- P-ISSN1226-0657
- E-ISSN2287-6081
- KCI
ISSN : 1226-0657
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Vol.22 No.1
Abstract
The present paper is concerned with the notions of Lipschitz and asymptotic for perturbed functional differential system knowing the corresponding stability of functional differential system. We investigate Lipschitz and asymptotic stability for perturbed functional differential systems. The main tool used is integral inequalities of the Bihari-type, and all that sort of things.
Abstract
We introduce a decomposition on a symplectic subspace determined by symplectic structure and study its properties. As a consequence, we give an elementary proof of the deformation of the Grassmannians of symplectic subspaces to the complex Grassmannians.
Abstract
In this paper we characterize the isogonal and isotomic conjugates of conic. Every conic can be expressed by a quadratic rational B<TEX>$\acute{e}$</TEX>zier curve having control polygon <TEX>$b_0b_1b_2$</TEX> with weight w > 0. We show that the isotomic conjugate of parabola and hyperbola with respect to <TEX>${\Delta}b_0b_1b_2$</TEX> is ellipse, and that the isotomic conjugate of ellipse with the weight <TEX>$w={\frac{1}{2}}$</TEX> is identical. We also find all cases of the isogonal conjugate of conic with respect to <TEX>${\Delta}b_0b_1b_2$</TEX>. Our characterizations are derived easily due to the expression of conic by the quadratic rational B<TEX>$\acute{e}$</TEX>ezier curve in standard form.
Abstract
In this paper, we classify all nonconstant smooth CR maps from a sphere <TEX>$S_{n,1}{\subset}\mathbb{C}^n$</TEX> with n > 3 to the Shilov boundary <TEX>$S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$</TEX> of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of <TEX>$S_{n,1}$</TEX> and <TEX>$S_{p,q}$</TEX> or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.
Abstract
We define a hyperholomorphic function with values in split quaternions, provide split hyperholomorphic mappings on <TEX>${\Omega}{\subset}\mathbb{C}^2$</TEX> and research the properties of split hyperholomorphic functions.
Abstract
In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.
Abstract
In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of <TEX>$W_{1,2}$</TEX> norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.
Abstract
A normal surface is determined by how the surface under consideration meets each tetrahedron in a given triangulation. We call such a nice embedded disk, which is a component of the intersection of the surface with a tetrahedron, an elementary disk. We classify all elementary disk types in a truncated ideal triangulation.