We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces as discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geome...

We obtain a bosonization prescription that allows to represent the energy-momentum tensor and supersymmetry generators of non-critical superstring theories with minimal matter as those of topological supergravity. Superstrings with N = 1 and N = 2 world-sheet supersymmetry are considered. The topological symmetry associated with the topological supergravity representation is studied. It is show...

In this chapter we define the topology of 2D asymmetric tensor fields in terms of two graphs corresponding to the eigenvalue and eigenvector analysis for the tensor fields, respectively. Asymmetric tensor field topology can not only yield a concise representation of the field, but also provide a framework for spatial-temporal tracking of field features. Furthermore, inherent topological constra...

Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: tensor product and multiplicity varieties. These varieties are closely related to Nakajima’s quiver varieties and should play an important role in the geometric constructions of tensor products and intertwining operators. In particular, it is shown that the set ...

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces as discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geome...

SUMMARY This paper proposes a novel signal estimation method that uses a tensor product expansion. When a bivariable function, which is expressed by two-dimensional matrix, is subjected to conventional tensor product expansion, two single variable functions are calculated by minimizing the mean square error between the input vector and its outer product. A tensor product expansion is useful for...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

4 Derived Tensor 15 4.1 Tensor Product of Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Hoflat Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Derived Tensor Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Change of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...