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Book review: "Control and Estimation of Distributed Parameter Systems" by W. Desch, F. Kappel and K. Kunisch,

Control and Cybernetics

A new method of exact controllability in short time and applications

Annales de la Faculté des sciences de Toulouse : Mathématiques

Oscillations of anharmonic Fourier series and the wave equation.

Revista Matemática Iberoamericana

In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of ⎧     utt + (-1)m Δmu = 0     (t,x) ∈ R x Ω ⎨ ⎩     u = ... = Δm-1 u = 0     t ∈ R. These results rely on the study of a sign of almost periodic functions of a special form restricted...

Acta Arithmetica

Ingham type theorems and applications to control theory

Bollettino dell'Unione Matematica Italiana

Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.

A two-dimensional univoque set

Fundamenta Mathematicae

Let J ⊂ ℝ² be the set of couples (x,q) with q > 1 such that x has at least one representation of the form $x={\sum }_{i=1}^{\infty }{c}_{i}{q}^{-i}$ with integer coefficients ${c}_{i}$ satisfying $0\le {c}_{i}, i ≥ 1. In this case we say that $\left({c}_{i}\right)=c₁c₂...$ is an expansion of x in base q. Let U be the set of couples (x,q) ∈ J such that x has exactly one expansion in base q. In this paper we deduce some topological and combinatorial properties of the set U. We characterize the closure of U, and we determine its Hausdorff dimension. For (x,q) ∈ J, we also prove new properties...

Well posedness and control of semilinear wave equations with iterated logarithms

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.

Characterization of the unique expansions $1={\sum }_{i=1}^{\infty }{q}^{-{n}_{i}}$ and related problems

Bulletin de la Société Mathématique de France

A simplified multidimensional integral

Czechoslovak Mathematical Journal

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.

Generalized golden ratios of ternary alphabets

Journal of the European Mathematical Society

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in dependence...

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