Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q. In this note, block representations for the group inverse of L and Q are given. The resistance distance in a graph can be obtained from the block representation of the group inverse of L.

Using the theory of the symmetry groups for PDEs of order two ([7], [17], [20]), one finds the symmetry group G associated to Ţiţeica surfaces PDE. One proves that Monge-Ampère-Ţiţeica PDE which is invariant with respect to G, where G is the maximal solvable subgroup of the symmetry group G, is just the PDE of Ţiţeica surfaces. One studies the inverse problem and one shows that the Ţiţeica surf...

background: autologous skin graft is frequently used in the field of plastic, and reconstructive surgery. the engraftment is dependent upon revascularization and angiogenesis, which can be regulated by different factors. in addition to its hematopoietic effects, erythropoietin is shown to positively affect the wound healing process. objectives: we studied effects of human erythropoietin on reva...

It is proved that the inverse homomorphic image of every language generated by a conjunctive grammar can be generated by a conjunctive grammar as well, and, given an arbitrary grammar G over an alphabet Γ and a homomorphism h : Σ∗ → Γ∗, a grammar for the language h−1(L(G)) ⊆ Σ∗ can be effectively constructed. Together with the known results on conjunctive grammars, this implies that the languag...

A graph G is said to be nonsingular (resp., singular) if its adjacency matrix A(G) is nonsingular (resp., singular). The inverse of a nonsingular graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s. Consider connected bipartite graphs with unique perfect matchings such that the graph obtained by contract...

PAD&APPROXIMANTS FOR THE SOLUTION OF A SYTEM OF NONLINEAR EQUATIONS ANNIE Cm-T? and PAUL VAN DER CRUYSSEN University of Antwerp, Department of Mathematics, Universiteitsplein 1, B-2610 Wihijk, Belgium (Receioed January 1981; and in revised form May 1982) Communicated by J. F. Traub Abstract-Let F: R4 *R’ and let x* be a simple root of the system of nonlinear equations F(x) = 0. We will construc...

In this paper an inverse problem of the weighted shortest arborescence problem is discussed. That is. given a directed graph G and a set of nonnegative costs on its arcs. we need to modify those costs as little as possible to ensure that T, a given (.I-arborescence of G, is the shortest one. It is found that only the cost of T needs modifying. An O(rz”) combinatorial algorithm is then proposed....

A divergence function defines a Riemannian metric g and dually coupled affine connections ∇ and ∇∗ with respect to it in a manifold M . When M is dually flat, that is flat with respect to ∇ and ∇∗, a canonical divergence is known, which is uniquely determined from (M, g,∇,∇∗). We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic ...

Over the past decade it has become accepted that G protein-coupled receptors (GPCRs) can activate G proteins and thus initiate signaling in the absence of agonist; this spontaneous receptor activity can be inhibited to varying degrees by antagonists, a phenomenon termed inverse ugonism. The modulation of spontaneous GPCR activity by the binding of specific ligands implies that receptors can int...

In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...