Let ? be a weight function defined on locally compact group G, 1?p<+?, S?G and let us assume that for any s?S, the left translation operator Ts is continuous from weighted Lp-space Lp(G,?) into itself. For given set ??C, vector f?Lp(G,?) said to (?,S)-dense if {?Tsf:???,s?S} dense in Lp(G,?). In this paper, we characterize existence of vectors terms ?.

Given a set S of points in the plane, a triangulation of S is a partition of the convex hull of S into triangles whose vertices are the points of S. A triangulation of S is said to be Delaunay if no point of S lies inside the triangles’ circumcircles. In this thesis, we study a generalization of these notions to a set S of disjoint segments in the plane. At first, we define a new family of diag...

It is known that if f : R → R is continuous then ẋ = f(x) with x(0) = x0 has at least one solution on some time interval [0, T (x0)). However, when f is not Lipschitz one cannot guarantee that the solutions are unique. In this paper we show that the set of points x0 ∈ R is a countable, nowhere dense set. (In particular, we show that if f(x0) 6= 0 then the solution must be locally unique.)

We provide a detailed construction of the three dimensional partition for the Julia set of an infinitely renormalizable quadratic polynomial. We show that for an unbranched infinitely renormalizable quadratic polynomial having complex bounds, the three-dimensional partition determines points in the Julia set dynamically. Furthermore, we construct a partition in the parameter space about a subse...

in today’s competitive market, for a business firm to win higher profit among its rivals, it is of necessity to evaluate, and rank its potential customer segments to improve its customer relationship management (crm). this brings the importance of having more efficient decision making methods considering the current fast growing information era. these decisions usually involve several criteria,...

A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we study connectedness and disconnectedness properties of groups G with the property that every closed subgroup of G is locally pseudocompact. We show that the completion of the component G0 of G contains every connected compact subgroup of the completion of G. We also prov...

Let M be the countably infinite metric fan. We show that Ck(M, 2) is sequential and contains a closed copy of Arens space S2. It follows that if X is metrizable but not locally compact, then Ck(X) contains a closed copy of S2, and hence does not have the property AP. We also show that, for any zero-dimensional Polish space X, Ck(X, 2) is sequential if and only if X is either locally compact or ...

A. We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distance-d dominating-set problem, also known as the (k, d)-centres problem, is fixed-parameter tractable on any class that is nowhere dense and closed under induced subgraphs. This generalises known re...

Let Z be the center of a nonnoetherian dimer algebra on torus. Although itself is also nonnoetherian, we show that it has Krull dimension 3, and locally noetherian an open dense set Max . Furthermore, reduced / nil depicted by Gorenstein singularity, contains precisely one closed point positive geometric dimension.