it is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. we introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. we deal with vietoris and hausdorff continuity concepts.stability of microperiodi...

In this paper, we introduce the notion of an extended metric space ($p$-metric space) as a new generalization of the concept of $b$-metric space. Also, we present the concept of $(psi ,varphi )_{Omega}$-contractive mappings and we establish some fixed point results for this class of mappings in ordered complete $p$-metric spaces. Our results generalize several well...

Clustering is one of the known techniques in the field of data mining where data with similar properties is within the set of categories. K-means algorithm is one the simplest clustering algorithms which have disadvantages sensitive to initial values of the clusters and converging to the local optimum. In recent years, several algorithms are provided based on evolutionary algorithms for cluster...

Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

A known case of nephrotic syndrome aged 32 months was admitted to ICU because of loss of consciousness. In physical exam he had tachycardia, tachypnea and hypotension. Lab data showed metabolic alkalosis and hypoxia. In CXR, vascular cut off was seen in right lung and perfusion lung scan showed absence of perfusion in the right lung.Treatment was started with heparin and streptokinase, bu...

We show how the zero structure of a basis of the null space of a positive semidefinite matrix can be exploited to very accurately compute its Cholesky factorization. We discuss consequences of this result for the solution of (constrained) linear systems and eigenvalue problems. The results are of particular interest if A and the null space basis are sparse.