A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D.Let Ωn,p1,p2,…,pn={z=（z2,z2,…,zn）′∈C^n：∑j=1^n｜zj）^Pj〈1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers.In this paper,we will prove that Φn,β2,γ2,…βn,γn（f）（z）=（f（z1）, preserves spirallikeness of type β and order α on Ωn,p1,p2,…,Pn.

On the time development of dispersion in electroosmotic flow througha rectangular channel

This is an analytical study on the time develop- ment of hydrodynamic dispersion of an inert species in elec- troosmotic flow through a rectangular channel. The objec- tive is to determine how the channel side walls may affect the dispersion coefficient at different instants of time. To this end, the generalized dispersion model, which is valid for short and long times, is employed in the present study. An- alytical expressions are derived for the convection and dis- persion coefficients as functions of time, the aspect ratio of the channel, and the Debye-Htickel parameter representing the thickness of the electric double layer. For transport in a channel of large aspect ratio, the dispersion may undergo several stages of transience. The initial, fast time develop- ment is controlled by molecular diffusion across the narrow channel height, while the later, slower time development is governed by diffusion across the wider channel breadth. For a sufficiently large aspect ratio, there can be an interlude between these two periods during which the coefficient is nearly steady, signifying the resemblance of the transport to that in a parallel-plate channel. Given a sufficiently long time, the dispersion coefficient will reach a fully-developed steady value that may be several times higher than that with- out the side wall effects. The time scales for these periods of transience are identified in this paper.

Optimal error estimates for Fourier spectral approximation of the generalized KdV equation

A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.

Fixed Point Theorems of the Iterated Function Systems

In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system.

Conditional Lie-Bcklund Symmetry and New Variable Separation Solutions of the Third Order KdV-Type Equations

The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-B¨acklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.

COOPERATIVE GAMES ON CONVEX GEOMETRIES WITH A COALITION STRUCTURE

This paper is mainly to discuss cooperative games on convex geometries with a coalition structure, which can be seen as an extension of cooperative games with a coalition structure. For this kind of games, the cooperation among unions and within each union will be the convex sets, i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively. The explicit form of the generalized Owen value for this kind of games is given, which can be seen as an extension of the Owen value. Eklrthermore, two special cases of this kind of games are researched. The corresponding Davoff indices are also stHdied. Fin~.llv ~n ilhl^r~＇i, ~r^l~ to ~