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Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods

Dieter Schott (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each...

Signatura of magic and Latin integer squares: isentropic clans and indexing

Ian Cameron, Adam Rogers, Peter D. Loly (2013)

Discussiones Mathematicae Probability and Statistics

The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin squares are included, including the order eight Franklin subset which is of direct relevance...

Singular Perturbations For Heart Image Segmentation Tracking

J. Pousin (2009)

Mathematical Modelling of Natural Phenomena

In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

Dryanov, Dimiter (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.We characterize Paley-Wiener-Schwartz space of entire functions as a union of three-parametric linear normed subspaces determined by the type of the entire functions, their polynomial asymptotic on the real line, and the index p ≥ 1 of a Sobolev type Lp-summability on the real line with an appropriate weight function. An entire function belonging to a sub-space of the decomposition is exactly recovered by a sampling series, locally...

Sobre el parámetro complejidad lineal y los filtros no lineales de segundo orden.

Amparo Fúster Sabater, Luis J. García Villalba (2000)

Revista Matemática Complutense

A new method of analysing the linear complexity of 2nd-order nonlinear filterings of m-sequences that is based on the concept of regular coset is present. The procedure considers any value of the LFSR's length, L, (prime or composite number). Emphasis is on the geometric interpretation of the regular cosets which produce degeneracies in the linear complexity of the filtered sequence. Numerical expressions to compute the linear complexity of such sequences are given as well as practical rules to...

Sobre el tamaño de muestra para experimentos aleatorios con imprecisión difusa.

M.ª Angeles Gil Alvarez, Pedro Gil Alvarez (1988)

Trabajos de Estadística

Statistical Inference deals with the drawing of conclusions about a random experiment on the basis of the information contained in a sample from it. A random experiment can be defined by means of the set of its possible outcomes (sample space) and the ability of observation of the experimenter. It is usually assumed that this ability allows the experimenter to describe the observable events as subsets of the sample space. In this paper, we will consider that the experimenter can only express the...

Some decompositions of Bernoulli sets and codes

Aldo de Luca (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

A decomposition of a set X of words over a d -letter alphabet A = { a 1 , ... , a d } is any sequence X 1 , ... , X d , Y 1 , ... , Y d of subsets of A * such that the sets X i , i = 1 , ... , d , are pairwise disjoint, their union is X , and for all i , 1 i d , X i a i Y i , where denotes the commutative equivalence relation. We introduce some suitable decompositions that we call good, admissible, and normal. A normal decomposition is admissible and an admissible decomposition is good. We prove that a set is commutatively prefix if and only if it has a normal decomposition. In particular,...

Some decompositions of Bernoulli sets and codes

Aldo de Luca (2010)

RAIRO - Theoretical Informatics and Applications

A decomposition of a set X of words over a d-letter alphabet A = {a1,...,ad} is any sequence X1,...,Xd,Y1,...,Yd of subsets of A* such that the sets Xi, i = 1,...,d, are pairwise disjoint, their union is X, and for all i, 1 ≤ i ≤ d, Xi ~ aiYi, where ~ denotes the commutative equivalence relation. We introduce some suitable decompositions that we call good, admissible, and normal. A normal decomposition is admissible and an admissible decomposition is good. We prove that a set is commutatively prefix...

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