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...

Let Map(K,X) denote the space of pointed continuous maps from a finite cell complex K to a space X. Let E∗ be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on K and X, Map(K,X) will send an E∗–isomorphism in either variable to a map that is monic in E∗ homology. Interesting examples arise by letting E∗ be K–theory, the finite complex K...

There are two distinct approaches to solving reinforcement learning problems, namely, searching in value function space and searching in policy space. Temporal di erence methods and evolutionary algorithms are well-known examples of these approaches. Kaelbling, Littman and Moore recently provided an informative survey of temporal di erence methods. This article focuses on the application of evo...

This paper studies the set of n × n matrices for which all row and column sums equal zero. By representing these matrices in a lower dimensional space, it is shown that this set is closed under addition and multiplication, and furthermore is isomorphic to the set of arbitrary (n−1)×(n−1) matrices. The Moore-Penrose pseudoinverse corresponds with the true inverse, (when it exists), in this lower...

Whereas Moore’s law continues to push the industry to ever more complex technologies (More Moore) supporting sophisticated digital applications, the so-called More than Moore technologies are finding more and more heterogeneous application domains. EDA challenges in More Moore are related to power optimisation, DfM and verification needs whereas the More than Moore technologies require EDA tool...

If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z) g-Drazin invertible, we study conditions under which the g-Drazin inverse AD(z) is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a matrix valued function and a result on diff...

Let G denote an associative iï-space with unit (e.g. a topological group). We will show that the relations between G and a classifying space B Q axe more readily displayed using a geometric analog of the resolutions of homological algebra. The analogy is quite sharp, the stages of the resolution, whose base is BQ, determine a filtration of BQ. The resulting spectral sequence for cohomology is i...

ontemporary ethical theory begins with G. E. Moore (1873–1958). Moore opened up new issues for consideration and altered the focus of ethical discussion. Much of twentieth-century analytic ethics, at least until recently, treated issues that were raised by Moore or by philosophers responding either to him or to other respondents. Although analytic ethical philosophers discussed many questions t...

A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical ω-category. This also has the structure of connections in the sense of Brown and Higgins, but cancellation of connections does not hold.

We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, assuming that every vertex of a given partite set is adjacent to the same number of vertices (δ) in each of the other independent sets. We determine when a Moore multipartite digraph is weakly distanceregular. Within this framework, some necessary conditions for the existence of a Moore r-parti...