High frequency S wave envelope synthesis using a multiple non-isotropic scattering model: application to aftershocks from the 2008 Wenchuan earthquake

Based on the formulation of a multiple non-isotropic scattering process, a characteristic source time is introduced to define the initial impulse width of energy density at the source. An analytical expression of the initial intensity spectral density of a seismic wave is incorporated into the integral equation of seismic wave energy density. And, a recursive formula of Green＇s function is derived to obtain the higher order Green＇s function, which is included to describe the stronger non-isotropic scattering process. Then, the effect of the scattering pattern on the energy density envelope is investigated by the modified scattering theory. Significant differences arc found in the decay of the energy density envelopes with distances using different scattering patterns. The envelope synthesized by the forward dominated scattering pattern is larger than the results obtained by the isotropic and backward dominated scattering pattern. Different scattering patterns are also used to fit the observation data from the aftershocks of the 2008 Wenchuan earthquake. It is concluded that the envelopes synthesized by the forward scattering pattern can match the data better than the isotropic and backward dominated scattering cases, and a new interpretation of the coda wave is given. Finally, using the forward dominated scattering pattern, the envelope broadening of the observed data is reproduced.

A NON-ISOTROPIC MULTIPLE-SCALE TURBULENCE MODEL

This paper describes a newly developednon-isotropic multiple-scale turbulence model (MS/ASM) for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model performs significantly better than the single-scale k-e model. The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.

Non-isotropic weighted L^p estimates for the -equation on piecewise smooth strictly pseudoconvex domains

In this paper we obtain non-isotropic weighted Lp estimates with the boundary distance weight function for the-equation on piecewise smooth strictly pseudoconvex domains under a hypoth- esis of complex transversality in Cn using the explicit formula of solutions by Berndtsson-Andersson.

Maximal Operators and Singular Integrals with Non-Isotropic Dilation on Product Domains

In this paper, the authors study the with non-isotropic dilation on product domains. LP-mapping properties of certain maximal operators As an application, the LP-boundedness of the corre- sponding nomisotropic multiple singular integral operator is also obtained. Here the integral kernel functions Ω belong to the spaces L（logL）a（E1 × E2） for some a 〉 0, which is optimal.

Spatial Nonparametric Regression Estimation: Non-isotropic Case

Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction are required.

Initial－boundary Value Problem for a Class of Quasilinear Degenerate Parabolic Equations

in this work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assume that is non characteristic for the system X,,..',Xm. Under some hypothesis for the boundary of domain and the elliptic structure condition for nonlinear coerfficients Aij, Bj, C,(i, j= 1, ..', m), we have proved that the existence and regularity of solution for aboveinitialboudary value problems.

Poincaré and Sobolev Inequalities for Vector Fields Satisfying Hrmander's Condition in Variable Exponent Sobolev Spaces

In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type. We obtain the first order Poincare inequalities for vector fields satisfying Hormander＇s condition in variable non-isotropic Sobolev spaces. We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups. Moreover, we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups. These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p（x）-subLaplacian. Our results are only stated and proved for vector fields satisfying Hormander＇s condition, but they also hold for Grushin vector fields as well with obvious modifications.

THE CHARACTERISTIC POLYNOMIAL OF A GEOMETRIC LATTICE IN SYMPLECTIC GEOMETRY OVER FINITE FIELDS

Let F be a field and V= Vn（F）={（a1,…, an）|ai∈F} be the row vector space of finite dimension n over F. Let be a finite set ofsubspaces of Vsuch that U=（0）. And let L= L（（?）） be the set of intersections of dements of. Partial order L by reverse inclusion has V as its minimal element and as its set of atoms. We denote the partial order-

Rough Marcinkiewicz Integrals with Mixed Homogeneity on Product Spaces

In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m × R^n（m, n ≥ 2） are studied. The LP-boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.

Bubble Tree ConVergence for the Harmonic Sequence of Harmonic Surfaces in CP^n

We show that any harmonic sequence determined by a harmonic map from a compact Riemannian surface M to CP^n has a terminating holomorphic （or anti-holomorphic） map from M to CP^n, or a ＂bubble tree limit＂ consisting of a harmonic map f： M → CP^n and a tree of bubbles hλ^μ： S^2 --→ CP^n.