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61.
Summary We prove that the error inn-point Gaussian quadrature, with respect to the standard weight functionw1, is of best possible orderO(n
–2) for every bounded convex function. This result solves an open problem proposed by H. Braß and published in the problem section of the proceedings of the 2. Conference on Numerical Integration held in 1981 at the Mathematisches Forschungsinstitut Oberwolfach (Hämmerlin 1982; Problem 2). Furthermore, we investigate this problem for positive quadrature rules and for general product quadrature. In particular, for the special class of Jacobian weight functionsw
, (x)=(1–x)(1+x), we show that the above result for Gaussian quadrature is not valid precisely ifw
, is unbounded.Dedicated to Prof. H. Braß on the occasion of his 55th birthday 相似文献
62.
63.
Georgi R. Grozev 《Numerische Mathematik》1989,56(4):331-343
Summary LetLM
N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x
i
}
1
n
,a <x
1 < ... <x
n
<b and an incidence matrixE = (e
ij
)
i=1
n
,
r-1
j=0
with
55044544427528/211_2005_Article_BF01396608_TeX2GIFIE2.gif" alt="
$$\left| E \right| = \sum\limits_{i = 1}^n {\sum\limits_{j = 0}^{r - 1} {e_{ij} \leqq N.} }$$
" align="middle" border="0">
Denote byLM
N
O
the subset ofLM
N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL
p-norms inLM
N belong toLM
N
O
.The results are reformulated as comparison theorems for quadrature formulae. 相似文献
64.
C. Lubich 《Numerische Mathematik》1988,52(2):129-145
Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals
相似文献
65.
A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x
1<...
66.
Olivia Vidoni Stefan Neumeier Nathalie Bardou Jean-Luc Pelouard Günter Schmid 《Journal of Cluster Science》2003,14(3):325-336
The elaboration of closed-packed monolayers of Au55(PPh3)12Cl6 clusters on oxidized and non-oxidized GaAs surfaces is reported. The first part of this work describes the use of silanethiol modified GaAs oxide surfaces to trap 18 nm gold colloids and Au55(PPh3)12Cl6 clusters. The surfaces characterized by AFM measurements present high-quality coverage on a quite long range for both metallic species. The second part is devoted to the elaboration of Au55(PPh3)12Cl6 cluster monolayers on non-oxidized p-type GaAs substrates, functionalized with dithiol molecules. AFM measurements demonstrate the presence of closed-packed two-dimensional arrangements of Au55 clusters. 相似文献
67.
Klaus-J. Engel 《Monatshefte für Mathematik》1995,119(4):259-265
In this note we prove some results on the m-accretivity of sums and products of linear operators. In particular we obtain the following theorem: LetA, B be two m-accretive operators on a reflexive Banach space. IfA is invertible and (A)–1
B is accretive thenBA
–1 andA+B are m-accretive. 相似文献
68.
For graphsA andB the relationA(B)
r
1
means that for everyr-coloring of the vertices ofA there is a monochromatic copy ofB inA. Forb (G) is the family of graphs which do not embedG. A familyof graphs is Ramsey if for all graphsBthere is a graphAsuch thatA(B)
r
1
. The only graphsG for which it is not known whether Forb (G) is Ramsey are graphs which have a cutpoint adjacent to every other vertex except one. In this paper we prove for a large subclass of those graphsG, that Forb (G) does not have the Ramsey property.This research has been supported in part by NSERC grant 69-1325. 相似文献
69.
Sia dato uno spazio topologicoE con azione di un monoide topologicoH e siaE→B una funzione continue che, su ogni apertoU di una partizione dell'unità diB, sia, a meno di omotopia, la proiezioneU×H→U (ovvero una fibrazione numerabile). Un classico risultato di A. Dold e R. Lashof (1959) permette di costruire, a partire
daE→B, una funzione continuaE
∞→B∞, conE
∞ debolmente contraibile e munito di azione diH: laH-fibrazione universale associata daH. Tale funzione, in generale, non è purtroppo numerabile e quindi non si presta alla classificazione delleH-fibrazioni numerabili. Successivamente (1971), M. Fuchs ha trovato un modo di modificare la costruzione di Dold-Lashof per
recuperare la numerabilità. La costruzione di Dold-Lashof-Fuchs è, da allora, uno dei principali strumenti nella teoria degli
spazi classificanti di monoidi topologici, anche se vi è un uso di topologie alquanto complesse e quindi poco maneggevoli.
In questo lavoro ci proponiamo di mostrare come, lavorando nella categoria conveniente deik-spazi, sia possibile descrivere la costruzione di Dold-Lashof-Fuchs in modo estremamente semplificato ed adattarla anche
alla classificazione delleF-fibrazioni numerabili.
Conferenza tenuta da R. Piccinini il 15 maggio 1995 相似文献 70.
S. Khazhomia 《Georgian Mathematical Journal》1995,2(1):55-77
|