1,088 research outputs found
Upper bound for the number of chords of a polygon which pass through a given point in a finite plane
No full text“Was Kepler Being Ironic? Ramus Professors of Mathematics and the Nature of Their Hypotheses in the Classroom”
No full textThe educational reformer Petrus Ramus stipulated in his will and publications that his proposed new chair of mathematics at Paris should have certain
attributes: be well-schooled in Greek and Latin, esteem reason over authority, place an emphasis on geometry, arithmetic, optics, and mechanics, and champion
an astronomy without hypotheses. This latter challenge was taken up by Johannes Kepler when he suggested that he himself met Ramus’ criteria. This chapter will
explore the multiple ways in which two prominent holders of, and one candidate for the chair presented astronomical hypotheses to students in the classrooms of France and Britain, offering multiple hypotheses that seem to run contrary to Ramus’ stipulations. However, their activities reflected an interpretation that Ramus’ intention had been—as Kepler suggested—a desire to go beyond unnecessary speculation grounded in unprovable natural philosophical conjecture in order
to find a true astronomical model grounded in the specialist aptitudes specified in his will
Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in L2(ℝ)
No full textSampled Gabor phase retrieval — the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice — is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, a classification of square-integrable signals which are not phase retrievable from Gabor measurements on parallel lines has been presented. This classification was used to exhibit a family of counterexamples to uniqueness in sampled Gabor phase retrieval. Here, we show that the set of counterexamples to uniqueness in sampled Gabor phase retrieval is dense in L2(ℝ), but is not equal to the whole of L2(ℝ) in general. Overall, our work contributes to a better understanding of the fundamental limits of sampled Gabor phase retrieval.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Analysi
Armament and Society in the Mirror of the Avar Archaelogy The Transdanubia-Phenomenon Revisited
No full textOne of the most significant problems of the A var archaeology is the question of
Germanic (mainly Gepidic) continuity in Transdanubia. In my paper I would like to
make some comments on the so-called Transdanubia-phenomenon of the Early A var
Carpathian Basin based on the analysis of weapon-combinations found in six
cemeteries of Eastern Transdanubia. I intend to answer the following questions: I.
How far the weapon-combinations of the East-Transdanubian cemeteries of the early
Avar Period (568-650) are identical or similar to the general picture of Avar armament
drawn by contemporary cemeteries? 2. Are the weapon-combinations or armament of
these cemeteries similar to that of the earlier Gepidic and Langobardic sites from the
early 6th centuries or to the contemporary Germanic (Alemannic, Frank or Bavarian)
cemeteries of the present-day Germany?
As a result, the early A var cemeteries of Transdanubia are characterized by the
relatively high number of close-combat weapons compared to other sites of the Avar
Khaganate. However, comparing to Merovingian sites the burials containing only
close-combat weapons are very low and in most of the cases the weapon-combinations
characteristic to this culture is missing
Gabor Frames for Model Sets
No full textWe generalize three main concepts of Gabor analysis for lattices to the setting of model sets: fundamental identity of Gabor analysis, Janssen’s representation of the frame operator and Wexler–Raz biorthogonality relations. Utilizing the connection between model sets and almost periodic functions, as well as Poisson’s summations formula for model sets we develop a form of a bracket product that plays a central role in our approach. Furthermore, we show that, if a Gabor system for a model set admits a dual which is of Gabor type, then the density of the model set has to be greater than one.© The Author(s) 201
A fast learning algorithm for Gabor transformation
Get PDFAn adaptive learning approach for the computation of the coefficients of the generalized nonorthogonal 2-D Gabor transform representation is introduced in this correspondence. The algorithm uses a recursive least squares (RLS) type algorithm. The aim is to achieve minimum mean squared error for the reconstructed image from the set of the Gabor coefficients. The proposed RLS learning offers better accuracy and faster convergence behavior when compared with the least mean squares (LMS)-based algorithms. Applications of this scheme in image data reduction are also demonstrated
Palmprint Identification Using Gabor and Wide Principal Line Features
No full textAbstractIn this paper proposed palmprint identification using Gabor features, Gabor and Wide Principal Line Image (WPLI) features. Extracted a fixed size ROI from palmprint images. Resize the extracted ROI into 64 x 64. Apply the Gabor filters to extract the features from the resized ROI. Dissimilarity distance is used to measure the dissimilarity between the query palmprint and database palmprint images. Experiments were conducted on Polyu Palmprint Database using Gabor features, Gabor and WPLI features. Experimental results shows that the proposed approach using Gabor and WPLI features obtains better results compared with the existing methods
The Mind/Body Connection
No full textPhysician and award winning author, Dr Gabor Mate, discusses his research at the intersection of addiction, science, psychology, and compassionhttps://digitalcommons.ciis.edu/publicprograms/1030/thumbnail.jp
Density of Gabor Systems Via the Short Time Fourier Transform
No full textWe apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof to Ramanathan and Steger’s well-known result regarding the density of Gabor frames and Gabor Riesz sequences. Moreover, this point of view allows us to extend this result in several directions. The approach we use was first observed by Olevskii and the third author in their study of exponential systems, here we develop and simplify it further
Absorbing new subjects: holography as an analog of photography
Get PDFI discuss the early history of holography and explore how perceptions, applications, and forecasts of the subject were shaped by prior experience. I focus on the work of Dennis Gabor (1900–1979) in England,Yury N. Denisyuk (b. 1924) in the Soviet Union, and Emmett N. Leith (1927–2005) and Juris Upatnieks (b. 1936) in the United States. I show that the evolution of holography was simultaneously promoted and constrained by its identification as an analog of photography, an association that influenced its assessment by successive audiences of practitioners, entrepreneurs, and consumers. One consequence is that holography can be seen as an example of a modern technical subject that has been shaped by cultural influences more powerfully than generally appreciated.
Conversely, the understanding of this new science and technology in terms of an older one helps
to explain why the cultural effects of holography have been more muted than anticipated by forecasters
between the 1960s and 1990s
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