Showing papers in "Annales Umcs, Mathematica in 2015"

On pseudo-BCI-algebras

Abstract: The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.

Proximinality and co-proximinality in metric linear spaces

Abstract: As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces.

Components with the expected codimension in the moduli scheme of stable spin curves

Abstract: Here we study the Brill–Noether theory of “extremal” Cornalba’s theta-characteristics on stable curves C of genus g, where “extremal” means that they are line bundles on a quasi-stable model of C with #(Sing(C)) exceptional components.

Pattern avoidance in partial words over a ternary alphabet

Abstract: Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with \(m\) distinct variables and of length at least \(2^m\) is avoidable over a ternary alphabet and if the length is at least \(3\cdot 2^{m-1}\) it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.

A multidimensional singular stochastic control problem on a finite time horizon

Abstract: A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time Moreover, we prove that an optimal control exists and is unique

A-manifolds on a principal torus bundle over an almost Hodge A-manifold base

Abstract: An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇ X Ric(X, X) = 0 This condition generalizes the Einstein condition We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds

Statuses and double branch weights of quadrangular outerplanar graphs

Abstract: In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C 4 . We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.

The natural transformations between r-th order prolongation of tangent and cotangent bundles over Riemannian manifolds

Abstract: If (M, g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM → T*M given by v → g(v, –) between the tangent TM and the cotangent T*M bundles of M In the present note first we generalize this isomorphism to the one J r TM → J r T*M between the r-th order prolongation J r TM of tangent TM and the r-th order prolongation J r T*M of cotangent T*M bundles of M Further we describe all base preserving vector bundle maps D M (g) : J r TM → J r T*M depending on a Riemannian metric g in terms of natural (in g) tensor fields on M