324 resultados para Part hausdo rff distance


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The Raman spectra of methyl alcohol, ethyl alcohol, n-propyl alcohol and n-butyl alcohol have been recorded using λ 2537 excitation. 35, 49, 45 and 51 Raman lines respectively have been identified in the spectra of these alcohols, in addition to the rotational 'wings'. In each case, a large number of additional lines have been recorded. The existence of Raman lines with frequency shifts greater than 3800 cm.-1, first reported by Bolla in the spectrum of ethyl alcohol, has been confirmed. Similar high-frequency shift Raman lines have also been recorded in the spectrum of methyl alcohol. They have been assigned as combinations. Proper assignments have been given for the prominent Raman lines appearing in the spectra of these alcohols.

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A mechanism for the isomerisation of ethyl 1-ethoxycarbonyl-2-oxocyclopentylacetate (I) into a cyclohexane β-keto-ester as proceeding through an intermediate bicyclic /gb-diketone (VII) has been considered as an alternative mechanism to one earlier suggested.1 The determination of the structure of the isomerised β-keto-ester as 2, 3-diethoxycarbonylcyclohexanone (V) has provided support for the earlier mechanism.

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Raman spectra of single crystals of β-malonic acid and β-succinic acid have been photographed using λ 2536·5 radiation. 32 Raman lines have been recorded in the case of β-malonic acid. Of these 21 lines have been recorded for the first time. The three intense lattice lines at 52, 90 and 144 cm.-1 have been attributed to rotational lattice oscillations. 29 Raman lines in the case of β-succinic acid have been recorded. The entire lattice spectrum and many internal frequencies have been recorded for the first time. The three intense lattice lines at 80, 135 and 160 cm.-1 have been assigned to the rotational oscillations of the two molecules of the succinic acid in the unit cell.

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A detailed investigation of the hydrolysis of nickel in the lower concentration range has been made. The results have been analysed on the basis of 'Core + links' theory and on the assumption of the formation of one predominant complex. Evidence is obtained for the formation of Ni2 (OH)62- and its stability constant is calculated to be 1038.78

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By observing mergers of compact objects, future gravity wave experiments would measure the luminosity distance to a large number of sources to a high precision but not their redshifts. Given the directional sensitivity of an experiment, a fraction of such sources (gold plated) can be identified optically as single objects in the direction of the source. We show that if an approximate distance-redshift relation is known then it is possible to statistically resolve those sources that have multiple galaxies in the beam. We study the feasibility of using gold plated sources to iteratively resolve the unresolved sources, obtain the self-calibrated best possible distance-redshift relation and provide an analytical expression for the accuracy achievable. We derive the lower limit on the total number of sources that is needed to achieve this accuracy through self-calibration. We show that this limit depends exponentially on the beam width and give estimates for various experimental parameters representative of future gravitational wave experiments DECIGO and BBO.

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Spectrophotometric and potentiometric investigations have been carried out on copper-diethanolamine system. Job plots at 900, 900 and 580 mμ have indicated the formation of CuD++, CuD2++ and CuD3++. The n- pA curves obtained indicate the formation of CuD++, CuD2++, CuD3++, CuDOH+, CuD2OH+ and CuD3OH+. The n- pA curves have been analyzed to obtain the stability constants of these complexes. Absorption curves of pure complexes have been computed by a graphical method. Gaussian analysis of the absorption curves of pure and hydroxy complexes show the presence of a second band, indicating that the structure is that of a distorted octahedron.

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neral expressions have been derived for the intensities of the three classes of Raman lines namely totally symmetric A, doubly degenerate E and triply degenerate F, in the case of cubic crystals under the following conditions. The direction of the incident beam which is polarised with its electric vector inclined at an angle α to the normal to the scattering plane makes an angle Θ with one of the cubic axes of the crystal. The transversely scattered light is analysed by a double image prism with its principal axes inclined at angle β to the normal to the scattering plane, which is horizontal. For incident unpolarised light and Θ=22 1/2°, and the scattered light being analysed by a double image prism rotated through 45° from the position when its principal axes are vertical and horizontal ρ{variant} for A lines is equal to one, for E lines >1 and for F lines <1. This gives a method of classifying the Raman lines of a cubic crystal in a single setting. The results have been experimentally verified in sodium chlorate.

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The kinetics of dimerization of 4-substituted- and unsubstituted o-benzoylbenzoyl chlorides, with iodide ion can be described by the expression, rate =k2[acid chloride][iodide]. The value for the reaction in dimethylformamide solution is –0·38. The entropy of activation for the reaction is –34·2 cal mol–1 K–1 and the activation energy is 10·7 kcal mol–1. These results have been interpreted as evidence for the formation of pseudo-iodide in the rate-determining step and its fast decomposition to radicals which combine to give a mixture of stereoisomeric dilactones.

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Ring-chain tautomeric equilibria of o-benzoylbenzamides in 95% ethanol, chloroform, dioxan, and acetonitrile have been estimated using u.v. spectroscopy. Unlike the case of acids, solvent polarity has only a small effect. In ethanol the cyclic form is favoured. Electron-withdrawing groups in the amide-bearing ring disfavour the cyclic form. Substitution of methyl, ethyl, and phenyl groups on the nitrogen atom of the amide function results in increase of the proportion of the cyclic form in the first two cases and decrease in the last.

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In the title compound, C15H12ClN3O, the quinoline ring system is essentially planar, with a maximum deviation of 0.017 (1) angstrom. The crystal packing is stabilized by pi-pi stacking interactions between the quinoline rings of adjacent molecule, with a centroid-centroid distance of 3.5913 (8) angstrom. Aweak C-H center dot center dot center dot pi contact is also observed between molecules.

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In the title molecule, C21H15ClN4S, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.054 (2) angstrom and a maximum deviation of 0.098 (2) angstrom from the mean plane for the triazole ring C atom that is bonded to the thiazole ring. The thiazole and benzene rings are twisted by 66.36 (7) and 56.32 (7)degrees respectively, with respect to the mean plane of the triazoloisoquinoline ring system. In the crystal structure, molecules are linked by intermolecular C-H center dot center dot center dot N interactions along the a axis. The molecular conformation is stabilized by a weak intramolecular pi-pi interaction involving the thiazole and benzene rings, with a centroid-centroid distance of 3.6546 (11) angstrom . In addition, two other intermolecular pi-pi stacking interactions are observed, between the triazole and benzene rings and between the dihydropyridine and benzene rings [centroid-centroid distances = 3.6489 (11) and 3.5967 (10) angstrom, respectively].

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A detailed mechanics based model is developed to analyze the problem of structural instability in slender aerospace vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic pressure and the propulsive thrust of the vehicle. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. Condition under which a flexible body with internal stress waves behaves like a perfect rigid body is derived. Two methods are developed for finite element discretization of the system: (1) A time-frequency Fourier spectral finite element method and (2) h-p finite element method. Numerical results using the above methods are presented in Part II of this paper. (C) 2010 Elsevier Ltd. All rights reserved.

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This paper makes explicit the relation between relative part position and kinematic freedom of the parts which is implicitly available in the literature. An extensive set of representative papers in the areas of assembly and kinematic modelling is reviewed to specifically identify how the ideas in the two areas are related and influencing the development of each other. The papers are categorised by the approaches followed in the specification, representation, and solution of the part relations. It is observed that the extent of the part geometry is not respected in modelling schemes and as a result, the causal flow of events (proximity–contact–mobility) during the assembling process is not realised in the existing modelling paradigms, which are focusing on either the relative positioning problem or the relative motion problem. Though an assembly is a static description of part configuration, achievement of this configuration requires availability of relative motion for bringing parts together during the assembly process. On the other hand, the kinematic freedom of a part depends on the nature of contacting regions with other parts in its static configuration. These two problems are thus related through the contact geometry. The chronology of the approaches that significantly contributed to the development of the subject is also included in the paper.

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This is the second part of a two part review on the state-of-the-art in holographic optical elements (HOEs). The aspects of fabrication, evaluation, and applications of HOEs, are discussed in this part. It details the direction of future efforts towards finding work-horse type recording media, developing new methods for the evaluation of HOE, and identifying the areas of application where HOEs are to be considered as indispensable components/tools. Finally a summary of all the suggestions for future work made in the two parts is displayed in Table 2 of this part of the review.