We consider the Schrödinger equation with a nondispersive logarithmic nonlinearity and repulsive harmonic potential. For suitable range of coefficients, there exist two positive stationary solutions, each one generating continuous family solitary waves. These solutions are Gaussian, turn out to be orbitally unstable. also discuss notion ground state in this setting: for any natural definition, ...

We consider the three forms of self-duality that can be exhibited by a planar graph G, map self-duality, graph self-duality and matroid self-duality. We show how these concepts are related with each other and with the connectivity of G. We use the geometry of self-dual polyhedra together with the structure of the cycle matroid to construct all self-dual graphs. 1.1. Forms of Self-duality. Given...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

Let G be a locally compact group, π : G → U(H) be a strongly continuous unitary representation, and CB(B(H)) the space of normal completely bounded maps on B(H). We study the range of the map Γπ : M(G)→ CB(B(H)), Γπ(μ) = Z G π(s)⊗ π(s)dμ(s) where we identify CB(B(H)) with the extended Haagerup tensor product B(H)⊗ B(H). We use the fact that the C*-algebra generated by integrating π to L(G) is u...

Suppose k is a positive integer, G and H are graphs, and / is a k-to-l correspondence from a vertex set of G onto a vertex set of H. Conditions on the adjacency matrices are given that are necessary and sufficient for / to extend to a continuous k-to-l map from G onto H .

In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor’s K-group of the real numbers into the additive group of real numbers. Usi...

This paper proposes an extension of an SOM called the “SOM of SOMs,” or SOM, in which objects to be mapped are self-organizing maps. In SOM, each nodal unit of a conventional SOM is replaced by a function module of SOM. Therefore, SOM can be regarded as a variation of a modular network SOM (mnSOM). Since each child SOM module in SOM is trained to represent an individual map, the parent map in S...

This paper presents a new mapping to construct the self-organizing map on the curved seamless surface. This mapping is developed for the planar triangle surface derived from the conformal selforganizing map [C.-Y. Liou, Y.-T. Kuo, Conformal self-organizing map for a genus-zero manifold, Visual Comput. 21(5) (2005) 340–353]. It shows how to construct a seamless surface for the genus-zero manifol...