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Edoardo Vesentini (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.
Yves Dutrieux, Nigel J. Kalton (2005)
Studia Mathematica
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We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L. ...
D. W. Hajek (1982)
Matematički Vesnik
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James R. Lee, Manor Mendel, Mohammad Moharrami (2012)
Fundamenta Mathematicae
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For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).
Themis Mitsis (2004)
Studia Mathematica
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We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
T. Przymusiński (1976)
Colloquium Mathematicae
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Lu-ming Shen (2010)
Acta Arithmetica
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Piotr Borodulin-Nadzieja, David Chodounský (2015)
Fundamenta Mathematicae
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We define and study two classes of uncountable ⊆*-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.
Mattila, Pertti, Orobitg, Joan (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Jaroslav Hančl, Radhakrishnan Nair, Lukáš Novotný, Jan Šustek (2012)
Acta Arithmetica
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Balázs Bárány (2009)
Fundamenta Mathematicae
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We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...
Antti Käenmäki, Markku Vilppolainen (2008)
Fundamenta Mathematicae
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It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.
Yan-Yan Liu, Jun Wu (2001)
Acta Arithmetica
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Alejandro Ramírez-Páramo (2010)
Colloquium Mathematicae
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We use the Hausdorff pseudocharacter to bound the cardinality and the Lindelöf degree of κ-Lindelöf Hausdorff spaces.
Veerman, J.J.P., Stošić, B.D. (2000)
Experimental Mathematics
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T. W. Körner (2008)
Studia Mathematica
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There is no non-trivial constraint on the Hausdorff dimension of sums of a set with itself.
Rodney S. Rambally (1973)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si considerano generali sistemi di equazioni differenziali ordinarie ed in particolare lineari e si danno condizioni sufficienti alle quali devono soddisfare perturbazioni dei dati, determinanti la soluzione dei detti sistemi, affinché questa si mantenga entro confini prescritti.
J. Mioduszewski (1978)
Colloquium Mathematicae
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Quansheng Liu (1993)
Publications mathématiques et informatique de Rennes
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Michał Rams (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.
Roy O. Davies (1979)
Colloquium Mathematicae
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Balázs Bárány (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate properties of the zero of the subadditive pressure which is a most important tool to estimate the Hausdorff dimension of the attractor of a non-conformal iterated function system (IFS). Our result is a generalization of the main results of Miao and Falconer [Fractals 15 (2007)] and Manning and Simon [Nonlinearity 20 (2007)].
Massimo Tessarotto (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si studiano soluzioni perturbative dell'equazione cinetica di Fokker-Planck nella approssimazione «di raggio di Larmor piccolo» che corrispondono a stati iniziali in presenza di moti non rigidi del plasma. Quali esempi si considerano, in particolare, configurazioni di equilibrio idromagnetico spazialmente simmetriche.
Massimo Tessarotto (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si studiano soluzioni perturbative dell'equazione cinetica di Fokker-Planck nella approssimazione «di raggio di Larmor piccolo» che corrispondono a stati iniziali in presenza di moti non rigidi del plasma. Quali esempi si considerano, in particolare, configurazioni di equilibrio idromagnetico spazialmente simmetriche.
Eda Cesaratto, Brigitte Vallée (2006)
Acta Arithmetica
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Massimo Nicoletti, Claudio Petrucciani (1973)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Nell'altopiano etiopico centro-orientale e nelle scarpate che da questo scendono nella fossa dancala e nel Main Ethiopian Rift affiorano estensivamente rioliti alcaline e trachirioliti. Le età K-Ar ottenute da una cinquantina di campioni hanno permesso di stabilire che tali rioliti appartengono a due cicli vulcanici distinti. Il ciclo più antico, oggetto di questo lavoro, rappresentato dalle «rioliti di Alagi», si è iniziato 32 M.A. fa ed è finito circa 20 M.A. fa. Il secondo, rappresentato...
Guifeng Huang, Lidong Wang (2014)
Annales Polonici Mathematici
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A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every s ∈ (0,1), we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is s.
K. Leśniak (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.