The proof of Wagner's Conjecture by Robertson and Seymour gives a nite description of any family of graphs which is closed under the minor ordering. This description is a nite set of graphs called the obstructions of the family. Since the intersection and the union of two minor closed graph families is again a minor closed graph family, an interesting question is that of computing the obstructi...

Let K be an algebraically closed field of prime characteristic p, let X be a semiabelian variety defined over a finite subfield of K, let Φ : X −→ X be a regular self-map defined over K, let V ⊂ X be a subvariety defined over K, and let α ∈ X(K). The Dynamical Mordell-Lang Conjecture in characteristic p predicts that the set S = {n ∈ N : Φ(α) ∈ V } is a union of finitely many arithmetic progres...

Ehrenfeucht's Conjecture is equivalent with the ascending chain condition for word equations. A related conjecture concerns the descending chain condition for word equations. We show that if this conjecture holds then an arbitrary in nite language L possesses a nite subset F such that the language L F is a disjoint union of its nite test sets. We prove this consequence of the descending chain c...

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are int...

the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open ...

Let R be a real closed field. The Pierce-Birkhoff conjecture says that any piecewise polynomial function f on Rn can be obtained from the polynomial ring R[x1, . . . , xn] by iterating the operations of maximum and minimum. The purpose of this paper is twofold. First, we state a new conjecture, called the Connectedness conjecture, which asserts the existence of connected sets in the real spectr...

closed families of sets. Poonen showed that if a finite union-closed family of sets S contains three of the 3−sets in some 4−set, then one of the elements of that 4−set is contained in at least half the members of the family S. This condition intrigued us, and we began to investigate collections of 3−sets for which it fails. The alternative statement that no 4−set contain more than two 3−sets i...

  Abstract   Background: The tibial diaphyseal fractures are the most common type of long   bone fractures encountered by most orthopedic surgeons. In accordance with descriptive indices of tibia fractures on the basis of their location in the bone, distal tibia   fractures have the second incidence of all tibia fractures after the middle tibia fractures.   The purpose of the study was to asses...