We give a Coulson integral formula and Coulson-Jacobs for the p-Schatten energy of bipartite graphs. use these formulas to compare different trees by using quasiorder, establishing maximality paths minimality stars among all trees.

The C* -algebra extensions of a topological space can be made into an abelian group which is naturally equivalent to the Khomology group of odd dimension [1] which has a close relation with index theory and is one of the starting points of KK theory [8]. The Cp -smoothness of an extension of a manifold was introduced in [3, 4], where Cp denotes the Schatten-von Neumann p-class [5]. We generaliz...

In this paper, we study the convexity of the integral operator

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

Schatten-IT sind Systeme, Organisationsstrukturen oder Prozesse, die Geschäftsprozesse unterstützen, aber weder technisch noch strategisch ins IT-Service-Management integriert sind. Um in Unternehmen ein Bewusstsein für Schatten-IT zu schaffen, wurde ein Lernspiel entwickelt, welches die Facetten von Schatten-IT spielerisch verdeutlichen soll. In diesem Paper wird der Prototyp dieses Spieles vo...

The CUR decomposition is a factorization of low-rank matrix obtained by selecting certain column and row submatrices it. We perform thorough investigation what happens to such decompositions in the presence noise. Since are nonuniquely formed, we investigate several variants give perturbation estimates for each terms magnitude noise broad class norms which includes all Schatten $p$-norms. given...

Let M be a von Neumann algebra and self-adjoint operator affiliated with M. We define the notion of an “integral symmetrically normed ideal” introduce space OC[k](R)⊆Ck(R) functions R→C such that following holds: for any integral ideal I f∈OC[k](R), function Isa∋b↦f(a+b)−f(a)∈I is k-times continuously Fréchet differentiable, formula its derivatives may written in terms multiple integrals. Moreo...