The two-sided Pompeiu problem for discrete groups

The Pompeiu problem

Let f ∈ Lloc(R) ∩ S ′, S ′ is the Schwartz class of distributions, and ∫ σ(D) f(x)dx = 0 ∀σ ∈ G, (∗) whereD ⊂ Rn, n ≥ 2, is a bounded domain, the closure D̄ of which is C1−diffeomorphic to a closed ball. Then the complement of D̄ is connected and path connected. Here G denotes the group of all rigid motions in Rn. This group consists of all translations and rotations. It is conjectured that if f ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The Patent System’s Two-Sided Agency Problem

Two-sided Pushdown Automata over Free Groups

In the two-sided pushdown automata discussed in this paper, their two-sided pushdowns are introduced over free groups rather than free monoids. It is demonstrated that these automata with pushdowns introduced in this way characterize the family of recursively enumerable languages.

On a Two-Sided Turan Problem

Given positive integers n, k, t, with 2 ≤ k ≤ n, and t < 2, let m(n, k, t) be the minimum size of a family F of nonempty subsets of [n] such that every k-set in [n] contains at least t sets from F , and every (k − 1)-set in [n] contains at most t− 1 sets from F . Sloan et. al [11] determined m(n, 3, 2) and Füredi et. al [6] studied m(n, 4, t) for t = 2, 3. We consider m(n, 3, t) and m(n, 4, t) ...