The Translational Hull of Strongly Inverse Wrpp Semigroups

In this paper, we obtain some characterizations of the translational hull of strongly inverse wrpp semigroups. And we prove that the translational hull of a strongly inverse wrpp semigroup is still of the same type.

Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.

Towards a Theoretical Background for Strong-Scattering Inversion–Direct Envelope Inversion and Gel’fand-Levitan-Marchenko Theory

Strong-scattering inversion or the inverse problem for strong scattering has different physical-mathematical foundations from the weak-scattering case.Seismic inversion based on wave equation for strong scattering cannot be directly solved by Newton’s local optimization method which is based on weak-nonlinear assumption.Here I try to illustrate the connection between the Schr̈odinger inverse scattering(inverse problem for Schr̈odinger equation)by GLM(Gel’fand-Levitan-Marchenko)the-ory and the direct envelope inversion(DEI)using reflection data.The difference between wave equation and Schr̈odinger equation is that the latter has a potential independent of frequency while the former has a frequency-square dependency in the potential.I also point out that the traditional GLM equation for potential inversion can only recover the high-wavenumber components of impedance profile.I propose to use the Schr̈odinger impedance equation for direct impedance inversion and introduce a singular impedance function which also corresponds to a singular potential for the reconstruction of impedance profile,including discontinuities and long-wavelength velocity structure.I will review the GLM theory and its application to impedance inversion including some numerical examples.Then I analyze the recently developed multi-scale direct envelope inversion(MS-DEI)and its connection to the inverse Schr̈odinger scattering.It is conceivable that the combination of strong-scattering inversion(inverse Schr̈odinger scattering)and weak-scattering inversion(local optimization based inversion)may create some inversion methods working for a whole range of inversion problems in geophysical exploration.

Iterative Algorithms of Common Solutions for Quasi-Variational Inclusion and Fixed Point Problems

By introducing the resolvent operator associated with a maximal monotone mapping, the author obtains a strong convergence theorem of a generalized iterative algorithm for a class of quasi-variational inclusion problems, which extends and unifies some recent results.

A NOTE ON CLINE'S FORMULA FOR TWO SUBCLASSES OF GENERALIZED DRAZIN INVERSES

For a Banach algebra A with identity and a, b, c, d ∈ A, the relations between the extended g-Drazin inverse(resp. generalized strong Drazin inverse)of ac and that of bd are given, when bac = bdb and cac = cdb.