We develop an algebraic underpinning of backtracking monad transformers in the general setting of monoidal categories. As our main technical device, we introduce Eilenberg–Moore monoids, which combine monoids with algebras for strong monads. We show that Eilenberg–Moore monoids coincide with algebras for the list monad transformer (‘done right’) known from Haskell libraries. From this, we obtai...

We propose a rich class FL(L) of temporal logics, parametrized by a class L of modalities, evaluated over forests, that is, ordered tuples of ordered but unranked finite trees, an algebraic product operation (which we call the Moore product) of forest automata, and show that these logically defined classes of forest languages are characterized precisely via the Moore product. As an application ...

We propose a method and algorithm for computing the weighted MoorePenrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial matrix. These methods and algorithms are generalizations of the method or computing the weighted Moore-Penrose inverse for constant matrices, originated in [2...

This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a result, the enumeration of the class of geodetic graphs homeomorphic to certain Moore graphs has been performed.

K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity ofcompacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $...

carefully weeded of difficult generalities; and at a later stage a philosophical theory. To begin with the latter would be to my mind a mistake; the appeal would be to too limited a class. Professor E.H. Moore, the vice-president of the Society, was also concerned with “fundamental ideas” in calculus, delivering an address titled “Certain fundamental ideas which should be emphasized throughout ...

We prove a converse to well-known results by E. Cartan and J. D. Moore. Let f:Mcn?Qc˜n+p be an isometric immersion of Riemannian manifold with constant sectional curvature c into space form c˜, free weak-umbilic points if c>c˜. show that the substantial codimension f is p=n?1 if, as shown Moore, first normal bundle possesses lowest possible rank n?1. These submanifolds are class has been extens...

The Milnor-Moore theorem shows that the Q-elliptic spaces are precisely those spaces which have the rational homotopy type of finite, 1-connected CW complexes and have finite total rational homotopy rank. This class of spaces is important because of the dichotomy theorem (the subject of the book [8]) which states that a finite, 1-connected complex either has finite total rational homotopy rank ...

This paper addresses the problem of estimating the mean vector of a singular multivariate normal distribution with an unknown singular covariance matrix. The maximum likelihood estimator is shown to be minimax relative to a quadratic loss weighted by the Moore-Penrose inverse of the covariance matrix. An unbiased risk estimator relative to the weighted quadratic loss is provided for a Baranchik...