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ISSN : 1226-0657
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Vol.9 No.2
Abstract
The study of fractal hedgehogs is a recent development in the ambit of fractal theory and nonlinear analysis. The intent of this paper is to present a study of fractal hedgehogs along with some of their special constructions. The main result is a new fractal hedgehog theorem. As a consequence, a fractal projective hedgehog theorem of Martinez-Maure is obtained as a special case, and several fractal hedgehogs and similar images are discussed.
Abstract
In this article, we prove various properties and some Liouville type theorems for quasi-strongly p-harmonic maps. We also describe conditions that quasi-strongly p-harmonic maps become p-harmonic maps. We prove that if <TEX>$\phi$</TEX> : <TEX>$M\;\longrightarrow\;N$</TEX> is a quasi-strongly p-harmonic map (\rho\; <TEX>$\geq\;2$</TEX>) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive sectional curvature such that the <TEx>$(2\rho－2)$</TEX>-energy, <TEX>$E_{2p-2}(\phi)$</TEX> is finite, then <TEX>$\phi$</TEX> is constant.
Abstract
Definition and some properties of the degree-n bifurcation set are introduced. It is proved that the interval formed by the intersection of the degree-n bifurcation set with the real line is explicitly written as a function of n. The functionality of the interval is computationally and geometrically confirmed through numerical examples. Our study extends the result of Carleson & Gamelin ［2］.
Abstract
We here characterize semigroups (which are called completely right projective semigroups) for which every S-automaton is projective, and then examine some of the relationships with the semigroups (which are called completely right injective semigroups) in which every S-automaton is injective.