40 resultados para Eigenfunctions Hydrogen Atom Schrodinger Elliptical Spherical Polar


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We have followed the morphological evolution and crystallization process of spherical micelles formed by the mixture of polystyrene-b-poly(acrylic acid) (PS-b-PAA) and polystyrene-b-poly(2-vinylpyridine)b-poly(ethylene oxide) (PS-b-P2VP-b-PEO) (the core of the spherical micelles was made of P2VP and PAA blocks through hydrogen bonding in neutral solvent N,N-dimethylformamide, DMF) via DMF vapor treatment. Different phenomena, such as rupture of the film, formation of cylinder aggregates and regular square lamellae, were observed when the micelle film was treated in DMF for different times. At the early stage of annealing in DMF vapor, the micelle film became unstable and ruptured. Cylinder aggregates, within which the PEO blocks achieved the association and primary chain folding, formed as the mesophases before the nucleation of the PEO single crystals at this stage. Further treatment in DMF vapor resulted in the nucleation of the PEO blocks at the corners of quasi-square lamellae. Then a quite regular "sandwich" lamellar structure, constructed by a PEO single-crystal layer covered by two tethered layers of other amorphous blocks on the top and bottom crystal basal surfaces, formed when the film of micelles was annealed in DMF vapor for sufficient times.

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A novel amperometric biosensor for quantification of the electrochemically inert polar organic solvents based on tyrosinase electrode was preliminarily reported. The biosensor was fabricated by simply syringing an aqueous solution of tyrosinase/PVAVP (PVAVP: copolymer of poly(vinyl alcohol) grafting with 4-vinylpyridine) onto glassy carbon electrode surface followed by drying the modified electrode at +4 degrees C in a refrigerator. The current generated from electrochemical reduction of quinone is a probe signal. The biosensor can be used for quantification of polar organic solvents, and its mechanism was characterized with in situ steady-state amperometry-quartz crystal microbalance experiments. The detection limit, sensitivity, and dynamic range for certain organic solvents are dependent on the kind and concentration of the substrate probe and the hydrophobicity of the immobilization matrix. The response time for all the tested organic solvents is less than 2 min.

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SmCl3, reacted with CpNa (Cp = Cyclopentadienyl) in the ratio of 1:3 in THF, which then was reacted with (S)-(+)-N-1-(phenylethyl) salicylideneamine/toluene to yield the title complex, [GRAPHICS] The X-ray crystal structure determination of the title complex reveals that 1 is a dimer with intramolecular C-C bond formation and hydrogen transfer, which leads to the configuration turnover of the carbon atom at the benzyl position of the ligand, while those of the newly formed asymmetric centers may have either Ii or S type configurations. (C) 1998 Elsevier Science Ltd. All rights reserved.

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Three new bimetallic complexes were synthesized and crystalized by reactions of (CF3CO2)(3)Ln With R(1) AlR(2)(Ln=Nd and Y, R(1)=H, R=i-C4H9; Ln=Eu, R=R(1)=C2H5) in tetrahydrofuran solution, and their crystal structures were determined using a X-ray diffraction method. The structures and the questions on valence state and noncoplanarity in the structures were confirmed and cracked by means of H-1 NMR and C-13 NMR spectra, especially by C-13-H-1 COSY 2D NMR technique. A general formula of molecules of the three rare earth complexes was defined as follows: [(mu-CF3CO2)(2)Ln(mu-CF3CHO2)AlR(2) . 2THF](2) A mechanism on the formation of the new complexes was also proposed through the following five steps: alkylating, beta-elimination (or hydrogenation), hydrogen transfer, linkage and association. Both Y-Al and Eu-Al complexes function as a catalyst in polymerization of MMA and ECH. The polymer obtained from the first monomer is mainly syndiotactic chain structure and the polymerization of the last monomer shows higher catalytic activity. The Y-Al complex also capable of ring-opening polymerization of THF in case of adding-vary small amount of ECH and a oxonium ion mechanism of THF polymerization was suggested from the analysis of THF polymer terminal.

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The effective property has been investigated theoretically in graded elliptical cylindrical composite's consisting of inhomogeneous graded elliptical cylinders and an isotropic matrix under external uniform electric field. As a theoretical model, the dielectric gradient profile in the elliptical cylinder is modeled by a power-law function of short semi-axis variable parameter (xi(2) - 1) in the elliptical cylindrical coordinates, namely epsilon(i)(xi) = c(k) (xi(2) - 1)(k), where c(k) and k are the parameters, and xi is the long semi-axis space variable in an elliptical cylindrical inclusion region. In the dilute limit, the local analytical potentials in inclusion and matrix regions are derived exactly by means of the hyper-geometric function, and the formulas are given for estimating the effective dielectric responses under the external lfield along (x) over cap- and (y) over cap -directions, respectively. Furthermore, we have demonstrated that our effective response formulas can be reduced to the well-known results of homogeneous isotropic elliptical cylindrical composites if we take the limit k -> 0 in graded elliptical cylindrical composites. (c) 2006 Elsevier B.V. All rights reserved.

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The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

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Experimental investigations on the ignition and combustion stabilization of kerosene with pilot hydrogen in Mach 2.5 airflows were conducted using two test combustors, with cross sections of 30.5 x 30 and 51 x 70 mm, respectively. Various integrated modules, including the combinations of different pilot injection schemes and recessed cavity flameholders with different geometries, were designed and tested. The stagnation pressure of vitiated air varied within the range of 1.1-1.8 NiPa, while the stagnation temperature varied from 1500 to 1900 K. Specifically, effects of the pilot hydrogen injection scheme, cavity geometry, and combustor scaling on the minimally required pilot hydrogen equivalence ratio were systematically examined. Results indicated that the cavity depth and length had significant effects on the ignition and flameholding, whereas the slanted angle of the aft wall was relatively less important. Two cavities in tandem were shown to be a more effective flameholding mechanism than that with a single cavity. The minimally required pilot hydrogen equivalence ratio for kerosene ignition and stable combustion was found to be as low as 0.02. Furthermore, combustion efficiency of 80% was demonstrated to be achievable for kerosene with the simultaneous use of pilot hydrogen and a recessed cavity to promote the ignition and global burning.

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The complete proof of the virial theorem in refined Thomas-Fermi-Dirac theory for all electrons of an atom in a solid is given.

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研究表明,保证经典轨道具有封闭性的Bertrand定理可以进一步推广,在适当的角动量睛,仍存在着非椭圆的闭合轨道。对于屏蔽Coulomb场,可获得广义Runge-Lenz矢量。这种轨道封闭性与径向Schrodinger方程因式分解相对应。

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Ultrafine diamond (UFD) was synthesized under high pressure and high temperatures generated by explosive detonation. The structure, composition, surface and thermal stability of UFD were studied by use of XRD, TEM, Raman Spectroscopy, FTIR, etc. The influences of the synthesis conditions and purification conditions on the properties of UFD were analyzed. The UFD had an average size of 4-6 nm, commonly exhibiting a spherical shape. The highest yield was of up to 10 mass% of the explosive. Attempts were made to use UFD as an additive to metal-diamond sintering and as crystallite seeds of CVD diamond films. The results show that UFD can decrease the coefficient of friction of the composite by 30%, and raise the nucleation density in CVD diamond films by 2-3 times.