Next article On the Convergence of an Algorithm for Best Tchebycheff ApproximationsJ. R. RiceJ. R. Ricehttps://doi.org/10.1137/0107011PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956x+307 MR0095369 0072.28403 Google Scholar[2] C. de la Vallée Poussin, Leçons sur l'Approximation des Fonctions d'une Variable Réelle, Gauthier-Villars, Paris, 1919 Google Scholar[3] C. de la Vallée Poussin, Sur la méthode de l'approximation minimum, Ann. Soc. Sci. Bruxelles, Ser. I, 35 (1911), 1–16 Google Scholar[4] A. A. Goldstein and , Ward Cheney, A finite algorithm for the solution of consistent linear equations and inequalities and for the Tchebycheff approximation of inconsistent linear equations, Mathematical pre-print series No. 7, Convair Astronautics, San Diego, 1957 0084.01902 Google Scholar[5] T. S. Motzkin and , J. L. Walsh, Least pth power polynomials on a finite point set, Trans. Amer. Math. Soc., 83 (1956), 371–396 MR0081991 0072.25206 Google Scholar[6] Abe Shenitzer, Chebyshev approximation of a continuous function by a class of functions, J. Assoc. Comput. Mach., 4 (1957), 30–35 MR0093892 CrossrefISIGoogle Scholar[7] S. I. Zuhovickii˘, An algorithm for the solution of the Čebyšev approximation problem in the case of a finite system of incompatible linear equations, Doklady Akad. Nauk SSSR (N.S.), 79 (1951), 561–564, See also this Journal, 6 (1958), pp. 233–239 MR0043559 Google Scholar Next article FiguresRelatedReferencesCited byDetails On $L_1 $ Approximation I: Computation for Continuous Functions and Continuous Dependence14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 4, No. 1AbstractPDF (1337 KB)Methods—Old and New—for Solving the Tchebycheff Approximation ProblemE. Stiefel14 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 1, No. 1AbstractPDF (1029 KB)Overdetermined Systems of Linear Equations18 July 2006 | SIAM Review, Vol. 5, No. 1AbstractPDF (1162 KB) Volume 7, Issue 2| 1959Journal of the Society for Industrial and Applied Mathematics History Submitted:10 September 1958Published online:10 July 2006 InformationCopyright © 1959 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0107011Article page range:pp. 133-142ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics
Two types of elastomeric light valves , their fabrication, performance, and application, are described. Both are thin blocks of poly(dimethylsiloxane), PDMS, with relief structures on their surfaces, either an array of square pyramids or an array of retroreflective corner cubes (see Figure). Use of the valves in a display device is demonstrated, in which the transparency can be controlled by mechanical compression. magnified image
It is shown that long-wavelength elastic scattering data from an arbitrary localized defect in a uniform isotropic medium has a maximum information content of 22 parameters which are characteristic of the defect. These parameters are shown to consist of the mass excess δM and the 21 independent components of a fourth-rank tensor Dijkl, that depends on the elastic moduli variation δcijkl and static response properties of the defect region. This tensor and the contracted forms Dij (=Dijkk/3) and D (=Dkk/3) allow partial ’’inversion’’ of scattering data to determine properties of the defect. In particular, it is shown how to estimate the orientation and maximum stress intensity factor for defects in the form of planar cracks, to obtain lower bounds to maximum defect dimensions, and to represent defects in the form of inclusions or voids as approximately equivalent ellipsoids. The results are pertinent to the quantification of nondestructive examination of materials for defects in their interiors.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTFree radical intermediates in the reaction of neophyllithium with oxygenEdward J. Panek and George M. WhitesidesCite this: J. Am. Chem. Soc. 1972, 94, 25, 8768–8775Publication Date (Print):December 1, 1972Publication History Published online1 May 2002Published inissue 1 December 1972https://doi.org/10.1021/ja00780a021RIGHTS & PERMISSIONSArticle Views122Altmetric-Citations25LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (985 KB) Get e-Alerts Get e-Alerts
Nanoscale materials enable unique opportunities at the interface between the physical and life sciences, and the interface between nanoelectronic devices and biological systems makes possible communication between these two diverse systems at the length scale relevant to biological function. In this presentation, the development of nanowire nanoelectronic devices and their application as powerful tools for the life sciences will be discussed. First, a brief introduction to nanowire nanoelectronic devices as well as comparisons to other electrophysiological tools will be presented to illuminate the unique strengths and opportunities enabled at the nanoscale. Second, illustration of detection capabilities including signal-to-noise and applications for real-time label-free detection of biochemical markers down to the level of single molecules will be described. Third, the use of nanowire nanoelectronics for building interfaces to cells and tissues will be reviewed. Multiplexed measurements made from nanowire devices fabricated on flexible and transparent substrates recording signal propagation across cultured cells, acute tissue slices and intact organs will be illustrated, including quantitative analysis of the high simultaneous spatial and temporal resolution achieved with these nanodevices. Specific examples of subcellular and near point detection of extracellular potential will be used to illustrate the unique capabilities, such as recording localized potential changes due to neuronal activities simultaneously across many length scales, which provide key information for functional neural circuit studies. Last, emerging opportunities for the creation of powerful new probes based on controlled synthesis and/or bottom-up assembly of nanomaterials will be described with an emphasis on the creation of kinked nanowire probes capable of first intracellular transistor recordings. The prospects for blurring the distinction between nanoelectronic and living systems in the future will be highlighted.
The biomimetic self-assembly of an operating electrical circuit is described. The circuit, self-assembled via the hydrophobic effect from two different, but shape-complementary, non-functional subunits, contains a light-emitting diode (LED), a gold cathode, and a magnesium anode. It is shown that the system, when immersed in a suitable electrolyte (potassium ferricyanide), constitutes an electrochemical cell—the LED is powered through a reaction involving the dissolution of magnesium(0) at the anode and the reduction of ferricyanide to ferrocyanide at the cathode.