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Zoekopdracht: faculteit: "UvA" en publicatiejaar: "2000"

AuteurJ. Korevaar
TitelProblems of Chebyshev quadrature on sphere and circle
Instituut/afd.UvA: Universiteitsbibliotheek
TrefwoordChebyshev quadrature, extremal problems for $N$-tuples,
potential energy functions, separation of extremal points, spherical designs, uniform distribution.
SamenvattingThe principal problem is to find optimal or nearly optimal $N$-tuples of nodes for Chebyshev quadrature on the unit sphere when $N$ is large. One tries to obtain such nodes as solutions to suitable extremal problems. In earlier work the author has described a complex-analytic method which would show that the extremal $N$-tuples provide good Chebyshev nodes. These are nodes such that, for constants $A,\,b,\,c>0$, the quadrature remainder is $\le Ae^{-b\sqrt N}$ for the polynomials of degree $\le c\sqrt N$ and sup norm $1$. However, in order to apply this method it is necessary to establish uniform distribution and good separation of the extremal points. In this note uniform distribution is proved with the aid of potential theory. It is plausible that one also has adequate separation. Indeed, there is such separation in the corresponding extremal problems for the unit circle which are considered at length.SR4480821419191919Growth of power series with square root gapsuva/uba/fnwi/kvi114549Korevaar;;Jacob;;For entire functions $f$ whose power series have Hadamard gaps with ratio $\alpha$ $(>1)$, Gaier has shown that the condition $|f(x)|\le e^x$ for $x\ge 0$ implies $|f(z)|\le C_\alpha e^{|z|}$ $(*)$ for all $z$. Here the result is extended to the case of square root gaps, that is, $f(z)=\sum b_{p_k}z^{p_k}$ with $p_{k+1}-p_k\ge \alpha \sqrt{p_k}$ where $\alpha>0$. Smaller gaps cannot work. In connection with his proof of the general high indices theorem for Borel summability, Gaier had shown that square root gaps imply $b_n={\cal O}(e^{c\sqrt n}/n!)$. Having such an estimate, one can adapt Pitt's Tauberian method for the restricted Borel high indices theorem to show that, in fact, $|b_n|\le c_\alpha\sqrt n/n!$ which implies $(*)$. The author also states an equivalent distance formula involving monomials $x^{p_k}e^{-x}$ in $L^\infty(0,\infty)$.SR4490120519891989Gezin, school en ontwikkelingen in intelligentie tussen zes en twaalf jaar.111624N.R. 4411181191uva/uba/fmg/pow124790Guldemond;;H.;;1001911;1;01;95004000;;;01;01;01-01-1987Boomsma;;A.;;4500120519891989De maatschappelijke positie van oud-lom-leerlingen.31478514619302320uva/uba/fmg/pow124791Drenth;;H.;;1001911;1;01;95004000;;;01;01;01-01-19874510320519941994The lex talionis: On vengeance239289uva/uba/fmg/psychHillsdale, NJLawrence Erlabum Associates0805812075Emotions: Essays on emotion theory1162221003421;1;03;94004000;;;01;06;12-10-1992Goozen;;S.H.M.;Poll;van de;Nanne;4520120520032003A further look at the language-as-fixed-effect fallacy.289586573141151uva/uba/fmg/psych11821002311;1;01;94004000;;;01;01;01-09-1992The proper analysis of experiments using language materials has been a source of controversy and debate among researchers. We summarize the main issues and discuss the solutions that have been presented. Even though the major issues have been dealt with extensively in the literature, there still exists quite a bit of confusion about how to analyze the data from such experiments. We discuss a number of the most frequently voiced objections. In particular, we discuss the issue of what happens if in a counterbalanced design only some of the items show the treatment effect. Finally, a possible solution is discussed for the case where only partial matching of items between conditions is possible.4530120519981998Functional connectivity within the visual cortex of the rat shows state changes.1144751041814901507uva/uba/fmg/psych120319Togt;van der;C.;;1001687;1;02;13000000;13040000;13200800;14;01;01-01-1994Spekreijse;;H.;prof. dr.;The aim of this study was to investigate the dynamics of the horizontal functional connectivity within the visual cortex during spontaneous activity or during visual stimulation. Two arrays of 16 electrodes were inserted in the visual cortex of a rat. From these electrodes a depth profile was Obtained of the local spiking activity. The crosscorrelations between all electrodes were estimated. Three types of cross-correlation peaks were identified an
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