33 research outputs found
Computing many faces in arrangements of lines and segments
No full textWe present randomized algorithms for computing many faces in an arrangement of lines or of segments in the plane, which are considerably simpler and slightly faster than the previously known ones. pn The main new idea is a simple randomized O(n log n) expected time algorithm for computing root n cells in an arrangement of n lines.A part of this work was done while the first and third authors were visiting Charles University and while the first author was visiting Utrecht University. The first author has been supported by National Science Foundation Grant CCR-93-01259 and an NYI aword. The second author has been supported by Charles University grant No. 351 and Czech Republic Grant GACR 201/93/2167. The third author has been supported by the Netherlands' Organization for Scientific Research (NWO) and partially supported by ESPRIT Basic Research Action No. 7141 (project ALCOM 2:Algorithms and Complexity)
From Disruption to Post-pandemic Scenario
No full textFollowing the previous Chapter 18, this concluding this chapter (Part 2 of two) puts forward options for regulators triggered by COVID-19, bringing to the conclusion that the pandemic is an unprecedented opportunity to redefining boundaries and refocusing the priority on innovation for transparency. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Flow Mechanism of Sand-Water Mixtures in Pipelines
No full textMechanical Maritime and Materials Engineerin
On Galleries With No Bad Points
No full textFor any k we construct a simply connected compact set (art gallery) in IR 3 whose every point sees a positive fraction (in fact, more than 5 9 ) of the gallery, but the whole gallery cannot be guarded by k guards. This disproves a conjecture of Kavraki, Latombe, Motwani, and Raghavan. 1 Introduction Consider an art gallery (i.e., compact set) X of Lebesgue measure 1 in IR d ; d 2, such that a guard placed anywhere in the gallery sees a region of Lebesgue measure at least ". Kavraki, Latombe, Motwani, and Raghavan [KLMR] conjectured that if X has at most h holes then it can be guarded by at most f d (h; ") guards, for some function f d polynomial in h and 1 " . Kalai and Matousek [KM] proved a weaker form of the planar version of the conjecture (their function f 2 was not polynomial in h). Following some ideas of Kalai and Matousek, the author [Va] proved the planar version of the conjecture with f 2 (h; ") = (2 + o(1)) 1 " log 1 " log 2 (h + 2). Kalai and Matousek [KM]..
A lower bound on the size of Lipschitz subsets in dimension 3
No full textA set S R is C-Lipschitz in the x i -coordinate, where C > 0 is a real number, if for every two points a; b 2 S, we have ja i b i j C maxfja j b j j : j = 1; 2; : : : ; d; j 6= ig. Motivated by a problem of Laczkovich, the author asked whether every n-point set in R contains a subset of size at least cn that is C-Lipschitz in one of the coordinates, for suitable constants C and c > 0 (depending on d). This wa
Engineering Design A Systematic Approach
No full textTO THE GERMAN EDITION This book is addressed to those engineering students who are prepared to work-not to such as are content to refurbish existing designs without taking the trouble to understand the trains of thought and the considerations which are needed in true design work. It is a well-established fact that the beginner, confronted by the simplest of design problems, and lacking a pattern or model to suggest a solution, loses his way in endless trial and error unless given positive guidance. In this book, therefore, the author has drawn on his long teaching experience in an attempt to present in a readily understandable and systematic manner a methodical work plan which will enable the beginner practising design problems to reach his objective by a rational route. This approach has the further advantage. con firmed by experience, that in adopting it the student will find his interest and pleasure in design work growing, and his self-confidence increasing. Written with the requirements of general mechanical engineering in mind, the book does not deal with the manufacturing methods typical of light precision engineering. To prevent the book from taking on a size which would have detracted from its clear layout and obscured the main principles presented, the numerical tables, graphs, etc. available for reference in pocket books and textbooks have been omitte
Shifted Excitation Raman Difference Spectroscopy Combined with Wide Area Illumination and Sample Rotation for Wood Species Classification
No full textEfficient Partition Trees
No full textWe prove a theorem on partitioning point sets in Ed (d fixed) and give an efficient construction of partition trees based on it. Such a partition tree for n points uses O(n) space, can be constructed in O(n log n) de-terministic time, and it can be used to answer simplex range queries (counting or general semigroup ones) in time O(nl–lld(log n) O[lJ). If we allow O(nl+d) pre-processing time, where 6 is some positive constant, a more complicated data structure yields query time O(nl-lld(loglog n) O(lJ). J?or dimensions d = 2,3 and if the weights of the points lie in a group, we get query time 0(nl-11d20(10g ” ‘)). This attains the lower bounds due to [Chazelle 89] upto polylogarithrnic factors, im-proving the results of [Chazelle et al. 90], making the preprocessing deterministic without loss of efficiency and simplifying the query answering algorithm. Dy-namization of our data structures and tradeoffs between preprocessing (and storage) and query time are also possible. The partition result is also applied for a deterministic computation of c-cuttings. E.g., given a collection of n lines in the plane and a parameter r < nl- $ for a fixed 6>0, the plane can be subdivided into O(r2) triangles, each intersected by at most n/r of the given lines, in time O(nl/2r3/2 + n log r), thus in almost linear time for r < n113. ●Part of thk research waa performed while the author was visiting at the Freie Universit5t Berlin
Temperature spatially offset Raman spectroscopy (T-SORS): subsurface chemically specific measurement of temperature in turbid media using anti-Stokes spatially offset Raman Spectroscopy.
No full textPublishedJournal ArticleThis is the author accepted manuscript. The final version is available from ACS via http://dx.doi.org/10.1021/acs.analchem.5b03360Here we propose and demonstrate a new analytical method for the noninvasive measurement of subsurface temperatures within diffusely scattering (turbid) media in combination with high chemical selectivity. The method is based upon the first combination of Stokes/anti-Stokes light scattering measurements and the recently developed spatially offset Raman spectroscopy (SORS). This approach has been conceptually demonstrated by measuring material-specific temperatures within a turbid sublayer of poly(tetrafluoroethylene) (PTFE) through a highly diffusely scattering overlayer of poly(oxymethylene) POM (3 mm thick). Root-mean-square errors (RMSEs) of 0.16-0.71 °C were achieved when measuring temperatures over ranges between 24 and 45 °C. This unique capability complements the array of existing, predominantly surface-based, temperature measurement techniques. It paves the way for a wide range of topical applications including subsurface, chemically specific, noninvasive temperature measurements within translucent media including the human body, subsurface monitoring of chemical or catalytic processes in manufacture quality and process control, and research
Theoretical and Practical Considerations of Spatially Offset Raman Spectroscopy (SORS) and Micro-SORS
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