A remark on T-duality and quantum volumes of zero-brane moduli spaces. T-duality (Fourier-Mukai duality) and properties of classical instanton moduli spaces can be used to deduce some properties of α ′-corrected moduli spaces of branes for Type IIA string theory compactified on K3 or T 4. Some interesting differences between the two compactifications are exhibited.

The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...

A convenient technique for proving kernel theorems for (LF)spaces (countable inductive limits of Fréchet spaces)is developed. The proposed approach is based on introducing a suitable modification of the functor of the completed inductive topological tensor product. Using such modified tensor products makes it possible to prove kernel theorems without assuming the completeness of the considered ...

The present paper investigates approximation spaces in the context of topological structures which axiomatise the notion of nearness. Starting with the framework of information quanta which distinguishes two levels of information structures, namely property systems (the first level) and information quantum relational systems (the second level), we shall introduce the notion of Pawlak’s property...

Topological quantum field theory led recently to a spectacular progress in numerical algebraic geometry. It was shown that generating functions of certain charactertistic numbers of modular spaces of stable algebraic curves with labelled points satisfy remarkable differential equations of KP -type (E. Witten, M. Kontsevich). In a later series of developments, this was generalized, partly conjec...

In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of...

A logic extending classical reasoning and supporting quantum reasoning is presented. The quantum logic is obtained by applying the exogenous semantics approach to propositional logic. The design is guided by the postulates of quantum mechanics and inspired by applications in quantum computation and information. The models of the quantum logic are superpositions of classical valuations. In order...