We define here e-chaos and study its interrelationships with P -chaos and Ruelle-Takens chaos. We show that a continuous self map f on a compact metric space is e-chaotic (P -chaotic) need not imply the induced map f̄ : K(X) → K(X) is e-chaotic (P -chaotic) and vice-versa, where K(X) is the space of all non-empty compact subsets of X endowed with Hausdorff metric. Mathematics Subject Classificat...

For a bounded domain Ω equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from (Ω, g) to a compact Riemannian manifold (N, h) ↪→ Rk without boundary. We generalize the notion of stationary harmonic maps and prove their partial regularity. We also discuss the global Lipschitz and piecewise C1,α-regularity of harmonic maps from (Ω, g) to manifolds that su...

In this article, the use of the self-organizing map (SOM) is approached on the basis of current theories of learning. Possibilities of computer and networked platforms that aim at helping human learning are also inspected. It is shown how the SOM can be considered a model of constructive learning. The area of constructive learning is outlined and two cases of using the self-organizing map in co...

We study the interplay of spin and orbital degrees of freedom in a triplet superconductor-ferromagnet junction. Using a self-consistent spatially dependent mean-field theory, we show that increasing the angle between the ferromagnetic moment and the triplet vector order parameter enhances or suppresses the p-wave gap close to the interface, according to whether the gap antinodes are parallel or...

For two not necessarily commutative topological groups G and T , let H(G, T ) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G, T ) is a k-space. As a consequence we obtain that if G1 is a dense subgroup of G then H(G1, T ) is homeomorphic to H(G,T ), and if G is separable h-complete, then the...

Let G be a real semisimple Lie group. Harish-Chandra has defined the Schwartz space, V[G), on G. A tempered distribution on G is a continuous linear functional on R G ) . If the real rank of G equals one, Harish-Chandra has published a version of the Plancherel formula for I^(G) [3(k), 5241. We restrict the Fourier transform map to %(G), and we compute the image of the space V(G) [Theorem 31. T...

suppose $f$ is a map from a non-empty finite set $x$ to a finite group $g$. define the map $zeta^f_g: glongrightarrow mathbb{n}cup {0}$ by $gmapsto |f^{-1}(g)|$. in this article, we show that for a suitable choice of $f$, the map $zeta^f_g$ is a character. we use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin g$) is a character, where $w(t_1,t...

where F : T × R → CK(R) is a set-valued map and g : T × T → R is a single-valued continuous map (CK(R) denotes the set of nonempty, closed, and convex subsets of R). In Section 3 some general existence principles for inclusions (1.1) are derived by using fixed point theory discussed in [1]. In Section 4 we present a specific function g such that y is a solution of (1.1) if and only if y is a so...

A self-dual map $G$ is said to be \emph{antipodally self-dual} if the dual $G^*$ antipodal embedded in $\mathbb{S}^2$ with respect $G$. In this paper, we investigate necessary and/or sufficient conditions for a antipodally self-dual. particular, present combinatorial characterization terms of certain \emph{involutive labelings}. The latter lead us obtain \emph{strongly involutive} (a notion rel...