124 resultados para Multiplicity of positive solutions


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Molecular dynamics simulations are used to examine the changes in water density and hydration characteristics of NaCl solutions confined in slit-shaped graphitic pores. Using a structural signature, we define the hydration limit as the salt concentration at which a sharp drop in the hydration number is observed. At small pores (H = 8.0-10 angstrom), confined water does not possess bulk-like features and remains in a layered arrangement between two surfaces. Despite this high degree of confinement, ions are able to form a quasi-2D hydration shell between two surfaces. Our results indicate the strong propensity of ions to form the first hydration shell, even under extremely confined aqueous environments. The hydration of ions is seen to weakly perturb the oxygen density distributions between two surfaces. The hydration number of Na+ reduces to about 4.15 at a pore width of H = 0.8 nm, when compared with the bulk hydration number of 6.25. At larger pore widths, above H = 16 angstrom, where bulk-like water densities are observed in the central regions of the pore, the hydration number is above 6.

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Local heating is an important parameter in compaction of thermally sensitive solids since local hot spots could conceivably raise the temperature of the system by several hundred degrees. To understand the importance of local hot spots, 20 g of ammonium perchlorate (AP) and potassium perchlorate (KP) were pressed together at 1500 kg cm−2 for 5 min. The surface structural examination of the compact revealed a secondary phase at the interfaces between the grains in the compositions ranging from 50% AP-50% KP to 10% AP-90% KP. The observation of the secondary phase only at the interfaces has been attributed to the short life times of temperature pulses present during the compaction. An interesting aspect of the investigation is the formation of a series of solid solutions of AP-KP.

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The superfluid state of fermion-antifermion fields developed in our previous papers is generalized to include higher orbital and spin states. In addition to single-particle excitations, the system is capable of having real and virtual bound or quasibound composite excitations which are akin to bosons of spinJ P equal to0 �, 1�, 2+, etc. These pseudoscalar, vector, and tensor bosons can be massive or massless and provide the vehicles for strong, electromagnetic, weak, and gravitational interactions. The concept that the basic (unmanifest) fermion-antifermion interaction can lead to a multiplicity of manifest interactions seems to provide a basis for a unified field theory.

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The paper presents a general method of structural synthesis which can be used to derive all possible simple- and multiple-jointed chains of positive, zero or negative degree-of-freedom. In this method all possible chains with N links and F degrees-of-freedom are derived by the transformation of the corresponding “binary chains” with N binary links and F degrees-of-freedom. The method is illustrated by applying to the case of chains with degrees-of-freedom 1,2,0 and −1.

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A class of self-propagating linear and nonlinear travelling wave solutions for compressible rotating fluid is studied using both numerical and analytical techiques. It is shown that, in general, a three dimensional linear wave is not periodic. However, for some range of wave numbers depending on rotation, horizontally propagating waves are periodic. When the rotation ohgr is equal to $$\sqrt {(\gamma - 1)/(4\gamma )}$$ , all horizontal waves are periodic. Here, gamma is the ratio of specific heats. The analytical study is based on phase space analysis. It reveals that the quasi-simple waves are periodic only in some plane, even when the propagation is horizontal, in contrast to the case of non-rotating flows for which there is a single parameter family of periodic solutions provided the waves propagate horizontally. A classification of the singular points of the governing differential equations for quasi-simple waves is also appended.

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Fine-particle metal chromites (MCr2O4, where M = Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn) have been prepared by the combustion of aqueous solutions containing the respective metal nitrate, chromium(III) nitrate, and urea in stoichiometric amounts. The mixtures, when rapidly heated to 350°C, ignite and yield voluminous chromites with surface areas ranging from 5 to 25 m2/g. MgCr2O4, sintered in air at 1500°C for 5 h, has a density of 4.0 g/cm3.

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Ten different tRNAGly1 genes from the silk worm, Bombyx mori, have been cloned and characterized. These genes were transcribed in vitro in homologous nuclear extracts from the posterior silk gland (PSG) or nuclear extracts derived from the middle silk gland or ovarian tissues. Although the transcription levels were much higher in the PSG nuclear extracts, the transcriptional efficiency of the individual genes followed a similar pattern in all the extracts. Based on the levels of in vitro transcription, the ten tRNAGly1 genes could be divided into three groups, viz., those which were transcribed at very high levels (e.g., clone pR8), high to medium levels (e.g., pBmil, pBmpl, pBmhl, pBmtl) and low to barely detectable levels (e.g., pBmsl, pBmjl and pBmkl). The coding sequences of all these tRNA genes being identical, the differential transcription suggested that the flanking sequences modulate their transcriptional efficiency. The presence of positive and negative regulatory elements in the 5' flanking regions of these genes was confirmed by transcription competition experiments. A positive element was present in the immediate upstream A + T-rich sequences in all the genes, but no consensus sequences correlating to the transcriptional status could be generated. The presence of negative elements on the other hand was indicated only in some of the genes and therefore may have a role in the differential transcription of these tRNAGly genes in vivo.

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Fine particle AlPO4, LaPO4 and KTiOPO4 have been prepared by the flash combustion of aqueous solutions containing metal nitrate, ammonium hydrogen phosphate, ammonium nitrate or ammonium perchlorate and carbohydrazide or tetraformal trisazine. When rapidly heated at 400 °C, the solution containing the redox mixtures ignites to undergo self-propagating, gas-producing, exothermic reactions. Formation of crystalline phosphates was confirmed by powder X-ray diffraction patterns and IR spectra. The metal phosphates formed are fine and have 20�78 m2 g?1 surface area.

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An important problem regarding pin joints in a thermal environment is addressed. The motivation emerges from structural safety requirements in nuclear and aerospace engineering. A two-dimensional model of a smooth, rigid misfit pin in a large isotropic sheet is considered as an abstraction. The sheet is subjected to a biaxial stress system and far-field unidirectional heat flow. The thermoelastic analysis is complex due to non-linear load-dependent contact and separation conditions at the pin-hole interface and the absence of existence and uniqueness theorems for the class of frictionless thermoelastic contact problems. Identification of relevant parameters and appropriate synthesis of thermal and mechanical variables enables the thermomechanical generalization of pin-joint behaviour. This paper then proceeds to explore the possibility of multiple solutions in such problems, especially interface contact configuration.

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This paper deals with the direct position kinematics problem of a general 6-6 Stewart platform, the complete solution of which is not reported in the literature until now and even establishing the number of possible solutions for the general case has remained an unsolved problem for a long period. Here a canonical formulation of the direct position kinematics problem for a general 6-6 Stewart platform is presented. The kinematic equations are expressed as a system of six quadratic and three linear equations in nine unknowns, which has a maximum of 64 solutions. Thus, it is established that the mechanism, in general, can have up to 64 closures. Further reduction of the system is shown arriving at a set of three quartic equations in three unknowns, the solution of which will yield the assembly configurations of the general Stewart platform with far less computational effort compared to earlier models.

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The coefficient of thermochromism of polyaniline solutions has been found to be solvent dependent and the solvent effect is not negligible. Hence, thermochromism of polyaniline solutions cannot be explained solely on the basis of conformational change induced by a change in temperature. Further, comparison of the solvatochromism of polyaniline and polytoluidine shows a higher solvatochromic shift for the former. It implies that the higher energy associated with the exciton peak of polytoluidine is not due to the higher ring torsional angle induced by the higher steric repulsion of the methyl group, as widely accepted, but is due to its less solvatochromic red-shift as compared to polyaniline.

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Pure Y2O3 and Y2O3---ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0–30% ZrO2 and precursors with 0–50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D53). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D53 structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

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Pure Y2O3 and Y2O3-ZrO2 solid solutions have been prepared by melt atomization and by pyrolysis of nitrate solutions. Extended solubility is readily achieved in both techniques for the entire composition range investigated: melts with 0-30% ZrO2 and precursors with 0-50% ZrO2. However, solidification of under cooled droplets yields almost exclusively single phase powders with the structure of cubic yttria (D5(3)). In contrast, the pyrolysis route leads to a sequence of metastable microstructures beginning with a nanocrystalline disordered fluorite-based (C1) solid solution. Further heating leads to the evolution of much larger (micron size) flake crystals with a {001} texture, concurrent with partial ordering of the oxygen ions to the sites occupied in the D5(3) structure. The driving force for ordering and the rate of grain growth decrease with increasing ZrO2 addition. Abrupt heating to high temperatures or electron irradiation can induce ordering without substantial grain growth. There is no significant reduction in porosity during the recrystallization, which with the other observations suggests that grain growth is driven by the free energy available for the ordering transformation from fluorite to the yttria structure. This route offers opportunities for single crystal thin film development at relatively low processing temperatures.

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Computer simulations have shown a novel geodesic splitting on the paraboloid of revolution leading to a multiplicity of surface ray paths. Such a phenomenon would have wide ramifications for wave propagation problems in general, besides applications in target-detection problems and the computational requirements of ray-theoretic formulations such as the UTD, in computing the antenna characteristics in the high-frequency domain.