The space CMO of functions of finite central mean oscillation is an analogue of BMO where the condition that the sharp maximal function is bounded is replaced by the convergence of the sharp function at the origin. In this paper it is shown that each element of CMO is a singular integral image of an element of the Beurling space B2 of functions whose Hardy-Littlewood maximal function converges ...

For simplicity, we adopt the following rules: x, X are sets, i, n, m are natural numbers, r, s are real numbers, c, c1, c2, d are complex numbers, f , g are complex-valued functions, g1 is an n-element complex-valued finite sequence, f1 is an n-element real-valued finite sequence, T is a non empty topological space, and p is an element of En T. Let R be a binary relation and let X be an empty s...

We show that isochronous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of such synchronization ...

Cayley-Dickson algebras are non-associative R-algebras that generalize the well-known algebras R, C, H, and O. We study zero-divisors in these algebras. In particular, we show that the annihilator of any element of the 2n-dimensional Cayley-Dickson algebra has dimension at most 2n−4n+4. Moreover, every multiple of 4 between 0 and this upper bound occurs as the dimension of some annihilator. Alt...

This paper considers the notion of decentralized fixed zeros for linear, time-invariant, finite-dimensional systems. For an -channel plant that is free of unstable decentralized fixed modes, an unstable decentralized fixed zero of Channel (1 ) is defined as an element of the closed right half-plane, which remains as a blocking zero of that channel under the application of every set of 1 control...

Two results are established concerning the ability of a set to cover any element of a class of sets under the action of an ergodic flow. The classes considered are the class of countable sets and the class of sets of measure zero. RESUME. Deux résultats sont demontres concernant la possibilité pour un ensemble de recouvrir, sous l’action d’un flot ergodique, tous les elements d’une classe d’ens...

This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is based on motivic integration, works both in characteristic zero and in positive characteristic. As an application, the Fundamental Lemma for this class of integ...

The multiplicity of a zero of a (univariate, polynomial) spline is defined in terms of its B-spline coefficients, thus making certain bounds trivial while, at the same time, adhering to the principle that the multiplicity of a zero indicates the number of simple zeros nearby achievable by a nearby element from the same class. In particular, the multiplicity depends on the class to which the fun...