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...

Let X be a Banach space and let G be a closed bounded subset of X. For x1, x2, . . . , xm ∈ X, we set ρ x1, x2, . . . , xm,G sup{max1≤i≤m‖xi−y‖ : y ∈ G}. The setG is called simultaneously remotal if, for any x1, x2, . . . , xm ∈ X, there exists g ∈ G such that ρ x1, x2, . . . , xm,G max1≤i≤m‖xi−g‖. In this paper, we show that if G is separable simultaneously remotal in X, then the set of ∞Bochn...

We say that X×Y satisfies the Uniquely Universal property (UU) iff there exists an open set U ⊆ X × Y such that for every open set W ⊆ Y there is a unique cross section of U with Ux = W . Michael Hrus̆ák raised the question of when does X × Y satisfy UU and noted that if Y is compact, then X must have an isolated point. We consider the problem when the parameter space X is either the Cantor spac...

When we have two data sets and want to find the nearest neighbour of each point in the first dataset among points in the second one, we need the all nearest neighbour operator. This is an operator in spatial databases that has many application in different fields such as GIS and VLSI circuit design. Existing algorithms for calculating this operator assume that there is no pre computation on the...