How large dimension guarantees a given angle?

We study the following two problems: (1) Given $n\ge 2$ and \al, how large Hausdorff dimension can a compact set A\su\Rn have if $A$ does not contain three points that form an angle \al? (2) Given \al and \de, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the \de-neighborhood of \al? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\circ$, the angles $60^\circ,90^\circ$ and $120^\circ$ also play special role in problem (2): the maximal dimension is smaller for these special angles than for the other angles. In problem (1) the angle $90^\circ$ seems to behave differently from other angles

A Phase Transition for Circle Maps and Cherry Flows

We study $C^{2}$ weakly order preserving circle maps with a flat interval. The main result of the paper is about a sharp transition from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval. We prove that the non-wandering set has zero Hausdorff dimension in the case of degenerate geometry and it has Hausdorff dimension strictly greater than zero in the case of bounded geometry. Our results about circle maps allow to establish a sharp phase transition in the dynamics of Cherry flows

Digestibility Estimates Based on a Grass Growth Model Are Distributed via Internet to Finnish Farmers

Optimising the harvesting time of grass in primary growth is difficult under Finnish climatic conditions, because the digestibility of grass decreases on average by 0.5 percentage units daily. We constructed a model based on cumulative temperature and geographical location which estimates the digestibility of grass. This model is used to produce estimates utilising real time weather information. The estimates are presented as a map, which is revised daily. Farmers have free access to the maps via Internet

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.Comment: 20 pages, 1 figur

Hyvinvoinnin turvaamisen rajat : Näköaloja talouskriisiin ja hyvinvointivaltion kehitykseen Suomessa

Miten syksyllä 2008 alkanut globaali talouskriisi vaikuttaa pitkällä aikavälillä suomalaiseen hyvinvointivaltioon? Jos olisimme antiikin Kreikassa, voisimme mennä Delfoin oraakkelin luo Apollonin temppeliin ja esittää tämän kysymyksen ennuspapittarelle. Eräänä lokakuun päivänä 2009 Kelan tiloihin kokoontui joukko suomalaisia hyvinvointivaltion huippuasiantuntijoita. He kertoivat julkisen talouden, kansalaisten toimeentulon ja terveyden näkökulmista kolmelle ”professori-oraakkelille” eli tanskalaiselle Nina Smithille, ruotsalaiselle Johan Fritzellille ja saksalaisille Karl Hinrichsille Suomen kokemuksista edellisestä, 1990-luvun alun lamasta, sen jälkeisestä kehityksestä sekä omista tulevaisuuden arvioistaan. Seuraavana päivänä oraakkelit lausuivat ennustuksensa, joka paljastetaan tässä raportissa.10,00 euro

Temperature and pressure-induced spin-state transitions in LaCoO3

We report the continuous variation of the spin moment of cobalt in LaCoO3 across its temperature and pressure-induced spin transitions evidenced with K\beta emission spectra. The first thermal transition is best described by a transition to an orbitally nondegenerate intermediate spin (S=1) state. In parallel, continuous redistribution of the 3d electrons is also indicated by partial fluorescence yield X-ray absorption spectra. At high pressure, our study confirms that the material becomes low spin between 40 and 70 kbar at room temperature

Comments on ``The first detections of the Extragalactic Background Light at 3000, 5500, and 8000 A'' by Bernstein, Freedman and Madore

A critical discussion is presented of the data analysis applied by Bernstein, Freedman and Madore (2002 ApJ, 571, 56; and ApJ 571, 85) in their measurement of the Extragalactic Background Light. There are questionable assumptions in the analysis of the ground-based observations of the Zodiacal Light. The modeling of the Diffuse Galactic Light is based on an underestimated value of the dust column density along the line of sight. Comparison with the previously presented results from the same observations reveals a puzzling situation: in spite of a large difference in the atmospheric scattered light corrections the derived Extragalactic Background Light values are exactly the same. The claim of the paper of a ``detection of the Extragalactic Background Light'' appears premature.Comment: 6 pages, accepted for Ap

Lipschitz equivalence of subsets of self-conformal sets

We give sufficient conditions to guarantee that if two self-conformal sets E and F have Lipschitz equivalent subsets of positive measure, then there is a bilipschitz map of E into, or onto, F