A single-step HSS method for non-Hermitian positive definite linear systems

In this paper, based on the Hermitian and skew-Hermitian splitting (HSS) iteration method, a single-step HSS (SHSS) iteration method is introduced to solve the non-Hermitian positive definite linear systems. Theoretical analysis shows that, under a loose restriction on the iteration parameter, the SHSS method is convergent to the unique solution of the linear system. Furthermore, we derive an upper bound for the spectral radius of the SHSS iteration matrix, and the quasi-optimal parameter is obtained to minimize the above upper bound. Numerical experiments are reported to the efficiency of the SHSS method; numerical comparisons show that the proposed SHSS method is superior to the HSS method under certain conditions.     

A generalized preconditioned HSS method for non-Hermitian positive definite linear systems

Based on the HSS (Hermitian and skew-Hermitian splitting) and preconditioned HSS methods, we will present a generalized preconditioned HSS method for the large sparse non-Hermitian positive definite linear system. Our method is essentially a two-parameter iteration which can extend the possibility to optimize the iterative process. The iterative sequence produced by our generalized preconditioned HSS method can be proven to be convergent to the unique solution of the linear system. An exact parameter region of convergence for the method is strictly proved. A minimum value for the upper bound of the iterative spectrum is derived, which is relevant to the eigensystem of the products formed by inverse preconditioner and splitting. An efficient preconditioner based on incremental unknowns is presented for the actual implementation of the new method. The optimality and efficiency are effectively testified by some comparisons with numerical results.     

Methods for wave equation prestack depth migration and numerical experiments

In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical re-     

A shadowing lemma for quasi-hyperbolic strings of flows

In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article.     

POTENTIAL INVERSION PROBLEMS FOR COUPLED SYSTEM OF DOWNGOING AND UPCOMING ONE-WAY WAVE EQUATIONS

1.IntroductionInthispaperthefollowingpotentialinversionproblemisconsideredThatis,givinganimpulseatthesurfacez~0,todeterminethewavefleldpandpotentialvfromtheimpulseresponseh.Inone-dimensionalcase3byfactorizingthewaveoperator,thewavefieldcanbesplitintoupcominganddowngoingwaves,sothewaveequationcanbeeasilyreducedtoacoupledfirst-ordersystem.Thedirectproblemandthecoefficiellt-inversionproblemcanbetreatedasCauchyproblemsintimeandinthedirectionofdepthregardedasthetime-likevariable[1].Theseproblemsar…     

Local detection of strongly irreducible Heegaard splittings

Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained and the allowable configurations are simple and useful. Splitting surfaces not conforming to these simple local pictures must be weakly reducible.     

Origination of In‐Phase Oscillations of Thin Plates with Aeroelastic Interaction

Synchronization of oscillations of thin elastic plates that are walls of a gasfilled channel is considered. The gas motion is described by a system of Navier–Stokes equations, which is solved using the secondorder MacCormack method with time splitting. The motion of the channel walls is described by a system of geometrically nonlinear dynamic equations of the theory of this plates, which is solved by the finitedifference method. Kinematic and dynamic contact conditions are imposed at the interface between the media. A numerical experiment is performed to determine typical dynamic regimes and study the transition of the aeroelastic system to inphase oscillations.     

An unconventional method for measuring the Tc L3‐edge of technetium compounds

Tc L₃‐edge XANES spectra have been collected on powder samples of SrTcO₃ (octahedral Tc⁴⁺) and NH₄TcO₄ (tetrahedral Tc⁷⁺) immobilized in an epoxy resin. Features in the Tc L₃‐edge XANES spectra are compared with the pre‐edge feature of the Tc K‐edge as well as other 4d transition metal L₃‐edges. Evidence of crystal field splitting is obvious in the Tc L₃‐edge, which is sensitive to the coordination number and oxidation state of the Tc cation. The Tc L₃ absorption edge energy difference between SrTcO₃ (Tc⁴⁺) and NH₄TcO₄ (Tc⁷⁺) shows that the energy shift at the Tc L₃‐edge is an effective tool for studying changes in the oxidation states of technetium compounds. The Tc L₃‐edge spectra are compared with those obtained from Mo and Ru oxide standards with various oxidation states and coordination environments. Most importantly, fitting the Tc L₃‐edge to component peaks can provide direct evidence of crystal field splitting that cannot be obtained from the Tc K‐edge.     

A Mössbauer study of hyperfine interaction in the systems Co x Mn3−x−y Fe y O4 and Ni x Mn3−x−y Fe y O4

A Mössbauer study of systems Co _x Mn_3?x?y Fe _y O₄ and Ni _x Mn_3?x?y Fe _y O₄ for values ofx=0·1, 0·5, 1·0 andy ranging from 0·1 to 2·0 in steps of 0·2 have been made. At room temperature samples fory values ranging in between 0·1 to 0·5 exhibit paramagnetic behaviour while all spectra for values ofy between 0·6 to 0·8 show relaxation effects. Well-defined hyperfine Zeeman spectra are observed for all the samples withy>0·8 and resolved in two sextets corresponding to octahedral and tetrahedral site symmetries and a central doublet probably due to the presence of super-paramagnetic particles in the system. The hyperfine field at⁵⁷Fe nucleus reduces with decreasing iron cobalt and nickel concentration. These observations have been explained in terms of site preference of cations and exchange interactions.     

二维潜水运动方程的分裂解法

本文通过对二维潜水运动方程的变形，按其在形式上所代表的意义不同，用和分裂方法，把它分解成“对流”和“扩散”两部分．对前者，用交替方向有限差分法求解；对后者，用交替方向Ｐｉｃａｒｄ迭代法进行计算，从而达到获得整个问题的解的目的．最后，用数值例子验证了所提方法的有效性，并与线性化的有限差分法作了对比，证明本文所提方法在计算精度上有所提高。