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Let C2k denote the cycle of length 2k and Cg = {C3, C4, . . . , Cg}. The girth of a graph G containing a cycle is the length of a shortest cycle in G, so a graph has girth at least g + 1 if it is Cg-free. The distance between vertices u and v in a graph G, denoted dG(u, v) is the minimum length of a uv-path in G. Then dG(·, ·) is a metric on V (G). The diameter of a connected graph G is max{dG(...

Dretske, F. 1970. Epistemic operators. Journal of Philosophy 67: 1007–23. Dretske, F. 1981. The pragmatic dimension of knowledge. Philosophical Studies 40: 363–78. Lewis, D. 1979. Scorekeeping in a language game. Journal of Philosophical Logic 8: 339–59. Lewis, D. 1996. Elusive knowledge. Australasian Journal of Philosophy 74: 549–67. Stine, G. C. 1976. Skepticism, relevant alternatives, and de...

Since its inception just over a century ago, the field of tumor virology has provided insights into the causes for many cancers. Patrick Moore, director of the Cancer Virology Program at the University of Pittsburgh, is a leading contributor to the field, having codiscovered two of the seven known human cancer-causing viruses. In 1994, with wife and collaborator Yuan Chang, Moore identified Kap...

In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.

A new formula for the pseudoinverse of a sum of symmetric matrices is presented, valid for arbitrary symmetric matrices without any restrictions relating to their column — or row — spaces. As an application of this formula a generalized version of the estimate minimizing the penalty is developed. This makes it possible to show that in a general case of estimation the problem is decomposed into ...

Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...

In this thesis I deal with the design of optimal interconnection networks. Optimality is interpreted as the largest possible number of nodes in the network, under given constraints on the number of connections attached to a node (degree of the node), and on the length of shortest paths between any two nodes (diameter of the network). Any interconnection network with bidirectional channels can b...