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Monomorphisms in spaces with Lindelöf filters

Richard N. Ball, Anthony W. Hager (2007)

Czechoslovak Mathematical Journal

𝐒𝐩𝐅𝐢 is the category of spaces with filters: an object is a pair ( X , ℱ ) , X a compact Hausdorff space and ℱ a filter of dense open subsets of X . A morphism f ( Y , 𝒢 ) → ( X , ℱ ) is a continuous function f Y → X for which f - 1 ( F ) ∈ 𝒢 whenever F ∈ ℱ . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically address only one of these...

Monotone interval eigenproblem in max–min algebra

Martin Gavalec, Ján Plavka (2010)

Kybernetika

The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.

Monotonicity of the maximum of inner product norms

Boris Lavrič (2004)

Commentationes Mathematicae Universitatis Carolinae

Let 𝕂 be the field of real or complex numbers. In this note we characterize all inner product norms p 1 , ... , p m on 𝕂 n for which the norm x ↦ max { p 1 ( x ) , ... , p m ( x ) } on 𝕂 n is monotonic.

Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix

Hiroshi Kurata, Ravindra B. Bapat (2016)

Special Matrices

By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix B, and vice...

Moore-Penrose inverses of Gram operators on Hilbert C*-modules

M. S. Moslehian, K. Sharif, M. Forough, M. Chakoshi (2012)

Studia Mathematica

Let t be a regular operator between Hilbert C*-modules and t † be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator t*t. More precisely, we study some conditions ensuring that t † = ( t * t ) † t * = t * ( t t * ) † and ( t * t ) † = t † t * † . As an application, we get some results for densely defined closed operators on Hilbert C*-modules over C*-algebras of compact operators.

Multi-agent solver for non-negative matrix factorization based on optimization

Zhipeng Tu, Weijian Li (2021)

Kybernetika

This paper investigates a distributed solver for non-negative matrix factorization (NMF) over a multi-agent network. After reformulating the problem into the standard distributed optimization form, we design our distributed algorithm (DisNMF) based on the primal-dual method and in the form of multiplicative update rule. With the help of auxiliary functions, we provide monotonic convergence analysis. Furthermore, we show by computational complexity analysis and numerical examples that our distributed...

Multichannel deblurring of digital images

Michal Šorel, Filip Šroubek, Jan Flusser (2011)

Kybernetika

Blur is a common problem that limits the effective resolution of many imaging systems. In this article, we give a general overview of methods that can be used to reduce the blur. This includes the classical multi-channel deconvolution problems as well as challenging extensions to spatially varying blur. The proposed methods are formulated as energy minimization problems with specific regularization terms on images and blurs. Experiments on real data illustrate very good and stable performance of...

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