Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj−2Fij . When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting ...

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

INTRODUCTION The Theory of Distance Geometry [1] allows coordinate-free formulations for most position analysis problems. Using such formulations, the inverse kinematics of a serial robot can be performed by using a distance matrix, one whose entries are squared distances between pairs of points selected on the axes of the robot. While some of these distances are known (such as the distances be...

Y. Huang acknowledges partial support from a UCF Graduate College Presidential Fellowship and National Science Foundation (NS F) grant No. 1200566. C. Li acknowledges partial support from NSF grants No. 0806931 and No. 0963146. M. Georgiopoulos acknowledges partial support from NSF grants No. 1161228 and No. 0525429. G. G. Anagnostopoulos acknowledges partial support from NSF grant No. 1263011....

Let T be a tree on n vertices and let the n− 1 edges e1, e2, . . . , en−1 have weights that are s× s matrices W1,W2, . . . ,Wn−1, respectively. For two vertices i, j, let the unique ordered path between i and j be pi,j = er1er2 . . . erk . Define the distance between i and j as the s × s matrix Ei,j = ∏k p=1Wep . Consider the ns × ns matrix D whose i, j-th block is the matrix Ei,j . We give a f...

Adipose tissue-derived microvascular fragments (ad-MVF) represent promising vascularisation units for bioengineered Integra® matrix wound dressing (MWD). However, due to the sheet-like structure with small pore sizes, the seeding of this matrix with ad-MVF is mainly limited to its surface. Integra® flowable wound matrix (FWM) may be suitable to achieve a more homogeneous distribution and, thus,...