The extensive study of metric spaces and their embeddings
has so far focused on embeddings that preserve pairwise distances.
A very intriguing concept introduced by Feige
allows us to quantify the extent to which larger
structures are preserved by a given embedding.
We investigate this concept, focusing on several major graph families
such as paths, trees, cubes, and expanders.
We find some similarities to the regular (pairwise) distortion,
as well as some striking differences. 相似文献
We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated. 相似文献
We study the Ginzburg-Landau functional
for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation
of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional.
Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001 相似文献
The objective of this study was to determine the incidence of vocal problems in young choir singers and to correlate vocal problems with demographic and behavioral information. A questionnaire addressing vocal habits and hygiene was offered to 571 young choir singers, up to 25 years of age, who sing at least weekly; 129 (22.6%) responded. More than one-half of the respondents had experienced vocal difficulty, particularly older adolescents. Detrimental behaviors and circumstances surveyed were not reflective of the incidence of vocal difficulty, except for morning hoarseness, chronic fatigue, insomnia, and female gender after puberty. Voice care professionals should be aware that self-reported voice difficulties are common among young choral singers, especially postpubescent girls, and children with symptoms consistent with reflux (morning hoarseness) and emotional stress (insomnia). Laryngologists should communicate with choral conductors and singing teachers to enhance early identification and treatment of children with voice complaints, and to develop choral educational strategies that help decrease their incidence. 相似文献
Introduction of a 2-isopropoxycarbonyl or 2-NN-dimethylcarbamoyl group into homochiral 1-p-tolyl- or 1-t-butyl-sulfinylnaphthalenes, via directed metalation reaction, followed by ligand coupling reaction with 1-naphthylmagnesium bromide, furnished atropisomeric 1,1′-binaphthyls in 82–95% enantiomeric excess (e.e.). 相似文献
Stochastic models with varying degrees of complexity are increasingly widespread in the oceanic and atmospheric sciences. One application is data assimilation, i.e., the combination of model output with observations to form the best picture of the system under study. For any given quantity to be estimated, the relative weights of the model and the data will be adjusted according to estimated model and data error statistics, so implementation of any data assimilation scheme will require some assumption about errors, which are considered to be random. For dynamical models, some assumption about the evolution of errors will be needed. Stochastic models are also applied in studies of predictability.
The formal theory of stochastic processes was well developed in the last half of the twentieth century. One consequence of this theory is that methods of simulation of deterministic processes cannot be applied to random processes without some modification. In some cases the rules of ordinary calculus must be modified.
The formal theory was developed in terms of mathematical formalism that may be unfamiliar to many oceanic and atmospheric scientists. The purpose of this article is to provide an informal introduction to the relevant theory, and to point out those situations in which that theory must be applied in order to model random processes correctly. 相似文献
A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site. 相似文献