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Quadratic differentials $(A (z - a) (z - b) / {(z - c)}^{2}) d z^{2}$ and algebraic Cauchy transform

Mohamed Jalel Atia, Faouzi Thabet (2016)

Czechoslovak Mathematical Journal

We discuss the representability almost everywhere (a.e.) in $ℂ$ of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials $A (z - a) (z - b) {(z - c)}^{- 2} d z^{2}$ . More precisely, we give a necessary and sufficient condition on the complex numbers $a$ and $b$ for these quadratic differentials to have finite critical trajectories....

Quantifying vasculature: new measures applied to arterial trees in the quail chorioallantoic membrane.

Lubkin, Sharon R., Funk, Sarah E., Sage, E.Helene (2005)

Journal of Theoretical Medicine

Quantitative estimates of N.N. Luzin's C-property for classes of integrable functions

K. Oskolkow (1979)

Banach Center Publications

Quantitative recurrence results.

Michael D. Boshernitzan (1993)

Inventiones mathematicae

Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

Mrinal Kanti Roychowdhury (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension $D_{r} (ν)$ of ν and bounded above by a unique number $κ_{r} \in (0, \infty)$ , related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.

Quantization Dimension Function and Ergodic Measure with Bounded Distortion

Mrinal Kanti Roychowdhury (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.

Quantum diffusion and generalized Rényi dimensions of spectral measures

Jean-Marie Barbaroux, François Germinet, Serguei Tcheremchantsev (2000)

Journées équations aux dérivées partielles

We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order $p$ at time $T$ for the state $ψ$ defined by $[\frac{1}{T} \int_{0}^{T} ∥ | X |^{p / 2} e^{- i t H} ψ ∥^{2} d t]$ . We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure $μ_{ψ}$ associated to the hamiltonian $H$ and the state $ψ$ . We especially concentrate on continuous models.

Quantum logics with classically determined states

Paolo de Lucia, Pavel Pták (1999)

Colloquium Mathematicae

Quasi-compacité de contractions positives d’un espace $L^{1}$ (suivant Brunel et Revuz)

C. Kipnis (1973/1974)

Séminaire Équations aux dérivées partielles (Polytechnique)

Quasi-compactness and uniform ergodicity of Markov operators

Michael Lin (1975)

Annales de l'I.H.P. Probabilités et statistiques

Quasiconformal dimensions of self-similar fractals.

Jeremy T. Tyson, Jang-Mei Wu (2006)

Revista Matemática Iberoamericana

The Sierpinski gasket and other self-similar fractal subsets of Rd, d ≥ 2, can be mapped by quasiconformal self-maps of Rd onto sets of Hausdorff dimension arbitrarily close to one. In R2 we construct explicit mappings. In Rd, d ≥ 3, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically...

Quasi-Invariance of Measures under Translation.

Srishti D. Chatterji (1977)

Mathematische Zeitschrift

Quasinormal convergence

Zuzana Bukovská (1991)

Mathematica Slovaca

Quasiregular Points and Time Changes.

William A. Veech (1978)

Monatshefte für Mathematik

Quasisymmetrically thick sets.

Staples, Susan G., Ward, Lesley A. (1998)

Annales Academiae Scientiarum Fennicae. Mathematica

Quelques curieuses topologies sur $M_{μ} (T)$ et $M_{β} (T)$

Henri Buchwalter (1977)

Annales de l'institut Fourier

Pour tout compact complètement régulier $T$ , on désigne par $M_{β} (T)$ l’espace des mesures de Radon sur le compactifié de Stone-Cech $β T$ de $T$ et par $M_{σ} (T)$ son sous-espace formé des mesures $σ$ -régulières au sens de Varadarajan. On décrit alors sur ces deux espaces des topologies $T_{p}$ , $1 \leq p \leq + \infty$ , qui possèdent des propriétés curieuses parmi lesquelles il convient de citer la suivante : pour $1 < p \leq + \infty$ et pour tout $T$ non pseudocompact, l’espace $(M_{σ} (T), T_{p})$ est non quasi-complet mais ses précompacts sont relativement compacts. Ce résultat permet...

Quelques espaces fonctionnels associés à des processus gaussiens

Z. Ciesielski, G. Kerkyacharian, B. Roynette (1993)

Studia Mathematica

The first part of the paper presents results on Gaussian measures supported by general Banach sequence spaces and by particular spaces of Besov-Orlicz type. In the second part, a new constructive isomorphism between the just mentioned sequence spaces and corresponding function spaces is established. Consequently, some results on the support function spaces for the Gaussian measure corresponding to the fractional Brownian motion are proved. Next, an application to stochastic equations is given. The...

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