Bentea and Tu{a}rnu{a}uceanu~(An. c{S}tiinc{t}. Univ. Al. I.Cuza Iac{s}, Ser. Nouv{a}, Mat., {bf 54(1)} (2008), 209-220)proposed the following problem: Find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$Q_8times mathbb{Z}_n$ where $Q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. In this paper weconsider more general grou...

Generalized semi-infinite optimization problems (GSIP) are considered. The difference between GSIP and standard semi-infinite problems (SIP) is illustrated by examples. By applying the ’Reduction Ansatz’, optimality conditions for GSIP are derived. Numerical methods for solving GSIP are considered in comparison with methods for SIP. From a theoretical and a practical point of view it is investi...

We introduce the concepts of T-generalized state machines and coverings of products of them. Also some of algebraic properties of them are investigated. Finely some products such as direct sum and sum of Tgeneralized state machines are introduced. An interesting distributive property of cascade product over the sum of Tgeneralized state machines concern to covering of T-generalized state machin...

1. Results. It is well known [2] that if A and B are n and msquare matrices respectively then (1) det(^ ® B) = (det(A))m(det(B))» where A®B is the tensor or direct product of A and B. By taking absolute values on both sides of (1) we can rewrite the equality as (2) I det(4 B) |2 = (det(4^*))'»(det(73*P))«, where A* is the conjugate transpose of A. The main result is a direct extension of (2...

We consider a generalized semi-infinite programming problem (GSIP) with one semi-infinite constraint where the index set depends on the variable to be minimized. Keeping in mind the integral global optimization method of Zheng & Chew and its modifications we would like to outline theoretical considerations for determining coarse approximations of a solution of (GSIP) via global optimization of ...

Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory. Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly. Indeed, this technique can be generalized for an extended set of gates, the so called Ck hierarchy gates, intro...