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Construction of sampling and interpolating sequences for multi-band signals. the two-band case

Sergei Avdonin, Anna Bulanova, William Moran (2007)

International Journal of Applied Mathematics and Computer Science

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.

Construction, properties and applications of finite neofields

Anthony Donald Keedwell (2000)

Commentationes Mathematicae Universitatis Carolinae

We give a short account of the construction and properties of left neofields. Most useful in practice seem to be neofields based on the cyclic group and particularly those having an additional divisibility property, called D-neofields. We shall give examples of applications to the construction of orthogonal latin squares, to the design of tournaments balanced for residual effects and to cryptography.

Continuous limits of discrete perimeters

Antonin Chambolle, Alessandro Giacomini, Luca Lussardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula. These functionals, based on submodular interactions, arise in discrete optimization and are known as a large class of problems which can be solved in polynomial time. In particular, some of them can be solved very efficiently by maximal flow algorithms and are quite popular in the image processing community. We study the limit in the continuum of these functionals, show that they always converge...

Controllability of partial differential equations on graphs

Sergei Avdonin, Victor Mikhaylov (2008)

Applicationes Mathematicae

We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in L₂-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the heat equation...

Convexity inequalities for estimating generalized conditional entropies from below

Alexey E. Rastegin (2012)

Kybernetika

Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional α -entropy and two kinds of non-extensive conditional α -entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain...

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