phenoxido-bridged dinuclear nickel(II) complexes, namely [Ni-2(L-1)(2)(NCS)(2)] (1), [Ni-2(L-2)(2)(NCS)(2)] (2), and [Ni-2(L-3)(2)(NCS)(2)] (3) have been synthesized using the reduced tridentate Schiff-base ligands 2-[1-(3-methylamino-propylamino)-ethyl]-phenol (HL1), 2-[1-(2-dimethylamino-ethylamino)-ethyl]-phenol (HL2), and 2-[1-(3-dimethylarnino-propylamino)-ethyl]-phenol (HL3), respectively. The coordination compounds have been characterized by X-ray structural analyses, magnetic-susceptibility measurements, and various spectroscopic methods. In all complexes, the nickel(II) ions are penta-coordinated in a square-pyramidal environment, which is severely distorted in the case of 1 (Addison parameter tau = 0.47) and 3 (tau = 0.29), while it is almost perfect for 2 (tau = 0.03). This arrangement leads to relatively strong antiferromagnetic interactions between the Ni(II) (S = 1) metal centers as mediated by double phenoxido bridges (with J values of -23.32 (1), -35.45 (2), and -34.02 (3) cm(3) K mol(-1), in the convention H = -2JS(1)S(2)). The catalytic activity of these Ni compounds has been investigated for the aerial oxidation of 3,5-di-tert-butylcatechol. Kinetic data analysis following Michaelis-Menten treatment reveals that the catecholase activity of the complexes is influenced by the flexibility of the ligand and also by the geometry around the metal ion. Electrospray ionization mass spectroscopy (ESI-MS) studies (in the positive mode) have been performed for all the coordination compounds in the presence of 3,5-DTBC to characterize potential complex-substrate intermediates. The mass-spectrometry data, corroborated by electron paramagnetic resonance (EPR) measurements, suggest that the metal centers are involved in the catecholase activity exhibited by the complexes.
Resumo:
We present a new subcortical structure shape modeling framework using heat kernel smoothing constructed with the Laplace-Beltrami eigenfunctions. The cotan discretization is used to numerically obtain the eigenfunctions of the Laplace-Beltrami operator along the surface of subcortical structures of the brain. The eigenfunctions are then used to construct the heat kernel and used in smoothing out measurements noise along the surface. The proposed framework is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shape. We detected a significant age effect on hippocampus in accordance with the previous studies. In addition, we also detected a significant gender effect on amygdala. Since we did not find any such differences in the traditional volumetric methods, our results demonstrate the benefit of the current framework over traditional volumetric methods.
Resumo:
Reaction of Cu(ClO(4))(2)center dot 6H(2)O with the 1:2 condensate of benzildihydrazone and 2-acetylpyridine, in methanol in equimolar ratio yields a green compound which upon recrystallisation from 1:1 CH(2)Cl(2)-C(6)H(6) mixture affords [CuL(H(2)O)](ClO(4))(2)center dot 1/2C(6)H(6). The complex crystallises in the space group P-1 with a = 8.028(11) angstrom, b = 12.316(17) angstrom, c = 18.14(3) angstrom, alpha = 97.191(10)degrees, beta = 94.657(10)degrees and gamma = 108.039(10)degrees. It is single helical with the metal having a distorted trigonal bipyramidal N(4)O coordination sphere. The acid dissociation constant of the Cu(I) complex in CH(3)CN is 3.34 +/- 0.19. The X band EPR spectrum of the compound is rhombic with g(1) = 2.43, g(2) = 2.10 g(3) = 2.02 and A(1) = 79.3 x 10(-4) cm(-1). The Cu(II/I) potential of the complex in CH(2)Cl(2) at a glassy carbon electrode is 0.43 V vs SCE. It is argued that the copper-water bond persists in the corresponding copper(I) species. Its implications on the single helix-double helix interconversion in copper helicates are discussed. DFT calculations at the B3LYP/6-311G** level shows that the binding energy of water in the single helicol live-coordinate copper(I) species [CuL(H(2)O)](+) is similar to 40 kJ mol(-1).
Resumo:
The crystal structure of the ruthenium DNA ‘light-switch’ complex -[Ru(TAP)2(11-Cl-dppz)]2+ (TAP = tetraazaphenanthrene, dppz = dipyrido[3,2-a':2',3'-c]phenazine)) bound to the oligonucleotide duplex d(TCGGCGCCGA)2 is reported. The synthesis of the racemic ruthenium complex is described for the first time, and the racemate was used in this study. The crystal structure, at atomic resolution (1.0 Å), shows one ligand as a wedge in the minor groove, resulting in the 51 kinking of the double helix, as with the parent lambda-[Ru(TAP)2(dppz)]2+. Each complex binds to one duplex by intercalation of the dppz ligand and also by semi-intercalation of one of the orthogonal TAP ligands into a second symmetrically equivalent duplex. The 11-Cl substituent binds with the major component (66%) oriented with the 11-chloro substituent on the purine side of the terminal step of the duplex.
Resumo:
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.