In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

We show that the transformation (xn)n≥1 → (1/(1 + x1 + . . . + xn))n≥1 of the compact set of sequences (xn)n≥1 of numbers from the unit interval [0, 1] has a unique fixed point, which is attractive. The fixed point turns out to be a Hausdorff moment sequence studied in [3]. 2010 Mathematics Subject Classification: primary 37C25; secondary 44A60.

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].

We show that if G is a compact connected Abelian group such that, for some n ∈ N and some closed subgroup H of G(n) = {a ∈ G | na = 0}, the set G \H is disconnected, then G is topologically isomorphic with the circle group T.

For n ≥ 2 let ∆ be a Dynkin diagram of rank n and let I = {1, . . . , n} be the set of labels of ∆. A group G admits a weak Phan system of type ∆ over C if G is generated by subgroups Ui, i ∈ I , which are central quotients of simply connected compact semisimple Lie groups of rank one, and contains subgroups Ui,j = 〈Ui, Uj〉, i 6= j ∈ I , which are central quotients of simply connected compact s...

Industrial circuits contain, in addition to the binary logic elements n]and, n]or and n]xor gates, other logic elements such as three-state elements, busses and bidirectionals. Previous published work on automatic test pattern generation (ATPG) can not handle all of the above mentioned circuit elements, generates too large test sets, or generates test patterns which can cause circuit damage. A ...