Abstract We prove an extension of the Moore–Schmidt theorem on triviality first cohomology class cocycles for action arbitrary discrete group measure space and with values in compact Hausdorff abelian group. The proof relies a ‘conditional’ Pontryagin duality spaces abstract measurable maps.

Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary c...

We study the size of Boyer-Moore automata introduced in Knuth, Morris & Pratt's famous paper on pattern matching. We experimentally exhibit a nite class of binary patterns, which produce large Boyer-Moore automata. The best approximation curve for their sizes is a polynomial O(m 7), or even an exponential O(2 0:4m), in the length m of the patterns. All the previously known maximal sizes were at...

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We introduce three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of inputoutput t...

We consider here the problem of estimating p×p scale matrix Σ a multivariate linear regression model when distribution observed belongs to large class elliptically symmetric distributions. Any estimator Σˆ is assessed through data-based loss tr(S+Σ(Σ−1Σˆ−Ip)2) where S sample covariance and S+ its Moore–Penrose inverse.

Maximally monotone operators are fundamental objects in modern optimization. The main classes of subdifferential and matrices with a positive semidefinite symmetric part. In this paper, we study nice class operators: displacement mappings isometries finite order. We derive explicit formulas for resolvents, Yosida approximations, (set-valued Moore-Penrose) inverses. illustrate our results by con...

An iterative algorithm for estimating the Moore-Penrose generalized inverse is developed. The main motive for the construction of algorithm is simultaneous usage of Penrose equations (2) and (4). Convergence properties of the introduced method are considered as well as their first-order and the second-order error terms. Numerical experience is also presented. AMS Subj. Class.: 15A09.