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In this note, we point out two errors in the article “On the Neumann function and the method of images in spherical and ellipsoidal geometry” by Dassios and Sten. Two corrections are then proposed. 相似文献
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We consider a model for gene regulatory networks that is a modification of Kauffmann's J Theor Biol 22 (1969), 437–467 random Boolean networks. There are three parameters: $n = {\rm the}$ number of nodes, $r = {\rm the}$ number of inputs to each node, and $p = {\rm the}$ expected fraction of 1'sin the Boolean functions at each node. Following a standard practice in thephysics literature, we use a threshold contact process on a random graph on n nodes, in which each node has in degree r, to approximate its dynamics. We show that if $r\ge 3$ and $r \cdot 2p(1-p)>1$ , then the threshold contact process persists for a long time, which correspond to chaotic behavior of the Boolean network. Unfortunately, we are only able to prove the persistence time is $\ge \exp(cn^{b(p)})$ with $b(p)>0$ when $r\cdot 2p(1-p)> 1$ , and $b(p)=1$ when $(r-1)\cdot 2p(1-p)>1$ . © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 相似文献
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Kim Plofker 《Historia Mathematica》2001,28(4):283
It has been repeatedly noted, but not discussed in detail, that certain so-called “third-order Taylor series approximations” found in the school of the medieval Keralese mathematician M
dhava are inaccurate. That is, these formulas, unlike the other series expansions brilliantly developed by M
dhava and his followers, do not correspond exactly to the terms of the power series subsequently discovered in Europe, by whose name they are generally known. We discuss a Sanskrit commentary on these rules that suggests a possible derivation explaining this discrepancy, and in the process re-emphasize that the Keralese work on such series was rooted in geometric approximation rather than in analysis per se. © 2001 Elsevier Science (USA).Es ist mehrfach festgestellt bisher aber nicht ausführlich diskutiert worden, daß einige sogenannte Taylor-reihennäherungswerte dritter Ordnung, die in der mittelalterlichen Schule keralesischen M
dhava gefunden werden, ungenau sind. Das heißt, diesc Formeln sind den Termen der Potenzreihe, die später in Europa entwickelt wurde und unter dem Namen Taylorreihe bekannt ist, nicht äquivalent, im Gegensatz zu den anderen Entwicklungen von Reihen, die glänzend von M
dhava und seinen Nachfolgern entwickelt werden. Wir behandeln einen Sanskritkommentar zu den Regeln, der eine mögliche Herleitung suggeriert, die diese Diskrepanz erklärt. Dabei betonen wir nochmals, daß die keralesische Arbeit über solche Reihen eher in geometrischen Näherungen als in der Analysis an sich ihre Wurzeln hat. © 2001 Elsevier Science (USA).MSC subject classification: 01A32. 相似文献
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Ge and Huang (1989) proposed an approach to transform nonlinear integer programming problems into nonlinear global optimization problems, which are then solved by the filled function transformation method. The approach has recently attracted much attention. This note indicates that the formulae to determine a penalty parameter in two fundamental theorems are incorrect, and presents the corrected formulae and revised theorems. 相似文献
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Hein van der Holst 《Journal of Graph Theory》2002,41(1):24-52
Let la(G) be the invariant introduced by Colin de Verdière [J. Comb. Theory, Ser. B., 74:121–146, 1998], which is defined as the smallest integer n≥0 such that G is isomorphic to a minor of Kn×T, where Kn is a complete graph on n vertices and where T is an arbitrary tree. In this paper, we give an alternative definition of la(G), which is more in terms of the tree‐width of a graph. We give the collection of minimal forbidden minors for the class of graphs G with la(G)≤k, for k=2, 3. We show how this work on la(G) can be used to get a forbidden minor characterization of the graphs with (G)≤3. Here, (G) is another graph parameter introduced in the above cited paper. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 24–52, 2002 相似文献
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Let ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have
(1-δ(x))ζ(x)+αδ(x)<ζ(x+1)<(1-δ(x))ζ(x)+βδ(x),