Arithmetic based fractals associated with Pascal's triangle

Our goal is to study Pascal-Sierpinski gaskets, which are certain fractal sets defined in terms of divisibility of entries in Pascal's triangle. The principal tool is a "carry rule" for the addition of the base-q representation of coordinates of points in the unit square. In the case that q = p is prime, we connect the carry rule to the power of p appearing in the prime factorization of binomialcoefficients. We use the carry rule to define a family of fractal subsets Bqr of the unit square, and we show that when q = p is prime, Bqr coincides with the Pascal-Sierpinski gasket corresponding to N = pr . We go on to describe Bqr as the limit of an iterated function system of "partial similarities", and we determine its Hausdorff dimension. We consider also the corresponding fractal sets in higher-dimensional Euclidean space

Nevanlinna-Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.Comment: 31 pages. The question left open at the end of version 1 has been answered in the affirmative; see Theorem 1.12 and Corollary 1.13 in version

Structure and Stability of the Iodide Elpasolite, Cs2AgBiI6

Iodide elpasolites (or double perovskites, A2B'B"I6, B' = M+, B" = M3+) are predicted to be promising alternatives to lead-based perovskite semiconductors for photovoltaic and optoelectronic applications, but no iodide elpasolite has ever been definitively prepared or structurally characterized. Iodide elpasolites are widely predicted to be unstable due to favorable decomposition to the competing A3B2I9 (B = M3+) phase. Here, we report the results of synchrotron XRD and X-ray total scattering measurements on putative Cs2AgBiI6 nanocrystals made via anion exchange from parent Cs2AgBiBr6 nanocrystals. Rietveld refinement of XRD and PDF data shows that these nanocrystals indeed exhibit a tetragonal (I4-m) elpasolite structure, making them the first example of a structurally characterized iodide elpasolite. A series of experiments probing structural relaxation and the effects of surface ligation or grain size all point to the critical role of surface free energy in stabilizing the iodide elpasolite phase in these nanocrystals.Comment: 7 figures, 1 scheme, plus supporting information fil

Cluster values of analytic functions on a Banach space

We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for the open unit balls of c0 and ℓ2, in which all but one of the functions comprising the corona data extend to be weak-star continuous on the closed unit ball.Fil: Aron, Richard Martin. Kent State University; Estados UnidosFil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Gamelin, T. W.. University of California at Los Angeles; Estados UnidosFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Maestre, Manuel. Universidad de Valencia; Españ

Экспериментальная автоматизированная система гидрометеорологических измерений и обработки данных для береговых станций

Разработан действующий макет автоматизированной системы прибрежных гидрометеорологических измерений для морской сети Госгидромета Украины. В течение 2000 – 2004 гг. проведены испытания и опытная эксплуатация метеорологических (ветер, температура воздуха, атмосферное давление) и гидрологических (уровень, температура и соленость воды) измерительных блоков, установленных в стандартных условиях морской станции «Севастополь». Приводятся данные о структуре, основных технологических принципах автоматизированной системы и некоторые результаты квазинепрерывных метеорологических и гидрологических измерений.Developed is functioning model of automated system of coastal hydrometeorological measurements for the marine net of State Hydrometeorological Institution of Ukraine. In 2000 – 2004 the tests and experimental exploitation of meteorological (wind, atmospheric temperature, atmospheric pressure) and hydrological (water level, temperature and salinity) measuring blocks installed in standard conditions of marine station “Sevastopol” were held. Data on structure, general technological principles of the automated system and some results of quazi-continuous meteorological and hydrological measurements is presented

Validity of the Polar V800 heart rate monitor to measure RR intervals at rest

Purpose To assess the validity of RR intervals and short-term heart rate variability (HRV) data obtained from the Polar V800 heart rate monitor, in comparison to an electrocardiograph (ECG). Method Twenty participants completed an active orthostatic test using the V800 and ECG. An improved method for the identification and correction of RR intervals was employed prior to HRV analysis. Agreement of the data was assessed using intra-class correlation coefficients (ICC), Bland–Altman limits of agreement (LoA), and effect size (ES). Results A small number of errors were detected between ECG and Polar RR signal, with a combined error rate of 0.086 %. The RR intervals from ECG to V800 were significantly different, but with small ES for both supine corrected and standing corrected data (ES 0.999 for both supine and standing corrected intervals. When analysed with the same HRV software no significant differences were observed in any HRV parameters, for either supine or standing; the data displayed small bias and tight LoA, strong ICC (>0.99) and small ES (≤0.029). Conclusions The V800 improves over previous Polar models, with narrower LoA, stronger ICC and smaller ES for both the RR intervals and HRV parameters. The findings support the validity of the Polar V800 and its ability to produce RR interval recordings consistent with an ECG. In addition, HRV parameters derived from these recordings are also highly comparable

On badly approximable functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21738/1/0000131.pd