In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an $H_{nu}$- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible...

The notion of partial fidelities as invented recently by A.Uhlmann for pairs of finite dimensional density matrices will be extended to the vNalgebraic context and is considered and thoroughly discussed in detail from a mathematical point of view. Especially, in the case of semifinite vN-algebras formulae and estimates for the partial fidelity between the functionals of a dense cone of inner de...

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

This paper considers when one can invert general recursive operators which map a class of functions F to F . In this regard, we study four different notions of inversion. We additionally consider enumeration of operators which cover all general recursive operators which map F to F in the sense that for every general recursive operator Ψ mapping F to F , there is a general recursive operator in ...

(b) We know that T is invertible if and only if its matrix is invertible with respect to any basis; we also know that a matrix is invertible if and only if its determinant is zero. If A is a matrix representing T in some basis, then T is invertible if and only if A is invertible if and only if det(T ) = det(A) 6= 0. (c) If T has matrix A under some basis, then T−1 has matrix A−1 under the same ...

On the topology of the group of invertible elements – A Survey – The topological structure of the group of invertible elements in a unital Banach algebra (regular group for short) has attracted topologists from the very beginning of homotopy theory. Be it for its own sake simply to show the instrumental power of newly invented methods or because there were important applications, the most notab...

Stabilization problems of linear systems with right invertible constraints have mostly been solved for both global and semi-global frameworks. Linear systems subject to non-right invertible constraints have completely different characteristics compared to those with right invertible constraints. This paper addresses the control problems of linear systems subject to non-right invertible constrai...