Complexiton Solutions of a Special Coupled mKdV System

For a special coupled mKdV system, which can be derived from a two-layer fluid model, Hirota＇s bilinear direct method is used to construct and yield the complexiton solutions. The detailed physical properties of complexitons are filrther illustrated graphically.

Painlevé Property and Complexiton Solutions of a Special Coupled KdV Equation

A special coupled KdV equation is proved to be the Painleve property by the Kruskal＇s simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota＇s bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical eomplexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically.

ON THE BROAD OPTIMALITY OF THE ORTHOGONAL DESIGN WITH ANY ORDER INTERACTION EFFECTS

The problem on the optimality of the orthogonal design has been studied and proved that the orthogonal design is A-, D-, E-optimal for the experiment designs under the additive model of the main effect. In Ref. [2], it has been obtained

THE BIEBERBACH CONJECTURE FOR UNIVALENT FUNCTIONS WITH RESTRICTED SECOND AND THIRD COEFFICIENTS

Let S denote the class of all univalent and analytical functions f(Z) in the unit disk |Z|<1, with the

PROPERTIES OF H_p FUNCTIONS

Let Hp be the class of functions f(z), each of which is regular in |z|<1 and satisfies Schur improved Hilbert’s inequality into the fol-