International Nuclear Information System (INIS)
Temperley, D.J.
1976-01-01
In this paper we consider fully developed, laminar, unidirectional flow of uniformly conducting, incompressible fluid through a rectangular duct of uniform cross-section. An externally applied magnetic field acts parallel to one pair of opposite walls and induced velocity and magnetic fields are generated in a direction parallel to the axis of the duct. The governing equations and boundary conditions for the latter fields are introduced and study is then concentrated on the special case of a duct having all walls non-conducting. For values of the Hartmann number M>>1, classical asymptotic analysis reveals the leading terms in the expansions of the induced fields in all key regions, with the exception of certain boundary layers near the corners of the duct. The order of magnitude of the affect of the latter layers on the flow-rate is discussed and closed-form solutions are obtained for the induced fields near the corners of the duct. Attempts were made to formulate a concise Principle of Minimum Singularity to enable the correct choice of eigen functions for the various field components in the boundary layers on the walls parallel to the applied field. It was found, however, that these components are best found by taking the outer expansion of the closed-form solution in those boundary-layers near the corners of the duct where classical asymptotic analysis is not applicable. (author)
Heping, Wang; Xiaoguang, Li; Duyang, Zang; Rui, Hu; Xingguo, Geng
2017-11-01
This paper presents an exploration for phase separation in a magnetic field using a coupled lattice Boltzmann method (LBM) with magnetohydrodynamics (MHD). The left vertical wall was kept at a constant magnetic field. Simulations were conducted by the strong magnetic field to enhance phase separation and increase the size of separated phases. The focus was on the effect of magnetic intensity by defining the Hartmann number (Ha) on the phase separation properties. The numerical investigation was carried out for different governing parameters, namely Ha and the component ratio of the mixed liquid. The effective morphological evolutions of phase separation in different magnetic fields were demonstrated. The patterns showed that the slant elliptical phases were created by increasing Ha, due to the formation and increase of magnetic torque and force. The dataset was rearranged for growth kinetics of magnetic phase separation in a plot by spherically averaged structure factor and the ratio of separated phases and total system. The results indicate that the increase in Ha can increase the average size of separated phases and accelerate the spinodal decomposition and domain growth stages. Specially for the larger component ratio of mixed phases, the separation degree was also significantly improved by increasing magnetic intensity. These numerical results provide guidance for setting the optimum condition for the phase separation induced by magnetic field.
Laparoscopic reversal of Hartmann's procedure
DEFF Research Database (Denmark)
Svenningsen, Peter Olsen; Bulut, Orhan; Jess, Per
2010-01-01
of Hartmann's procedure as safely as in open surgery and with a faster recovery, shorter hospital stay and less blood loss despite a longer knife time. It therefore seems reasonable to offer patients a laparoscopic procedure at departments which are skilled in laparoscopic surgery and use it for standard...
Effect of Hartmann layer resolution for MHD flow in a straight ...
Indian Academy of Sciences (India)
851–861. c Indian Academy of Sciences. Effect of Hartmann layer resolution for MHD flow in a straight, conducting duct at high Hartmann numbers. SHARANYA SUBRAMANIAN1,∗, P K SWAIN2,. A V DESHPANDE1 and P SATYAMURTHY2. 1Mechanical Engineering Department, Veermata Jijabai Technological Institute,.
Transition to turbulence in the Hartmann boundary layer
Energy Technology Data Exchange (ETDEWEB)
Thess, A.; Krasnov, D.; Boeck, T.; Zienicke, E. [Dept. of Mechanical Engineering, Ilmenau Univ. of Tech. (Germany); Zikanov, O. [Dept. of Mechanical Engineering, Univ. of Michigan, Dearborn, MI (United States); Moresco, P. [School of Physics and Astronomy, The Univ. of Manchester (United Kingdom); Alboussiere, T. [Lab. de Geophysique Interne et Tectonophysique, Observatoire des Science de l' Univers de Grenoble, Univ. Joseph Fourier, Grenoble (France)
2007-07-01
The Hartmann boundary layer is a paradigm of magnetohydrodynamic (MHD) flows. Hartmann boundary layers develop when a liquid metal flows under the influence of a steady magnetic field. The present paper is an overview of recent successful attempts to understand the mechanisms by which the Hartmann layer undergoes a transition from laminar to turbulent flow. (orig.)
Reversal of Hartmann's procedure following acute diverticulitis: is timing everything?
LENUS (Irish Health Repository)
Fleming, Fergal J
2012-02-01
BACKGROUND: Patients who undergo a Hartmann\\'s procedure may not be offered a reversal due to concerns over the morbidity of the second procedure. The aims of this study were to examine the morbidity post reversal of Hartmann\\'s procedure. METHODS: Patients who underwent a Hartmann\\'s procedure for acute diverticulitis (Hinchey 3 or 4) between 1995 and 2006 were studied. Clinical factors including patient comorbidities were analysed to elucidate what preoperative factors were associated with complications following reversal of Hartmann\\'s procedure. RESULTS: One hundred and ten patients were included. Median age was 70 years and 56% of the cohort were male (n = 61). The mortality and morbidity rate for the acute presentation was 7.3% (n = 8) and 34% (n = 37) respectively. Seventy six patients (69%) underwent a reversal at a median of 7 months (range 3-22 months) post-Hartmann\\'s procedure. The complication rate in the reversal group was 25% (n = 18). A history of current smoking (p = 0.004), increasing time to reversal (p = 0.04) and low preoperative albumin (p = 0.003) were all associated with complications following reversal. CONCLUSIONS: Reversal of Hartmann\\'s procedure can be offered to appropriately selected patients though with a significant (25%) morbidity rate. The identification of potential modifiable factors such as current smoking, prolonged time to reversal and low preoperative albumin may allow optimisation of such patients preoperatively.
Shack-Hartmann reflective micro profilometer
Gong, Hai; Soloviev, Oleg; Verhaegen, Michel; Vdovin, Gleb
2018-01-01
We present a quantitative phase imaging microscope based on a Shack-Hartmann sensor, that directly reconstructs the optical path difference (OPD) in reflective mode. Comparing with the holographic or interferometric methods, the SH technique needs no reference beam in the setup, which simplifies the system. With a preregistered reference, the OPD image can be reconstructed from a single shot. Also, the method has a rather relaxed requirement on the illumination coherence, thus a cheap light source such as a LED is feasible in the setup. In our previous research, we have successfully verified that a conventional transmissive microscope can be transformed into an optical path difference microscope by using a Shack-Hartmann wavefront sensor under incoherent illumination. The key condition is that the numerical aperture of illumination should be smaller than the numerical aperture of imaging lens. This approach is also applicable to characterization of reflective and slightly scattering surfaces.
Coded Shack-Hartmann Wavefront Sensor
Wang, Congli
2016-12-01
Wavefront sensing is an old yet fundamental problem in adaptive optics. Traditional wavefront sensors are limited to time-consuming measurements, complicated and expensive setup, or low theoretically achievable resolution. In this thesis, we introduce an optically encoded and computationally decodable novel approach to the wavefront sensing problem: the Coded Shack-Hartmann. Our proposed Coded Shack-Hartmann wavefront sensor is inexpensive, easy to fabricate and calibrate, highly sensitive, accurate, and with high resolution. Most importantly, using simple optical flow tracking combined with phase smoothness prior, with the help of modern optimization technique, the computational part is split, efficient, and parallelized, hence real time performance has been achieved on Graphics Processing Unit (GPU), with high accuracy as well. This is validated by experimental results. We also show how optical flow intensity consistency term can be derived, using rigor scalar diffraction theory with proper approximation. This is the true physical law behind our model. Based on this insight, Coded Shack-Hartmann can be interpreted as an illumination post-modulated wavefront sensor. This offers a new theoretical approach for wavefront sensor design.
Corneal topographer based on the Hartmann test.
Mejía, Yobani; Galeano, Janneth C
2009-04-01
The purpose of this article is to show the performance of a topographer based on the Hartmann test for convex surfaces of F/# approximately 1. This topographer, called "Hartmann Test topographer (HT topographer)," is a prototype developed in the Physics Department of the Universidad Nacional de Colombia. From the Hartmann pattern generated by the surface under test, and by the Fourier analysis and the optical aberration theory we obtain the sagitta (elevation map) of the surface. Then, taking the first and the second derivatives of the sagitta in the radial direction we obtain the meridional curvature map. The method is illustrated with an example. To check the performance of the HT topographer a toric surface, a revolution aspherical surface, and two human corneas were measured. Our results are compared with those obtained with a Placido ring topographer (Tomey TMS-4 videokeratoscope), and we show that our curvature maps are similar to those obtained with the Placido ring topographer. The HT topographer is able to reconstruct the corneal topography potentially eradicating the skew ray problem, therefore, corneal defects can be visualized more. The results are presented by elevation and meridional curvature maps.
Morbidity and Mortality of Hartmann's Procedure for Sigmoid ...
African Journals Online (AJOL)
Background: The restoration of intestinal continuity following Hartmann's procedure is associated with high morbidity and mortality rates and low restoration rate. Objective: To determine the causes of complications and deaths associated with Hartmann's procedure and the secondary restoration of digestive continuity for ...
Combined shearing interferometer and hartmann wavefront sensor
International Nuclear Information System (INIS)
Hutchin, R. A.
1985-01-01
A sensitive wavefront sensor combining attributes of both a Hartmann type of wavefront sensor and an AC shearing interferometer type of wavefront sensor. An incident wavefront, the slope of which is to be detected, is focussed to first and second focal points at which first and second diffraction gratings are positioned to shear and modulate the wavefront, which then diverges therefrom. The diffraction patterns of the first and second gratings are positioned substantially orthogonal to each other to shear the wavefront in two directions to produce two dimensional wavefront slope data for the AC shearing interferometer portion of the wavefront sensor. First and second dividing optical systems are positioned in the two diverging wavefronts to divide the sheared wavefront into an array of subapertures and also to focus the wavefront in each subaperture to a focal point. A quadrant detector is provided for each subaperture to detect the position of the focal point therein, which provides a first indication, in the manner of a Hartmann wavefront sensor, of the local wavefront slope in each subaperture. The total radiation in each subaperture, as modulated by the diffraction grating, is also detected by the quadrant detector which produces a modulated output signal representative thereof, the phase of which relative to modulation by the diffraction grating provides a second indication of the local wavefront slope in each subaperture, in the manner of an AC shearing interferometer wavefront sensor. The data from both types of sensors is then combined by long term averaging thereof to provide an extremely sensitive wavefront sensor
Sorting method to extend the dynamic range of the Shack-Hartmann wave-front sensor
International Nuclear Information System (INIS)
Lee, Junwon; Shack, Roland V.; Descour, Michael R.
2005-01-01
We propose a simple and powerful algorithm to extend the dynamic range of a Shack-Hartmann wave-front sensor. In a conventional Shack-Hartmann wave-front sensor the dynamic range is limited by the f-number of a lenslet, because the focal spot is required to remain in the area confined by the single lenslet. The sorting method proposed here eliminates such a limitation and extends the dynamic range by tagging each spot in a special sequence. Since the sorting method is a simple algorithm that does not change the measurement configuration, there is no requirement for extra hardware, multiple measurements, or complicated algorithms. We not only present the theory and a calculation example of the sorting method but also actually implement measurement of a highly aberrated wave front from nonrotational symmetric optics
Exact solutions of continuous states for Hartmann potential
International Nuclear Information System (INIS)
Chen Changyuan; Lu Falin; Sun Dongsheng
2004-01-01
In this Letter, we obtain the exact solutions of continuous states for the Hartmann potential. The normalized wave functions of continuous states on the 'k/2π scale' and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed
Ekman-Hartmann layer in a magnetohydrodynamic Taylor-Couette flow.
Szklarski, Jacek; Rüdiger, Günther
2007-12-01
We study magnetic effects induced by rigidly rotating plates enclosing a cylindrical magnetohydrodynamic (MHD) Taylor-Couette flow at the finite aspect ratio HD=10 . The fluid confined between the cylinders is assumed to be liquid metal characterized by small magnetic Prandtl number, the cylinders are perfectly conducting, an axial magnetic field is imposed with Hartmann number Ha approximately 10 , and the rotation rates correspond to Reynolds numbers of order 10(2)-10(3). We show that the end plates introduce, besides the well-known Ekman circulation, similar magnetic effects which arise for infinite, rotating plates, horizontally unbounded by any walls. In particular, there exists the Hartmann current, which penetrates the fluid, turns in the radial direction, and together with the applied magnetic field gives rise to a force. Consequently, the flow can be compared with a Taylor-Dean flow driven by an azimuthal pressure gradient. We analyze the stability of such flows and show that the currents induced by the plates can give rise to instability for the considered parameters. When designing a MHD Taylor-Couette experiment, special care must be taken concerning the vertical magnetic boundaries so that they do not significantly alter the rotational profile.
Aquina, Christopher T; Probst, Christian P; Becerra, Adan Z; Hensley, Bradley J; Iannuzzi, James C; Noyes, Katia; Monson, John R T; Fleming, Fergal J
2016-11-01
Colostomy reversal after Hartmann's procedure for diverticulitis is a morbid procedure, and studies investigating factors associated with outcomes are lacking. This study identifies patient, surgeon, and hospital-level factors associated with perioperative outcomes after stoma reversal. The Statewide Planning and Research Cooperative System was queried for urgent/emergency Hartmann's procedures for diverticulitis between 2000-2012 in New York State and subsequent colostomy reversal within 1 year of the procedure. Surgeon and hospital volume were categorized into tertiles based on the annual number of colorectal resections performed each year. Bivariate and mixed-effects analyses were used to assess the association between patient, surgeon, and hospital-level factors and perioperative outcomes after colostomy reversal, including a laparoscopic approach; duration of stay; intensive care unit admission; complications; mortality; and 30-day, unscheduled readmission. Among 10,487 patients who underwent Hartmann's procedure and survived to discharge, 63% had the colostomy reversed within 1 year. After controlling for patient, surgeon, and hospital-level factors, high-volume surgeons (≥40 colorectal resections/yr) were independently associated with higher odds of a laparoscopic approach (unadjusted rates: 14% vs 7.6%; adjusted odds ratio = 1.84, 95% confidence interval = 1.12, 3.00), shorter duration of stay (median: 6 versus 7 days; adjusted incidence rate ratio = 0.87, 95% confidence interval = 0.81, 0.95), and lower odds of 90-day mortality (unadjusted rates: 0.4% vs 1.0%; adjusted odds ratio = 0.30, 95% confidence interval = 0.10, 0.88) compared with low-volume surgeons (1-15 colorectal resections/yr). High-volume surgeons are associated with better perioperative outcomes and lower health care utilization after Hartmann's reversal for diverticulitis. These findings support referral to high-volume surgeons for colostomy reversal. Copyright © 2016
MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow
International Nuclear Information System (INIS)
Jirkovsky, L.; Bo-ot, L. Ma.; Chiang, C. M.
2010-01-01
We derive higher order magneto-hydrodynamic (MHD) equations from a microscopic picture using projection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number. (physics of gases, plasmas, and electric discharges)
Hartmann test of the COMPASS RICH-1 optical telescopes
Polak, J; Alekseev, M; Angerer, H; Apollonio, M; Birsa, R; Bordalo, P; Bradamante, F; Bressan, A; Busso, L; Chiosso, V M; Ciliberti, P; Colantoni, M L; Costa, S; Dibiase, N; Dafni, T; Dalla Torre, S; Diaz, V; Duic, V; Delagnes, E; Deschamps, H; Eyrich, W; Faso, D; Ferrero, A; Finger, M; Finger, M Jr; Fischer, H; Gerassimov, S; Giorgi, M; Gobbo, B; Hagemann, R; von Harrach, D; Heinsius, F H; Joosten, R; Ketzer, B; Königsmann, K; Kolosov, V N; Konorov, I; Kramer, D; Kunne, F; Levorato, S; Maggiora, A; Magnon, A; Mann, A; Martin, A; Rebourgeard, P; Mutter, A; Nähle, O; Neyret, D; Nerling, F; Pagano, P; Paul, S; Panebianco, S; Panzieri, D; Pesaro, G; Pizzolotto, C; Menon, G; Rocco, E; Robinet, F; Schiavon, P; Schill, C; Schoenmeier, P; Silva, L; Slunecka, M; Steiger, L; Sozzi, F; Sulc, M; Svec, M; Tessarotto, F; Teufel, A; Wollny, H
2008-01-01
The central region of COMPASS RICH-1 has been equipped with a new photon detection system based on MultiAnode PhotoMultiplier Tubes (MAPMT). The Cherenkov photons are focused by an array of 576 fused silica telescopes onto 576 MAPMTs. The quality and positioning of all optical components have been tested by Hartmann method. The validation procedures are described. The quality of the optical concentrators was checked and alignment corrections were made. The upgraded detector showed excellent performances during 2006 data taking.
International Nuclear Information System (INIS)
Baker, K.L.
2005-01-01
This article details a multigrid algorithm that is suitable for least-squares wave-front reconstruction of Shack-Hartmann and shearing interferometer wave-front sensors. The algorithm detailed in this article is shown to scale with the number of subapertures in the same fashion as fast Fourier transform techniques, making it suitable for use in applications requiring a large number of subapertures and high Strehl ratio systems such as for high spatial frequency characterization of high-density plasmas, optics metrology, and multiconjugate and extreme adaptive optics systems
Directory of Open Access Journals (Sweden)
Lucia Leao
2011-07-01
Full Text Available In August 18, 2010, Frank Hartmann was present at the Post Graduate Program in Communication and Semiotics of PUC-SP, where he lectured on the following theme: “Towards an aesthetics of communication”. Frank Hartmann is full professor at the Bauhaus University, Weimar in Germany and external faculty member at the Dept. of Communication, University of Vienna, Austria. He is the author, among others, of: Medien und Kommunikation (2008; Mediologie - Ansatz einer der Medientheorie Kulturwissenschaften (2003, and Medienphilosophie (2000. More information on his website: http://www.medienphilosophie.net/f_hartmann.htmlFrank Hartmann esteve no dia 18 de agosto de 2010 no Programa de Pós-Graduação em Comunicação e Semiótica da PUC-SP, onde proferiu a palestra “Towards an aesthetics of communication”. Hartmann é professor titular da Universidade Bauhaus, em Weimar, na Alemanha e professor convidado do Departamento de Comunicação da Universidade de Viena, na Áustria. É autor, entre outros, de: Medien und Kommunikation (2008; Mediologie – Ansätze einer Medientheorie der Kulturwissenschaften (2003; e Medienphilosophie (2000. Mais informações em seu site: http://www.medienphilosophie.net/f_hartmann.html
Optimal Shack-Hartmann Wavefront Sensing For Low-Light-Levels
National Research Council Canada - National Science Library
Solomon, Christopher
1997-01-01
.... He will analyze the sensitivity gains achievable in shack-hartmann wavefront sensors using bayesian estimators and compare the results with those achieved using a standard least squares approach...
Kaegbein, Paul
2007-01-01
Arvustus: Stefan Hartmann. Revaler Handwerker im Spiegel fer Ratsprotokolle von 1722 bis 1755. In : Ostseeprovinzen, baltische Staaten und das Nationale. Münster : LIT, 2005. lk. 89-112. Kanuti gildi koondunud ametite organisatsioonist ja struktuurist
DEFF Research Database (Denmark)
Gehrman, J.; Angenete, E; Björholt, I.
2016-01-01
Background: Open surgery with resection and colostomy (Hartmann's procedure) has been the standard treatment for perforated diverticulitis with purulent peritonitis. In recent years laparoscopic lavage has emerged as an alternative, with potential benefits for patients with purulent peritonitis...
More about tunnelling times and superluminal tunnelling (Hartmann effect)
International Nuclear Information System (INIS)
Olkhovsky, V.S.; Recami, E.; Raciti, F.; Zaichenko, A.
1995-05-01
Aims of the present paper are: i) presenting and analysing the results of various numerical calculations on the penetration and return times Pen >, Ret >, during tunnelling inside a rectangular potential barrier, for various penetration depths x f ; ii) putting forth and discussing suitable definitions, besides of the mean values, also of the variances (or dispersions) D τT and D τR for the time durations of transmission and reflection processes; iii)mentioning, moreover, that our definition T > for the average transmission time results to constitute an improvement of the ordinary dwell- time formula; iv) commenting, at last, on the basis of the new numerical results, upon some recent criticism by C.R. Leavens. The paper stresses that numerical evaluations confirm that the approach implied, and implies, the existence of the Hartmann effect: an effect that in these days (due to the theoretical connections between tunnelling and evanescent-wave propagation) is receiving - at Cologne, Berkeley, Florence and Vienna - indirect, but quite interesting, experimental verification
Brightness checkerboard lattice method for the calibration of the coaxial reverse Hartmann test
Li, Xinji; Hui, Mei; Li, Ning; Hu, Shinan; Liu, Ming; Kong, Lingqin; Dong, Liquan; Zhao, Yuejin
2018-01-01
The coaxial reverse Hartmann test (RHT) is widely used in the measurement of large aspheric surfaces as an auxiliary method for interference measurement, because of its large dynamic range, highly flexible test with low frequency of surface errors, and low cost. And the accuracy of the coaxial RHT depends on the calibration. However, the calibration process remains inefficient, and the signal-to-noise ratio limits the accuracy of the calibration. In this paper, brightness checkerboard lattices were used to replace the traditional dot matrix. The brightness checkerboard method can reduce the number of dot matrix projections in the calibration process, thus improving efficiency. An LCD screen displayed a brightness checkerboard lattice, in which the brighter checkerboard and the darker checkerboard alternately arranged. Based on the image on the detector, the relationship between the rays at certain angles and the photosensitive positions of the detector coordinates can be obtained. And a differential de-noising method can effectively reduce the impact of noise on the measurement results. Simulation and experimentation proved the feasibility of the method. Theoretical analysis and experimental results show that the efficiency of the brightness checkerboard lattices is about four times that of the traditional dot matrix, and the signal-to-noise ratio of the calibration is significantly improved.
Automatic centroid detection and surface measurement with a digital Shack–Hartmann wavefront sensor
International Nuclear Information System (INIS)
Yin, Xiaoming; Zhao, Liping; Li, Xiang; Fang, Zhongping
2010-01-01
With the breakthrough of manufacturing technologies, the measurement of surface profiles is becoming a big issue. A Shack–Hartmann wavefront sensor (SHWS) provides a promising technology for non-contact surface measurement with a number of advantages over interferometry. The SHWS splits the incident wavefront into many subsections and transfers the distorted wavefront detection into the centroid measurement. So the accuracy of the centroid measurement determines the accuracy of the SHWS. In this paper, we have presented a new centroid measurement algorithm based on an adaptive thresholding and dynamic windowing method by utilizing image-processing techniques. Based on this centroid detection method, we have developed a digital SHWS system which can automatically detect centroids of focal spots, reconstruct the wavefront and measure the 3D profile of the surface. The system has been tested with various simulated and real surfaces such as flat surfaces, spherical and aspherical surfaces as well as deformable surfaces. The experimental results demonstrate that the system has good accuracy, repeatability and immunity to optical misalignment. The system is also suitable for on-line applications of surface measurement
Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances.
Téllez-Quiñones, Alejandro; Malacara-Doblado, Daniel; Flores-Hernández, Ricardo; Gutiérrez-Hernández, David A; León-Rodríguez, Miguel
2016-03-20
In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.
Life Cycle Management at Brødrene Hartmann A/S - strategy,- organisation and implementation
DEFF Research Database (Denmark)
Pedersen, Claus Stig; Alting, Leo; Mortensen, Anna Lise
1997-01-01
decisionmaking is under development.The implementation of life cycle management in Hartmann is organised with respect to the divisional areas: strategic management, product development, purchase, production, sale and distribution. The implementation of life cycle managment is assisted by tools to support...... decision making. The tools are developed in coorporation with the Department of Manufacturing Engineering at the Technical University of Denmark.This paper presents- The Hartmann environmental strategy, based on the life cycle concept- Experiences and results from developing a life cycle orientated...... organisation- Experiences and results from developing and implementing tools for life cycle management...
Geometrical error calibration in reflective surface testing based on reverse Hartmann test
Gong, Zhidong; Wang, Daodang; Xu, Ping; Wang, Chao; Liang, Rongguang; Kong, Ming; Zhao, Jun; Mo, Linhai; Mo, Shuhui
2017-08-01
In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, ray tracing of the modeled testing system is performed to reconstruct the test surface error. Careful calibration of system geometry is required to achieve high testing accuracy. To realize the high-precision surface testing with reverse Hartmann test, a computer-aided geometrical error calibration method is proposed. The aberrations corresponding to various geometrical errors are studied. With the aberration weights for various geometrical errors, the computer-aided optimization of system geometry with iterative ray tracing is carried out to calibration the geometrical error, and the accuracy in the order of subnanometer is achieved.
CMOS optical centroid processor for an integrated Shack-Hartmann wavefront sensor
Pui, Boon Hean
2004-01-01
A Shack Hartmann wavefront sensor is used to detect the distortion of light in an optical wavefront. It does this by sampling the wavefront with an array of lenslets and measuring the displacement of focused spots from reference positions. These displacements are linearly related to the local wavefront tilts from which the entire wavefront can be reconstructed. In most Shack Hartmann wavefront sensors, a CCD is used to sample the entire wavefront, typically at a rate of 25 to 60 Hz, and a who...
International Nuclear Information System (INIS)
Poynee, L A
2003-01-01
Shack-Hartmann based Adaptive Optics system with a point-source reference normally use a wave-front sensing algorithm that estimates the centroid (center of mass) of the point-source image 'spot' to determine the wave-front slope. The centroiding algorithm suffers for several weaknesses. For a small number of pixels, the algorithm gain is dependent on spot size. The use of many pixels on the detector leads to significant propagation of read noise. Finally, background light or spot halo aberrations can skew results. In this paper an alternative algorithm that suffers from none of these problems is proposed: correlation of the spot with a ideal reference spot. The correlation method is derived and a theoretical analysis evaluates its performance in comparison with centroiding. Both simulation and data from real AO systems are used to illustrate the results. The correlation algorithm is more robust than centroiding, but requires more computation
International Nuclear Information System (INIS)
Schaefer, B.; Luebbecke, M.; Mann, K.
2006-01-01
The suitability of the Hartmann-Shack technique for the determination of the propagation parameters of a laser beam is faced against the well known caustic approach according to the ISO 11146 standard. A He-Ne laser (543 nm) was chosen as test beam, both in its fundamental mode as well as after intentional distortion, introducing a moderate amount of spherical aberration. Results are given for the most important beam parameters M 2 , divergence, and beam widths, indicating an agreement of better than 10% and for adapted beam diameter <5%. Furthermore, the theoretical background, pros and cons, as well as some features of the software implementation for the Hartmann-Shack sensor are briefly reviewed
2016-11-01
Free Electron Density in Laser-Produced Plasmas by Anthony R Valenzuela Approved for public release; distribution is...AND SUBTITLE Shack-Hartmann Electron Densitometer (SHED): An Optical System for Diagnosing Free Electron Density in Laser-Produced Plasmas 5a...SUPPLEMENTARY NOTES 14. ABSTRACT The Shack-Hartmann Electron Densitometer is a novel method to diagnose ultrashort pulse laser–produced plasmas
A video Hartmann wavefront diagnostic that incorporates a monolithic microlens array
International Nuclear Information System (INIS)
Toeppen, J.S.; Bliss, E.S.; Long, T.W.; Salmon, J.T.
1991-07-01
we have developed a video Hartmann wavefront sensor that incorporates a monolithic array of microlenses as the focusing elements. The sensor uses a monolithic array of photofabricated lenslets. Combined with a video processor, this system reveals local gradients of the wavefront at a video frame rate of 30 Hz. Higher bandwidth is easily attainable with a camera and video processor that have faster frame rates. When used with a temporal filter, the reconstructed wavefront error is less than 1/10th wave
Benito Lopez, Pablo; Radhakrishnan, Hema; Nourrit, Vincent
2015-02-01
To determine whether an unmodified commercial wavefront aberrometer (irx3) can be used to estimate forward light scattering and how this assessment matches estimations obtained from the C-Quant straylight meter. University of Manchester, Manchester, United Kingdom. Prospective comparative study. Measurements obtained with a straylight meter and with Shack-Hartmann spot patterns using a previously reported metric were compared. The method was first validated in a model eye by spraying an aerosol over 4 contact lenses to generate various levels of scattering. Measurements with both methods were subsequently obtained in healthy eyes. The study comprised 33 healthy participants (mean age 38.9 years ± 13.1 [SD]). A good correlation was observed between the density of droplets over the contact lenses and the objective scatter value extracted from the hartmanngrams (r = 0.972, P meter and the metric derived from the Shack-Hartmann method (r = 0.133, P = .460). The hartmanngrams provided a valid objective measurement of the light scatter in a model eye; the measurements in human eyes were not significantly correlated with those of the light scatter meter. The straylight meter assesses large-angle scattering, while the Shack-Hartmann method collates information from a narrow angle around the center of the point-spread function; this could be the reason for the difference in measurements. No author has a financial or proprietary interest in any material or method mentioned. Copyright © 2015 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.
Rapid and highly integrated FPGA-based Shack-Hartmann wavefront sensor for adaptive optics system
Chen, Yi-Pin; Chang, Chia-Yuan; Chen, Shean-Jen
2018-02-01
In this study, a field programmable gate array (FPGA)-based Shack-Hartmann wavefront sensor (SHWS) programmed on LabVIEW can be highly integrated into customized applications such as adaptive optics system (AOS) for performing real-time wavefront measurement. Further, a Camera Link frame grabber embedded with FPGA is adopted to enhance the sensor speed reacting to variation considering its advantage of the highest data transmission bandwidth. Instead of waiting for a frame image to be captured by the FPGA, the Shack-Hartmann algorithm are implemented in parallel processing blocks design and let the image data transmission synchronize with the wavefront reconstruction. On the other hand, we design a mechanism to control the deformable mirror in the same FPGA and verify the Shack-Hartmann sensor speed by controlling the frequency of the deformable mirror dynamic surface deformation. Currently, this FPGAbead SHWS design can achieve a 266 Hz cyclic speed limited by the camera frame rate as well as leaves 40% logic slices for additionally flexible design.
Stafford, Caitlin; Francone, Todd D; Marcello, Peter W; Roberts, Patricia L; Ricciardi, Rocco
2018-03-01
Treatment of left-sided colorectal anastomotic leaks often requires fecal stream diversion for prevention of further septic complications. To manage anastomotic leak, it is unclear if diverting ileostomy provides similar outcomes to Hartmann resection with colostomy. We identified all patients who developed anastomotic leak following left-sided colorectal resections from 1/2012 through 12/2014 using the American College of Surgeons National Surgical Quality Improvement Program. Then, we examined the risk of mortality and abdominal reoperation in patients treated with diverting ileostomy as compared to Hartmann resection. There were 1745 patients who experienced an anastomotic leak in a cohort of 63,748 patients (3.7%). Two hundred thirty-five patients had a reoperation for anastomotic leak involving the formation of a diverting ileostomy (n = 77) or Hartmann resection (n = 158). There was no difference in mortality or abdominal reoperation in patients treated with diverting ileostomy (3.9, 7.8%) versus Hartmann resection (3.8, 6.3%) (p = 0.8). There was no difference in the outcomes of mortality or need for second abdominal reoperation in patients treated with diverting ileostomy as compared to Hartmann resection for left-sided colorectal anastomotic leak. Thus, select patients with left-sided colorectal anastomotic leaks may be safely managed with diverting ileostomy.
Numerical Evaluation of Parameter Correlation in the Hartmann-Tran Line Profile
Adkins, Erin M.; Reed, Zachary; Hodges, Joseph T.
2017-06-01
The partially correlated quadratic, speed-dependent hard-collision profile (pCqSDHCP), for simplicity referred to as the Hartmann-Tran profile (HTP), has been recommended as a generalized lineshape for high resolution spectroscopy. The HTP parameterizes complex collisional effects such as Dicke narrowing, speed dependent narrowing, and correlations between velocity-changing and dephasing collisions, while also simplifying to simpler profiles that are widely used, such as the Voigt profile. As advanced lineshape profiles are adopted by more researchers, it is important to understand the limitations that data quality has on the ability to retrieve physically meaningful parameters using sophisticated lineshapes that are fit to spectra of finite signal-to-noise ratio. In this work, spectra were simulated using the HITRAN Application Programming Interface (HAPI) across a full range of line parameters. Simulated spectra were evaluated to quantify the precision with which fitted lineshape parameters can be determined at a given signal-to-noise ratio, focusing on the numerical correlation between the retrieved Dicke narrowing frequency and the velocity-changing and dephasing collisions correlation parameter. Tran, H., N. Ngo, and J.-M. Hartmann, Journal of Quantitative Spectroscopy and Radiative Transfer 2013. 129: p. 89-100. Tennyson, et al., Pure Appl. Chem. 2014, 86: p. 1931-1943. Kochanov, R.V., et al., Journal of Quantitative Spectroscopy and Radiative Transfer 2016. 177: p. 15-30. Tran, H., N. Ngo, and J.-M. Hartmann, Journal of Quantitative Spectroscopy and Radiative Transfer 2013. 129: p. 199-203.
X-ray active mirror coupled with a Hartmann wavefront sensor
International Nuclear Information System (INIS)
Idir, Mourad; Mercere, Pascal; Modi, Mohammed H.; Dovillaire, Guillaume; Levecq, Xavier; Bucourt, Samuel; Escolano, Lionel; Sauvageot, Paul
2010-01-01
This paper reports on the design and performances of a test prototype active X-ray mirror (AXM) which has been designed and manufactured in collaboration with the French Small and Medium Enterprise mechanical company ISP System for the national French storage ring SOLEIL. Coupled with this active X-ray mirror and also in collaboration with another French Small and Medium Enterprise (Imagine Optic) a lot of efforts have been done in order to design and fabricate a wavefront X-ray analyzer based on the Hartmann principle (Hartman wavefront sensor, HWS).
Prandtl number of toroidal plasmas
International Nuclear Information System (INIS)
Itoh, K.; Itoh, S.; Fukuyama, A.; Yagi, M.; Azumi, M.
1993-06-01
Theory of the L-mode confinement in toroidal plasmas is developed. The Prandtl number, the ratio between the ion viscosity and the thermal conductivity is obtained for the anomalous transport process which is caused by the self-sustained turbulence in the toroidal plasma. It is found that the Prandtl number is of order unity both for the ballooning mode turbulence in tokamaks and for the interchange mode turbulence in helical system. The influence on the anomalous transport and fluctuation level is evaluated. Hartmann number and magnetic Prandtl number are also discussed. (author)
Trenti, Loris; Biondo, Sebastiano; Golda, Thomas; Monica, Millan; Kreisler, Esther; Fraccalvieri, Domenico; Frago, Ricardo; Jaurrieta, Eduardo
2011-03-01
Hartmann's procedure (HP) still remains the most frequently performed procedure for diffuse peritonitis due to perforated diverticulitis. The aims of this study were to assess the feasibility and safety of resection with primary anastomosis (RPA) in patients with purulent or fecal diverticular peritonitis and review morbidity and mortality after single stage procedure and Hartmann in our experience. From January 1995 through December 2008, patients operated for generalized diverticular peritonitis were studied. Patients were classified into two main groups: RPA and HP. A total of 87 patients underwent emergency surgery for diverticulitis complicated with purulent or diffuse fecal peritonitis. Sixty (69%) had undergone HP while RPA was performed in 27 patients (31%). At the multivariate analysis, RPA was associated with less post-operative complications (P clinical anastomotic leakage and needed re-operation. RPA can be safely performed without adding morbidity and mortality in cases of diffuse diverticular peritonitis. HP should be reserved only for hemodynamically unstable or high-risk patients. Specialization in colorectal surgery improves mortality and raises the percentage of one-stage procedures.
Real-time wavefront correction system using a zonal deformable mirror and a Hartmann sensor
International Nuclear Information System (INIS)
Salmon, J.T.; Bliss, E.S.; Long, T.W.; Orham, E.L.; Presta, R.W.; Swift, C.D.; Ward, R.S.
1991-07-01
We have developed an adaptive optics system that corrects up to five waves of 2nd-order and 3rd-order aberrations in a high-power laser beam to less than 1/10th wave RMS. The wavefront sensor is a Hartmann sensor with discrete lenses and position-sensitive photodiodes; the deformable mirror uses piezoelectric actuators with feedback from strain gauges bonded to the stacks. The controller hardware uses a VME bus. The system removes thermally induced aberrations generated in the master-oscillator-power-amplifier chains of a dye laser, as well as aberrations generated in beam combiners and vacuum isolation windows for average output powers exceeding 1 kW. The system bandwidth is 1 Hz, but higher bandwidths are easily attainable
Comparison of sorting algorithms to increase the range of Hartmann-Shack aberrometry.
Bedggood, Phillip; Metha, Andrew
2010-01-01
Recently many software-based approaches have been suggested for improving the range and accuracy of Hartmann-Shack aberrometry. We compare the performance of four representative algorithms, with a focus on aberrometry for the human eye. Algorithms vary in complexity from the simplistic traditional approach to iterative spline extrapolation based on prior spot measurements. Range is assessed for a variety of aberration types in isolation using computer modeling, and also for complex wavefront shapes using a real adaptive optics system. The effects of common sources of error for ocular wavefront sensing are explored. The results show that the simplest possible iterative algorithm produces comparable range and robustness compared to the more complicated algorithms, while keeping processing time minimal to afford real-time analysis.
Generalized method for sorting Shack-Hartmann spot patterns using local similarity
International Nuclear Information System (INIS)
Smith, Daniel G.; Greivenkamp, John E.
2008-01-01
The sensitivity and dynamic range of a Shack-Hartmann wavefront sensor is enhanced when the spots produced by the lenslet array are allowed to shift more than one lenslet radius from their on-axis positions. However, this presents the problem of accurately and robustly associating the spots with their respective subapertures. This paper describes a method for sorting spots that takes advantage of the local spot position distortions to unwrap the spot pattern. The described algorithm is both simple and robust and also applicable to any lenslet array geometry that can be described as a two-dimensional lattice, including hexagonal arrays, which are shown here to be more efficient than square arrays
Li, Xuxu; Li, Xinyang; wang, Caixia
2018-03-01
This paper proposes an efficient approach to decrease the computational costs of correlation-based centroiding methods used for point source Shack-Hartmann wavefront sensors. Four typical similarity functions have been compared, i.e. the absolute difference function (ADF), ADF square (ADF2), square difference function (SDF), and cross-correlation function (CCF) using the Gaussian spot model. By combining them with fast search algorithms, such as three-step search (TSS), two-dimensional logarithmic search (TDL), cross search (CS), and orthogonal search (OS), computational costs can be reduced drastically without affecting the accuracy of centroid detection. Specifically, OS reduces calculation consumption by 90%. A comprehensive simulation indicates that CCF exhibits a better performance than other functions under various light-level conditions. Besides, the effectiveness of fast search algorithms has been verified.
Scholl, A; Marcus, M A; Doran, A; Nasiatka, J R; Young, A T; MacDowell, A A; Streubel, R; Kent, N; Feng, J; Wan, W; Padmore, H A
2018-05-01
Aberration correction by an electron mirror dramatically improves the spatial resolution and transmission of photoemission electron microscopes. We will review the performance of the recently installed aberration corrector of the X-ray Photoemission Electron Microscope PEEM-3 and show a large improvement in the efficiency of the electron optics. Hartmann testing is introduced as a quantitative method to measure the geometrical aberrations of a cathode lens electron microscope. We find that aberration correction leads to an order of magnitude reduction of the spherical aberrations, suggesting that a spatial resolution of below 100 nm is possible at 100% transmission of the optics when using x-rays. We demonstrate this improved performance by imaging test patterns employing element and magnetic contrast. Published by Elsevier B.V.
Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing.
Guo, Wenjiang; Zhao, Liping; Li, Xiang; Chen, I-Ming
2012-01-01
In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation. © 2012 Optical Society of America
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Liao Guoqing
2005-11-01
Full Text Available Abstract Background Rectovaginal fistula is uncommon after lower anterior resection for rectal cancer. The most leading cause of this complication is involvement of the posterior wall of the vagina into the staple line when firing the circular stapler. Case presentation A 50-year-old women underwent resection for obstructed carcinoma of the sigmoid colon with Hartmann procedure. Four months later she underwent restorative surgery with circular stapler. Following which she developed rectovaginal fistula. A transvaginal repair was performed but stool passing from vagina not per rectum. Laporotomy revealed colovaginal anastomosis, which was corrected accordingly. Patient had an uneventful recovery. Conclusion Inadvertent formation of colovaginal anastomosis associated with a rectovaginal fistula is a rare complication caused by the operator's error. The present case again highlights the importance of ensuring that the posterior wall of vagina is away from the staple line.
Hough transform used on the spot-centroiding algorithm for the Shack-Hartmann wavefront sensor
Chia, Chou-Min; Huang, Kuang-Yuh; Chang, Elmer
2016-01-01
An approach to the spot-centroiding algorithm for the Shack-Hartmann wavefront sensor (SHWS) is presented. The SHWS has a common problem, in that while measuring high-order wavefront distortion, the spots may exceed each of the subapertures, which are used to restrict the displacement of spots. This artificial restriction may limit the dynamic range of the SHWS. When using the SHWS to measure adaptive optics or aspheric lenses, the accuracy of the traditional spot-centroiding algorithm may be uncertain because the spots leave or cross the confined area of the subapertures. The proposed algorithm combines the Hough transform with an artificial neural network, which requires no confined subapertures, to increase the dynamic range of the SHWS. This algorithm is then explored in comprehensive simulations and the results are compared with those of the existing algorithm.
Oral histories in meteoritics and planetary science—XXIV: William K. Hartmann
Sears, Derek W. G.
2014-06-01
In this interview, William Hartmann (Bill, Fig. 1) describes how he was inspired as a teenager by a map of the Moon in an encyclopedia and by the paintings by Chesley Bonestell. Through the amateur journal "Strolling Astronomer," he shared his interests with other teenagers who became lifelong colleagues. At college, he participated in Project Moonwatch, observing early artificial satellites. In graduate school, under Gerard Kuiper, Bill discovered Mare Orientale and other large concentric lunar basin structures. In the 1960s and 1970s, he used crater densities to study surface ages and erosive/depositional effects, predicted the approximately 3.6 Gyr ages of the lunar maria before the Apollo samples, discovered the intense pre-mare lunar bombardment, deduced the youthful Martian volcanism as part of the Mariner 9 team, and proposed (with Don Davis) the giant impact model for lunar origin. In 1972, he helped found (what is now) the Planetary Science Institute. From the late 1970s to early 1990s, Bill worked mostly with Dale Cruikshank and Dave Tholen at Mauna Kea Observatory, helping to break down the Victorian paradigm that separated comets and asteroids, and determining the approximately 4% albedo of comet nuclei. Most recently, Bill has worked with the imaging teams for several additional Mars missions. He has written three college textbooks and, since the 1970s, after painting illustrations for his textbooks, has devoted part of his time to painting, having had several exhibitions. He has also published two novels. Bill Hartmann won the 2010 Barringer Award for impact studies and the first Carl Sagan Award for outreach in 1997.
Hartmann wavefront sensing of the corrective optics for the Hubble Space Telescope
Davila, Pam S.; Eichhorn, William L.; Wilson, Mark E.
1994-06-01
aberration content of the corrected images. Also, from only this test it was difficult to measure important pupil parameters, such as pupil intensity profiles and pupil sizes and location. To measure the COSTAR wavefront accurately and to determine pupil parameters, another very important test was performed on the COSTAR optics. A Hartmann test of the optical system consisting of the RAS and COSTAR was conducted by the Goddard Independent Verification Team (IVT). In this paper, we first describe the unique Hartmann sensor that was developed by the IVT. Then we briefly describe the RAS and COSTAR optical systems and the test setup. Finally, we present the results of the test and compare our results with results obtained from optical analysis and from image tests with the BIA.
Ontologie della resistenza: note sul concetto di materia in N. Hartmann e G. Lukács
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D’Anna, Giuseppe
2010-01-01
Full Text Available The essay discusses the topic of matter in N. Hartmann and G. Lukács. It shows how both of them use their own concepts of matter in order to counter correlativistic philosophies – such as Phenomenology, Neo-Kantianism, Existentialism, Pragmatism, Positivism, Empirio-Criticism or Conventionalism – which reduce the real world to the laws of thought, to those of the absolute consciousness or to scientific laws, therefore eliminating the resistance of the reality and the meaning of praxis and dialectic in front of the givenness of the world. While Hartmann uses the concept of matter in order to revive the idea of a reality going beyond the laws of thought, Lukács uses Hartmann’s ontology in order to counter the philosophies that, by excluding the exceedance of reality and matter, provide theories which appear to him functional to the capitalist society.
Energy Technology Data Exchange (ETDEWEB)
Krasnov, D.; Boeck, T. [Technische Univ. Ilmenau (Germany). Inst. of Thermodynamics and Fluid Mechanics; Braiden, L.; Molokov, S. [Conventry Univ. (United Kingdom). Dept. of Mathematics and Physics; Buehler, L. [Karlsruher Institut fuer Technologie (Germany). Inst. fuer Kern- und Energietechnik, Programm Kernfusion
2016-07-01
Pressure-driven magnetohydrodynamic duct flows in a transverse, wall-parallel and uniform field have been studied by direct numerical. The conducting Hartmann walls give rise to a laminar velocity distribution with strong jets at the side walls, which are susceptible to flow instability. The onset of time-dependent flow as well as fully developed turbulent flow have been explored in a wide range of parameters.
Peak-locking centroid bias in Shack-Hartmann wavefront sensing
Anugu, Narsireddy; Garcia, Paulo J. V.; Correia, Carlos M.
2018-05-01
Shack-Hartmann wavefront sensing relies on accurate spot centre measurement. Several algorithms were developed with this aim, mostly focused on precision, i.e. minimizing random errors. In the solar and extended scene community, the importance of the accuracy (bias error due to peak-locking, quantization, or sampling) of the centroid determination was identified and solutions proposed. But these solutions only allow partial bias corrections. To date, no systematic study of the bias error was conducted. This article bridges the gap by quantifying the bias error for different correlation peak-finding algorithms and types of sub-aperture images and by proposing a practical solution to minimize its effects. Four classes of sub-aperture images (point source, elongated laser guide star, crowded field, and solar extended scene) together with five types of peak-finding algorithms (1D parabola, the centre of gravity, Gaussian, 2D quadratic polynomial, and pyramid) are considered, in a variety of signal-to-noise conditions. The best performing peak-finding algorithm depends on the sub-aperture image type, but none is satisfactory to both bias and random errors. A practical solution is proposed that relies on the antisymmetric response of the bias to the sub-pixel position of the true centre. The solution decreases the bias by a factor of ˜7 to values of ≲ 0.02 pix. The computational cost is typically twice of current cross-correlation algorithms.
Li, Xinji; Hui, Mei; Zhao, Zhu; Liu, Ming; Dong, Liquan; Kong, Lingqin; Zhao, Yuejin
2018-05-01
A differential computation method is presented to improve the precision of calibration for coaxial reverse Hartmann test (RHT). In the calibration, the accuracy of the distance measurement greatly influences the surface shape test, as demonstrated in the mathematical analyses. However, high-precision absolute distance measurement is difficult in the calibration. Thus, a differential computation method that only requires the relative distance was developed. In the proposed method, a liquid crystal display screen successively displayed two regular dot matrix patterns with different dot spacing. In a special case, images on the detector exhibited similar centroid distributions during the reflector translation. Thus, the critical value of the relative displacement distance and the centroid distributions of the dots on the detector were utilized to establish the relationship between the rays at certain angles and the detector coordinates. Experiments revealed the approximately linear behavior of the centroid variation with the relative displacement distance. With the differential computation method, we increased the precision of traditional calibration 10-5 rad root mean square. The precision of the RHT was increased by approximately 100 nm.
Accuracy of Shack-Hartmann wavefront sensor using a coherent wound fibre image bundle
Zheng, Jessica R.; Goodwin, Michael; Lawrence, Jon
2018-03-01
Shack-Hartmannwavefront sensors using wound fibre image bundles are desired for multi-object adaptive optical systems to provide large multiplex positioned by Starbugs. The use of a large-sized wound fibre image bundle provides the flexibility to use more sub-apertures wavefront sensor for ELTs. These compact wavefront sensors take advantage of large focal surfaces such as the Giant Magellan Telescope. The focus of this paper is to study the wound fibre image bundle structure defects effect on the centroid measurement accuracy of a Shack-Hartmann wavefront sensor. We use the first moment centroid method to estimate the centroid of a focused Gaussian beam sampled by a simulated bundle. Spot estimation accuracy with wound fibre image bundle and its structure impact on wavefront measurement accuracy statistics are addressed. Our results show that when the measurement signal-to-noise ratio is high, the centroid measurement accuracy is dominated by the wound fibre image bundle structure, e.g. tile angle and gap spacing. For the measurement with low signal-to-noise ratio, its accuracy is influenced by the read noise of the detector instead of the wound fibre image bundle structure defects. We demonstrate this both with simulation and experimentally. We provide a statistical model of the centroid and wavefront error of a wound fibre image bundle found through experiment.
Novel Detecting Methods of Shack-Hartmann Wavefront Sensor at Low Light Levels
International Nuclear Information System (INIS)
Zhang, A; Rao, C H; Zhang, Y D; Jiang, W H
2006-01-01
A study of novel detecting methods of Shack-Hartmann wavefront sensor at low light levels has been made. Three methods of images processing before slope estimating are presented: Linear Enhancing (LE), Exponential Enhancing (EE) and Fourier Spectrum Filtering (FSF). The idea of LE method is to time the image intensity with a special coefficient before slope estimation. The image points are powered by a selected exponent in EE method. The FSF method is based on the spectrum difference between signal and noise. Most of noise spectrum is filtered and the noise is restrained. The simulated and experimental results show that the LE method does not work effectively, and the other two methods can improve the slope estimation when the Signal-to-noise ratio is higher than 3.0. When the Signal-to-noise ratio is less than 3.0, especially when it is less than 1.0, the FSF is the only method that can overcome the readout noise of the CCD detector
International Nuclear Information System (INIS)
Vargas, Javier; Gonzalez-Fernandez, Luis; Quiroga, Juan Antonio; Belenguer, Tomas
2010-01-01
In the optical quality measuring process of an optical system, including diamond-turning components, the use of a laser light source can produce an undesirable speckle effect in a Shack-Hartmann (SH) CCD sensor. This speckle noise can deteriorate the precision and accuracy of the wavefront sensor measurement. Here we present a SH centroid detection method founded on computer-based techniques and capable of measurement in the presence of strong speckle noise. The method extends the dynamic range imaging capabilities of the SH sensor through the use of a set of different CCD integration times. The resultant extended range spot map is normalized to accurately obtain the spot centroids. The proposed method has been applied to measure the optical quality of the main optical system (MOS) of the mid-infrared instrument telescope smulator. The wavefront at the exit of this optical system is affected by speckle noise when it is illuminated by a laser source and by air turbulence because it has a long back focal length (3017 mm). Using the proposed technique, the MOS wavefront error was measured and satisfactory results were obtained.
Comparison of performance of some common Hartmann-Shack centroid estimation methods
Thatiparthi, C.; Ommani, A.; Burman, R.; Thapa, D.; Hutchings, N.; Lakshminarayanan, V.
2016-03-01
The accuracy of the estimation of optical aberrations by measuring the distorted wave front using a Hartmann-Shack wave front sensor (HSWS) is mainly dependent upon the measurement accuracy of the centroid of the focal spot. The most commonly used methods for centroid estimation such as the brightest spot centroid; first moment centroid; weighted center of gravity and intensity weighted center of gravity, are generally applied on the entire individual sub-apertures of the lens let array. However, these processes of centroid estimation are sensitive to the influence of reflections, scattered light, and noise; especially in the case where the signal spot area is smaller compared to the whole sub-aperture area. In this paper, we give a comparison of performance of the commonly used centroiding methods on estimation of optical aberrations, with and without the use of some pre-processing steps (thresholding, Gaussian smoothing and adaptive windowing). As an example we use the aberrations of the human eye model. This is done using the raw data collected from a custom made ophthalmic aberrometer and a model eye to emulate myopic and hyper-metropic defocus values up to 2 Diopters. We show that the use of any simple centroiding algorithm is sufficient in the case of ophthalmic applications for estimating aberrations within the typical clinically acceptable limits of a quarter Diopter margins, when certain pre-processing steps to reduce the impact of external factors are used.
OPERA, an automatic PSF reconstruction software for Shack-Hartmann AO systems: application to Altair
Jolissaint, Laurent; Veran, Jean-Pierre; Marino, Jose
2004-10-01
When doing high angular resolution imaging with adaptive optics (AO), it is of crucial importance to have an accurate knowledge of the point spread function associated with each observation. Applications are numerous: image contrast enhancement by deconvolution, improved photometry and astrometry, as well as real time AO performance evaluation. In this paper, we present our work on automatic PSF reconstruction based on control loop data, acquired simultaneously with the observation. This problem has already been solved for curvature AO systems. To adapt this method to another type of WFS, a specific analytical noise propagation model must be established. For the Shack-Hartmann WFS, we are able to derive a very accurate estimate of the noise on each slope measurement, based on the covariances of the WFS CCD pixel values in the corresponding sub-aperture. These covariances can be either derived off-line from telemetry data, or calculated by the AO computer during the acquisition. We present improved methods to determine 1) r0 from the DM drive commands, which includes an estimation of the outer scale L0 2) the contribution of the high spatial frequency component of the turbulent phase, which is not corrected by the AO system and is scaled by r0. This new method has been implemented in an IDL-based software called OPERA (Performance of Adaptive Optics). We have tested OPERA on Altair, the recently commissioned Gemini-North AO system, and present our preliminary results. We also summarize the AO data required to run OPERA on any other AO system.
Hernández-Gómez, Geovanni; Malacara-Hernández, Zacarías; Malacara-Hernández, Daniel
2014-02-20
The measurement of astigmatic lenses, optical surfaces or wavefronts are a highly studied problem and many different instruments have been commercially fabricated to perform this task. Many of them use a Hartmann arrangement to obtain the result. In this paper, we analyze with detail the algorithms that can be used to make the necessary calculations and propose several alternatives with different advantages and disadvantages. Different mathematical algorithms that are involved in the calculation process have been given whereas any description of the instrument itself is not proposed, but only the different mathematical algorithms that are involved in the calculation process.
Colostomia tipo hartmann em ratos: alterações morfológicas e dosagem de hidroxiprolina
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João Carlos Simões
Full Text Available A colostomia tem sido um procedimento cirúrgico freqüentemente empregado nas doenças colônicas, lesões traumáticas e neoplásicas. Este trabalho experimental, em ratos, visou estudar as progressivas mudanças morfológicas no cólon proximal e distal , após uma laparotomia e colostomia terminal, tipo Hartmann, que foram estudadas histologicamente e através da dosagem tecidual de hidroxiprolina. Utilizaram-se 40 ratos, machos, raça Wistar, com peso médio de 200 gramas, alocados em dois grupos (grupo I ou experimento e grupo II ou controle, subdivididos em quatro subgrupos: A,B,C e D com 10 animais em cada subgrupo. Os animais do grupo I (subgrupos A e B foram submetidos à colostomia tipo Hartmann, no cólon distal, a 7,5cm do canal anal. Nos ratos do grupo II foi praticada apenas uma laparotomia mediana. Os animais dos subgrupo A e C foram sacrificados no 30º dia de P.O., enquanto que os animais dos subgrupos B e D o sacrifício foi no 60º dia de P.O. A análise histológica dos segmentos colônicos permitiu observar infiltrado inflamatório agudo e crônico na lâmina própria, achatamento pronunciado das criptas, diminuição do número de criptas e da celularidade epitelial, redução das células caliciformes e da mucossecreção, adelgaçamento da muscular da mucosa, mais intensos no coto colônico distal dos animais submetidos à colostomia terminal tipo Hartmann (subgrupos A e B. Os segmentos proximais apresentavam estas alterações, porém mais discretas. A dosagem de hidroxiprolina nos tecidos colônicos não revelou alterações estatisticamente significativas quanto ao conteúdo de colágeno ou do peso desidratado. Estes achados permitem demonstrar alterações morfológicas inflamatórias e hipotróficas mais pronunciadas no cólon distal de ratos submetidos à colostomia tipo Hartmann.
A Shack-Hartmann Sensor for Single-Shot Multi-Contrast Imaging with Hard X-rays
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Tomy dos Santos Rolo
2018-05-01
Full Text Available An array of compound refractive X-ray lenses (CRL with 20 × 20 lenslets, a focal distance of 20cm and a visibility of 0.93 is presented. It can be used as a Shack-Hartmann sensor for hard X-rays (SHARX for wavefront sensing and permits for true single-shot multi-contrast imaging the dynamics of materials with a spatial resolution in the micrometer range, sensitivity on nanosized structures and temporal resolution on the microsecond scale. The object’s absorption and its induced wavefront shift can be assessed simultaneously together with information from diffraction channels. In contrast to the established Hartmann sensors the SHARX has an increased flux efficiency through focusing of the beam rather than blocking parts of it. We investigated the spatiotemporal behavior of a cavitation bubble induced by laser pulses. Furthermore, we validated the SHARX by measuring refraction angles of a single diamond CRL, where we obtained an angular resolution better than 4 μ rad.
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Bruin Sjoerd C
2010-10-01
Full Text Available Abstract Background Recently, excellent results are reported on laparoscopic lavage in patients with purulent perforated diverticulitis as an alternative for sigmoidectomy and ostomy. The objective of this study is to determine whether LaparOscopic LAvage and drainage is a safe and effective treatment for patients with purulent peritonitis (LOLA-arm and to determine the optimal resectional strategy in patients with a purulent or faecal peritonitis (DIVA-arm: perforated DIVerticulitis: sigmoidresection with or without Anastomosis. Methods/Design In this multicentre randomised trial all patients with perforated diverticulitis are included. Upon laparoscopy, patients with purulent peritonitis are treated with laparoscopic lavage and drainage, Hartmann's procedure or sigmoidectomy with primary anastomosis in a ratio of 2:1:1 (LOLA-arm. Patients with faecal peritonitis will be randomised 1:1 between Hartmann's procedure and resection with primary anastomosis (DIVA-arm. The primary combined endpoint of the LOLA-arm is major morbidity and mortality. A sample size of 132:66:66 patients will be able to detect a difference in the primary endpoint from 25% in resectional groups compared to 10% in the laparoscopic lavage group (two sided alpha = 5%, power = 90%. Endpoint of the DIVA-arm is stoma free survival one year after initial surgery. In this arm 212 patients are needed to significantly demonstrate a difference of 30% (log rank test two sided alpha = 5% and power = 90% in favour of the patients with resection with primary anastomosis. Secondary endpoints for both arms are the number of days alive and outside the hospital, health related quality of life, health care utilisation and associated costs. Discussion The Ladies trial is a nationwide multicentre randomised trial on perforated diverticulitis that will provide evidence on the merits of laparoscopic lavage and drainage for purulent generalised peritonitis and on the optimal resectional strategy
Bridoux, Valerie; Regimbeau, Jean Marc; Ouaissi, Mehdi; Mathonnet, Muriel; Mauvais, Francois; Houivet, Estelle; Schwarz, Lilian; Mege, Diane; Sielezneff, Igor; Sabbagh, Charles; Tuech, Jean-Jacques
2017-12-01
About 25% of patients with acute diverticulitis require emergency intervention. Currently, most patients with diverticular peritonitis undergo a Hartmann's procedure. Our objective was to assess whether primary anastomosis (PA) with a diverting stoma results in lower mortality rates than Hartmann's procedure (HP) in patients with diverticular peritonitis. We conducted a multicenter randomized controlled trial conducted between June 2008 and May 2012: the DIVERTI (Primary vs Secondary Anastomosis for Hinchey Stage III-IV Diverticulitis) trial. Follow-up duration was up to 18 months. A random sample of 102 eligible participants with purulent or fecal diverticular peritonitis from tertiary care referral centers and associated centers in France were equally randomized to either a PA arm or to an HP arm. Data were analyzed on an intention-to-treat basis. The primary end point was mortality rate at 18 months. Secondary outcomes were postoperative complications, operative time, length of hospital stay, rate of definitive stoma, and morbidity. All 102 patients enrolled were comparable for age (p = 0.4453), sex (p = 0.2347), Hinchey stage III vs IV (p = 0.2347), and Mannheim Peritonitis Index (p = 0.0606). Overall mortality did not differ significantly between HP (7.7%) and PA (4%) (p = 0.4233). Morbidity for both resection and stoma reversal operations were comparable (39% in the HP arm vs 44% in the PA arm; p = 0.4233). At 18 months, 96% of PA patients and 65% of HP patients had a stoma reversal (p = 0.0001). Although mortality was similar in both arms, the rate of stoma reversal was significantly higher in the PA arm. This trial provides additional evidence in favor of PA with diverting ileostomy over HP in patients with diverticular peritonitis. ClinicalTrials.gov Identifier: NCT 00692393. Copyright © 2017. Published by Elsevier Inc.
Directory of Open Access Journals (Sweden)
Daniel Rubens Santiago da Silva
2016-12-01
Full Text Available O artigo se trata de um estudo teórico onde são apresentados alguns pontos da Ontologia Dimensional de Nicolai Hartmann e a relação destes com a Antropologia Ontológico-Dimensional de Viktor Frankl. Além dos pontos em que se percebe uma clara influência de Hartmann no pensamento frankliano, procurou-se chegar a elementos do pensamento do primeiro para além daquilo que serve de fundamento à Logoterapia. Quanto à influência de Hartmann, concluiu-se pela centralidade de sua Ontologia Dimensional no esquema frankliano, atestada pelas concessões ao condicionamento “psicofísico” e pela crítica ao pandeterminismo e ao reducionismo. O resultado é a fórmula: “autonomia apesar da dependência”. Quanto aos elementos que estão para além daquilo que serve de fundamento à Logoterapia, perceberam-se possibilidades fecundas de diálogo, como por ocasião da discussão em torno da vida espiritual “a-temporal” e do “espírito objetivo”.
Xiang, Huazhong; Guo, Hang; Fu, Dongxiang; Zheng, Gang; Zhuang, Songlin; Chen, JiaBi; Wang, Cheng; Wu, Jie
2018-05-01
To precisely measure the whole-surface characterization of freeform progressive addition lenses (PALs), considering the multi-optical-axis conditions is becoming particularly important. Spherical power and astigmatism (cylinder) measurements for freeform PALs, using a Hartmann-Shack wavefront sensor (HSWFS) are proposed herein. Conversion formulas for the optical performance results were provided as HSWFS Zernike polynomial expansions. For each selected zone, the studied PALs were placed and tilted to simulate the multi-optical-axis conditions. The results of two tested PALs were analyzed using MATLAB programs and represented as contour plots of the spherical equivalent and cylinder of the whole-surface. The proposed experimental setup can provide a high accuracy as well as a possibility of choosing 12 lines and positions of 193 measurement zones on the entire surface. This approach to PAL analysis is potentially an efficient and useful method to objectively evaluate the optical performances, in which the full lens surface is defined and expressed as the contour plots of power in different regions (i.e., the distance region, progressive region, and near region) of the lens for regions of interest.
International Nuclear Information System (INIS)
Yin Xiaoming; Li Xiang; Zhao Liping; Fang Zhongping
2009-01-01
A Shack-Hartmann wavefront sensor (SWHS) splits the incident wavefront into many subsections and transfers the distorted wavefront detection into the centroid measurement. The accuracy of the centroid measurement determines the accuracy of the SWHS. Many methods have been presented to improve the accuracy of the wavefront centroid measurement. However, most of these methods are discussed from the point of view of optics, based on the assumption that the spot intensity of the SHWS has a Gaussian distribution, which is not applicable to the digital SHWS. In this paper, we present a centroid measurement algorithm based on the adaptive thresholding and dynamic windowing method by utilizing image processing techniques for practical application of the digital SHWS in surface profile measurement. The method can detect the centroid of each focal spot precisely and robustly by eliminating the influence of various noises, such as diffraction of the digital SHWS, unevenness and instability of the light source, as well as deviation between the centroid of the focal spot and the center of the detection area. The experimental results demonstrate that the algorithm has better precision, repeatability, and stability compared with other commonly used centroid methods, such as the statistical averaging, thresholding, and windowing algorithms.
The Ekman-Hartmann layer in MHD Taylor-Couette flow
Szklarski, Jacek; Rüdiger, Günther
2007-01-01
We study magnetic effects induced by rigidly rotating plates enclosing a cylindrical MHD Taylor-Couette flow at the finite aspect ratio $H/D=10$. The fluid confined between the cylinders is assumed to be liquid metal characterized by small magnetic Prandtl number, the cylinders are perfectly conducting, an axial magnetic field is imposed $\\Ha \\approx 10$, the rotation rates correspond to $\\Rey$ of order $10^2-10^3$. We show that the end-plates introduce, besides the well known Ekman circulati...
Marcos, Susana; Diaz-Santana, Luis; Llorente, Lourdes; Dainty, Chris
2002-06-01
Ocular aberrations were measured in 71 eyes by using two reflectometric aberrometers, employing laser ray tracing (LRT) (60 eyes) and a Shack-Hartmann wave-front sensor (S-H) (11 eyes). In both techniques a point source is imaged on the retina (through different pupil positions in the LRT or a single position in the S-H). The aberrations are estimated by measuring the deviations of the retinal spot from the reference as the pupil is sampled (in LRT) or the deviations of a wave front as it emerges from the eye by means of a lenslet array (in the S-H). In this paper we studied the effect of different polarization configurations in the aberration measurements, including linearly polarized light and circularly polarized light in the illuminating channel and sampling light in the crossed or parallel orientations. In addition, completely depolarized light in the imaging channel was obtained from retinal lipofuscin autofluorescence. The intensity distribution of the retinal spots as a function of entry (for LRT) or exit pupil (for S-H) depends on the polarization configuration. These intensity patterns show bright corners and a dark area at the pupil center for crossed polarization, an approximately Gaussian distribution for parallel polarization and a homogeneous distribution for the autofluorescence case. However, the measured aberrations are independent of the polarization states. These results indicate that the differences in retardation across the pupil imposed by corneal birefringence do not produce significant phase delays compared with those produced by aberrations, at least within the accuracy of these techniques. In addition, differences in the recorded aerial images due to changes in polarization do not affect the aberration measurements in these reflectometric aberrometers.
Reconstrução de trânsito intestinal após confecção de colostomia à Hartmann
Directory of Open Access Journals (Sweden)
Rodrigo Gomes da Silva
Full Text Available OBJETIVO: O objetivo desse estudo foi avaliar as taxas de morbidade e de mortalidade da tentativa de reversão do procedimento de Hartmann. MÉTODOS: Foram estudados retrospectivamente 29 pacientes submetidos à operação para reconstrução do trânsito intestinal após procedimento de Hartmann no Hospital das Clínicas da Universidade Federal de Minas Gerais no período de janeiro de 1998 a dezembro de 2006. Foram avaliados dados pré-operatório, intra-operatórios e pós-operatórios. RESULTADOS: A média de idade dos pacientes submetidos à operação para reconstrução de trânsito intestinal após realização de colostomia a Hartmann foi de 52,6 anos, sendo 16 pacientes do sexo masculino (55,2%. O tempo médio da permanência da colostomia foi de 17,6 meses (variando de 1 a 84 meses. O tempo operatório médio foi de 300 minutos (variando de 180 a 720 minutos. O sucesso na reconstrução do trânsito intestinal foi alcançado em 27 pacientes (93%. Dois pacientes apresentaram fístula anastomótica (7% e seis tiveram infecção de parede (22%. Ocorreu um óbito (3,4% em paciente com fístula anastomótica e sepse abdominal. Dentre os fatores relacionados ao insucesso na reconstrução da colostomia a Hartmann observou-se associação estatisticamente significativa com a tentativa prévia de reconstrução (p = 0,007, a utilização prévia de quimioterapia (p = 0,037 e o longo tempo de permanência da colostomia (p = 0,025 CONCLUSÃO: O intervalo entre a confecção e a tentativa de reversão não deve ser muito longo e os pacientes devem ser alertados que, numa pequena porcentagem dos casos, a reconstrução do trânsito intestinal pode ser impossível devido às condições locais do reto excluído.
International Nuclear Information System (INIS)
Tucker, H.E.; Day, R.D.; Hedges, R.O.; Hanlon, J.A.; Kortegaard, B.L.
1981-01-01
The MHB has been in operation for about nine months and has been performing quite well. It has provided the Helios laser fusion facility with additional target illumination flexibility so that many additional parameters can be investigated in the realm of target implosion physics
Cerviño, Alejandro; Bansal, Dheeraj; Hosking, Sarah L; Montés-Micó, Robert
2008-07-01
To apply software-based image-analysis tools to objectively determine intraocular scatter determined from clinically derived Hartmann-Shack patterns. Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom, and Department of Optics, University of Valencia, Valencia, Spain. Purpose-designed image-analysis software was used to quantify scatter from centroid patterns obtained using a clinical Hartmann-Shack analyzer (WASCA, Zeiss/Meditec). Three scatter values, as the maximum standard deviation within a lenslet for all lenslets in the pattern, were obtained in 6 model eyes and 10 human eyes. In the model-eye sample, patterns were obtained in 4 sessions: 2 without realigning between measurements, 1 with realignment, and 1 with an angular shift of 6 degrees from the instrument axis. Three measurements were made in the human eyes with the C-Quant straylight meter (Oculus) to obtain psychometric and objective measures of retinal straylight. Analysis of variance, intraclass correlation coefficients, coefficient of repeatability (CoR), and correlations were used to determine intrasession and intersession repeatability and the relationship between measures. No significant differences were found between the sessions in the model eye (P=.234). The mean CoR was less than 10% in all model- and human-eye sessions. After incomplete patterns were removed, good correlation was achieved between psychometric and objective scatter measurements despite the small sample size (n=6; r=-0.831; P=.040). The methodology was repeatable in model and human eyes, strong against realignment and misalignment, and sensitive. Clinical application would benefit from effective use of the sensor's dynamic range.
Bennett, Ruth, Ed.; And Others
An introduction to the Hupa number system is provided in this workbook, one in a series of numerous materials developed to promote the use of the Hupa language. The book is written in English with Hupa terms used only for the names of numbers. The opening pages present the numbers from 1-10, giving the numeral, the Hupa word, the English word, and…
Indian Academy of Sciences (India)
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Triangular number, figurate num- ber, rangoli, Brahmagupta–Pell equation, Jacobi triple product identity. Figure 1. The first four triangular numbers. Left: Anuradha S Garge completed her PhD from. Pune University in 2008 under the supervision of Prof. S A Katre. Her research interests include K-theory and number theory.
Directory of Open Access Journals (Sweden)
Schwarzweller Christoph
2015-02-01
Full Text Available In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.
Mendonça, J. Ricardo G.
2012-01-01
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.
Zhang, Lin; Zhou, Wenchen; Naples, Neil J; Yi, Allen Y
2018-05-01
A novel fabrication method by combining high-speed single-point diamond milling and precision compression molding processes for fabrication of discontinuous freeform microlens arrays was proposed. Compared with slow tool servo diamond broaching, high-speed single-point diamond milling was selected for its flexibility in the fabrication of true 3D optical surfaces with discontinuous features. The advantage of single-point diamond milling is that the surface features can be constructed sequentially by spacing the axes of a virtual spindle at arbitrary positions based on the combination of rotational and translational motions of both the high-speed spindle and linear slides. By employing this method, each micro-lenslet was regarded as a microstructure cell by passing the axis of the virtual spindle through the vertex of each cell. An optimization arithmetic based on minimum-area fabrication was introduced to the machining process to further increase the machining efficiency. After the mold insert was machined, it was employed to replicate the microlens array onto chalcogenide glass. In the ensuing optical measurement, the self-built Shack-Hartmann wavefront sensor was proven to be accurate in detecting an infrared wavefront by both experiments and numerical simulation. The combined results showed that precision compression molding of chalcogenide glasses could be an economic and precision optical fabrication technology for high-volume production of infrared optics.
de Castro, Alberto; Sawides, Lucie; Qi, Xiaofeng; Burns, Stephen A
2017-08-20
Retinal imaging with an adaptive optics (AO) system usually requires that the eye be centered and stable relative to the exit pupil of the system. Aberrations are then typically corrected inside a fixed circular pupil. This approach can be restrictive when imaging some subjects, since the pupil may not be round and maintaining a stable head position can be difficult. In this paper, we present an automatic algorithm that relaxes these constraints. An image quality metric is computed for each spot of the Shack-Hartmann image to detect the pupil and its boundary, and the control algorithm is applied only to regions within the subject's pupil. Images on a model eye as well as for five subjects were obtained to show that a system exit pupil larger than the subject's eye pupil could be used for AO retinal imaging without a reduction in image quality. This algorithm automates the task of selecting pupil size. It also may relax constraints on centering the subject's pupil and on the shape of the pupil.
International Nuclear Information System (INIS)
Zhu Zhao-Yi; Li Da-Yu; Hu Li-Fa; Mu Quan-Quan; Yang Cheng-Liang; Cao Zhao-Liang; Xuan Li
2016-01-01
High signal-to-noise ratio can be achieved with the electron multiplying charge-coupled-device (EMCCD) applied in the Shack–Hartmann wavefront sensor (S–H WFS) in adaptive optics (AO). However, when the brightness of the target changes in a large scale, the fixed electron multiplying (EM) gain will not be suited to the sensing limitation. Therefore an auto-gain-control method based on the brightness of light-spots array in S–H WFS is proposed in this paper. The control value is the average of the maximum signals of every light spot in an array, which has been demonstrated to be kept stable even under the influence of some noise and turbulence, and sensitive enough to the change of target brightness. A goal value is needed in the control process and it is predetermined based on the characters of EMCCD. Simulations and experiments have demonstrated that this auto-gain-control method is valid and robust, the sensing SNR reaches the maximum for the corresponding signal level, and especially is greatly improved for those dim targets from 6 to 4 magnitude in the visual band. (special topic)
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
Indian Academy of Sciences (India)
Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.
Ji, Caleb; Khovanova, Tanya; Park, Robin; Song, Angela
2015-01-01
In this paper, we consider a game played on a rectangular $m \\times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \\times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we p...
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Barnes, John
2016-01-01
In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...
Number names and number understanding
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 syste...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....
Yasuoka, Fatima M. M.; Matos, Luciana; Cremasco, Antonio; Numajiri, Mirian; Marcato, Rafael; Oliveira, Otavio G.; Sabino, Luis G.; Castro N., Jarbas C.; Bagnato, Vanderlei S.; Carvalho, Luis A. V.
2016-03-01
An optical system that conjugates the patient's pupil to the plane of a Hartmann-Shack (HS) wavefront sensor has been simulated using optical design software. And an optical bench prototype is mounted using mechanical eye device, beam splitter, illumination system, lenses, mirrors, mirrored prism, movable mirror, wavefront sensor and camera CCD. The mechanical eye device is used to simulate aberrations of the eye. From this device the rays are emitted and travelled by the beam splitter to the optical system. Some rays fall on the camera CCD and others pass in the optical system and finally reach the sensor. The eye models based on typical in vivo eye aberrations is constructed using the optical design software Zemax. The computer-aided outcomes of each HS images for each case are acquired, and these images are processed using customized techniques. The simulated and real images for low order aberrations are compared using centroid coordinates to assure that the optical system is constructed precisely in order to match the simulated system. Afterwards a simulated version of retinal images is constructed to show how these typical eyes would perceive an optotype positioned 20 ft away. Certain personalized corrections are allowed by eye doctors based on different Zernike polynomial values and the optical images are rendered to the new parameters. Optical images of how that eye would see with or without corrections of certain aberrations are generated in order to allow which aberrations can be corrected and in which degree. The patient can then "personalize" the correction to their own satisfaction. This new approach to wavefront sensing is a promising change in paradigm towards the betterment of the patient-physician relationship.
Directory of Open Access Journals (Sweden)
Theodore M. Porter
2012-12-01
Full Text Available The struggle over cure rate measures in nineteenth-century asylums provides an exemplary instance of how, when used for official assessments of institutions, these numbers become sites of contestation. The evasion of goals and corruption of measures tends to make these numbers “funny” in the sense of becoming dis-honest, while the mismatch between boring, technical appearances and cunning backstage manipulations supplies dark humor. The dangers are evident in recent efforts to decentralize the functions of governments and corporations using incen-tives based on quantified targets.
Murty, M Ram
2014-01-01
This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Indian Academy of Sciences (India)
this is a characteristic difference between finite and infinite sets and created an immensely useful branch of mathematics based on this idea which had a great impact on the whole of mathe- matics. For example, the question of what is a number (finite or infinite) is almost a philosophical one. However Cantor's work turned it ...
Directory of Open Access Journals (Sweden)
Luis Alberto Carvalho
2003-06-01
Full Text Available In this project we are developing an instrument for measuring the wave-front aberrations of the human eye using the Hartmann-Shack sensor. A laser source is directed towards the eye and its diffuse reflection at the retina generates an approximately spherical wave-front inside the eye. This wave-front travels through the different components of the eye (vitreous humor, lens, aqueous humor, and cornea and then leaves the eye carrying information about the aberrations caused by these components. Outside the eye there is an optical system composed of an array of microlenses and a CCD camera. The wave-front hits the microlens array and forms a pattern of spots at the CCD plane. Image processing algorithms detect the center of mass of each spot and this information is used to calculate the exact wave-front surface using least squares approximation by Zernike polynomials. We describe here the details of the first phase of this project, i. e., the construction of the first generation of prototype instruments and preliminary results for an artificial eye calibrated with different ametropias, i. e., myopia, hyperopia and astigmatism.Neste projeto estamos desenvolvendo instrumento para medidas das aberrações de frente de onda do olho humano usando um sensor Hartmann-Shack. Uma fonte de luz laser é direcionada ao olho e sua reflexão difusa na retina gera frente de onda aproximadamente esférica dentro do olho. Esta frente de onda atravessa os diferentes componentes do olho (humor vítreo, lente, humor aquoso e córnea trazendo informações sobre as aberrações ópticas causadas por estes componentes. No meio externo ao olho existe sistema óptico formado por uma matriz de microlentes e uma câmera CCD. A frente de onda incide nesta matriz e forma um padrão aproximadamente matricial de "spots" no plano do CCD. Algoritmos de processamento de imagens são utilizados para detectar os centróides de cada "spot" e esta informação é utilizada para
International Nuclear Information System (INIS)
Yamamoto, Yoshinobu; Kunugi, Tomoaki
2015-01-01
Graphical abstract: - Highlights: • For the first time, the MHD heat transfer DNS database corresponding to the typical nondimensional parameters of the fusion blanket design using molten salt, were established. • MHD heat transfer correlation was proposed and about 20% of the heat transfer degradation was evaluated under the design conditions. • The contribution of the turbulent diffusion to heat transfer is increased drastically with increasing Hartmann number. - Abstract: The high-Prandtl number passive scalar transport of the turbulent channel flow imposed a wall-normal magnetic field is investigated through the large-scale direct numerical simulation (DNS). All essential turbulence scales of velocities and temperature are resolved by using 2048 × 870 × 1024 computational grid points in stream, vertical, and spanwise directions. The heat transfer phenomena for a Prandtl number of 25 were observed under the following flow conditions: the bulk Reynolds number of 14,000 and Hartman number of up to 28. These values were equivalent to the typical nondimensional parameters of the fusion blanket design proposed by Wong et al. As a result, a high-accuracy DNS database for the verification of magnetohydrodynamic turbulent heat transfer models was established for the first time, and it was confirmed that the heat transfer correlation for a Prandtl number of 5.25 proposed by Yamamoto and Kunugi was applicable to the Prandtl number of 25 used in this study
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, Yoshinobu, E-mail: yamamotoy@yamanashi.ac.jp [Department of Mechanical Systems Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu 400-8511 (Japan); Kunugi, Tomoaki [Department of Nuclear Engineering, Kyoto University Yoshida, Sakyo, Kyoto 606-8501 (Japan)
2015-01-15
Graphical abstract: - Highlights: • For the first time, the MHD heat transfer DNS database corresponding to the typical nondimensional parameters of the fusion blanket design using molten salt, were established. • MHD heat transfer correlation was proposed and about 20% of the heat transfer degradation was evaluated under the design conditions. • The contribution of the turbulent diffusion to heat transfer is increased drastically with increasing Hartmann number. - Abstract: The high-Prandtl number passive scalar transport of the turbulent channel flow imposed a wall-normal magnetic field is investigated through the large-scale direct numerical simulation (DNS). All essential turbulence scales of velocities and temperature are resolved by using 2048 × 870 × 1024 computational grid points in stream, vertical, and spanwise directions. The heat transfer phenomena for a Prandtl number of 25 were observed under the following flow conditions: the bulk Reynolds number of 14,000 and Hartman number of up to 28. These values were equivalent to the typical nondimensional parameters of the fusion blanket design proposed by Wong et al. As a result, a high-accuracy DNS database for the verification of magnetohydrodynamic turbulent heat transfer models was established for the first time, and it was confirmed that the heat transfer correlation for a Prandtl number of 5.25 proposed by Yamamoto and Kunugi was applicable to the Prandtl number of 25 used in this study.
Donnelly, William J., III
Purpose. The purpose of this research is to determine if Shack/Hartmann (S/H) wavefront sensing (SHWS) can be used to objectively quantify ocular forward scatter. Methods. Patient S/H images from an study of nuclear cataract were analyzed to extract scattering data by examining characteristics of the lenslet point spread functions. Physical and computer eye models with simulated cataract were developed to control variables and to test the underlying assumptions for using SHWS to measure aberrations and light scatter from nuclear cataract. Results. (1) For patients with nuclear opalescence (NO) >=2.5, forward scatter metrics in a multiple regression analysis account for 33% of variance in Mesopic Low Contrast acuity. Prediction of visual acuity was improved by employing a multiple regression analysis that included both backscatter and forward scatter metrics (R2 = 51%) for Mesopic High Contrast acuity. (2) The physical and computer models identified areas of instrument noise (e.g., stray light and unwanted reflections) improving the design of a second generation SHWS for measuring both wavefront error and scatter. (3) Exposure time had the most influence on, and pupil size had negligible influence on forward scatter metrics. Scatter metric MAX_SD predicted changes in simulated cataract up to R2 = 92%. There were small but significant differences (alpha = 0.05) between 1.5-pass and 1-pass wavefront measurements inclusive of variable simulated nuclear cataract and exposure; however, these differences were not visually significant. Improvements to the SHWS imaging hardware, software, and test protocol were implemented in a second generation SHWS to be used in a longitudinal cataract study. Conclusions. Forward light scatter in real eyes can be quantified using a SHWS. In the presence of clinically significant nuclear opalescence, forward scatter metrics predicted acuity better than the LOCS III NO backscatter metric. The superiority of forward scatter metrics over back
Magnetohydrodynamic duct and channel flows at finite magnetic Reynolds numbers
Energy Technology Data Exchange (ETDEWEB)
Bandaru, Vinodh Kumar
2015-11-27
Lorentz force is found to show an R{sub m}{sup -1} dependence. After this, the phenomenon of dynamic runaway due to magnetic flux expulsion in a two-dimensional channel flow is studied. Comparison with an existing one-dimensional model shows a close agreement for the Hartmann regime and the bifurcation location but the model overpredicts the core velocities in the Poisuelle regime significantly. Parametric studies indicate the importance of the streamwise wavenumber of the imposed magnetic field on the bifurcation point. Finally, turbulent Hartmann duct flow is investigated at moderate values of R{sub m}. A higher R{sub m} is found to delay the onset of relaminarization to a higher value of Hartmann number. Large scale turbulence is induced at moderate R{sub m} and the effect increases with R{sub m}. Between the core and the Shercliff layers, Reynolds stresses decrease with increase in R{sub m}, leading to larger mean velocities in that region.
Butt, A. R.; Abdullah, M.; Raza, N.; Imran, M. A.
2017-10-01
In this work, semi analytical solutions for the heat and mass transfer of a fractional MHD Jeffery fluid over an infinite oscillating vertical plate with exponentially heating and constant mass diffusion via the Caputo-Fabrizio fractional derivative are obtained. The governing equations are transformed into dimensionless form by introducing dimensionless variables. A modern definition of the Caputo-Fabrizio derivative has been used to develop the fractional model for a Jeffery fluid. The expressions for temperature, concentration and velocity fields are obtained in the Laplace transformed domain. We have used the Stehfest's and Tzou's algorithm for the inverse Laplace transform to obtain the semi analytical solutions for temperature, concentration and velocity fields. In the end, in order to check the physical impact of flow parameters on temperature, concentration and velocity fields, results are presented graphically and in tabular forms.
Number Sense on the Number Line
Woods, Dawn Marie; Ketterlin Geller, Leanne; Basaraba, Deni
2018-01-01
A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…
Directory of Open Access Journals (Sweden)
Germán Javier MALAGA RODRIGUEZ
2006-10-01
Full Text Available Objetivos: Comparar el efecto de una solución de dextrosa hipotónica y de una solución isotónica (Hartmann en los niveles séricos de electrolitos y el equilibrio ácido base en pacientes ancianos hospitalizados. Materiales y métodos: Se evaluaron prospectivamente a 18 pacientes mayores de 60 años hospitalizados en el departamento de Medicina del Hospital Nacional Cayetano Heredia que recibieron fluidos endovenosos al menos por 48 horas. El primer grupo (G1 recibió una solución de dextrosa al 5%, 71 mmol/L de ClNa y 27 mmol/L de cloruro de potasio. El segundo grupo (G2 recibió solución Hartmann, más una solución glucosada de 100 cc al 50% simultáneamente. Se controlaron los valores de los electrolitos y los gases sanguíneos a las 0, 24 y 48 horas de iniciada la observación. Resultados: Ambos grupos presentaron condiciones comparables al ingreso. A las 48 horas los valores del sodio para el G1 fueron 134,5±4,4 mEq/L y para el G2 140±2,4 mEq/L (p<0,01, el pH del G1 fue 7,32±0,07 y el del G2 fue 7,4±0,03 (p<0,01, y el bicarbonato fue 16,6±2,2 mEq/L para el G1 y 22,3±1,6 mEq/L para el G2 (p<0,001. La diferencia entre los valores a las 0 (delta y 48 horas fueron: sodio -6,1±3,78(G1, 0,9±2,25(G2 en mEq/L, (p<0,001; potasio 0,01±0,43(G1, -0,61±0,56(G2 en mEq/L, (p<0,05; pH -0,09±0,07(G1, -0,01±0,04(G2, (p<0,01; bicarbonato -6,34±1,21(G1, -0,27±1,43(G2 en mEq/L, (p<0,001; pCO2 -6,25±5,33 (G1, 1,4±4,52(G2 en mmHg, (p<0,01. Conclusiones: Los pacientes ancianos hospitalizados que recibieron solución de dextrosa hipotónica, tuvieron niveles significativamente menores de sodio, pH, bicarbonato y pCO2 después de 48 horas comparados con quienes recibieron solución de Hartmann. No se observaron diferencias en los niveles de cloruro, pO2 y anion gap.(Rev Med Hered 2006;17:189-195.
Richardson, Thomas M.
2014-01-01
We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.
Lopez, Karen M; Fleming, Gregory J; Mylniczenko, Natalie D
2016-12-01
Reports of equine herpesvirus (EHV) 1 and EHV-9 causing clinical disease in a wide range of species have been well documented in the literature. It is thought that zebras are the natural hosts of EHV-9 both in the wild and in captive collections. Concerns about potential interspecies transmission of EHV-1 and EHV-9 in a mixed species savannah exhibit prompted serologic and polymerase chain reaction surveys. Eighteen Burchell's zebras ( Equus quagga ), 11 Hartmann's mountain zebras ( Equus zebra hartmannae), and 14 Thomson's gazelles ( Eudorcas thomsonii ) cohabitating the same exhibit were examined for EHV-1 virus neutralization titers, and evidence of virus via EHV 1-5 polymerase chain reactions. None of the animals had previous exposure to vaccination with EHV-1 or EHV-4. All tested zebras had positive EHV-1 titers, ranging from 4 to 384. All zebras and Thomson's gazelles had negative polymerase chain reaction results for all targeted equine herpesviruses. EHV-9-specific assays are not available but EHV-1, EHV-4, and EHV-9 cross-react serologically. Positive serology results indicate a potential latent equine herpesvirus in the zebra population, which prompted initiation of an equine herpesvirus vaccine protocol, changes in pregnant zebra mare management, and equine herpesvirus polymerase chain reaction screening prior to shipment to or from the study site.
Number words and number symbols a cultural history of numbers
Menninger, Karl
1992-01-01
Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.
Directory of Open Access Journals (Sweden)
T. Pathinathan
2015-01-01
Full Text Available In this paper we define diamond fuzzy number with the help of triangular fuzzy number. We include basic arithmetic operations like addition, subtraction of diamond fuzzy numbers with examples. We define diamond fuzzy matrix with some matrix properties. We have defined Nested diamond fuzzy number and Linked diamond fuzzy number. We have further classified Right Linked Diamond Fuzzy number and Left Linked Diamond Fuzzy number. Finally we have verified the arithmetic operations for the above mentioned types of Diamond Fuzzy Numbers.
Koninck, Jean-Marie De
2009-01-01
Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new n
Burkhart, Jerry
2009-01-01
Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…
Vazzana, Anthony; Garth, David
2007-01-01
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.
On the number of special numbers
Indian Academy of Sciences (India)
without loss of any generality to be the first k primes), then the equation a + b = c has .... This is an elementary exercise in partial summation (see [12]). Thus ... This is easily done by inserting a stronger form of the prime number theorem into the.
Grešak, Rozalija
2015-01-01
The field of real numbers is usually constructed using Dedekind cuts. In these thesis we focus on the construction of the field of real numbers using metric completion of rational numbers using Cauchy sequences. In a similar manner we construct the field of p-adic numbers, describe some of their basic and topological properties. We follow by a construction of complex p-adic numbers and we compare them with the ordinary complex numbers. We conclude the thesis by giving a motivation for the int...
On the number of special numbers
Indian Academy of Sciences (India)
We now apply the theory of the Thue equation to obtain an effective bound on m. Indeed, by Lemma 3.2, we can write m2 = ba3 and m2 − 4 = cd3 with b, c cubefree. By the above, both b, c are bounded since they are cubefree and all their prime factors are less than e63727. Now we have a finite number of. Thue equations:.
International Nuclear Information System (INIS)
Kaneko, K.
1987-01-01
A relationship between the number projection and the shell model methods is investigated in the case of a single-j shell. We can find a one-to-one correspondence between the number projected and the shell model states
Gallistel, C R
2017-12-01
The representation of discrete and continuous quantities appears to be ancient and pervasive in animal brains. Because numbers are the natural carriers of these representations, we may discover that in brains, it's numbers all the way down.
DEFF Research Database (Denmark)
Andersen, Torben
2014-01-01
had a marked singular and an unmarked plural. Synchronically, however, the singular is arguably the basic member of the number category as revealed by the use of the two numbers. In addition, some nouns have a collective form, which is grammatically singular. Number also plays a role...
DEFF Research Database (Denmark)
Elvik, Rune; Bjørnskau, Torkel
2017-01-01
Highlights •26 studies of the safety-in-numbers effect are reviewed. •The existence of a safety-in-numbers effect is confirmed. •Results are consistent. •Causes of the safety-in-numbers effect are incompletely known....
de Mestre, Neville
2008-01-01
Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…
International Nuclear Information System (INIS)
Todorov, T.D.
1980-01-01
The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed
Niederreiter, Harald
2015-01-01
This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters...
DEFF Research Database (Denmark)
Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert
numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular......We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto......, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”....
Ore, Oystein
2017-01-01
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
Godefroy, Gilles
2004-01-01
Numbers are fascinating. The fascination begins in childhood, when we first learn to count. It continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we learn that numbers not only help us to measure the world, but also to understand it and, to some extent, to control it. In The Adventure of Numbers, Gilles Godefroy follows the thread of our expanding understanding of numbers to lead us through the history of mathematics. His goal is to share the joy of discovering and understanding this great adventure of the mind. The development of mathematics has been punctuated by a n
DEFF Research Database (Denmark)
Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl
2016-01-01
We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers...... as formalized in recent behavioral theory. In particular, players tend to bet less on numbers that have been drawn in the preceding week, as suggested by the ‘gambler’s fallacy’, and bet more on a number if it was frequently drawn in the recent past, consistent with the ‘hot-hand fallacy’....
Diamond, Harold G; Cheung, Man Ping
2016-01-01
"Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L^2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the ...
Intuitive numbers guide decisions
Directory of Open Access Journals (Sweden)
Ellen Peters
2008-12-01
Full Text Available Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a perceived differences between numbers, b the extent to which proportional differences are weighed in decisions, and, ultimately, c the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.
Hirst, Keith
1994-01-01
Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc
General lexicography in Europe | Hartmann | Lexikos
African Journals Online (AJOL)
On the basis of several surveys of experts, centres and projects in lexicography, and against the author's own experience of metalexicography, the paper traces the recent progress of academic lexicography, especially in Europe. Particular attention is paid to 'dictionary research' in four of its divisions. One special concern is ...
Skolko pogibshihh v Tshetshenskoi voine? / Jens Hartmann
Hartmann, Jens
2005-01-01
Tšetšeenia Riiginõukogu esimehe Tauss Dzhabrailovi sõnul on kahe Tšetšeenia sõja vältel hukkunud 160 000 inimest. Inimõigusorganisatsiooni Memorial andmetel aga tapeti kahe sõja vältel 75 000 tsiviilisikut ja 14 000 sõjaväelast
Templates, Numbers & Watercolors.
Clemesha, David J.
1990-01-01
Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)
International Nuclear Information System (INIS)
Coveyou, R.R.
1974-01-01
The subject of random number generation is currently controversial. Differing opinions on this subject seem to stem from implicit or explicit differences in philosophy; in particular, from differing ideas concerning the role of probability in the real world of physical processes, electronic computers, and Monte Carlo calculations. An attempt is made here to reconcile these views. The role of stochastic ideas in mathematical models is discussed. In illustration of these ideas, a mathematical model of the use of random number generators in Monte Carlo calculations is constructed. This model is used to set up criteria for the comparison and evaluation of random number generators. (U.S.)
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Cohn, Harvey
1980-01-01
""A very stimulating book ... in a class by itself."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.The book is divided into three parts
Crossley, John N
1987-01-01
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the deve
Professor Stewart's incredible numbers
Stewart, Ian
2015-01-01
Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of - real, imaginary, rational, irrational, positive and negative - along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes,
LeVeque, William J
1996-01-01
This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha
Kneusel, Ronald T
2015-01-01
This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numb
Sierpinski, Waclaw
1988-01-01
Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian
Directory of Open Access Journals (Sweden)
R. A. Mollin
1986-01-01
Full Text Available A powerful number is a positive integer n satisfying the property that p2 divides n whenever the prime p divides n; i.e., in the canonical prime decomposition of n, no prime appears with exponent 1. In [1], S.W. Golomb introduced and studied such numbers. In particular, he asked whether (25,27 is the only pair of consecutive odd powerful numbers. This question was settled in [2] by W.A. Sentance who gave necessary and sufficient conditions for the existence of such pairs. The first result of this paper is to provide a generalization of Sentance's result by giving necessary and sufficient conditions for the existence of pairs of powerful numbers spaced evenly apart. This result leads us naturally to consider integers which are representable as a proper difference of two powerful numbers, i.e. n=p1−p2 where p1 and p2 are powerful numbers with g.c.d. (p1,p2=1. Golomb (op.cit. conjectured that 6 is not a proper difference of two powerful numbers, and that there are infinitely many numbers which cannot be represented as a proper difference of two powerful numbers. The antithesis of this conjecture was proved by W.L. McDaniel [3] who verified that every non-zero integer is in fact a proper difference of two powerful numbers in infinitely many ways. McDaniel's proof is essentially an existence proof. The second result of this paper is a simpler proof of McDaniel's result as well as an effective algorithm (in the proof for explicitly determining infinitely many such representations. However, in both our proof and McDaniel's proof one of the powerful numbers is almost always a perfect square (namely one is always a perfect square when n≢2(mod4. We provide in §2 a proof that all even integers are representable in infinitely many ways as a proper nonsquare difference; i.e., proper difference of two powerful numbers neither of which is a perfect square. This, in conjunction with the odd case in [4], shows that every integer is representable in
Corry, Leo
2015-01-01
The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the
Dudley, Underwood
2008-01-01
Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamenta
African Journals Online (AJOL)
OLUWOLE
Agro-Science Journal of Tropical Agriculture, Food, Environment and Extension. Volume 9 Number 1 ... of persistent dumping of cheap subsidized food imports from developed ... independence of the inefficiency effects in the two estimation ...
High Reynolds Number Turbulence
National Research Council Canada - National Science Library
Smits, Alexander J
2007-01-01
The objectives of the grant were to provide a systematic study to fill the gap between existing research on low Reynolds number turbulent flows to the kinds of turbulent flows encountered on full-scale vehicles...
International Development Research Centre (IDRC) Digital Library (Canada)
Operating a Demographic Surveillance System (DSS) like this one requires a blend of high-tech number-crunching ability and .... views follow a standardized format that takes several ... general levels of health and to the use of health services.
Quantum random number generator
Pooser, Raphael C.
2016-05-10
A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.
Solar Indices - Sunspot Numbers
National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes a variety of indices related to solar activity contributed by a number of national and private solar observatories located worldwide. This...
Schwartz, Richard Evan
2014-01-01
In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual i...
Indian Academy of Sciences (India)
One could endlessly churn out congruent numbers following the method in Box 1 without being certain when a given number n (or n x m 2, for some integer m) will ap- pear on the list. Continuing in this way ·would exhaust one's computing resources, not to mention one's patience! Also, this procedure is of no avail if n is not ...
DEFF Research Database (Denmark)
Korsby, Trine Mygind
2017-01-01
Taking a point of departure in negotiations for access to a phone number for a brothel abroad, the article demonstrates how a group of pimps in Eastern Romania attempt to extend their local business into the rest of the EU. The article shows how the phone number works as a micro-infrastructure in......Taking a point of departure in negotiations for access to a phone number for a brothel abroad, the article demonstrates how a group of pimps in Eastern Romania attempt to extend their local business into the rest of the EU. The article shows how the phone number works as a micro...... in turn cultivate and maximize uncertainty about themselves in others. When making the move to go abroad into unknown terrains, accessing the infrastructure generated by the phone number can provide certainty and consolidate one’s position within criminal networks abroad. However, at the same time......, mishandling the phone number can be dangerous and in that sense produce new doubts and uncertainties....
Energy Technology Data Exchange (ETDEWEB)
Nelson, R.N. (ed.)
1985-05-01
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.
International Nuclear Information System (INIS)
Nelson, R.N.
1985-05-01
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name
DEFF Research Database (Denmark)
Levin, Bruce R; McCall, Ingrid C.; Perrot, Veronique
2017-01-01
We postulate that the inhibition of growth and low rates of mortality of bacteria exposed to ribosome-binding antibiotics deemed bacteriostatic can be attributed almost uniquely to these drugs reducing the number of ribosomes contributing to protein synthesis, i.e., the number of effective......-targeting bacteriostatic antibiotics, the time before these bacteria start to grow again when the drugs are removed, referred to as the post-antibiotic effect (PAE), is markedly greater for constructs with fewer rrn operons than for those with more rrn operons. We interpret the results of these other experiments reported...... here as support for the hypothesis that the reduction in the effective number of ribosomes due to binding to these structures provides a sufficient explanation for the action of bacteriostatic antibiotics that target these structures....
Quantum random number generator
Soubusta, Jan; Haderka, Ondrej; Hendrych, Martin
2001-03-01
Since reflection or transmission of a quantum particle on a beamsplitter is inherently random quantum process, a device built on this principle does not suffer from drawbacks of neither pseudo-random computer generators or classical noise sources. Nevertheless, a number of physical conditions necessary for high quality random numbers generation must be satisfied. Luckily, in quantum optics realization they can be well controlled. We present an easy random number generator based on the division of weak light pulses on a beamsplitter. The randomness of the generated bit stream is supported by passing the data through series of 15 statistical test. The device generates at a rate of 109.7 kbit/s.
Alizée Dauvergne
2010-01-01
What makes the LHC the biggest particle accelerator in the world? Here are some of the numbers that characterise the LHC, and their equivalents in terms that are easier for us to imagine. Feature Number Equivalent Circumference ~ 27 km Distance covered by beam in 10 hours ~ 10 billion km a round trip to Neptune Number of times a single proton travels around the ring each second 11 245 Speed of protons first entering the LHC 299 732 500 m/s 99.9998 % of the speed of light Speed of protons when they collide 299 789 760 m/s 99.9999991 % of the speed of light Collision temperature ~ 1016 °C ove...
Samuel, Pierre
2008-01-01
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal
Iwaniec, Henryk
2004-01-01
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques. The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercis
CONFUSION WITH TELEPHONE NUMBERS
Telecom Service
2002-01-01
he area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service
CONFUSION WITH TELEPHONE NUMBERS
Telecom Service
2002-01-01
The area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service
Earthquake number forecasts testing
Kagan, Yan Y.
2017-10-01
We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness
Wetherell, Chris
2017-01-01
This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.
Bell, Eric Temple
1991-01-01
From one of the foremost interpreters for lay readers of the history and meaning of mathematics: a stimulating account of the origins of mathematical thought and the development of numerical theory. It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how ""number magic"" has influenced religion, philosophy, science, and mathematics
International Nuclear Information System (INIS)
Khan, T.A.; Baum, J.W.; Beckman, M.C.
1993-10-01
This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the 'tyranny' of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment
Uniform random number generators
Farr, W. R.
1971-01-01
Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.
International Nuclear Information System (INIS)
1994-01-01
The key numbers of energy give statistical data related to production, consumption, and to foreign trade of each energy in the World and in France. A chapter is dedicated to environment and brings quantitative elements on pollutant emissions connected to energy uses
Directory of Open Access Journals (Sweden)
Oli Brown
2008-10-01
Full Text Available Estimates of the potential number of ‘climate changemigrants’ vary hugely. In order to persuade policymakers ofthe need to act and to provide a sound basis for appropriateresponses, there is an urgent need for better analysis, betterdata and better predictions.
Trudgian, Timothy
2009-01-01
One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Typical Complexity Numbers. Say. 1000 tones,; 100 Users,; Transmission every 10 msec. Full Crosstalk cancellation would require. Full cancellation requires a matrix multiplication of order 100*100 for all the tones. 1000*100*100*100 operations every second for the ...
Indian Academy of Sciences (India)
IAS Admin
improved by Selberg [4] in 1941 who showed that a pos- ... be seen by entries of his first letter to G H Hardy in ... tary in the technical sense of the word, employed com- ..... III: On the expression of a number as a sum of primes, Acta Math.,.
1985-02-01
of the blade. The Darrieus VAWT has more complex aerodynamics. This type of wind turbine produces power as a result of the tangential thrust as...Horizontal Axis Propeller-Type b) Verticle Axis Darrieus -Type Figure 78. Wind Turbine Configurations 0 6 Q K [_ 2 -, C 4 UJ UJ...Sailplanes 23 5.2 Wind Turbines 23 6. CONCLUDING REMARKS 24 7. RECOMMENDATIONS FOR FUTURE RESEARCH 24 REFERENCES 25 FIGURES 32 yv/ LOW REYNOLDS NUMBER
LeVeque, William J
2002-01-01
Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symb
DEFF Research Database (Denmark)
Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik
2006-01-01
Random numbers are used for a great variety of applications in almost any field of computer and economic sciences today. Examples ranges from stock market forecasting in economics, through stochastic traffic modelling in operations research to photon and ray tracing in graphics. The construction...... distributions into others with most of the required characteristics. In essence, a uniform sequence which is transformed into a new sequence with the required distribution. The subject of this article is to consider the well known highly uniform Halton sequence and modifications to it. The intent is to generate...
van Gijn, J
2000-01-01
The round figure for the current year has stirred people's minds in anticipation. Numbers have acquired great significance also in today's medical science. The Paris physician Pierre Charles Alexandre Louis (1787-1872) is considered the founding father of the numerical method in medicine. At first the principle of aggregating data from different individuals aroused much resistance and even disgust: Claude Bernard was a leading figure among those who warned that one will never find a mean in nature, and that grouping findings together obscures the true relationship between biological phenomena. True enough, statistical significance is not a characteristic of nature itself. Significant differences or risk reductions do not necessarily imply clinical relevance, and results obtained in a group of patients are rarely applicable to an individual patient in the consultation room. Likewise, the health of a human being cannot be captured in biochemical, radiological or other technical measures, nor in disease-specific scales that reduce well-being to one or two digits. The editors of this journal will remain keen on publishing numerical studies that contribute to evidence-based medicine, but at the same time they will continue to foster the art of reporting illness from the point of view of the sick person.
Lepton family number violation
International Nuclear Information System (INIS)
Herczeg, P.
1999-01-01
At present there is evidence from neutrino oscillation searches that the neutrinos are in fact massive particles and that they mix. If confirmed, this would imply that the conservation of LFN is not exact. Lepton family number violation (LFNV) has been searched for with impressive sensitivities in many processes involving charged leptons. The present experimental limits on some of them (those which the author shall consider here) are shown in Table 1. These stringent limits are not inconsistent with the neutrino oscillation results since, given the experimental bounds on the masses of the known neutrinos and the neutrino mass squared differences required by the oscillation results, the effects of LFNV from neutrino mixing would be too small to be seen elsewhere (see Section 2). The purpose of experiments searching for LFNV involving the charged leptons is to probe the existence of other sources of LFNV. Such sources are present in many extensions of the SM. In this lecture the author shall discuss some of the possibilities, focusing on processes that require muon beams. Other LFNV processes, such as the decays of the kaons and of the τ, provide complementary information. In the next Section he shall consider some sources of LFNV that do not require an extension of the gauge group of the SM (the added leptons or Higgs bosons may of course originate from models with extended gauge groups). In Section 3 he discusses LFNV in left-right symmetric models. In Section 4 he considers LFNV in supersymmetric models, first in R-parity conserving supersymmetric grand unified models, and then in the minimal supersymmetric standard model with R-parity violation. The last section is a brief summary of the author's conclusions
Straight flavor of Binary Number in Decimal Number System
MD. Abdul Awal Ansary; Sushanta Acharjee
2012-01-01
Different number systems are available on the basis of their base numbers. For instance, decimal number system is of base 10, hexadecimal number system which base is 16 and, Binary number system which base is 2 etc. Some numbers systems are easy to understand by the human being and some are easy to understand by electronics machine for instance digital computers. Computers only can understand data and instructions that are stored in binary form, though we input the data and instruction in dec...
Neutrino number of the universe
International Nuclear Information System (INIS)
Kolb, E.W.
1981-01-01
The influence of grand unified theories on the lepton number of the universe is reviewed. A scenario is presented for the generation of a large (>> 1) lepton number and a small (<< 1) baryon number. 15 references
[Intel random number generator-based true random number generator].
Huang, Feng; Shen, Hong
2004-09-01
To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.
Bell numbers, determinants and series
Indian Academy of Sciences (India)
In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients. Keywords. p-adic series; Bell numbers. 1. Introduction. Bell numbers, Bn [2] ...
Cosmic numbers the numbers that define our universe
Stein, James D
2011-01-01
Our fascination with numbers begins when we are children and continues throughout our lives. We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers , mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers lik
Fermion number in supersymmetric models
International Nuclear Information System (INIS)
Mainland, G.B.; Tanaka, K.
1975-01-01
The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.)
Leng, Xueyuan; Kolesnikov, Yurii B.; Krasnov, Dmitry; Li, Benwen
2018-01-01
The effect of an axial homogeneous magnetic field on the turbulence in the Taylor-Couette flow confined between two infinitely long conducting cylinders is studied by the direct numerical simulation using a periodic boundary condition in the axial direction. The inner cylinder is rotating, and the outer one is fixed. We consider the case when the magnetic Reynolds number Rem ≪ 1, i.e., the influence of the induced magnetic field on the flow is negligible that is typical for industry and laboratory study of liquid metals. Relevance of the present study is based on the similarity of flow characteristics at moderate and high magnetic field for the cases with periodic and end-wall conditions at the large flow aspect ratio, as proven in the earlier studies. Two sets of Reynolds numbers 4000 and 8000 with several Hartmann numbers varying from 0 to 120 are employed. The results show that the mean radial induced electrical current, resulting from the interaction of axial magnetic field with the mean flow, leads to the transformation of the mean flow and the modification of the turbulent structure. The effect of turbulence suppression is dominating at a strong magnetic field, but before reaching the complete laminarization, we capture the appearance of the hairpin-like structures in the flow.
The Mental Number Line in Dyscalculia: Impaired Number Sense or Access from Symbolic Numbers?
Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël
2017-01-01
Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a…
THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Misfeldt, Morten
Different countries have different names for numbers. These names are often related in a regular way to the base-10 place value system used for writing numbers as digits. However, in several languages, this regularity breaks down (e.g., between 10 and 20), and there is limited knowledge of how th......, a second, regular set of number names is introduced in primary school. The study’s findings suggest that the regularity of number names influences the development of number concepts and creates a positive impact on the understanding of the base-10 system....
The theory of algebraic numbers
Pollard, Harry
1998-01-01
An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.
Elementary number theory with programming
Lewinter, Marty
2015-01-01
A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con
Distribution theory of algebraic numbers
Yang, Chung-Chun
2008-01-01
The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.
Random Numbers and Quantum Computers
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
International Nuclear Information System (INIS)
Ônishi, Yoshihiro
2011-01-01
The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.
2016 Gainesville Number Theory Conference
Garvan, Frank
2017-01-01
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find th...
Photon number projection using non-number-resolving detectors
International Nuclear Information System (INIS)
Rohde, Peter P; Webb, James G; Huntington, Elanor H; Ralph, Timothy C
2007-01-01
Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters
Bernoulli numbers and zeta functions
Arakawa, Tsuneo; Kaneko, Masanobu
2014-01-01
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...
Compendium of Experimental Cetane Numbers
Energy Technology Data Exchange (ETDEWEB)
Yanowitz, Janet [Ecoengineering, Sharonville, OH (United States); Ratcliff, Matthew A. [National Renewable Energy Lab. (NREL), Golden, CO (United States); McCormick, Robert L. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Taylor, J. D. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Murphy, M. J. [Battelle, Columbus, OH (United States)
2017-02-22
This report is an updated version of the 2014 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single-compound cetane number data found in the scientific literature up until December 2016 as well as a number of previously unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This version of the compendium contains cetane values for 496 pure compounds, including 204 hydrocarbons and 292 oxygenates. 176 individual measurements are new to this version of the compendium, all of them collected using ASTM Method D6890, which utilizes an Ignition Quality Tester (IQT) a type of constant-volume combustion chamber. For many compounds, numerous measurements are included, often collected by different researchers using different methods. The text of this document is unchanged from the 2014 version, except for the numbers of compounds in Section 3.1, the Appendices, Table 1. Primary Cetane Number Data Sources and Table 2. Number of Measurements Included in Compendium. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines. It is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant-volume combustion chamber. Values in the previous compendium derived from octane numbers have been removed and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane number has been expanded, and the data have been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.
Dynamic Virtual Credit Card Numbers
Molloy, Ian; Li, Jiangtao; Li, Ninghui
Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.
Number-unconstrained quantum sensing
Mitchell, Morgan W.
2017-12-01
Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here, we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies when each is optimized for particle number.
Schmidt number for quantum operations
International Nuclear Information System (INIS)
Huang Siendong
2006-01-01
To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided
Random number generation and creativity.
Bains, William
2008-01-01
A previous paper suggested that humans can generate genuinely random numbers. I tested this hypothesis by repeating the experiment with a larger number of highly numerate subjects, asking them to call out a sequence of digits selected from 0 through 9. The resulting sequences were substantially non-random, with an excess of sequential pairs of numbers and a deficit of repeats of the same number, in line with previous literature. However, the previous literature suggests that humans generate random numbers with substantial conscious effort, and distractions which reduce that effort reduce the randomness of the numbers. I reduced my subjects' concentration by asking them to call out in another language, and with alcohol - neither affected the randomness of their responses. This suggests that the ability to generate random numbers is a 'basic' function of the human mind, even if those numbers are not mathematically 'random'. I hypothesise that there is a 'creativity' mechanism, while not truly random, provides novelty as part of the mind's defence against closed programming loops, and that testing for the effects seen here in people more or less familiar with numbers or with spontaneous creativity could identify more features of this process. It is possible that training to perform better at simple random generation tasks could help to increase creativity, through training people to reduce the conscious mind's suppression of the 'spontaneous', creative response to new questions.
Unsolved problems in number theory
Guy, Richard K
1994-01-01
Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, not only extensive new material has been added, but corrections and additions have been included throughout the book.
Complex numbers in n dimensions
Olariu, Silviu
2002-01-01
Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbe...
Directory of Open Access Journals (Sweden)
J. Y. Kang
2013-01-01
Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.
BKP and projective Hurwitz numbers
Natanzon, Sergey M.; Orlov, Aleksandr Yu.
2017-06-01
We consider d-fold branched coverings of the projective plane RP^2 and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for weighted sums of the related Hurwitz numbers. In particular, we get the RP^2 analogues of the CP^1 generating functions proposed by Okounkov and by Goulden and Jackson. Other examples are Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials. We also consider integrals of tau functions which generate Hurwitz numbers related to base surfaces with arbitrary Euler characteristics sc {e}, in particular projective Hurwitz numbers sc {e}=1.
Indian Academy of Sciences (India)
016-0309-0. Generalized r-Lah numbers. MARK SHATTUCK. Department of ...... of Dowling lattices, Discrete Math. 312. (2012) 2337–2348. [7] Hsu L C and Shiue P J-S, A unified approach to generalized Stirling numbers, Adv. Appl. Math.
Ore, Oystein
1988-01-01
A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.
Investigating the Randomness of Numbers
Pendleton, Kenn L.
2009-01-01
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
Fractions, Number Lines, Third Graders
Cramer, Kathleen; Ahrendt, Sue; Monson, Debra; Wyberg, Terry; Colum, Karen
2017-01-01
The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…
Pseudo-Random Number Generators
Howell, L. W.; Rheinfurth, M. H.
1984-01-01
Package features comprehensive selection of probabilistic distributions. Monte Carlo simulations resorted to whenever systems studied not amenable to deterministic analyses or when direct experimentation not feasible. Random numbers having certain specified distribution characteristic integral part of simulations. Package consists of collector of "pseudorandom" number generators for use in Monte Carlo simulations.
On Counting the Rational Numbers
Almada, Carlos
2010-01-01
In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…
Core Knowledge, Language, and Number
Spelke, Elizabeth S.
2017-01-01
The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…
The Algebra of Complex Numbers.
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Salman, M.; Broersma, Haitze J.
2003-01-01
For two given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest positive integer $p$ such that for every graph $F$ on $p$ vertices the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers
Salman, M.; Broersma, Haitze J.
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers
Salman, M.; Broersma, Haitze J.
2007-01-01
For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers
From natural numbers to quaternions
Kramer, Jürg
2017-01-01
This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.
Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
Energy Technology Data Exchange (ETDEWEB)
Onishi, Yoshihiro [Faculty of Education Human Sciences, University of Yamanashi, Takeda, Kofu (Japan)
2011-10-31
The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.
Low energy fermion number violation
International Nuclear Information System (INIS)
Peccei, R.D.
1989-01-01
After a brief aside on charge quantization in the standard electroweak theory, I concentrate on various aspects of anomaly induced fermion number violation in the standard model. A critical analysis of the role of sphalerons for the universe's baryon asymmetry is presented and the importance of calculating directly fermion number violating Green's functions is stressed. A physical interpretation of the recent observation of Ringwald, that coherent effects in the electroweak theory lead to catastrophic fermion number violation at 100 TeV, is discussed. Possible quantum effects which might spoil this semi-classical picture are examined
Gallistel, C R
2017-02-19
After listing functional constraints on what numbers in the brain must do, I sketch the two's complement fixed-point representation of numbers because it has stood the test of time and because it illustrates the non-obvious ways in which an effective coding scheme may operate. I briefly consider its neurobiological implementation. It is easier to imagine its implementation at the cell-intrinsic molecular level, with thermodynamically stable, volumetrically minimal polynucleotides encoding the remembered numbers, than at the circuit level, with plastic synapses encoding them.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).
Fundamental number theory with applications
Mollin, Richard A
2008-01-01
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition Removal of all advanced material to be even more accessible in scope New fundamental material, including partition theory, generating functions, and combinatorial number theory Expa
Classical theory of algebraic numbers
Ribenboim, Paulo
2001-01-01
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...
Microcomputer Unit: Generating Random Numbers.
Haigh, William E.
1986-01-01
Presents an activity, suitable for students in grades 6-12, on generating random numbers. Objectives, equipment needed, list of prerequisite experiences, instructional strategies, and ready-to-copy student worksheets are included. (JN)
Number theory via Representation theory
Indian Academy of Sciences (India)
2014-11-09
Number theory via Representation theory. Eknath Ghate. November 9, 2014. Eightieth Annual Meeting, Chennai. Indian Academy of Sciences1. 1. This is a non-technical 20 minute talk intended for a general Academy audience.
Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...
Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...
Additive theory of prime numbers
Hua, L K
2009-01-01
Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial x^k is replaced by an arbitrary polynomial of degree k. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Advanced number theory with applications
Mollin, Richard A
2009-01-01
Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...
Integral Presentations of Catalan Numbers
Dana-Picard, Thierry
2010-01-01
We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.
Numbers their history and meaning
Flegg, Graham
2003-01-01
Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." - Choice.
Poison control center - emergency number
For a POISON EMERGENCY call: 1-800-222-1222 ANYWHERE IN THE UNITED STATES This national hotline number will let you ... is a free and confidential service. All local poison control centers in the United States use this ...
Women In Numbers - Europe workshop
Bucur, Alina; Feigon, Brooke; Schneps, Leila
2015-01-01
Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.
Digital random-number generator
Brocker, D. H.
1973-01-01
For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.
Random numbers from vacuum fluctuations
International Nuclear Information System (INIS)
Shi, Yicheng; Kurtsiefer, Christian; Chng, Brenda
2016-01-01
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
Numbers for reducible cubic scrolls
Directory of Open Access Journals (Sweden)
Israel Vainsencher
2004-12-01
Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.
Random numbers from vacuum fluctuations
Energy Technology Data Exchange (ETDEWEB)
Shi, Yicheng; Kurtsiefer, Christian, E-mail: christian.kurtsiefer@gmail.com [Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Center for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Chng, Brenda [Center for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)
2016-07-25
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
Banner prints social security numbers
Robbins RA
2014-01-01
No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1). The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pion...
Directory of Open Access Journals (Sweden)
Saveliev Peter
2005-01-01
Full Text Available Suppose , are manifolds, are maps. The well-known coincidence problem studies the coincidence set . The number is called the codimension of the problem. More general is the preimage problem. For a map and a submanifold of , it studies the preimage set , and the codimension is . In case of codimension , the classical Nielsen number is a lower estimate of the number of points in changing under homotopies of , and for an arbitrary codimension, of the number of components of . We extend this theory to take into account other topological characteristics of . The goal is to find a "lower estimate" of the bordism group of . The answer is the Nielsen group defined as follows. In the classical definition, the Nielsen equivalence of points of based on paths is replaced with an equivalence of singular submanifolds of based on bordisms. We let , then the Nielsen group of order is the part of preserved under homotopies of . The Nielsen number of order is the rank of this group (then . These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.
Dimensionless numbers in additive manufacturing
Mukherjee, T.; Manvatkar, V.; De, A.; DebRoy, T.
2017-02-01
The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.
Grammatical typology and frequency analysis: number availability and number use
Directory of Open Access Journals (Sweden)
Dunstan Brown
2013-12-01
Full Text Available The Smith-Stark hierarchy, a version of the Animacy Hierarchy, offers a typology of the cross-linguistic availability of number. The hierarchy predicts that the availability of number is not arbitrary. For any language, if the expression of plural is available to a noun, it is available to any noun of a semantic category further to the left of the hierarchy. In this article we move one step further by showing that the structure of the hierarchy can be observed in a statistical model of number use in Russian. We also investigate three co-variates: plural preference, pluralia tantum and irregularity effects; these account for an item's behaviour being different than that solely expected from its animacy position.
Directory of Open Access Journals (Sweden)
Luis Alberto Carvalho
2006-04-01
Full Text Available PURPOSE: There is a general acceptance among the scientific community of Cartesian symmetry wavefront sensors (such as the Hartmann-Shack (HS sensor as a standard in the field of optics and vision science. In this study it is shown that sensors of different symmetries and/or configurations should also be tested and analyzed in order to quantify and compare their effectiveness when applied to visual optics. Three types of wave-aberration sensors were developed and tested here. Each sensor has a very different configuration and/or symmetry (dodecagonal (DOD, cylindrical (CYL and conventional Hartmann-Shack (HS. METHODS: All sensors were designed and developed in the Physics Department of the Universidade de São Paulo - São Carlos. Each sensor was mounted on a laboratory optical bench used in a previous study. A commercial mechanical eye was used as control. This mechanical eye has a rotating mechanism that allows the retinal plane to be positioned at different axial distances. Ten different defocus aberrations were generated: 5 cases of myopia from -1D to -5D and 5 cases of hyperopia, from +1D to +5D, in steps of 1D following the scale printed on the mechanical eye. For each wavefront sensor a specific image-processing and fitting algorithm was implemented. For all three cases, the wavefront information was fit using the first 36 VSIA standard Zernike polynomials. Results for the mechanical eye were also compared to the absolute Zernike surface generated from coefficients associated with the theoretical sphere-cylinder aberration value. RESULTS: Precision was analyzed using two different methods: first, a theoretical approach was used by generating synthetic Zernike coefficients from the known sphere-cylinder aberrations, simply by applying sphere-cylinder equations in the backward direction. Then comparisons were made of these coefficients with the ones obtained in practice. Results for DOD, HS and CYL sensors were, respectively, as follows
From Natural Numbers to Numbers and Curves in Nature - II
Indian Academy of Sciences (India)
line grows from C towards both left and right. Suppose ... Let there be n steps of growth to the left, and n-l to the right. Then n .... right-hand spirals is 8 and that of left-hand .... [4] I Stewart, Nature's Numbers - Discovering Order and Pattern in the.
Number Meaning and Number Grammar in English and Spanish
Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique
2012-01-01
Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…
The MIXMAX random number generator
Savvidy, Konstantin G.
2015-11-01
In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.
Experimental determination of Ramsey numbers.
Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank
2013-09-27
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.
Stream ciphers and number theory
Cusick, Thomas W; Renvall, Ari R
2004-01-01
This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields. · Unique book on interactions of stream ciphers and number theory. · Research monograph with many results not available elsewhere. · A revised edition with the most recent advances in this subject. · Over thirty research problems for stimulating interactions between the two areas. · Written by leading researchers in stream ciphers and number theory.
Sequences, groups, and number theory
Rigo, Michel
2018-01-01
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Negative numbers and antimatter particles
International Nuclear Information System (INIS)
Tsan, Ung Chan
2012-01-01
Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter
Generation of photon number states
International Nuclear Information System (INIS)
Waks, Edo; Diamanti, Eleni; Yamamoto, Yoshihisa
2006-01-01
The visible light photon counter (VLPC) has the capability to discriminate photon number states, in contrast to conventional photon counters which can only detect the presence or absence of photons. We use this capability, along with the process of parametric down-conversion, to generate photon number states. We experimentally demonstrate generation of states containing 1, 2, 3 and 4 photons with high fidelity. We then explore the effect the detection efficiency of the VLPC has on the generation rate and fidelity of the created states
World Epidemiology Review, Number 105.
1978-09-13
respectively last year. Not Siberian The official stated that the Soviet virus is not related to the famous pathogenic agent which appeared in the Siberian...numbers of aphids are due to appear on the alfalfa in the near future. The infestation has approached and even exceeded the extent at which serious
Counting problems for number rings
Brakenhoff, Johannes Franciscus
2009-01-01
In this thesis we look at three counting problems connected to orders in number fields. First we study the probability that for a random polynomial f in Z[X] the ring Z[X]/f is the maximal order in Q[X]/f. Connected to this is the probability that a random polynomial has a squarefree
Linking numbers and variational method
International Nuclear Information System (INIS)
Oda, I.; Yahikozawa, S.
1989-09-01
The ordinary and generalized linking numbers for two surfaces of dimension p and n-p-1 in an n dimensional manifold are derived. We use a variational method based on the properties of topological quantum field theory in order to derive them. (author). 13 refs, 2 figs
From Calculus to Number Theory
Indian Academy of Sciences (India)
A. Raghuram
2016-11-04
Nov 4, 2016 ... diverges to infinity. This means given any number M, however large, we can add sufficiently many terms in the above series to make the sum larger than M. This was first proved by Nicole Oresme (1323-1382), a brilliant. French philosopher of his times.
RELATIONSHIP BETWEEN SLUDGE DEWATERABILITY NUMBER ...
African Journals Online (AJOL)
A representative of a sludge sample collected from the same source was filtered under the same environmental condition and the result analysed with two different concepts. One method of analysis uses Sludge Dewaterability Number, while the second employed the Carman's Specific resistance concept in sludge ...
Materiales, 1995
1995-01-01
Four booklets present articles on Spanish language and culture aimed at teachers of Spanish in the United States for student use in their classes. Number 17, "Los Jovenes Espanoles" (Spanish Youth), includes articles on Spanish youth sports, music, gangs, thoughts, and t-shirt slogans: (1) "Young Spanish Athletes"; (2)…
Materiales, 1997
1997-01-01
These three journals of contemporary cultural, historical, and social interest contain activities designed to enhance the awareness of students of Spanish as a foreign language regarding the entire panorama of daily life in Spain. Number 21 focuses on the role of modern Spanish women; their career status; female authors; and the changing place of…
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
Models for Rational Number Bases
Pedersen, Jean J.; Armbruster, Frank O.
1975-01-01
This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)
Residual number processing in dyscalculia.
Cappelletti, Marinella; Price, Cathy J
2014-01-01
Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.
Residual number processing in dyscalculia
Directory of Open Access Journals (Sweden)
Marinella Cappelletti
2014-01-01
Full Text Available Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.
Residual number processing in dyscalculia☆
Cappelletti, Marinella; Price, Cathy J.
2013-01-01
Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia. PMID:24266008
Learning Potentials in Number Blocks
DEFF Research Database (Denmark)
Majgaard, Gunver; Misfeldt, Morten; Nielsen, Jacob
2012-01-01
This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher....
An introduction to Catalan numbers
Roman, Steven
2015-01-01
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice o...
Strouhal number for free swimming
Saadat, Mehdi; van Buren, Tyler; Floryan, Daniel; Smits, Alexander; Haj-Hariri, Hossein
2015-11-01
In this work, we present experimental results to explore the implications of free swimming for Strouhal number (as an outcome) in the context of a simple model for a fish that consists of a 2D virtual body (source of drag) and a 2D pitching foil (source of thrust) representing cruising with thunniform locomotion. The results validate the findings of Saadat and Haj-Hariri (2012): for pitching foils thrust coefficient is a function of Strouhal number for all gaits having amplitude less than a certain critical value. Equivalently, given the balance of thrust and drag forces at cruise, Strouhal number is only a function of the shape, i.e. drag coefficient and area, and essentially a constant for high enough swimming speeds for which the mild dependence of drag coefficient on the speed vanishes. Furthermore, a dimensional analysis generalizes the findings. A scaling analysis shows that the variation of Strouhal number with cruising speed is functionally related to the variation of body drag coefficient with speed. Supported by ONR MURI Grant N00014-14-1-0533.
Directory of Open Access Journals (Sweden)
Peter Saveliev
2005-04-01
Full Text Available Suppose X, Y are manifolds, f,g:XÃ¢Â†Â’Y are maps. The well-known coincidence problem studies the coincidence set C={x:f(x=g(x}. The number m=dimÃ¢Â€Â‰XÃ¢ÂˆÂ’dimÃ¢Â€Â‰Y is called the codimension of the problem. More general is the preimage problem. For a map f:XÃ¢Â†Â’Z and a submanifold Y of Z, it studies the preimage set C={x:f(xÃ¢ÂˆÂˆY}, and the codimension is m=dimÃ¢Â€Â‰X+dimÃ¢Â€Â‰YÃ¢ÂˆÂ’dimÃ¢Â€Â‰Z. In case of codimension 0, the classical Nielsen number N(f,Y is a lower estimate of the number of points in C changing under homotopies of f, and for an arbitrary codimension, of the number of components of C. We extend this theory to take into account other topological characteristics of C. The goal is to find a Ã¢Â€Âœlower estimateÃ¢Â€Â of the bordism group ÃŽÂ©p(C of C. The answer is the Nielsen group Sp(f,Y defined as follows. In the classical definition, the Nielsen equivalence of points of C based on paths is replaced with an equivalence of singular submanifolds of C based on bordisms. We let Sp'(f,Y=ÃŽÂ©p(C/Ã¢ÂˆÂ¼N, then the Nielsen group of order p is the part of Sp'(f,Y preserved under homotopies of f. The Nielsen number Np(F,Y of order p is the rank of this group (then N(f,Y=N0(f,Y. These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.
Gaussian distribution of LMOV numbers
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri–Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (! and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects.
Energy Technology Data Exchange (ETDEWEB)
Nakayama, Kazunori [Theory Center, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Takahashi, Fuminobu, E-mail: fumi@tuhep.phys.tohoku.ac.jp [Department of Physics, Tohoku University, Sendai 980-8578 (Japan); Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan); Yanagida, Tsutomu T. [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan); Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)
2011-05-23
We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1){sub B-L} gauge symmetry, Z{sub 2}(B-L). We introduce a set of chiral fermions charged under the U(1){sub B-L} in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1){sub B-L} gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z{sub 2}(B-L).
International Nuclear Information System (INIS)
Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.
2011-01-01
We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1) B-L gauge symmetry, Z 2 (B-L). We introduce a set of chiral fermions charged under the U(1) B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1) B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z 2 (B-L).
Gyori, Ervin; Lovasz, Laszlo
2006-01-01
This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.
Large number discrimination by mosquitofish.
Directory of Open Access Journals (Sweden)
Christian Agrillo
Full Text Available BACKGROUND: Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4 were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish. METHODOLOGY/PRINCIPAL FINDINGS: Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance. Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1:2 or 2:3 but not when the ratio was 3:4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish. CONCLUSIONS/SIGNIFICANCE: Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all
DISCRETE MATHEMATICS/NUMBER THEORY
Mrs. Manju Devi*
2017-01-01
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Number systems and combinatorial problems
Yordzhev, Krasimir
2014-01-01
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in combinatorial analysis and most of all when proving some combinatorial identities. To demonstrate discussed in this article method we have chosen several suitable mathematical tasks.
World Epidemiology Review, Number 109.
1978-10-11
infantilism, "lung color," monale, followed by cardiac deficiency, cyanosis, intestinal stenosis ; glomerulonephritis and neurological symptoms. Many...Bursa were infected by rabid dogs and cats. The following breakdown was given for the number of persons infected during the succeeding 7 months of...area it is much more difficult to save his life. One of the six dogs taken into custody under the suspicion of being rabid during the past 8 months
Number theory meets Higgs physics
CERN. Geneva
2014-01-01
Inspired by results from modern number theory and algebraic geometry, a lot of progress has recently been made regarding the computation of multi-loop integrals and scattering amplitudes. I will discuss various new approaches to the computation of loop integrals, and illustrate them on the first computation of a quantity at N3LO in perturbative QCD, the soft-virtual part of the inclusive Higgs-boson cross section in gluon fusion at N3LO.
Residual number processing in dyscalculia ?
Cappelletti, Marinella; Price, Cathy J.
2013-01-01
Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and ca...
International Nuclear Information System (INIS)
Bursa, M.
1988-01-01
The secular Love number of Phobos was estimated k s =10.4. It only deviates by one order of magnitude from that corresponding to the ideal equilibrium state. It is not in contradiction with the theory of the origin of Phobos as a result of the accretion around Mars. In its early history, the rotation period of Phobos had been estimated to be approx. 2.4 hours. (author). 1 tab., 4 refs
When a number is not only a number
DEFF Research Database (Denmark)
Christensen, Ken Ramshøj; Roepstorff, Andreas; Saddy, Douglas
at. 1999, 2004). Furthermore, lesions studies have shown that damage to the posterior inferior parietal cortex leads to severe difficulties with performing simple calculation, such as stepwise computation (Joseph 2000: 463). The same frontal-parietal network is also involved in working memory (WM......MRI study which involves numerical processing as well as WM and error detection. Three types of stimuli: (a) repeated chunks (x, y, z, x, y, z…), (b) smaller structured chunks requiring minimal calculation (x, x+1, y, y+1, z, z+1…), and (c) strings with an increased calculation requirement (x = x+3......). The control condition consists of simple x = x+1 strings (e.g. 1, 2, 3, 4, 5, 6…). The subjects have to press a button when they detect error to the general patterns, i.e., when a number does not conform to the numerical string. Using a block design to investigate the numerical processing, all three...
Propulsion at low Reynolds number
International Nuclear Information System (INIS)
Najafi, Ali; Golestanian, Ramin
2005-01-01
We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium
Propulsion at low Reynolds number
Energy Technology Data Exchange (ETDEWEB)
Najafi, Ali [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of); Faculty of Science, Zanjan University, Zanjan 313 (Iran, Islamic Republic of); Golestanian, Ramin [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of)
2005-04-13
We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.
Fedosov differentials and Catalan numbers
Energy Technology Data Exchange (ETDEWEB)
Loeffler, Johannes, E-mail: j.j.loeffler@web.d [Muehlgasse 19, 78549 Spaichingen (Germany)
2010-06-11
The aim of the paper is to establish a non-recursive formula for the general solution of Fedosov's 'quadratic' fixed-point equation (Fedosov 1994 J. Diff. Geom. 40 213-38). Fedosov's geometrical fixed-point equation for a differential is rewritten in a form similar to the functional equation for the generating function of Catalan numbers. This allows us to guess the solution. An adapted example for Kaehler manifolds of constant sectional curvature is considered in detail. Also for every connection on a manifold a familiar classical differential will be introduced.
Fedosov differentials and Catalan numbers
Löffler, Johannes
2010-06-01
The aim of the paper is to establish a non-recursive formula for the general solution of Fedosov's 'quadratic' fixed-point equation (Fedosov 1994 J. Diff. Geom. 40 213-38). Fedosov's geometrical fixed-point equation for a differential is rewritten in a form similar to the functional equation for the generating function of Catalan numbers. This allows us to guess the solution. An adapted example for Kaehler manifolds of constant sectional curvature is considered in detail. Also for every connection on a manifold a familiar classical differential will be introduced. Dedicated to the memory of Nikolai Neumaier.
2014-12-01
at $23,200 an hour. So that’s another $1.2M a day. Pete: Don’t they shoot at you? Joe: Well, we usually wire together a bunch of microwave ovens we...Officer, to break his vow never to sail on a “ bird farm.” MORS welcomes Kevin Williams as the new AF sponsor. He became the Director of...person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number
Random Generators and Normal Numbers
Bailey, David H.; Crandall, Richard E.
2002-01-01
Pursuant to the authors' previous chaotic-dynamical model for random digits of fundamental constants, we investigate a complementary, statistical picture in which pseudorandom number generators (PRNGs) are central. Some rigorous results are achieved: We establish b-normality for constants of the form $\\sum_i 1/(b^{m_i} c^{n_i})$ for certain sequences $(m_i), (n_i)$ of integers. This work unifies and extends previously known classes of explicit normals. We prove that for coprime $b,c>1$ the...
DEFF Research Database (Denmark)
Krarup, Jakob
2016-01-01
Born in 1936 I was a schoolboy on the threshold of the secondary school when a knapsack-type game was played with a class mate around 1946–1947. To play the game well and fascinated by numbers in general since my early childhood, however, I realized soon the usefulness of knowing that 1001 = 7 × 11...... × 13. Today, about 70 years later, the game has been passed to some of my grandchildren who also should convince themselves that simple, arithmetic calculations do not necessarily require a pocket computer. As a side effect of the recent revival of the game I felt motivated to seek more insight...
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Cryptography and computational number theory
Shparlinski, Igor; Wang, Huaxiong; Xing, Chaoping; Workshop on Cryptography and Computational Number Theory, CCNT'99
2001-01-01
This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer s...
Signals of lepton number violation
Panella, O; Srivastava, Y N
1999-01-01
The production of like-sign-dileptons (LSD), in the high energy lepton number violating ( Delta L=+2) reaction, pp to 2jets+l/sup +/l /sup +/, (l=e, mu , tau ), of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is reported, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle. Numerical estimates of the corresponding signal cross-section that implement kinematical cuts needed to suppress the standard model background, are presented which show that in some regions of the parameter space the total number of LSD events is well above the background. Assuming non-observation of the LSD signal it is found that LHC would exclude a composite Majorana neutrino up to 700 GeV (if one requires 10 events for discovery). The sensitivity of LHC experiments to the parameter space is then compared to that of the next generation of neutrinoless double beta decay ( beta beta /sub 0 nu /) experiment, GENIUS, and i...
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Banner prints social security numbers
Directory of Open Access Journals (Sweden)
Robbins RA
2014-02-01
Full Text Available No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1. The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pioneer Accountable Care Organization, a government health-care plan that Banner serves. Banner generated its mailing list from information it received from the U.S. Centers for Medicare & Medicaid Services, which is an agency within the U.S. Department of Health & Human Services (HHS responsible for administration of several federal health-care programs. Although medical information has been protected by the Health Insurance Portability and Accountability Act (HIPAA since 1996, penalties were recently increased. Civil monetary penalties were increased from a maximum of $100 ...
Intersection numbers of spectral curves
Eynard, B.
2011-01-01
We compute the symplectic invariants of an arbitrary spectral curve with only 1 branchpoint in terms of integrals of characteristic classes in the moduli space of curves. Our formula associates to any spectral curve, a characteristic class, which is determined by the laplace transform of the spectral curve. This is a hint to the key role of Laplace transform in mirror symmetry. When the spectral curve is y=\\sqrt{x}, the formula gives Kontsevich--Witten intersection numbers, when the spectral curve is chosen to be the Lambert function \\exp{x}=y\\exp{-y}, the formula gives the ELSV formula for Hurwitz numbers, and when one chooses the mirror of C^3 with framing f, i.e. \\exp{-x}=\\exp{-yf}(1-\\exp{-y}), the formula gives the Marino-Vafa formula, i.e. the generating function of Gromov-Witten invariants of C^3. In some sense this formula generalizes ELSV, Marino-Vafa formula, and Mumford formula.
Topics in Number Theory Conference
Andrews, George; Ono, Ken
1999-01-01
From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci ence Foundation, The Penn State Conference Center and the Penn State Depart ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. ...
Directory of Open Access Journals (Sweden)
Christian Agrillo
Full Text Available BACKGROUND: Research on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals. METHODOLOGY/PRINCIPAL FINDINGS: Here we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task. CONCLUSIONS/SIGNIFICANCE: Mosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a 'last resort' strategy in fish, when no other
International Nuclear Information System (INIS)
Metcalfe, N.; Shanks, T.; Fong, R.; Jones, L.R.
1991-01-01
Using the Prime Focus CCD Camera at the Isaac Newton Telescope we have determined the form of the B and R galaxy number-magnitude count relations in 12 independent fields for 21 m ccd m and 19 m ccd m 5. The average galaxy count relations lie in the middle of the wide range previously encompassed by photographic data. The field-to-field variation of the counts is small enough to define the faint (B m 5) galaxy count to ±10 per cent and this variation is consistent with that expected from galaxy clustering considerations. Our new data confirm that the B, and also the R, galaxy counts show evidence for strong galaxy luminosity evolution, and that the majority of the evolving galaxies are of moderately blue colour. (author)
Polynomials formalism of quantum numbers
International Nuclear Information System (INIS)
Kazakov, K.V.
2005-01-01
Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru
The european emergency number 112 - the questionnaire
Directory of Open Access Journals (Sweden)
Krzysztof Goniewicz
2017-07-01
Conclusions. Most of the respondents (92% identify the 112 number as an emergency number that allows them to connect to emergency services from anywhere in the European Union. A significant number of respondents (47% identify the 112 number as an emergency number in Poland. One in three respondents will use the 999 number to contact the emergency services as a witness to an emergency in Poland. Non-medical university students more often (63% will use the 112 emergency number than medical college students (41%. Respondents (98% confirmed the usefulness of a unified emergency number throughout Europe, but decided that they were not sufficiently informed about 112 as the European emergency number.
Essays on the theory of numbers
Dedekind, Richard
1963-01-01
Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
How to be Brilliant at Numbers
Webber, Beryl
2010-01-01
How to be Brilliant at Numbers will help students to develop an understanding of numbers, place value, fractions and decimals. They will develop the language of number, and of the relationships between numbers. They will also use mathematics to solve problems and will develop mathematical reasoning. Using the worksheets in this book, pupils will learn about: ancient Greek numbers; coins; digits; consecutive numbers; magic ladders; fractions; matching pairs; multiples of 10; rounding; decimal un
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
Visuospatial Priming of the Mental Number Line
Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco
2008-01-01
It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response…
Fast integration using quasi-random numbers
International Nuclear Information System (INIS)
Bossert, J.; Feindt, M.; Kerzel, U.
2006-01-01
Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples
Fast integration using quasi-random numbers
Bossert, J.; Feindt, M.; Kerzel, U.
2006-04-01
Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples.
On domination multisubdivision number of unicyclic graphs
Directory of Open Access Journals (Sweden)
Joanna Raczek
2018-01-01
Full Text Available The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009, 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.
DEFF Research Database (Denmark)
Elmasry, Amr Ahmed Abd Elmoneim; Jensen, Claus; Katajainen, Jyrki
2010-01-01
We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit i...... is 2 i-1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg n) worst-case cost per delete, where n is the number of elements stored....
Observing Optional Number in DDC Edition 23
Directory of Open Access Journals (Sweden)
Rotmianto Mohamad
2018-01-01
Full Text Available Dewey Decimal Classification is a most popular classification system in the world because of its completeness and most up-to-date. There are many optional number in this classification system, although it rarely to be discussed even it is important to known well about that optional number, especially for a librarian as classifier. This paper is a literature study about Dewey Decimal Classification Edition 23, to describe about optional numbers, particularly the number in relationship with Indonesia’s subject and discipline. This paper is to avoid misunderstanding in interpreted about optional number among librarians, especially for who that does not understand well about optional numbers.
Some functional equations originating from number theory
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Moreover, we will also study some stability problems of those equations. ... Wisconsin in which he discussed a number of important unsolved problems [18]. ... According to a well-known theorem in number theory, a positive integer of the form.
Nielsen number of a covering map
Directory of Open Access Journals (Sweden)
Jezierski Jerzy
2006-01-01
Full Text Available We consider a finite regular covering over a compact polyhedron and a map admitting a lift . We show some formulae expressing the Nielsen number as a linear combination of the Nielsen numbers of its lifts.
Some inequalities for the Bell numbers
Indian Academy of Sciences (India)
Feng Qi
2017-08-19
Aug 19, 2017 ... Bell number determinant; product; inequality; generating function; derivative; absolutely monotonic function; completely monotonic func- tion; logarithmically absolutely monotonic function; logarithmically completely monotonic function; Stirling number of the second kind; induction; Faà di Bruno formula;.
A new definition of Bejan number
Directory of Open Access Journals (Sweden)
Awad Mohamed M.
2012-01-01
Full Text Available A new definition of Bejan number will be generated by replacing the thermal diffusivity with the mass diffusivity. For example, the Schmidt number is the mass transfer analog of the Prandtl number. For the case of Reynolds analogy (Sc = Pr = = 1, both current and new definitions of Bejan number are the same. This new definition is useful and needed for diffusion of mass (mass diffusion.
Hyperreal Numbers for Infinite Divergent Series
Bartlett, Jonathan
2018-01-01
Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent serie...
49 CFR 230.47 - Boiler number.
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall...
Developmental Changes in the Whole Number Bias
Braithwaite, David W.; Siegler, Robert S.
2018-01-01
Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under…
Altermatic number of categorical product of graphs
DEFF Research Database (Denmark)
Alishahi, Meysam; Hajiabolhassan, Hossein
2018-01-01
In this paper, we prove some relaxations of Hedetniemi's conjecture in terms of altermatic number and strong altermatic number of graphs, two combinatorial parameters introduced by the present authors Alishahi and Hajiabolhassan (2015) providing two sharp lower bounds for the chromatic number of ...
Thermal convection for large Prandtl numbers
Grossmann, Siegfried; Lohse, Detlef
2001-01-01
The Rayleigh-Bénard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra a maximum in the Nu(Pr) dependence is predicted. We moreover offer
Graphing Powers and Roots of Complex Numbers.
Embse, Charles Vonder
1993-01-01
Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)
Combinatorial Interpretation of General Eulerian Numbers
Tingyao Xiong; Jonathan I. Hall; Hung-Ping Tsao
2014-01-01
Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions { a, a+d, a+2d,...}.
Number to finger mapping is topological.
Plaisier, M.A.; Smeets, J.B.J.
2011-01-01
It has been shown that humans associate fingers with numbers because finger counting strategies interact with numerical judgements. At the same time, there is evidence that there is a relation between number magnitude and space as small to large numbers seem to be represented from left to right. In
20 CFR 404.1220 - Identification numbers.
2010-04-01
.... The special number will also be assigned to an interstate instrumentality if pre-1987 coverage is obtained and SSA will send a Form SSA-214-CD to the interstate instrumentality to notify it of the number.... SSA will send the State a Form SSA-214-CD, “Notice of Identifying Number,” to inform the State of the...
46 CFR Sec. 2 - Voyage numbers.
2010-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...
An adventurer's guide to number theory
Friedberg, Richard
1995-01-01
In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Written for readers with an understanding of arithmetic and beginning algebra, the book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes
Fibonacci and Catalan Numbers An Introduction
Grimaldi, Ralph
2012-01-01
In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers . The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers
Defense Horizons. Number 79, April 2015
2015-04-01
law , no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB...79, April 2015 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT...aggression. Even more issues emerged following the downing of Malaysian Airlines Flight 17 over Ukraine in July 2014, and cross-border ar- tillery renewed
What Do Numbers Do in Transnational Governance?
DEFF Research Database (Denmark)
Krause Hansen, Hans; Porter, Tony
2012-01-01
processes. Numbers have properties that differ from words, and shifts from one to the other in governance, for instance in the displacement of laws or norms with risk models or rankings based on numbers, have particular effects, including political effects on states, firms, individuals, and other actors......This study examines how numbers in transnational governance constitute actors, objects, and relationships, including relationships of power. We review the existing literatures on numbers for insights relevant to their role in transnational governance, including the ontology of numbers, the history...
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
Bugeaud, Yann; Evertse, Jan-Hendrik
2007-01-01
We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...
Solomon A. Keelson; Addo J. Odei
2014-01-01
The use of multiple mobile phone numbers in Ghana has become a dominate phenomenon in recent years. The introduction of mobile number portability (MNP) makes it possible for a subscriber to conveniently switch from one mobile network to another without losing his or her number. Because of mobile number portability, we expected that use of multiple numbers would become less attractive. This study examines how mobile number portability has affected the use of multiple phone numbers. We use top,...
Fibonacci number of the tadpole graph
Directory of Open Access Journals (Sweden)
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Certain number-theoretic episodes in algebra
Sivaramakrishnan, R
2006-01-01
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.
On the binary expansions of algebraic numbers
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
2003-07-01
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.
Interaction of Number Magnitude and Auditory Localization.
Golob, Edward J; Lewald, Jörg; Jungilligens, Johannes; Getzmann, Stephan
2016-01-01
The interplay of perception and memory is very evident when we perceive and then recognize familiar stimuli. Conversely, information in long-term memory may also influence how a stimulus is perceived. Prior work on number cognition in the visual modality has shown that in Western number systems long-term memory for the magnitude of smaller numbers can influence performance involving the left side of space, while larger numbers have an influence toward the right. Here, we investigated in the auditory modality whether a related effect may bias the perception of sound location. Subjects (n = 28) used a swivel pointer to localize noise bursts presented from various azimuth positions. The noise bursts were preceded by a spoken number (1-9) or, as a nonsemantic control condition, numbers that were played in reverse. The relative constant error in noise localization (forward minus reversed speech) indicated a systematic shift in localization toward more central locations when the number was smaller and toward more peripheral positions when the preceding number magnitude was larger. These findings do not support the traditional left-right number mapping. Instead, the results may reflect an overlap between codes for number magnitude and codes for sound location as implemented by two channel models of sound localization, or possibly a categorical mapping stage of small versus large magnitudes. © The Author(s) 2015.
International Nuclear Information System (INIS)
Maeda, Hiroko; Kawai, Takeshi; Kanasaki, Yoshiki; Akagi, Hiroaki
1981-01-01
This report is studied on CT number and CT images of the eight cases with fatty liver. Five of these cases showed the reversal of densities of the liver and vessels. In these cases, the diagnoses of the fatty liver were easible. In other cases, the diagnoses were possible only by comparison of the CT number of the liver and spleen because the CT number of normal liver were higher than those of the spleen. In the results which we examined the correlation of the CT number and specific gravities of the blood, normal saline, distilled water, mayonnaise, eatable iol, ethyl alcohol and lard, we observed the linear relationship between CT number and specific gravities. And so, we think that the diagnosis of the fatty liver and the degree of fatty infiltration can be guessed by the CT number of the liver and spleen. (author)
Observing Optional Number in DDC Edition 23
Directory of Open Access Journals (Sweden)
Mohamad Rotmianto
2015-04-01
Full Text Available Dewey Decimal Classification is a most popular classification system in the world because of its completeness and most up-to-date. There are many optional number in this classification system, although it rarely to be discussed even it is important to known well about that optional number, especially for a librarian as classifier. This paper is a literature study about Dewey Decimal Classification Edition 23, to describe about optional numbers, particularly the number in relationship with Indonesia’s subject and discipline. This paper is to avoid misunderstanding in interpreted about optional number among librarians, especially for who that does not understand well about optional numbers.
Self-correcting random number generator
Humble, Travis S.; Pooser, Raphael C.
2016-09-06
A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.
Relativistic theory of tidal Love numbers
International Nuclear Information System (INIS)
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
Cortical areas involved in Arabic number reading.
Roux, F-E; Lubrano, V; Lauwers-Cances, V; Giussani, C; Démonet, J-F
2008-01-15
Distinct functional pathways for processing words and numbers have been hypothesized from the observation of dissociated impairments of these categories in brain-damaged patients. We aimed to identify the cortical areas involved in Arabic number reading process in patients operated on for various brain lesions. Direct cortical electrostimulation was prospectively used in 60 brain mappings. We used object naming and two reading tasks: alphabetic script (sentences and number words) and Arabic number reading. Cortical areas involved in Arabic number reading were identified according to location, type of interference, and distinctness from areas associated with other language tasks. Arabic number reading was sustained by small cortical areas, often extremely well localized (area (Brodmann area 45), the anterior part of the dominant supramarginal gyrus (Brodmann area 40; p area (Brodmann area 37; p areas.
Neocortical glial cell numbers in human brains
DEFF Research Database (Denmark)
Pelvig, D.P.; Pakkenberg, H.; Stark, A.K.
2008-01-01
Stereological cell counting was applied to post-mortem neocortices of human brains from 31 normal individuals, age 18-93 years, 18 females (average age 65 years, range 18-93) and 13 males (average age 57 years, range 19-87). The cells were differentiated in astrocytes, oligodendrocytes, microglia...... while the total astrocyte number is constant through life; finally males have a 28% higher number of neocortical glial cells and a 19% higher neocortical neuron number than females. The overall total number of neocortical neurons and glial cells was 49.3 billion in females and 65.2 billion in males...... and neurons and counting were done in each of the four lobes. The study showed that the different subpopulations of glial cells behave differently as a function of age; the number of oligodendrocytes showed a significant 27% decrease over adult life and a strong correlation to the total number of neurons...
THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY
Reluga, Timothy C.; Medlock, Jan; Galvani, Alison
2009-01-01
The basic reproductive number, , and the effective reproductive number, , are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measur...
Analysis of android random number generator
Sarıtaş, Serkan
2013-01-01
Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013. Thesis (Master's) -- Bilkent University, 2013. Includes bibliographical references leaves 61-65. Randomness is a crucial resource for cryptography, and random number generators are critical building blocks of almost all cryptographic systems. Therefore, random number generation is one of the key parts of secure communication. Random number generatio...
Quality pseudo-random number generator
International Nuclear Information System (INIS)
Tarasiuk, J.
1996-01-01
The pseudo-random number generator (RNG) was written to match needs of nuclear and high-energy physics computation which in some cases require very long and independent random number sequences. In this random number generator the repetition period is about 10 36 what should be sufficient for all computers in the world. In this article the test results of RNG correlation, speed and identity of computations for PC, Sun4 and VAX computer tests are presented
Number conserving approach in quasiparticle representation
International Nuclear Information System (INIS)
Oudih, M.R.; Fellah, M.; Allal, N.H.
2003-01-01
An exact number conserving approach is formulated in the quasiparticle representation to show the effect of the particle-number projection on the ground and the first 0+ excited states. It is applied to the two-level pairing model, which allows an exact solution and a comparison to other approaches. The present method has proved to be an advantageous alternative as compared to the BCS and to the usual methods used to restore the particle number symmetry. (author)
Random walk of the baryon number
International Nuclear Information System (INIS)
Kazaryan, A.M.; Khlebnikov, S.Y.; Shaposhnikov, M.E.
1989-01-01
A new approach is suggested for the anomalous nonconservation of baryon number in the electroweak theory at high temperatures. Arguments are presented in support of the idea that the baryon-number changing reactions may be viewed as random Markov processes. Making use of the general theory of Markov processes, the Fokker--Planck equation for the baryon-number distribution density is obtained and kinetic coefficients are calculated
Trading volume and the number of trades
Marwan Izzeldin
2007-01-01
Trading volume and the number of trades are both used as proxies for market activity, with disagreement as to which is the better proxy for market activity. This paper investigates this issue using high frequency data for Cisco and Intel in 1997. A number of econometric methods are used, including GARCH augmented with lagged trading volume and number of trades, tests based on moment restrictions, regression analysis of volatility on volume and trades, normality of returns when standardized by...
Conferences on Combinatorial and Additive Number Theory
2014-01-01
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.
Asymptotics of quantum weighted Hurwitz numbers
Harnad, J.; Ortmann, Janosch
2018-06-01
This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.
Unique Physician Identification Number (UPIN) Directory
U.S. Department of Health & Human Services — The Unique Physician Identification Number (UPIN) Directory contains selected information on physicians, doctors of Osteopathy, limited licensed practitioners and...
Total dominator chromatic number of a graph
Directory of Open Access Journals (Sweden)
Adel P. Kazemi
2015-06-01
Full Text Available Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
Numbers and other math ideas come alive
Pappas, Theoni
2012-01-01
Most people don't think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive. Pappas explores mathematical ideas by looking behind the scenes of what numbers, points, lines, and other concepts are saying and thinking. In each story, properties and characteristics of math ideas are entertainingly uncovered and explained through the dialogues and actions of its math
Asymptotic numbers, asymptotic functions and distributions
International Nuclear Information System (INIS)
Todorov, T.D.
1979-07-01
The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)
Continental anthropogenic primary particle number emissions
Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus
2016-06-01
Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas-Air Pollution Interactions and Synergies) model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa), coke production (Russia and China), and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation) scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol-cloud interactions as well as particle number related adverse health effects, e.g. in response to tightening
Continental anthropogenic primary particle number emissions
Directory of Open Access Journals (Sweden)
P. Paasonen
2016-06-01
Full Text Available Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas–Air Pollution Interactions and Synergies model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa, coke production (Russia and China, and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol–cloud interactions as well as particle number related adverse health effects, e.g. in response
Analytic number theory an introductory course
Bateman, Paul T
2004-01-01
This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed.
Hello, I am not an NHS number.
Bates, Jane
2016-09-14
I was handed a request to return a patient's call and given a name, signs and symptoms and a number with ten digits, starting with a seven. There was no preceding zero, and assuming it must be a mistake I stuck one on, and dialled. The number was unobtainable.
Nonclassicality in phase-number uncertainty relations
International Nuclear Information System (INIS)
Matia-Hernando, Paloma; Luis, Alfredo
2011-01-01
We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.
Nonclassicality in phase-number uncertainty relations
Energy Technology Data Exchange (ETDEWEB)
Matia-Hernando, Paloma; Luis, Alfredo [Departamento de Optica, Facultad de Ciencias Fisicas, Universidad Complutense, 28040 Madrid (Spain)
2011-12-15
We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.
Savaaksrat Kisitchisit (Numbers 1-10).
Pulu, Tupou L.; And Others
This first grade workbook is designed for children in bilingual Inupiat-English programs in the Alaskan villages of Ambler, Kiana, Kobuk, Noorvik, Selawik, and Shungnak. Each page has a particular number, a corresponding picture with an appropriate caption, and lines for the child to use in writing the number. (CFM)
Hacking DNA copy number for circuit engineering.
Wu, Feilun; You, Lingchong
2017-07-27
DNA copy number represents an essential parameter in the dynamics of synthetic gene circuits but typically is not explicitly considered. A new study demonstrates how dynamic control of DNA copy number can serve as an effective strategy to program robust oscillations in gene expression circuits.
2010-01-01
... and entered on all sales tickets identifying and segregating the sales from the various shipments on hand. The lot number shall be entered on the sales tickets by the salesmen at the time of sale or by the produce dispatcher, and not by bookkeepers or others after the sales have been made. No lot number...
Search for lepton-family-number nonconservation
International Nuclear Information System (INIS)
Hoffman, C.M.
1986-01-01
A review of the status of lepton-family-number nonconservation is given. After a brief historical and theoretical discussion, a description of how experimental searches for lepton-family-number nonconservation are performed is presented. Finally, a summary of the results from past experiments and prospects for future experiments is given
On contact numbers in random rod packings
Wouterse, A.; Luding, Stefan; Philipse, A.P.
2009-01-01
Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well
Families of Linear Recurrences for Catalan Numbers
Gauthier, N.
2011-01-01
Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Numbering. 105-1.109 Section 105-1.109 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.109 Numbering. ...
Game chromatic number of lexicographic product graphs
Directory of Open Access Journals (Sweden)
R. Alagammai
2015-11-01
Full Text Available In this paper, we determine the exact values of the game chromatic number of lexicographic product of path P2 with path Pn, star K1,n and wheel Wn. Also we give an upper bound for the game chromatic number of lexicographic product of any two simple graphs G and H.
Teach Kids about Numbers All around Us
Hudson, Hannah Trierweiler
2011-01-01
Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers…
The Power of Numbers in Global Governance
DEFF Research Database (Denmark)
Krause Hansen, Hans; Mühlen-Schulte, Arthur
2012-01-01
of the historical and contemporary role of numbers in different governance settings. It includes a discussion of the capacity of numbers to foster social identities, relations and truths across national boundaries, to construct issue areas and to enable various modes of surveillance, communication and action...... and relations, as well as in relation to processes of politicisation and de-politicisation that transcend national spaces....
Lepton number violation searches at the LHC
Salvucci, Antonio; The ATLAS collaboration
2017-01-01
Lepton number is conserved in the Standard Model, therefore, any evidence for its violation would indicate the existence of new physics. This talk presents a review of the latest searches performed at the LHC concerning Lepton Number Violation (LNV) processes in the context of Left-Right Symmetric theory and Seesaw mechanism.
Cellular Automata Rules and Linear Numbers
Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika
2012-01-01
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
On the Concept Image of Complex Numbers
Nordlander, Maria Cortas; Nordlander, Edvard
2012-01-01
A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Atomic Fisher information versus atomic number
International Nuclear Information System (INIS)
Nagy, A.; Sen, K.D.
2006-01-01
It is shown that the Thomas-Fermi Fisher information is negative. A slightly more sophisticated model proposed by Gaspar provides a qualitatively correct expression for the Fisher information: Gaspar's Fisher information is proportional to the two-third power of the atomic number. Accurate numerical calculations show an almost linear dependence on the atomic number
The Ramsey Numbers of Paths Versus Fans
Salman, M.; Broersma, Haitze J.; Faigle, U.; Hurink, Johann L.; Pickl, Stefan; Woeginger, Gerhard
2003-01-01
For two given graphs G and H, the Ramsey number R(G,H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Fm), where Pn is
The prime numbers and their distribution
Tenenbaum, Gerald
2000-01-01
One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.
Andreescu, Titu
2014-01-01
It is impossible to imagine modern mathematics without complex numbers. The second edition of Complex Numbers from A to … Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics. The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them. The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. Many new problems and solutions have been added in this second edition. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented. The book reflects the unique experience of the authors. It distills a vast mathematical literature, most ...
On the nullity number of graphs
Directory of Open Access Journals (Sweden)
Mustapha Aouchiche
2017-10-01
Full Text Available The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007 60--67] that $\\eta \\le n - D$, where $\\eta$, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Topics from the theory of numbers
Grosswald, Emil
1984-01-01
Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: * divisibility * congruences * the Riemann zeta function * Diophantine equations and Fermat’s conjecture * the theory of partitions Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike. "In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at...
A conversational introduction to algebraic number theory
Pollack, Paul
2017-01-01
Gauss famously referred to mathematics as the "queen of the sciences" and to number theory as the "queen of mathematics". This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field \\mathbb{Q}. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three "fundamental theorems": unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise w...
Relativistic theory of surficial Love numbers
Landry, Philippe; Poisson, Eric
2014-06-01
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.
Random numbers spring from alpha decay
International Nuclear Information System (INIS)
Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.
1980-05-01
Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a 235 U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables
Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts
Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter
2004-01-01
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…
Alternative analysis: the prime numbers theory and an extension of the real numbers set
Sukhotin A.; Zvyagin M.
2016-01-01
Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) applicatio...
Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers
Kaneko, Hajime; Komatsu, Takao
2017-01-01
Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz numbers. In this paper, we study the second analogue of Stirling-Carlitz numbers and give some general formulae, including Bernoulli and Cauchy numbers in formal power series with complex coefficients, and Bernoulli-Carlitz and Cauchy-Carlitz numbers in function fields. We also give some applications of Hasse-Teichm...
Neocortical glial cell numbers in human brains.
Pelvig, D P; Pakkenberg, H; Stark, A K; Pakkenberg, B
2008-11-01
Stereological cell counting was applied to post-mortem neocortices of human brains from 31 normal individuals, age 18-93 years, 18 females (average age 65 years, range 18-93) and 13 males (average age 57 years, range 19-87). The cells were differentiated in astrocytes, oligodendrocytes, microglia and neurons and counting were done in each of the four lobes. The study showed that the different subpopulations of glial cells behave differently as a function of age; the number of oligodendrocytes showed a significant 27% decrease over adult life and a strong correlation to the total number of neurons while the total astrocyte number is constant through life; finally males have a 28% higher number of neocortical glial cells and a 19% higher neocortical neuron number than females. The overall total number of neocortical neurons and glial cells was 49.3 billion in females and 65.2 billion in males, a difference of 24% with a high biological variance. These numbers can serve as reference values in quantitative studies of the human neocortex.
Theory of analogous force on number sets
Energy Technology Data Exchange (ETDEWEB)
Canessa, Enrique [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
2003-08-01
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions p{sub x} for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering p{sub x} to describe complex phenomena, the theory leads to derive a distinct analogous force f{sub x} on number sets proportional to ({partial_derivative}p{sub x}/{partial_derivative}x){sub T} at an analogous system temperature T. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed. (author)
Language and number: a bilingual training study.
Spelke, E S; Tsivkin, S
2001-01-01
Three experiments investigated the role of a specific language in human representations of number. Russian-English bilingual college students were taught new numerical operations (Experiment 1), new arithmetic equations (Experiments 1 and 2), or new geographical or historical facts involving numerical or non-numerical information (Experiment 3). After learning a set of items in each of their two languages, subjects were tested for knowledge of those items, and new items, in both languages. In all the studies, subjects retrieved information about exact numbers more effectively in the language of training, and they solved trained problems more effectively than untrained problems. In contrast, subjects retrieved information about approximate numbers and non-numerical facts with equal efficiency in their two languages, and their training on approximate number facts generalized to new facts of the same type. These findings suggest that a specific, natural language contributes to the representation of large, exact numbers but not to the approximate number representations that humans share with other mammals. Language appears to play a role in learning about exact numbers in a variety of contexts, a finding with implications for practice in bilingual education. The findings prompt more general speculations about the role of language in the development of specifically human cognitive abilities.
Limits on hypothesizing new quantum numbers
International Nuclear Information System (INIS)
Goldstein, G.R.; Moravcsik, M.J.
1986-01-01
According to a recent theorem, for a general quantum-mechanical system undergoing a process, one can tell from measurements on this system whether or not it is characterized by a quantum number, the existence of which is unknown to the observer, even though the detecting equipment used by the observer is unable to distinguish among the various possible values of the ''secret'' quantum number and hence always averages over them. The present paper deals with situations in which this averaging is avoided and hence the ''secret'' quantum number remains ''secret.'' This occurs when a new quantum number is hypothesized in such a way that all the past measurements pertain to the system with one and the same value of the ''secret'' quantum number, or when the new quantum number is related to the old ones by a specific dynamical model providing a one-to-one correspondence. In the first of these cases, however, the one and the same state of the ''secret'' quantum number needs to be a nondegenerate one. If it is degenerate, the theorem can again be applied. This last feature provides a tool for experimentally testing symmetry breaking and the reestablishment of symmetries in asymptotic regions. The situation is illustrated on historical examples like isospin and strangeness, as well as on some contemporary schemes involving spaces of higher dimensionality
Low Nephron Number and Its Clinical Consequences
Directory of Open Access Journals (Sweden)
Valerie A. Luyckx
2011-10-01
Full Text Available decades ago, that developmental programming of the kidney impacts an individual’s risk for hypertension and renal disease in later life. Low birth weight is the strongest current clinical surrogate marker for an adverse intrauterine environment and, based on animal and human studies, is associated with a low nephron number. Other clinical correlates of low nephron number include female gender, short adult stature, small kidney size, and prematurity. Low nephron number in Caucasian and Australian Aboriginal subjects has been shown to be associated with higher blood pressures, and, conversely, hypertension is less prevalent in individuals with higher nephron numbers. In addition to nephron number, other programmed factors associated with the increased risk of hypertension include salt sensitivity, altered expression of renal sodium transporters, altered vascular reactivity, and sympathetic nervous system overactivity. Glomerular volume is universally found to vary inversely with nephron number, suggesting a degree of compensatory hypertrophy and hyperfunction in the setting of a low nephron number. This adaptation may become overwhelmed in the setting of superimposed renal insults, e.g. diabetes mellitus or rapid catch-up growth, leading to the vicious cycle of on-going hyperfiltration, proteinuria, nephron loss and progressive renal functional decline. Many millions of babies are born with low birth weight every year, and hypertension and renal disease prevalences are increasing around the globe. At present, little can be done clinically to augment nephron number; therefore adequate prenatal care and careful postnatal nutrition are crucial to optimize an individual’s nephron number during development and potentially to stem the tide of the growing cardiovascular and renal disease epidemics worldwide.
Standard random number generation for MBASIC
Tausworthe, R. C.
1976-01-01
A machine-independent algorithm is presented and analyzed for generating pseudorandom numbers suitable for the standard MBASIC system. The algorithm used is the polynomial congruential or linear recurrence modulo 2 method. Numbers, formed as nonoverlapping adjacent 28-bit words taken from the bit stream produced by the formula a sub m + 532 = a sub m + 37 + a sub m (modulo 2), do not repeat within the projected age of the solar system, show no ensemble correlation, exhibit uniform distribution of adjacent numbers up to 19 dimensions, and do not deviate from random runs-up and runs-down behavior.
Baryon number violation and string topologies
International Nuclear Information System (INIS)
Sjoestrand, T.; Skands, P.Z.
2003-01-01
In supersymmetric scenarios with broken R-parity, baryon number violating sparticle decays become possible. In order to search for such decays, a good understanding of expected event properties is essential. We here develop a complete framework that allows detailed studies. Special attention is given to the hadronization phase, wherein the baryon number violating vertex is associated with the appearance of a junction in the colour confinement field. This allows us to tell where to look for the extra (anti)baryon directly associated with the baryon number violating decay
The generative basis of natural number concepts.
Leslie, Alan M; Gelman, Rochel; Gallistel, C R
2008-06-01
Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes.
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Quantum numbers and band topology of nanotubes
Energy Technology Data Exchange (ETDEWEB)
Damnjanovic, M [Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade (Yugoslavia); Milosevic, I [Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade (Yugoslavia); Vukovic, T [Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade (Yugoslavia); Maultzsch, J [Institut fuer Festkoerper Physik, Technische Universitaet Berlin, Hardenbergstr. 36, 10623 Berlin (Germany)
2003-05-30
Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities.
Quantum numbers and band topology of nanotubes
International Nuclear Information System (INIS)
Damnjanovic, M; Milosevic, I; Vukovic, T; Maultzsch, J
2003-01-01
Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities
Quantum numbers and band topology of nanotubes
Damnjanovic, M; Vukovic, T; Maultzsch, J
2003-01-01
Nanotubes as well as polymers and quasi-1D subsystems of 3D crystals have line group symmetry. This allows two types of quantum numbers: roto-translational and helical. The roto-translational quantum numbers are linear and total angular (not conserved) momenta, while the helical quantum numbers are helical and complementary angular momenta. Their mutual relations determine some topological properties of energy bands, such as systematic band sticking or van Hove singularities related to parities. The importance of these conclusions is illustrated by the optical absorption in carbon nanotubes: parity may prevent absorption peaks at van Hove singularities.
Topological quantum numbers in nonrelativistic physics
Thouless, David James
1998-01-01
Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect,
Numbers at work a cultural perspective
Taschner , Rudolf
2007-01-01
Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, politics, and rational foundations of human thought. Each chapter focuses on the influence of mathematics in a specific field and on a specific historical figure, such as ""Pythagoras: Numbers and Symbol""; ""Bach: Numbers and Music""; ""Descartes: Numb
Generation of pseudo-random numbers
Howell, L. W.; Rheinfurth, M. H.
1982-01-01
Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.
Microcomputer-Assisted Discoveries: Random Numbers.
Kimberling, Clark
1983-01-01
A programing contest was designed to promote interest in mathematical randomness. Student-developed programs making clever uses of random numbers are presented. Modifications users might make are suggested. (MNS)
Using Random Numbers in Science Research Activities.
Schlenker, Richard M.; And Others
1996-01-01
Discusses the importance of science process skills and describes ways to select sets of random numbers for selection of subjects for a research study in an unbiased manner. Presents an activity appropriate for grades 5-12. (JRH)
Generalized catalan numbers, sequences and polynomials
KOÇ, Cemal; GÜLOĞLU, İsmail; ESİN, Songül
2010-01-01
In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.
Muon number nonconservation in gauge theories
International Nuclear Information System (INIS)
Cheng, T.P.; Li, L.F.
1977-01-01
The question of separate conservation of muon and electron number is considered in the context of unified gauge theories of weak and electromagnetic interactions. Theories with heavy neutral leptons, Higgs scalars, and doubly charged heavy leptons are discussed. 28 references
Biometric National Identification Number Generation for Secure ...
African Journals Online (AJOL)
Biometric National Identification Number Generation for Secure Network Authentication Based Fingerprint. ... Username, Password, Remember me, or Register ... In this paper an authentication based finger print biometric system is proposed ...
Distribution function of faint galaxy numbers
International Nuclear Information System (INIS)
Fesenko, L.M.
1981-01-01
The Lick observatory counts of galaxies are considered. The distribution of number of galaxies in elementary regions (ER) of 1 degx1 deg is investigated. Each field of 6 degx6 deg was treated separately At b>40 deg the probab+lity to observe of n galaxies in ER is an exponential decreasing function of n, if unequality n> were fulfilled. The mean apparent multiplicity of a galaxy (2.8+-0.9) was derived. The galaxy number distribution was simple model for the number of various systems of galaxies. The supperclustering of galaxies was not introduced. Based on that model the approximate expression for galaxy number distribution was considered and was compared with observed distributions. The agreement between these distributions become better with reducing of the interstellar absorption of light
New technique for number-plate recognition
Guo, Jie; Shi, Peng-Fei
2001-09-01
This paper presents an alternative algorithm for number plate recognition. The algorithm consists of three modules. Respectively, they are number plate location module, character segmentation module and character recognition module. Number plate location module extracts the number plate from the detected car image by analyzing the color and the texture properties. Different from most license plate location methods, the algorithm has fewer limits to the car size, the car position in the image and the image background. Character segmentation module applies connected region algorithm both to eliminate noise points and to segment characters. Touching characters and broken characters can be processed correctly. Character recognition module recognizes characters with HHIC (Hierarchical Hybrid Integrated Classifier). The system has been tested with 100 images obtained from crossroad and parking lot, etc, where the cars have different size, position, background and illumination. Successful recognition rate is about 92%. The average processing time is 1.2 second.
Introduction to the geometry of complex numbers
Deaux, Roland
2008-01-01
Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.
Opening the Door on Triangular Numbers
McMartin, Kimberley; McMaster, Heather
2016-01-01
As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.
Random Number Generation for High Performance Computing
2015-01-01
number streams, a quality metric for the parallel random number streams. * * * * * Atty. Dkt . No.: 5660-14400 Customer No. 35690 Eric B. Meyertons...responsibility to ensure timely payment of maintenance fees when due. Pagel of3 PTOL-85 (Rev. 02/11) Atty. Dkt . No.: 5660-14400 Page 1 Meyertons...with each subtask executed by a separate thread or process (henceforth, process). Each process has Atty. Dkt . No.: 5660-14400 Page 2 Meyertons
Hodge numbers for all CICY quotients
International Nuclear Information System (INIS)
Constantin, Andrei; Gray, James; Lukas, Andre
2017-01-01
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.
All-optical fast random number generator.
Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong
2010-09-13
We propose a scheme of all-optical random number generator (RNG), which consists of an ultra-wide bandwidth (UWB) chaotic laser, an all-optical sampler and an all-optical comparator. Free from the electric-device bandwidth, it can generate 10Gbit/s random numbers in our simulation. The high-speed bit sequences can pass standard statistical tests for randomness after all-optical exclusive-or (XOR) operation.
CAT-ASVAB Technical Bulletin Number 1
2006-03-01
CAT -ASVAB Technical Bulletin #1 Personnel Testing Division Defense Manpower Data Center March 2006 Report...2. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE CAT -ASVAB Technical Bulletin #1 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c...Hetter, R. D. "Psychometric Procedures for Administering CAT -ASVAB" (pp. 131-140) Chapter 4 Hetter, R. D., & Sympson J. B. "Item Exposure
Large number discrimination in newborn fish.
Directory of Open Access Journals (Sweden)
Laura Piffer
Full Text Available Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14 in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density, three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies.
International Nuclear Information System (INIS)
Falcon, Sergio; Plaza, Angel
2007-01-01
We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {F k,n } n=0 ∼ were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers are deduce directly from elementary matrix algebra
Fibonacci and Lucas numbers with applications
Koshy, Thomas
2011-01-01
[Koshy's] book is without doubt the most comprehensive and scholarly work on Fibonacci numbers to date and I am sure that it will quickly signal its presence and impose itself as an authoritative reference manual on Fibonacci numbers. -Napoleon Gauthier, Royal Military College of Canada, Kingston, ON What a gem this is! [...] My only regrest about the book is that it wasn't around years ago. It fills such a void. -Monte Zerger, Adams State College, Alamosa, CO
Hodge numbers for all CICY quotients
Energy Technology Data Exchange (ETDEWEB)
Constantin, Andrei [Department of Physics and Astronomy, Uppsala University, SE-751 20, Uppsala (Sweden); Gray, James [Physics Department, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)
2017-01-02
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.
Number skills are maintained in healthy ageing.
Cappelletti, Marinella; Didino, Daniele; Stoianov, Ivilin; Zorzi, Marco
2014-03-01
Numerical skills have been extensively studied in terms of their development and pathological decline, but whether they change in healthy ageing is not well known. Longer exposure to numbers and quantity-related problems may progressively refine numerical skills, similar to what happens to other cognitive abilities like verbal memory. Alternatively, number skills may be sensitive to ageing, reflecting either a decline of number processing itself or of more auxiliary cognitive abilities that are involved in number tasks. To distinguish between these possibilities we tested 30 older and 30 younger participants on an established numerosity discrimination task requiring to judge which of two sets of items is more numerous, and on arithmetical tasks. Older participants were remarkably accurate in performing arithmetical tasks although their numerosity discrimination (also known as 'number acuity') was impaired. Further analyses indicate that this impairment was limited to numerosity trials requiring inhibiting information incongruent to numerosity (e.g., fewer but larger items), and that this also correlated with poor inhibitory processes measured by standard tests. Therefore, rather than a numerical impairment, poor numerosity discrimination is likely to reflect elderly's impoverished inhibitory processes. This conclusion is supported by simulations with a recent neuro-computational model of numerosity perception, where only the specific degradation of inhibitory processes produced a pattern that closely resembled older participants' performance. Numeracy seems therefore resilient to ageing but it is influenced by the decline of inhibitory processes supporting number performance, consistent with the 'Inhibitory Deficit' Theory. Copyright © 2013 Elsevier Inc. All rights reserved.
Persistent consequences of atypical early number concepts
Directory of Open Access Journals (Sweden)
Michèle M. M. Mazzocco
2013-09-01
Full Text Available How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders’ number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes.
Complex architecture of primes and natural numbers.
García-Pérez, Guillermo; Serrano, M Ángeles; Boguñá, Marián
2014-08-01
Natural numbers can be divided in two nonoverlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.
A new pseudorandom number generator based on a complex number chaotic equation
International Nuclear Information System (INIS)
Liu Yang; Tong Xiao-Jun
2012-01-01
In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties
Number density structures in the inner heliosphere
Stansby, D.; Horbury, T. S.
2018-06-01
Aims: The origins and generation mechanisms of the slow solar wind are still unclear. Part of the slow solar wind is populated by number density structures, discrete patches of increased number density that are frozen in to and move with the bulk solar wind. In this paper we aimed to provide the first in-situ statistical study of number density structures in the inner heliosphere. Methods: We reprocessed in-situ ion distribution functions measured by Helios in the inner heliosphere to provide a new reliable set of proton plasma moments for the entire mission. From this new data set we looked for number density structures measured within 0.5 AU of the Sun and studied their properties. Results: We identified 140 discrete areas of enhanced number density. The structures occurred exclusively in the slow solar wind and spanned a wide range of length scales from 50 Mm to 2000 Mm, which includes smaller scales than have been previously observed. They were also consistently denser and hotter that the surrounding plasma, but had lower magnetic field strengths, and therefore remained in pressure balance. Conclusions: Our observations show that these structures are present in the slow solar wind at a wide range of scales, some of which are too small to be detected by remote sensing instruments. These structures are rare, accounting for only 1% of the slow solar wind measured by Helios, and are not a significant contribution to the mass flux of the solar wind.
Number theory in the spirit of Ramanujan
Berndt, Bruce C
2006-01-01
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of q-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematic...
Unpredictability and the transmission of numbers
Myers, John M.; Madjid, F. Hadi
2016-03-01
Curiously overlooked in physics is its dependence on the transmission of numbers. For example, the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.
On Generalizations of the Stirling Number Triangles
Lang, Wolfdieter
2000-09-01
Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinite-dimensional lower triangular matrices) of numbers will be denoted by S2(k;n,m) and S1(k;n,m) with k in Z. The original Stirling number triangles of the second and first kind arise when k = 1. S2(2;n,m) is identical with the unsigned S1(2;n,m) triangle, called S1p(2;n,m), which also represents the triangle of signless Lah numbers. Certain associated number triangles, denoted by s2(k;n,m) and s1(k;n,m), are also defined. Both s2(2;n,m) and s1(2;n + 1, m + 1) form Pascal's triangle, and s2(-1,n,m) turns out to be Catalan's triangle. Generating functions are given for the columns of these triangles. Each S2(k) and S1(k) matrix is an example of a Jabotinsky matrix. Therefore the generating functions for the rows of these triangular arrays constitute exponential convolution polynomials. The sequences of the row sums of these triangles are also considered. These triangles are related to the problem of obtaining finite transformations from infinitesimal ones generated by x^k d/dx, for k in Z.
Approximate particle number projection in hot nuclei
International Nuclear Information System (INIS)
Kosov, D.S.; Vdovin, A.I.
1995-01-01
Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab
True random numbers from amplified quantum vacuum.
Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V
2011-10-10
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.
The distribution of prime numbers and associated problems in number theory
International Nuclear Information System (INIS)
Nair, M.
1991-01-01
Some problems in number theory, namely the gaps between consecutive primes, the distribution of primes in arithmetic progressions, Brun-Titchmarsh theorem, Fermat's last theorem, The Thue equation, the gaps between square-free numbers are discussed
Microsoft Support Phone Number +1-877-353-1149(toll-free) Microsoft Helpline Phone Number
Allina willson
2018-01-01
Microsoft Helpline Phone Number Call Now: +1-877-353-1149 for Microsoft support and services. This is Trusted Microsoft Support number provide instant support.if you get any problem while using Microsoft office just relaxed because Microsoft support phone number +1-877-353-1149 is here to provide instant help of microsoft issues. Just dial our Microsoft support phone number +1-877-353-1149 and get instant online support.
Large numbers hypothesis. II - Electromagnetic radiation
Adams, P. J.
1983-01-01
This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.
Room Airflows with Low Reynolds Number Effects
DEFF Research Database (Denmark)
Topp, Claus; Nielsen, Peter V.; Davidson, Lars
The behaviour of room airflows under fully turbulent conditions is well known both in terms of experiments and, numerical calculations by computational fluid dynamics (CFD). For room airflows where turbulence is not fully developed though, i.e. flows at low Reynolds numbers, the existing knowledge...... is limited. It has been the objective to investigate the behaviour of a plane isothermal wall jet in a full-scale ventilated room at low Reynolds numbers, i.e. when the flow is not fully turbulent. The results are significantly different from known theory for fully turbulent flows. It was found that the jet...... constants are a strong function of the Reynolds number up to a level of Reh≈500....
Seniority Number in Valence Bond Theory.
Chen, Zhenhua; Zhou, Chen; Wu, Wei
2015-09-08
In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.
Baryon number nonconservation in extreme conditions
International Nuclear Information System (INIS)
Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Shaposhnikov, M.E.
1988-01-01
In gauge theories with the left-right asymmetric fermionic content (e.g. in standard electroweak theory) fermion number F is not conserved due to the anomaly. It is shown that anomalous processes, while being exponentially suppressed, under normal conditions, are in fact rapid. The mechanism of fermionic number nonconservation connected with a level crossing phenomenon in external gauge fields is described. The theory and experimental consequences of monopole catalysis of a proton decay is reviewed. It is shown that cold dense fermionic matter is stable only up to some limiting density. It is demonstrated that there is no exponential suppression of the rate F nonconservation at high temperatures. The cosmological implications of this fact are discussed. The strong anomalous fermionic number violation in decays of superheavy fermions technibaryons is considered
Lepton number violating processes and Majorana neutrinos
International Nuclear Information System (INIS)
Dib, C.; Schmidt, I.; Gribanov, V.; Kovalenko, S.
2001-01-01
Some generic properties of lepton number violating processes and their relation to different entries of the Majorana neutrino mass matrix are discussed. Present and near future experiments searching for these processes, except the neutrinoless double beta decay, are unable to probe light (eV mass region) and heavy (hundred GeV mass region) neutrinos. On the other hand, due to the effect of a resonant enhancement, some of lepton number violating decays can be very sensitive to the intermediate-mass neutrinos with typical masses in the hundred MeV region. These neutrinos may appear as admixtures of the three active and an arbitrary number of sterile neutrino species. The experimental constraints on these massive neutrino states are analyzed and their possible cosmological and astrophysical implications are discussed
Motzkin numbers out of Random Domino Automaton
Energy Technology Data Exchange (ETDEWEB)
Białecki, Mariusz, E-mail: bialecki@igf.edu.pl [Institute of Geophysics, Polish Academy of Sciences, ul. Ks. Janusza 64, 01-452 Warszawa (Poland)
2012-10-01
Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton. -- Highlights: ► Motzkin numbers are derived from stochastic cellular automaton with avalanches. ► Explicit solution of toy model of earthquakes is presented. ► Case with inverse-power distribution of avalanches is found.
Directory of Open Access Journals (Sweden)
Shetnikov, Andrey
2009-06-01
Full Text Available The paper concerns the concept of number (arithmos, important for dialectical method of later Plato. It becomes clear that the arithmos in Plato’s dialectics should be understood as a concrete operation, a sort of tekhne, such as counting, enumeration, compilation of a comprehensive and systematic list, etc., rather then the theoretical number of abstract arithmetic. The author analyses a series of grammatical, musical and rhetorical examples, supplied by Plato in the Philebus and other dialogues, and traces the usage of arithmos and similar words in the earlier tradition, particularly, in Homer, Hesiod, the classical tragedy, and Herodotus.
Dynamical real numbers and living systems
International Nuclear Information System (INIS)
Datta, Dhurjati Prasad
2004-01-01
Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical representation of the ordinary real number system. Every real number can be visualized as a living cell-like structure, endowed with a definite evolutionary arrow. We discuss the relevance of this extended calculus in the study of living systems. We also present an intelligent version of the Newton's first law of motion
Type number and rigidity of fibred surfaces
International Nuclear Information System (INIS)
Markov, P E
2001-01-01
Infinitesimal l-th order bendings, 1≤l≤∞, of higher-dimensional surfaces are considered in higher-dimensional flat spaces (for l=∞ an infinitesimal bending is assumed to be an analytic bending). In terms of the Allendoerfer type number, criteria are established for the (r,l)-rigidity (in the terminology of Sabitov) of such surfaces. In particular, an (r,l)-infinitesimal analogue is proved of the classical theorem of Allendoerfer on the unbendability of surfaces with type number ≥3 and the class of (r,l)-rigid fibred surfaces is distinguished
The number density of a charged relic
International Nuclear Information System (INIS)
Berger, C.F.; Kraml, S.; Palorini, F.
2008-07-01
We investigate scenarios in which a charged, long-lived scalar particle decouples from the primordial plasma in the Early Universe. We compute the number density at time of freeze-out considering both the cases of abelian and non-abelian interactions and including the effect of Sommerfeld enhancement at low initial velocity. We also discuss as extreme case the maximal cross section that fulfils the unitarity bound. We then compare these number densities to the exotic nuclei searches for stable relics and to the BBN bounds on unstable relics and draw conclusions for the cases of a stau or stop NLSP in supersymmetric models with a gravitino or axino LSP. (orig.)
Searches for violation of muon number conservation
International Nuclear Information System (INIS)
Redwine, R.P.
1981-01-01
The question of violation of muon number conservation is one which has occupied considerable attention and resources in recent years. The first generation of experiments at the medium energy accelerators has now been completed and the next generation of experiments is ready to begin. The history of muon number conservation is reviewed, including the reasons for the present belief that the conservation law may not be exact. The experiments that have been completed in the last few years are discussed. The new experiments that are being mounted and planned at several laboratories are discussed, and the relationship of these types of experiments to other studies, such as searches for neutrino oscillations, are considered
Energy information data base: report number codes
Energy Technology Data Exchange (ETDEWEB)
None
1979-09-01
Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used. (RWR)
The number density of a charged relic
Energy Technology Data Exchange (ETDEWEB)
Berger, C.F. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics]|[California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Covi, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kraml, S. [CNRS/IN2P3, Grenoble (France). Lab. de Physique Subatomique et de Cosmologie; Palorini, F. [Lyon Univ., UCBL, CNRS/IN2P3, Villeurbanne (France). IPN de Lyon
2008-07-15
We investigate scenarios in which a charged, long-lived scalar particle decouples from the primordial plasma in the Early Universe. We compute the number density at time of freeze-out considering both the cases of abelian and non-abelian interactions and including the effect of Sommerfeld enhancement at low initial velocity. We also discuss as extreme case the maximal cross section that fulfils the unitarity bound. We then compare these number densities to the exotic nuclei searches for stable relics and to the BBN bounds on unstable relics and draw conclusions for the cases of a stau or stop NLSP in supersymmetric models with a gravitino or axino LSP. (orig.)
Formulation of baryon number violating collisions
International Nuclear Information System (INIS)
Funakubo, Koichi; Otsuki, Shoichiro; Takenaga, Kazunori; Toyoda, Fumihiko.
1992-01-01
A new formalism based on path-integral expression of time-evolution operator during tunneling is presented. Instead of instanton calculus in the LSZ formalism, a classical bounce solution leading to sphaleron (instanton action) at high (low) energies is adopted as the tunneling configuration. The formalism is applied to O(3) nonlinear sigma model in two dimensions. For the coupling constant g 2 ≅ 0.1, which may be physical in the sense that the number of produced particles ≅ 100, comparable with that of electroweak theory, the baryon number violating cross section is smaller by orders of magnitude than the so-called unitarity bound. (author)
Number sense how the mind creates mathematics
Dehaene, Stanislas
2011-01-01
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudime
Nielsen number of a covering map
Directory of Open Access Journals (Sweden)
Jerzy Jezierski
2006-02-01
Full Text Available We consider a finite regular covering pH:XÃ‹ÂœHÃ¢Â†Â’X over a compact polyhedron and a map f:XÃ¢Â†Â’X admitting a lift fÃ‹Âœ:XÃ‹ÂœHÃ¢Â†Â’XÃ‹ÂœH. We show some formulae expressing the Nielsen number N(f as a linear combination of the Nielsen numbers of its lifts.
A finite particle number approach to physics
International Nuclear Information System (INIS)
Noyes, H.P.
1984-01-01
Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules the author constructs: the scale constants of physics (3, 10, 137, 1.7x10 38 ); 3+1 Minkowski space with a discrete metric and the algebraic bound ΔepsilonΔtau >= 1; the Einstein-deBroglie relation; algebraic 'double slit' interference; a single time momentum space scattering theory connected to laboratory experience; an approximation to 'wave functions'; 'local' phase severence and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; msub(p)/msub(e); a cosmology not in disagreement with current observations. (Auth.)
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
Number theory and the periodicity of matter
Boeyens, Jan C A
2008-01-01
Presents a fully scientific account of the use of the golden ratio and explores the observation that stable nucleides obey a number theory based general lawThe interest in number theory is worldwide and covers the entire spectrum of human knowledge. Those aspects covered here will not be immediately accessible to the general lay readership, but, scientists of all pursuations immediately appreciate the importance of the applications described hereThe well-known interest of engineers, medical practitioners and information technologists in popular scientific matters, should make this an attractive buy for such individuals. Undergraduate students in these disciplines should be equally interested.
History of the theory of numbers
Dickson, Leonard Eugene
2005-01-01
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include
Energy information data base: report number codes
International Nuclear Information System (INIS)
1979-09-01
Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used
The effect of the cranial bone CT numbers on the brain CT numbers
Energy Technology Data Exchange (ETDEWEB)
Fukuda, Hitoshi; Kobayashi, Shotai; Koide, Hiromi; Yamaguchi, Shuhei; Okada, Kazunori; Shimote, Koichi; Tsunematsu, Tokugoro (Shimane Medical Univ., Izumo (Japan))
1989-06-01
The effects of the cranial size and the computed tomography (CT) numbers of the cranial bone on that of the brain were studied in 70 subjects, aged from 30 to 94 years. The subjects had no histories of cerebrovascular accidents and showed no abnormalities in the central nervous system upon physical examinations and a CT scan. We measured the average attenuation values (CT numbers) of each elliptical region (165 pixels, 0.39 cm{sup 2}) at the bilateral thalamus and at twelve areas of the deep white matter. Multiple regression analysis was used to assess the effects of age, cranial size, and cranial bone CT numbers on the brain CT numbers. The effect of the cranial bone CT numbers on the brain CT numbers was statistically significant. The brain CT numbers increased with the increase in the cranial bone CT numbers. There was, however, no significant correlation between brain CT numbers and cranial size. In measuring the brain CT numbers, it is desirable that consideration be given to the cranial bone CT numbers. (author).
The Learning Potentials of Number Blocks
DEFF Research Database (Denmark)
Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten
2012-01-01
This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher...
The 17 GHz active region number
Energy Technology Data Exchange (ETDEWEB)
Selhorst, C. L.; Pacini, A. A. [IP and D-Universidade do Vale do Paraíba-UNIVAP, São José dos Campos (Brazil); Costa, J. E. R. [CEA, Instituto Nacional de Pesquisas Espaciais, São José dos Campos (Brazil); Giménez de Castro, C. G.; Valio, A. [CRAAM, Universidade Presbiteriana Mackenzie, São Paulo (Brazil); Shibasaki, K., E-mail: caius@univap.br [Nobeyama Solar Radio Observatory/NAOJ, Minamisaku, Nagano 384-1305 (Japan)
2014-08-01
We report the statistics of the number of active regions (NAR) observed at 17 GHz with the Nobeyama Radioheliograph between 1992, near the maximum of cycle 22, and 2013, which also includes the maximum of cycle 24, and we compare with other activity indexes. We find that NAR minima are shorter than those of the sunspot number (SSN) and radio flux at 10.7 cm (F10.7). This shorter NAR minima could reflect the presence of active regions generated by faint magnetic fields or spotless regions, which were a considerable fraction of the counted active regions. The ratio between the solar radio indexes F10.7/NAR shows a similar reduction during the two minima analyzed, which contrasts with the increase of the ratio of both radio indexes in relation to the SSN during the minimum of cycle 23-24. These results indicate that the radio indexes are more sensitive to weaker magnetic fields than those necessary to form sunspots, of the order of 1500 G. The analysis of the monthly averages of the active region brightness temperatures shows that its long-term variation mimics the solar cycle; however, due to the gyro-resonance emission, a great number of intense spikes are observed in the maximum temperature study. The decrease in the number of these spikes is also evident during the current cycle 24, a consequence of the sunspot magnetic field weakening in the last few years.
Defense Horizons. Number 78, March 2015
2015-03-01
and antelope Valley College (aVC) results in increases in number of scientists, engi- neers, and technicians from which to draw employees for the...should address best prac- tices for project valuation , what types of formalized arrangements are acceptable, and legal precedents that allow such
Identification of copy number variants in horses
Doan, R.; Cohen, N.; Harrington, J.; Veazy, K.; Juras, R.; Cothran, G.; McCue, M. E.; Skow, L.; Dindot, S. V.
2012-01-01
identical CNVs from each animal yielded 775 CNV regions (CNVRs), involving 1707 protein- and RNA-coding genes. The number of CNVs per animal ranged from 55 to 347, with median and mean sizes of CNVs of 5.3 kb and 99.4 kb, respectively. Approximately 6
Irrational Numbers Can "In-Spiral" You
Lewis, Leslie D.
2007-01-01
This article describes the instructional process of helping students visualize irrational numbers. Students learn to create a spiral, called "the wheel of Theodorus," which demonstrates irrational and rational lengths. Examples of student work help the reader appreciate the delightful possibilities of this project. (Contains 4 figures.)
Identifying jet quantum numbers event by event
International Nuclear Information System (INIS)
Teper, M.J.
1979-12-01
A method is proposed to identify the parton that gives rise to any particular jet. The method improves with the number of particles in the jet, and should indicate which of the jets in a three jet event at PETRA is the gluon jet. (author)
Natural occupation numbers: When do they vanish?
Giesbertz, K.J.H.; Van Leeuwen, R.
The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the
Chinese Number Words, Culture, and Mathematics Learning
Ng, Sharon Sui Ngan; Rao, Nirmala
2010-01-01
This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…
Distribution of squares modulo a composite number
Aryan, Farzad
2015-01-01
In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.
Improving Euler computations at low Mach numbers
Koren, B.; Leer, van B.; Deconinck, H.; Koren, B.
1997-01-01
The paper consists of two parts, both dealing with conditioning techniques for lowMach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of
Improving Euler computations at low Mach numbers
Koren, B.
1996-01-01
This paper consists of two parts, both dealing with conditioning techniques for low-Mach-number Euler-flow computations, in which a multigrid technique is applied. In the first part, for subsonic flows and upwind-discretized linearized 1-D Euler equations, the smoothing behavior of
Learning Random Numbers: A Matlab Anomaly
Czech Academy of Sciences Publication Activity Database
Savický, Petr; Robnik-Šikonja, M.
2008-01-01
Roč. 22, č. 3 (2008), s. 254-265 ISSN 0883-9514 R&D Projects: GA AV ČR 1ET100300517 Institutional research plan: CEZ:AV0Z10300504 Keywords : random number s * machine learning * classification * attribute evaluation * regression Subject RIV: BA - General Mathematics Impact factor: 0.795, year: 2008
Boundary induced nonlinearities at small Reynolds numbers
Sbragaglia, M.; Sugiyama, K.
2007-01-01
We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag
On gauged Baryon and Lepton numbers
International Nuclear Information System (INIS)
Rajpoot, S.
1990-01-01
The observation that Baryon number and Lepton number are conserved in nature provides strong motivation for associating gauge symmetries to these conserved numbers. This endeavor requires that the gauge group of electroweak interactions be extended from SU(2) L X U(1) Y to SU(2) L X U(1) R X U(1) Lepton where U(1) R couples only to the right-handed quarks and leptons. If it furthur postulated that right-handed currents exist on par with the left-handed ones, then the full electroweak symmetry is SU(2) L X SU(2) R X U(1) Baryon X U(1) Lepton . The SU(2) L X SU(2) R X U(1) Baryon X U(1) Lepton model is described in some detail. The triangle anomalies of the three families of quarks and leptons in the model are cancelled invoking leptoquark matter which is new fermionic matter that carries baryon as well as lepton numbers. In addition to the standard neutral boson (Z degree), the theory predicts two neutral gauge bosons with mass lower bounds of 120 GeV and 210 GeV which makes these particles prospective candidates for production at LEP, the TEVATRON and the SSC
Metric propositional neighborhood logics on natural numbers
DEFF Research Database (Denmark)
Bresolin, Davide; Della Monica, Dario; Goranko, Valentin
2013-01-01
Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is “met by” the current one and to an interval that “meets” the current one, plus an infinite set of length constraints, regarded as atomic propositions...
Production of Numbers about the Future
DEFF Research Database (Denmark)
Huikku, Jari; Mouritsen, Jan; Silvola, Hanna
of prominent Finnish business managers, auditors, analysts, investors, financial supervisory authority, academics and media, the paper extends prior research which has used large data. The paper analyses impairment testing as a process where network of human and non-human actors produce numbers about...
Some Functional Equations Originating from Number Theory
Indian Academy of Sciences (India)
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
Preferential solvation: dividing surface vs excess numbers.
Shimizu, Seishi; Matubayasi, Nobuyuki
2014-04-10
How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions.
Contributions to Analytic Number Theory | Lucht | Quaestiones ...
African Journals Online (AJOL)
This paper reports on some recent contributions to the theory of multiplicative arithmetic semigroups, which have been initiated by John Knopfmacher's work on analytic number theory. They concern weighted inversion theorems of the. Wiener type, mean-value theorems for multiplicative functions, and, Ramanujan
A Geometrical Application of Number Theory
Srinivasan, V. K.
2013-01-01
Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…
International Nuclear Information System (INIS)
Brekke, L.; Freund, P.G.O.
1993-01-01
The boundary of the ordinary open string world sheet is the real line. Along with the usual open string, one can consider p-adic open strings whose world sheet has as boundary the p-adic line instead (the points on this boundary are labelled by p-adic numbers rather than real numbers). The world sheet itself is then no longer a continuous manifold but becomes a discrete homogeneous Bethe lattice, or Bruhat-Tits tree of incidence number p + 1. The p-adic strings thus correspond to specific discretizations of the world sheet. Studying all these discretizations (one for each prime p) together, as suggested by number theory, sheds new light on the ordinary string, via adelic product formulae. One is also led this way to a new type of string, the adelic string. These issues and their generalization to closed strings are discussed after a self-contained mathematical introduction. Other physical systems with natural p-adic counterparts are considered and in their context the connection between p-adic theories and quantum groups is explored. (orig.)
IEEE Standard for Floating Point Numbers
Indian Academy of Sciences (India)
IAS Admin
Floating point numbers are an important data type in compu- tation which is used ... quite large! Integers are ... exp, the value of the exponent will be taken as (exp –127). The ..... bit which is truncated is 1, add 1 to the least significant bit, else.
Synesthesia and Number Cognition in Children
Green, Jennifer A. K.; Goswami, Usha
2008-01-01
Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…
Reproduction numbers of infectious disease models
Directory of Open Access Journals (Sweden)
Pauline van den Driessche
2017-08-01
Full Text Available This primer article focuses on the basic reproduction number, â0, for infectious diseases, and other reproduction numbers related to â0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of â0 determining whether or not the disease dies out. The next generation matrix method of calculating â0 in a compartmental model is described and illustrated. To address control strategies, type and target reproduction numbers are defined, as well as sensitivity and elasticity indices. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease, cholera in humans (a disease with two transmission pathways, anthrax in animals (a disease that can be spread by dead carcasses and spores, and Zika in humans (spread by mosquitoes and sexual contacts. Some parameter values from literature data are used to illustrate the results. Finally, references for other ways to calculate â0 are given. These are useful for more complicated models that, for example, take account of variations in environmental fluctuation or stochasticity. Keywords: Basic reproduction number, Disease control, West Nile virus, Cholera, Anthrax, Zika virus
9 CFR 355.8 - Official number.
2010-01-01
... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION, AND... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY...
Baryon number violation and particle collider experiments
International Nuclear Information System (INIS)
Klinkhamer, F.R.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1992-09-01
Baryon number non-conservation, due to non-perturbative effects (sphalerons) in the standard model, may have been important in the early Universe. In this paper the possibility is discussed that similar effects could show up at future particle collider experiments. (author). 16 refs.; 3 figs
Maple Explorations, Perfect Numbers, and Mersenne Primes
Ghusayni, B.
2005-01-01
Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.
New feature for an old large number
International Nuclear Information System (INIS)
Novello, M.; Oliveira, L.R.A.
1986-01-01
A new context for the appearance of the Eddington number (10 39 ), which is due to the examination of elastic scattering of scalar particles (ΠK → ΠK) non-minimally coupled to gravity, is presented. (author) [pt
About the lepton number non conservation
International Nuclear Information System (INIS)
Bernabeu, J
1989-01-01
The possibility of lepton number non conservation through the mixing of lepton flavours, as well as the IΔLI=2 lepton antilepton conversion, is discussed. The paper follows the scheme: i) Experimental Situation; ii) Relation with the Neutrino Mass problem; iii) Majorana Neutrinos?; iv) Extensions of the Standard Model; v) Lepton Flavour Violating Decays of μ and τ; vi) Z∞ Boson Decays. (Author)
Gauge transformations with fractional winding numbers
International Nuclear Information System (INIS)
Abouelsaood, A.
1996-01-01
The role which gauge transformations of noninteger winding numbers might play in non-Abelian gauge theories is studied. The phase factor acquired by the semiclassical physical states in an arbitrary background gauge field when they undergo a gauge transformation of an arbitrary real winding number is calculated in the path integral formalism assuming that a θFF term added to the Lagrangian plays the same role as in the case of integer winding numbers. Requiring that these states provide a representation of the group of open-quote open-quote large close-quote close-quote gauge transformations, a condition on the allowed backgrounds is obtained. It is shown that this representability condition is only satisfied in the monopole sector of a spontaneously broken gauge theory, but not in the vacuum sector of an unbroken or a spontaneously broken non-Abelian gauge theory. It is further shown that the recent proof of the vanishing of the θ parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed because certain gauge transformations needed for the proof, and whose existence is assumed, are either spontaneously broken or cannot be globally defined as a result of a topological obstruction. copyright 1996 The American Physical Society
Hidden supersymmetry and Fermion number fractionalization
International Nuclear Information System (INIS)
Akhoury, R.
1985-01-01
This paper discusses how a hidden supersymmetry of the underlying field theories can be used to interpret and to calculate fermion number fractionalization in different dimensions. This is made possible by relating it to a corresponding Witten index of the hidden supersymmetry. The closely related anomalies in odd dimensions are also discussed
Visualizing the Arithmetic of Complex Numbers
Soto-Johnson, Hortensia
2014-01-01
The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…
The number of expats is rather stable
DEFF Research Database (Denmark)
Andersen, Torben
2008-01-01
aggregate data from the Danish economist’s and the engineer’s trade unions show that during the last decade there has been stagnation in the number of expatriates. Taking into consideration that the three trade unions cover the very large majority of Danish knowledge workers occupying foreign jobs...
Radical Software. Number Two. The Electromagnetic Spectrum.
Korot, Beryl, Ed.; Gershuny, Phyllis, Ed.
1970-01-01
In an effort to foster the innovative uses of television technology, this tabloid format periodical details social, educational, and artistic experiments with television and lists a large number of experimental videotapes available from various television-centered groups and individuals. The principal areas explored in this issue include cable…
Forecasting distribution of numbers of large fires
Haiganoush K. Preisler; Jeff Eidenshink; Stephen Howard; Robert E. Burgan
2015-01-01
Systems to estimate forest fire potential commonly utilize one or more indexes that relate to expected fire behavior; however they indicate neither the chance that a large fire will occur, nor the expected number of large fires. That is, they do not quantify the probabilistic nature of fire danger. In this work we use large fire occurrence information from the...
Topics in the theory of numbers
Erdős, Paul
2003-01-01
This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdös. Janos Suranyis vast teaching experience successfully complements Paul Erdös'ability to initiate new directions of research by suggesting new problems and approaches. This book will surely arouse the interest of the student and the teacher alike. Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers. While his papers contributed to almost every area of mathematics, his main research interest was in the area of combinatorics, graph theory, and number theory. He is most famous for proposing...
Where Are All the Typical Numbers - 1
Indian Academy of Sciences (India)
inequality, independence. B V Rao was a Professor at the Indian Statistical. Institute, Kolkata. He is currently with the. Chennai Mathematical. Institute. The entire discussion below, except the first few paragraphs, takes place on the interval (0;1], so you can relax. In this two-part article, we show that decimal digits of numbers ...
Poison control center - Emergency number (image)
For a poison emergency call 1-800-222-1222 anywhere in the United States. This national hotline number will let you ... is a free and confidential service. All local poison control centers in the U.S. use this national ...
String fields, higher spins and number theory
Polyakov, Dimitri
2018-01-01
The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.
Directory of Open Access Journals (Sweden)
Konstantinos ePriftis
2012-02-01
Full Text Available Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL, an analogical, visuo-spatial representation of number magnitude. The MNL is left-to-right oriented, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in processing the left side of the MNL and show a rightward deviation in the mental bisection of numerical intervals. In the present study we investigated the effects of optokinetic stimulation (OKS -a technique inducing spatial attention shifts by means of activation of the optokinetic nystagmus- on mental number interval bisection. One patient with left neglect following right hemisphere stroke (BG and four control patients with right hemisphere damage, but without neglect, performed the mental number interval bisection task in three experimental conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, but again to the right of the midpoint following rightward OKS. In contrast, the performance of controls was not significantly affected by the direction of OKS. We argue that shifts of visuospatial attention, induced by OKS, may affect the mental number interval bisection, suggesting the presence of an interaction between the processing of number magnitude and the processing of the perceptual space, in patients with neglect for the mental number space.
Priftis, Konstantinos; Pitteri, Marco; Meneghello, Francesca; Umiltà, Carlo; Zorzi, Marco
2012-01-01
Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) – a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus – on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG’s performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the “indifference zone” that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space. PMID:22363280
Rational-number comparison across notation: Fractions, decimals, and whole numbers.
Hurst, Michelle; Cordes, Sara
2016-02-01
Although fractions, decimals, and whole numbers can be used to represent the same rational-number values, it is unclear whether adults conceive of these rational-number magnitudes as lying along the same ordered mental continuum. In the current study, we investigated whether adults' processing of rational-number magnitudes in fraction, decimal, and whole-number notation show systematic ratio-dependent responding characteristic of an integrated mental continuum. Both reaction time (RT) and eye-tracking data from a number-magnitude comparison task revealed ratio-dependent performance when adults compared the relative magnitudes of rational numbers, both within the same notation (e.g., fractions vs. fractions) and across different notations (e.g., fractions vs. decimals), pointing to an integrated mental continuum for rational numbers across notation types. In addition, eye-tracking analyses provided evidence of an implicit whole-number bias when we compared values in fraction notation, and individual differences in this whole-number bias were related to the individual's performance on a fraction arithmetic task. Implications of our results for both cognitive development research and math education are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Estimation of curve number by DAWAST model
Energy Technology Data Exchange (ETDEWEB)
Kim, Tai Cheol; Park, Seung Ki; Moon, Jong Pil [Chungnam National University, Taejon (Korea, Republic of)
1997-10-31
It is one of the most important factors to determine the effective rainfall for estimation of flood hydrograph in design schedule. SCS curve number (CN) method has been frequently used to estimate the effective rainfall of synthesized design flood hydrograph for hydraulic structures. But, it should be cautious to apply SCS-CN originally developed in U.S.A to watersheds in Korea, because characteristics of watersheds in Korea and cropping patterns especially like a paddy land cultivation are quite different from those in USA. New CN method has been introduced. Maximum storage capacity which was herein defined as U{sub max} can be calibrated from the stream flow data and converted to new CN-I of driest condition of soil moisture in the given watershed. Effective rainfall for design flood hydrograph can be estimated by the curve number developed in the watersheds in Korea. (author). 14 refs., 5 tabs., 3 figs.
Optimal Number of Questionnaire Response Categories
Directory of Open Access Journals (Sweden)
W. Paul Jones
2013-05-01
Full Text Available Two multi-instrument investigations in a university clinic/lab provided an opportunity to explore the impact of reducing the number of response alternatives in a scale measuring vocational personality traits. In a simulation study, a standard computer-based administration provided a numeric scale for each item ranging from 0 to 10. The tests were then rescored to simulate the effect of only three choices. For the follow-up study, two versions of the scale were created, one with two response options and the other with six response options, and were randomly assigned to participants. Typical relationships were evident between the vocational personality traits and scores on standard measures of core personality traits with negligible impact from reducing the number of response alternatives. Neither the ability of the participants nor the self-reported distress had a measurable impact on the utility of the results with the reduction in response alternatives.
Bridge Condition Assessment Using D Numbers
Hu, Yong
2014-01-01
Bridge condition assessment is a complex problem influenced by many factors. The uncertain environment increases more its complexity. Due to the uncertainty in the process of assessment, one of the key problems is the representation of assessment results. Though there exists many methods that can deal with uncertain information, however, they have more or less deficiencies. In this paper, a new representation of uncertain information, called D numbers, is presented. It extends the Dempster-Shafer theory. By using D numbers, a new method is developed for the bridge condition assessment. Compared to these existing methods, the proposed method is simpler and more effective. An illustrative case is given to show the effectiveness of the new method. PMID:24696639
Entanglement distillation protocols and number theory
International Nuclear Information System (INIS)
Bombin, H.; Martin-Delgado, M.A.
2005-01-01
We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z D n associated with Bell diagonal states is a module rather than a vector space. We find that a partition of Z D n into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D. When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively
Finite-particle-number approach to physics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1982-10-01
Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10/sup 38/); 3+1 Minkowski space with a discrete metric and the algebraic bound ..delta.. is an element of ..delta.. tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations.
Rational and irrational numbers from unit resistors
International Nuclear Information System (INIS)
Kasperski, Maciej; Kłobus, Waldemar
2014-01-01
We address the problem of constructing a network of unit resistors such that it enables the retrieval of an arbitrary value of equivalent resistance. In particular, we employ the notion of continued fractions to construct a ladder network by which we can easily obtain any fractional value resistance. In addition, since any irrational number is associated with an infinite continued fraction, we discuss the convergence of the equivalent resistance of an infinite resistive ladder and various aspects concerning the approximations of arbitrary numbers attained by adding additional resistors successively to the network. The presented methods can be easily implemented in an educational laboratory and offer an interesting addition to the topic of Ohm’s law. (paper)
Finite-particle-number approach to physics
International Nuclear Information System (INIS)
Noyes, H.P.
1982-10-01
Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10 38 ); 3+1 Minkowski space with a discrete metric and the algebraic bound δ is an element of δ tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations
European Science Notes. Volume 41, Number 7.
1987-07-01
college preparatory that the social constructionist view, as group. (Chances are only slightly better he describes it, offers anything more for the...new method for the recognition and positioning of two-dimensionl objects. The method uses segmented descriptions of the object contours to generate...and recursively evaluate a number of selected hypotheses. This article dis- cusses the method in detail. International Symposium on Simulation of
Baryon number transfer in hadronic interactions
International Nuclear Information System (INIS)
Arakelyan, G.H.; Capella, A.; Kaidalov, A.B.; Shabelski, Yu.M.
2002-01-01
The process of baryon number transfer due to string junction propagation in rapidity space is analyzed. It has a significant effect on the net baryon production in pp collisions at mid-rapidities and an even larger effect in the forward hemisphere in the cases of πp and γp interactions. The results of numerical calculations in the framework of the quark-gluon string model are in reasonable agreement with the data. (orig.)
European Scientific Notes. Volume 37, Number 2,
1983-02-28
potassium persulfate the initiator. ethylene. The method is to immerse the Particle nucleation, flocculation, and films in an aqueous solution of acrylic... polyacrylic acid in the aqueous solu- causing flocculation and coalescence. tion, water soluble inhibitors were The process of aggregation of ...AD-A127 548 EUROPEAN SCIENTIFIC 140TES VOLUME 37 NUMBER 2(U) OFFICE / OF NAVAL RESEARCH LONDON (ERGLAND) V TSTANNET ET AL 28 FER 83 ESN-37-2 UNCLAAS
European Scientific Notes. Volume 34. Number 5,
1980-05-31
of spontaneous and (Al, Nb), have been fabricated. Prop- induced photomagnetic properties; (3) erties of quantum interference for The ’discovery and...conducting quantum interference device) sputter deposition on a number of sub- has a periodic voltage response to an strates (e.g., Go, SiO. thermally...designed and MICROWAVE ANTE POLARIZATION tested. With one of the smaller cryo- DVERSITY AT tINDHOVAN UNIVERSITY stats, magnetic levitation of an "anten
Fermion production despite fermion number conservation
International Nuclear Information System (INIS)
Bock, W.; Hetrick, J.E.; Smit, J.
1995-01-01
Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. Both the sharp momentum cutoff and the lattice regulator break gauge invariance. In the case of the lattice model a mass counterterm for the gauge field is sufficient to restore gauge invariance in the perturbative regime. A study of the vacuum energy shows however that the perturbative counterterm is insufficient in a nonperturbative setting and that further quartic counterterms are needed. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories. ((orig.))
European Scientific Notes. Volume 36, Number 11.
1982-11-30
and polyisocyanides appear to by S. Piccarolo (Univ. of Palermo , Italy) of the be unique in their behavior in solution, thermal expansion of...of solvent down polyethylenes was investigated by D. Curto an activity gradient coupled with time- (Univ. of Palermo , Italy). When the rheo- dependent...ambitious in Paris. Projects are projected to start in program for a number of reasons, which were 1983 in Pakistan, India, Colombia , and Saudi discussed
Predicting Social Security numbers from public data
Acquisti, Alessandro; Gross, Ralph
2009-01-01
Information about an individual's place and date of birth can be exploited to predict his or her Social Security number (SSN). Using only publicly available information, we observed a correlation between individuals' SSNs and their birth data and found that for younger cohorts the correlation allows statistical inference of private SSNs. The inferences are made possible by the public availability of the Social Security Administration's Death Master File and the widespread accessibility of per...
Laser interrogation of latent vehicle registration number
Energy Technology Data Exchange (ETDEWEB)
Russo, R.E. [Lawrence Berkeley Lab., CA (United States). Energy and Environment Div.]|[Lawrence Livermore National Lab., CA (United States). Forensic Science Center; Pelkey, G.E. [City of Livermore Police Dept., CA (United States); Grant, P.; Whipple, R.E.; Andresen, B.D. [Lawrence Livermore National Lab., CA (United States). Forensic Science Center
1994-09-01
A recent investigation involved automobile registration numbers as important evidentiary specimens. In California, as in most states, small, thin metallic decals are issued to owners of vehicles each year as the registration is renewed. The decals are applied directly to the license plate of the vehicle and typically on top of the previous year`s expired decal. To afford some degree of security, the individual registration decals have been designed to tear easily; they cannot be separated from each other, but can be carefully removed intact from the metal license plate by using a razor blade. In September 1993, the City of Livermore Police Department obtained a blue 1993 California decal that had been placed over an orange 1992 decal. The two decals were being investigated as possible evidence in a case involving vehicle registration fraud. To confirm the suspicion and implicate a suspect, the department needed to known the registration number on the bottom (completely covered) 1992 decal. The authors attempted to use intense and directed light to interrogate the colored stickers. Optical illumination using a filtered white-light source partially identified the latent number. However, the most successful technique used a tunable dye laser pumped by a pulsed Nd:YAG laser. By selectively tuning the wavelength and intensity of the dye laser, backlit illumination of the decals permitted visualization of the underlying registration number through the surface of the top sticker. With optimally-tuned wavelength and intensity, 100% accuracy was obtained in identifying the sequence of latent characters. The advantage of optical techniques is their completely nondestructive nature, thus preserving the evidence for further interrogation or courtroom presentation.
Computational foundations of the visual number sense.
Stoianov, Ivilin Peev; Zorzi, Marco
2017-01-01
We provide an emergentist perspective on the computational mechanism underlying numerosity perception, its development, and the role of inhibition, based on our deep neural network model. We argue that the influence of continuous visual properties does not challenge the notion of number sense, but reveals limit conditions for the computation that yields invariance in numerosity perception. Alternative accounts should be formalized in a computational model.
From the Editor Vol: 6 number 2
Ugur Demiray
2005-01-01
From the Editor Dear TOJDES Readers Time flies. Another quarter has begun. It is a great pleasure to welcome you to the 18th issue, the Volume: 6, Number: 2 of The Turkish Online Journal of Distance Education (TOJDE), of looking forward. TOJDE has been driving and shaping by our editorial board, reviewers, authors and even unbelievable readers. In the April 2005 issue, TOJDE publishes peer-reviewed distance education articles under four umbrellas: applications, feature topics, researches, ...
GS Department
2009-01-01
The Green Plates Service, which is responsible for issuing the 431K/CD vehicle number plates , wishes to apologise for the delay in processing applications over the past weeks. The delay is outside the Service’s control, as it is due to the recent introduction of new rules governing the vehicle registration process in France. Normal service will be resumed as soon as possible. Thank you for your understanding. GS-SEM-LS – Green Plates Service
Health care delivery: strength in numbers.
DeVries, R A
1978-03-16
The number and types of multi-institutional arrangements among health care facilities are on the increase, and the days of the completely autonomous, independent hospital are coming to a close. Although by themselves hospital systems are no panacea in dealing with the challenges facing hospitals today, many such arrangements offer more opportunities than problems in coping with the rapid changes currently facing the health care industry. The pros and cons of seven arrangements are discussed in detail.
European Scientific Notes. Volume 36, Number 2,
1982-02-28
noted that the alleged Symptom-limited exercise testing is gen- immunity of marathon runners to coronary erally accepted as an integral part of any...marathon runners out of coronary patients. risk, and the motivation pf both physician and Wenger emphasized that there is no fixed dose patient...never 45 ESN 36-2 (1982) RESCUE KITE The accuracy of addition of columns of 2-digit numbers was significantly worse at In emergencies at sea, detection
Forcing clique immersions through chromatic number
Gauthier, Gregory; Le, Tien-Nam; Wollan, Paul
2017-01-01
Building on recent work of Dvo\\v{r}\\'ak and Yepremyan, we show that every simple graph of minimum degree $7t+7$ contains $K_t$ as an immersion and that every graph with chromatic number at least $3.54t + 4$ contains $K_t$ as an immersion. We also show that every graph on $n$ vertices with no stable set of size three contains $K_{2\\lfloor n/5 \\rfloor}$ as an immersion.
A note on Ramsey numbers for fans
Zhang, Yanbo; Broersma, Haitze J.; Chen, Yaojun
For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. A fan Fl is l triangles sharing exactly one vertex. In this note, it is shown that R(Fn,
Nowcasting sunshine number using logistic modeling
Czech Academy of Sciences Publication Activity Database
Brabec, Marek; Badescu, V.; Paulescu, M.
2013-01-01
Roč. 120, č. 1-2 (2013), s. 61-71 ISSN 0177-7971 R&D Projects: GA MŠk LD12009 Grant - others:European Cooperation in Science and Technology(XE) COST ES1002 Institutional research plan: CEZ:AV0Z1030915 Keywords : logistic regression * Markov model * sunshine number Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.245, year: 2013
European Science Notes. Volume 40, Number 4.
1986-04-01
increase during A representative governing board senescence; this suggests that basal oversees the activities of the Center. gluconeogenesis is...cultures of sensory neurons and they derive from the same number of Schwann cells that reproduce the morpho- cells. These and other results led to logical...bithorax function com- munoreactive neurons in the central pletely. Because of this observation, nervous system of DrosophiZa MeZanogas- Morata et al. have