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Basic relations valid for the Bernstein spaces B ² σ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, G. Schmeisser (2014)

Banach Center Publications

Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces B σ p are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from B σ p . The difficult situation of derivative-free error estimates is also covered.

Bi-infinitary codes

Do Long Van, D. G. Thomas, K. G. Subramanian, Rani Siromoney (1990)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Binary codes and partial permutation decoding sets from the odd graphs

Washiela Fish, Roland Fray, Eric Mwambene (2014)

Open Mathematics

For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, the set of all k-subsets of Ω = 1, 2, …, 2k +1, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k)...

Binomial-Poisson entropic inequalities and the M/M/∞ queue

Djalil Chafaï (2006)

ESAIM: Probability and Statistics

This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular the exponential dissipation of Φ-entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semi-group ...

Bound on extended f -divergences for a variety of classes

Pietro Cerone, Sever Silvestru Dragomir, Ferdinand Österreicher (2004)

Kybernetika

The concept of f -divergences was introduced by Csiszár in 1963 as measures of the ‘hardness’ of a testing problem depending on a convex real valued function f on the interval [ 0 , ∞ ) . The choice of this parameter f can be adjusted so as to match the needs for specific applications. The definition and some of the most basic properties of f -divergences are given and the class of χ α -divergences is presented. Ostrowski’s inequality and a Trapezoid inequality are utilized in order to prove bounds for an extension...

Bounded expansion in web graphs

Silvia Gago, Dirk Schlatter (2009)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study various models for web graphs with respect to bounded expansion. All the deterministic models even have constant expansion, whereas the copying model has unbounded expansion. The most interesting case turns out to be the preferential attachment model --- which we conjecture to have unbounded expansion, too.

Bounds for f -divergences under likelihood ratio constraints

Sever Silvestru Dragomir (2003)

Applications of Mathematics

In this paper we establish an upper and a lower bound for the f -divergence of two discrete random variables under likelihood ratio constraints in terms of the Kullback-Leibler distance. Some particular cases for Hellinger and triangular discimination, χ 2 -distance and Rényi’s divergences, etc. are also considered.

Bounds on the information divergence for hypergeometric distributions

Peter Harremoës, František Matúš (2020)

Kybernetika

The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In this paper we present upper and lower bounds on information divergence. These bounds are important for statistical testing and for a better understanding of the notion of exchangeability.

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