Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem

We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie--Weiss Ising model and includes as well all ferromagnetic Curie--Weiss Potts and Curie--Weiss Heisenberg models. By de Finetti's theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide examples showing that ``ferromagnetism'' is not however in itself sufficient and also study in some detail the Curie--Weiss Ising model with an additional 3-body interaction. Finally, we study the question of how much the antiferromagnetic Curie--Weiss Ising model can be extended. In this direction, we obtain sharp asymptotic results via a solution to a new moment problem. We also obtain a ``formula'' for the extension which is valid in many cases.Comment: Published at http://dx.doi.org/10.1214/009117906000001033 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Erdőszegélyek fajösszetételét és szerkezetét meghatározó tényezők

Vizsgálatainkat két eltérő termőhelyi viszonyok között kialakult e rdőtársulás esetében az erdőállomány és a szomszédos nyílt terület átmeneti zónájában végeztük. A Budai-hegységben két cseres- kocsánytalan tölgyes ( Quercetum petraeae-cerris S oó 1963) erdőállomány, illetve a szomszédos parlag - területek határán található, különböző égtáji kitettségű (ÉK, ÉNY, DK, DNY) erdőszegélyeket vizsgáltunk. Csáfordjánosfa határában egy síkvidéki üde tölgy-kőris-szil ligeterdő ( Fraxino pannonicae-Ulmetum S oó in A S zód 1935 corr. 1963), illetve a szomszédos dunántúli mocsárrét ( Deschampsietum caespitosae ) határán ki - alakult, az előbbiekkel megegyező égtáji kitettségű erdőszegélyeket vizsgáltuk. Célunk volt annak megállapítása, hogy van-e határozott különbség az átmeneti zóna egyes szerkezeti ele - meinek (nyílt terület, lágyszárú szegély, cserjés szegély, erdőköpeny, erdőbelső) fajösszetétele között, az egyes erdőtársulások, illetve a különböző égtáji kitettségű szegélyek esetében. Eredményeink alapján a cseres-kocsánytalan tölgyes és a tölgy-kőris-szil ligeterdő állományok szegélyei - nek fajösszetétele teljes mértékben eltér egymástól. Az erdőszegélyek fajösszetétele és szerkezete minden eset - ben az égtáji kitettségtől függően alakul

Synchronization versus stability of the invariant distribution for a class of globally coupled maps

We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant measure (acim), which is furthermore mixing. Interaction arises in the form of diffusive coupling, which involves a function that is discontinuous on the circle. We show that for sufficiently small coupling strength the coupled map system admits a unique absolutely continuous invariant distribution, which depends on the coupling strength $\varepsilon$. Furthermore, the invariant density exponentially attracts all initial distributions considered in our framework. We also show that the dependence of the invariant density on the coupling strength $\varepsilon$ is Lipschitz continuous in the BV norm. When the coupling is sufficiently strong, the limit behavior of the system is more complex. We prove that a wide class of initial measures approach a point mass with support moving chaotically on the circle. This can be interpreted as synchronization in a chaotic state

O-Arylation of Iodophenols with 2-Fluorobenzaldehyde Under Microwave Conditions

The arylation of 4-iodo-, 2-iodo- and 3-iodophenols with 2-fluorobenzaldehyde may be carried out in the presence of K2CO3 in DMF as the solvent under microwave conditions. The arylation of 4-iodophenole was promoted by the use of triethylbenzylammonium chloride (TEBAC) as the phase transfer catalyst. In the other model reactions, the use of TEBAC was harmful. By-products formed by isomerization and disproportionation were also detected

Synthesis of Homogeneous Manganese-Doped Titanium Oxide Nanotubes from Titanate Precursors

We report a novel synthesis route of homogeneously manganese-doped titanium dioxide nanotubes in a broad concentration range. The scroll-type trititanate (H(2)Ti(3)O(7)) nanotubes prepared by hydrothermal synthesis were used as precursors. Mn2+ ions were introduced by an ion exchange method resulting Mn(x)H(2-x)Ti(3)O(7). In a subsequent heat-treatment they were transformed into Mn(y)Ti(1-y)O(2) where y=x/(3+x). The state and the local environment of the Mn2+ ions in the precursor and final products were studied by Electron Spin Resonance (ESR) technique. It was found that the Mn2+ ions occupy two positions: the first having an almost perfect cubic symmetry while the other is in a strongly distorted octahedral site. The ratio of the two Mn2+ sites is independent of the doping level and amounts to 15:85 in Mn(x)H(2-x)Ti(3)O(7) and to 5:95 in Mn(y)Ti(1-y)O(2). SQUID magnetometry does not show long-range magnetic order in the homogeneously Mn2+-doped nanotubes.Comment: 7 pages, 6 figure

Simulating the weak death of the neutron in a femtoscale universe with near-Exascale computing

The fundamental particle theory called Quantum Chromodynamics (QCD) dictates everything about protons and neutrons, from their intrinsic properties to interactions that bind them into atomic nuclei. Quantities that cannot be fully resolved through experiment, such as the neutron lifetime (whose precise value is important for the existence of light-atomic elements that make the sun shine and life possible), may be understood through numerical solutions to QCD. We directly solve QCD using Lattice Gauge Theory and calculate nuclear observables such as neutron lifetime. We have developed an improved algorithm that exponentially decreases the time-to solution and applied it on the new CORAL supercomputers, Sierra and Summit. We use run-time autotuning to distribute GPU resources, achieving 20% performance at low node count. We also developed optimal application mapping through a job manager, which allows CPU and GPU jobs to be interleaved, yielding 15% of peak performance when deployed across large fractions of CORAL.Comment: 2018 Gordon Bell Finalist: 9 pages, 9 figures; v2: fixed 2 typos and appended acknowledgement