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61.
62.
Joseph W. Jerome 《Numerische Mathematik》2008,109(1):121-142
We consider nonlinear elliptic systems, with mixed boundary conditions, on a convex polyhedral domain Ω ⊂ R
N
. These are nonlinear divergence form generalizations of Δu = f(·, u), where f is outward pointing on the trapping region boundary. The motivation is that of applications to steady-state reaction/diffusion
systems. Also included are reaction/diffusion/convection systems which satisfy the Einstein relations, for which the Cole-Hopf
transformation is possible. For maximum generality, the theory is not tied to any specific application. We are able to demonstrate
a trapping principle for the piecewise linear Galerkin approximation, defined via a lumped integration hypothesis on integrals
involving f, by use of variational inequalities. Results of this type have previously been obtained for parabolic systems by Estep, Larson,
and Williams, and for nonlinear elliptic equations by Karátson and Korotov. Recent minimum and maximum principles have been
obtained by Jüngel and Unterreiter for nonlinear elliptic equations. We make use of special properties of the element stiffness
matrices, induced by a geometric constraint upon the simplicial decomposition. This constraint is known as the non-obtuseness
condition. It states that the inward normals, associated with an arbitrary pair of an element’s faces, determine an angle
with nonpositive cosine. Drăgănescu, Dupont, and Scott have constructed an example for which the discrete maximum principle
fails if this condition is omitted. We also assume vertex communication in each element in the form of an irreducibility hypothesis
on the off-diagonal elements of the stiffness matrix. There is a companion convergence result, which yields an existence theorem
for the solution. This entails a consistency hypothesis for interpolation on the boundary, and depends on the Tabata construction
of simple function approximation, based on barycentric regions.
This work was supported by the National Science Foundation under grant DMS-0311263. 相似文献
63.
64.
The initial/Neumann boundary-value enthalpy formulation for the two-phase Stefan problem is regularized by smoothing. Known estimates predict a convergence rate of 1/2, and this result is extended in this paper to include the case of a (nonzero) residual in the regularized problem. A modified Newton Kantorovich framework is established, whereby the exact solution of the regularized problem is replaced by one Newton iteration. It is shown that a consistent theory requires measure-theoretic hypotheses on the starting guess and the Newton iterate, otherwise residual decrease is not expected. The circle closes in one spatial dimension, where it is shown that the residual decrease of Newton's method correlates precisely with the 1/2 convergence theory. 相似文献
65.
An efficient synthesis of 2-amino-oxazolo[4,5-c]quinoline TRPV1 antagonists is described via a thiourea formation/carbodiimide cyclization sequence. Synthetic route optimization eliminates intermediate isolations and facilitates the rapid preparation of a series of novel pentacyclic TRPV1 antagonists. From this series, compound (S)-4 was identified as a potent and selective ligand for the TRPV1 ion channel. 相似文献
66.
This is a reprinting of a paper by Jerome Kristian and Rainer K. Sachs, first published in 1966, in which they proposed a
power-series scheme for reading out various parameters of the Universe directly from observations in a model-independent way.
The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series
of the journal. This republication is accompanied by an editorial note written by George Ellis and by a brief biography of
J. Kristian, compiled by A. Krasiński from internet sources. 相似文献
67.
2-Furoic acid (2FA), an organic third order nonlinear optical single crystal, has been synthesized and grown successfully by slow solvent evaporation technique. The space group and lattice parameters of the grown crystals were obtained by single crystal X-ray diffraction analysis. The presence of the functional groups was confirmed by Fourier Transform Infrared (FTIR) spectroscopy. Optical absorption studies reveal low absorption in the UV and visible regions and the UV cut-off wavelength is found to be at 240 nm. The thermal stability of the material examined by TGA analysis, reveals that the material is thermally stable up to 130 °C. The third order nonlinear optical parameters (nonlinear refractive index, nonlinear absorption coefficient and real and imaginary parts of the third order nonlinear optical susceptibility) were derived by Z-scan technique. This reveals that the crystal has a negative refractive index, which indicates the defocusing nature of the material. 相似文献
68.
K. ParasuramanK. Sakthi Murugesan R. UthrakumarS. Jerome Das B. Milton Boaz 《Physica B: Condensed Matter》2011,406(20):3856-3860
Good quality single crystals of pure and metal ion (Ni2+) doped bis-thiourea zinc chloride (BTZC) possessing excellent nonlinear optical properties have been grown from aqueous solution by the slow solvent evaporation technique. The lattice parameters of the grown crystals are determined by single crystal X-ray analysis. The well defined sharp peaks in the powder X-ray diffraction pattern reveals the crystalline perfection and the EDAX spectrum confirms the presence of dopant in the lattice of the parent crystal. The DRS UV-visible spectral study reveals improved transparency for the doped crystal, ascertaining the inclusion of metal ion in the lattice. The optical band gap of the pure and doped crystals was calculated to be 4.8 and 5.2 eV respectively from the UV transmission spectrum. The vickers hardness test brings forth higher hardness value for Ni2+doped BTZC as compared to pure BTZC crystal. The dielectric measurement exhibits very low dielectric constant and dielectric loss at higher frequencies for both the pure and Ni2+doped BTZC. The existence of second harmonic generation signals in the crystal also has been confirmed by performing the Kurtz powder test. 相似文献
69.
We report experiments on self-focusing of femtosecond diffraction-resistant vortex beams in water. These beams are higher-order Bessel beams with weak azimuthal modulation of the transverse intensity patterns. The modulation overrides the self-focusing dynamics and results in the formation of regular bottlelike filament distributions. The peak-power thresholds for filamentation, at a particular distance, are relatively accurately estimated by the adaptation of the Marburger formula derived earlier for Gaussian beams. The nonlinear conversion of the incident conical waves into the localized spatial wave packets propagating near the beam axis is observed. 相似文献
70.
Eric A. Voight Jerome F. Daanen Bhadra H. Shelat Daniel J. Plata 《Tetrahedron letters》2010,51(45):5904-5907
Starting from a variety of substituted chroman-4-ones, a highly enantioselective CBS reduction using in situ-generated B-H catalyst gave (S)-chroman-4-ols. Azide inversion and reduction gave crude (R)-chroman-4-amines, which could be purified without chromatography by isolation as the (R)-mandelic or d-tartaric acid salts with good yields and excellent ee. 相似文献