Given two Banach spaces X and Y, we analyze when the projective tensor product X?ˆ?Y has Corson's property (C) or is weakly Lindelöf determined (WLD), subspace of a compactly generated (WCG) space Hilbert space. For instance, show that: (i) WLD if only both Y are all operators from to Y? X? have separable range; (ii) WCG same holds for under assumption that every operator compact; (iii) ?p(?)?ˆ...

In this paper we consider Artinian modules over power series rings endowed with a Frobenius map. We describe a method for finding the set of all prime annihilators of submodules which are preserved by the given Frobenius map and on which the Frobenius map is not nilpotent. This extends the algorithm by Karl Schwede and the first author, which solved this problem for submodules of the injective ...

The Milne universe is an open Robertson-Walker universe with scale factor being equal to the cosmic time, which is therefore a locally flat spacetime. By analytically continuing the Schwarzschild spacetime, we obtain a generalized Milne space, in which the black hole horizon in the Schwarzschild spacetime turns to be a de Sitter-like horizon in the generalized Milne space. We present a solution...

We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states Hamiltonians (i.e., are quasi-locally Gibbsian) if conditional mutual information (CMI) any connected tripartition lattice is rapidly decaying in width middle region. For inject...

In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon–Nikod´ym property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the β-compactness, the β-...

In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called coreflexive coalgebras. Our approach in this note is an algebraically topological one. Introduction The concept of coreflexive coalgebras was studied, in the case of...

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

Bector et al., (1994) introduced the concept of univexity. Mishra (1998), Mishra and Reuda (2001) and Mishra et al., (2005) have applied and generalized these functions. Mathematical programming in complex spaces originated from Levinson’s discussion of linear problems (Levinson, 1966). Mishra and Reuda (2003) have generalized these upto first orders, second order with symmetric duality. Furthe...