In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is satisfied by a wide range of Banach spaces including all the classical spaces. We then investigate which constructions of new Banach spaces from old ones preserv...

A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs P1,P2, . . . ,Pn a vertex (P1,P2, . . . ,Pn)-partition of a graph G is a partition {V1, V2, . . . , Vn} of V (G) such that for each i = 1, 2, . . . , n the induced subgraph G[Vi] has property Pi. The class of all graphs having a vertex (P1,P2, . . . ,Pn)partition is denoted by P1◦P2◦ · · · ◦Pn....

using qcd factorization for the hadronic matrix elements, we show that existing data, inparticular the branching ratios br ( b →j/ψk) and br ( b →j/ψπ), can be accounted for in this approach.we analyze the decay b j /k( ) within the framework of qcd factorization. the calculation of therelevant hard-scattering kernels for twist-2 and twist-3 is completed. we calculate this decay in a special...

Abstract Properties can be tailored by tuning composition in high-order spaces. For spaces with complex phase behavior, modeling the properties as a function of and distribution remains formidable challenge. We present materials structure–property factorization (MSPF) an approach to automate such data identify synergistic interactions. MSPF is interpretable machine learning algorithm that coupl...

The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

1 Summary We investigated matrix factorization in three applications: mimimum mean square error decision feedback equalization (which uses a special form of the Cholesky factorization), code division multiple access (which uses a traditional form of the Cholesky factorization) and blind equalization (which uses the singular value decomposition). The MMSE-DFE application's factorization was both...

Recently, location-based social networks (LBSNs), such as Gowalla, Foursquare, Facebook, and Brightkite, etc., have attracted millions of users to share their social friendship and their locations via check-ins. The available check-in information makes it possible to mine users’ preference on locations and to provide favorite recommendations. Personalized Point-of-interest (POI) recommendation ...

Abstract. We extend our previous work on a convergent algorithm for uni-orthogonal nonnegative matrix factorization (UNMF) to the case where the data matrix is decomposed into three factors with two of them are constrained orthogonally and the third one is used to absorb the approximation error. Due to the way the factorization is performed, we name it as bi-orthogonal nonnegative matrix tri-fa...