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We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton–Jacobi equations of the form ut+H(Dxu)=0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws pt+DxH(p)=0, where p=Dxu. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as “large-time-step” Godunov-type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature.  相似文献   
134.
For a smooth domain with compact boundary we investigate the problem with Neumann boundary conditions, where f has superlinear but subcritical growth. Provided that is sufficiently small we show the existence of at least positive solutions with single maximum points that lie on . We replace the standard variational setting used in the case of homogeneous f by considering the restriction of the free functional to a suitable submanifold of the Sobolev Space . Received May 25, 1997 / Accepted October 3, 1997  相似文献   
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We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ π=3/2+ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.  相似文献   
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High-resolution laser fluorescence spectroscopy, using a single-mode dye laser acting on a collimated atomic beam, has been performed to determine the hyperfine-structure (hfs) constants in six states of the 6p 5d configuration of135Ba and137Ba. Isotope shifts (IS) for eleven transitions between the 6s 5d and the 6p 5d configurations have also been measured. From an analysis of the energy levels, intermediate angular wavefunctions have been deduced. The wavefunctions are used to evaluate experimental hyperfine parameters from the experimental hfs constants. The parameters are, for the magnetic-dipole interaction compared with theoretical values, and for the electricquadrupole interaction used to estimate the nuclear quadrupole moments for the odd isotopes. The IS in the measured transitions are analysed using a King-plot, with the first resonance line in Ba II as the reference. Specific mass and field shifts are evaluated for the measured transitions. The field shifts have been used to determine the change in mean-square radius between the natural abundant Ba-isotopes.  相似文献   
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Pion-nucleon scattering amplitudes as well as Born amplitudes are calculated in a constant-cutoff approach to the canonical quantization of skyrmions, with the subsidiary conditions imposed on the quantum fields and their conjugate momenta such that all infrared singularities from the zero-frequency modes are eliminated. It is shown that the Born terms with recoil corrections are reproduced by the pion-nucleon linear and quadratic interactions.  相似文献   
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