This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated minimum spanning tree problem (CMST). A surrogate constraint relaxation incorporating cutting planes is proposed to explore the dual solution space. In the dual RAMP approach, primal-feasible solutions are obtained by simple tabu searches that project dual solutions onto primal feasible space. A prima...

Let X be a non-locally convex F-space (complete metric linear space) whose dual X' separates the points of X. Then it is known that X possesses a closed subspace N which fails to be weakly closed (see [3]), or, equivalently, such that the quotient space XIN does not have a point separating dual. However the question has also been raised by Duren, Romberg and Shields [2] of whether X possesses a...

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any b...

virtual colonialism (ameli, 2011) is reflecting a new trend of colonialismin the virtual space parallel to the physical space. according to ameli(2007), withthe “dual spacization” of life,the imperial powers like the united states of americatake the advantage of the synchronization and translocality of the virtual space toexpand their realm of imperial power through the “attraction” and “persua...

Let AN be the symmetric operator given by the restriction of A toN , where A is a self-adjoint operator on the Hilbert space H and N is a linear dense set which is closed with respect to the graph norm on D(A), the operator domain of A. We show that any self-adjoint extension AΘ of AN such that D(AΘ)∩D(A) = N can be additively decomposed by the sum AΘ = Ā + TΘ, where both the operators Ā and TΘ...

In fuzzy algebra, fuzzy subspaces are basic concepts. They had been introduced by Katsaras and Liu 1 in 1977 as a generalization of the usual notion of vector spaces. Since then, many results of fuzzy subspaces had been obtained in the literature 1–4 . Moreover, many researches in fuzzy algebra are closely related to fuzzy subspaces, such as fuzzy subalgebras of an associative algebra 5 , fuzzy...

In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is...

We investigate the structure of invariant subspaces of backward shift operator Lf = (f − f(0))/ζ on a large class of abstract Hilbert spaces of analytic functions on the unit disc where the forward shift operator Mζf = ζf acts as a contraction. Our main results show that under certain regularity conditions on the norm of such a space, the functions in a nontrivial invariant subspace of L have m...

Let B be a class of point-line geometries. Given Γi ∈ B with subspace Si for i = 1, 2, does any isomorphism Γ1−S1 −→ Γ2−S2 extend to a unique isomorphism Γ1 −→ Γ2? It is known to be true if B is the class of almost all projective spaces or the class of almost all non-degenerate polar spaces. We show that this is true for the class of almost all strong parapolar spaces, including dual polar spac...