Sharanya Subramanian; P K Swain; A V Deshpande; P Satyamurthy
2015-05-01
Conventionally, obtaining a converged solution for a MagnetoHydro-Dynamic problem entails a highly resolved Hartmann boundary layer, leading to excessive time and computational requirements. For high Hartmann number flows through electrically conducting channels, majority of the current loops close through the walls and the Hartmann layer contributes only a small fraction of the global current path. Hence, the effect on flow parameters due to coarsening the mesh of the Hartmann Layer was investigated using the ANSYS FLUENT code. Numerical simulations have been carried out in square and rectangular ducts with wall conductance ratio of 0.156 and 0.078 respectively. Magnetic field was varied from 1T to 4T to obtain solution for Hartmann numbers $(Ha = Ba \\sqrt{\\sigma/\\mu})$ in the range of 260–1040 for the square duct, and 520–2080 for the rectangular duct. B, $\\alpha$, $\\mu$, and $\\sigma$ are the strength of applied magnetic field, characteristic length of the channel, dynamic viscosity and electrical conductivity of the fluid respectively. The errors in estimating core and side layer peak velocity and fully developed pressure gradient were found to be low even for a grid system having 46% coarser grid than a well-resolved system. The analysis indicated that for high Hartmann number flows through thick, conducting ducts, coarsening the mesh in the Hartmann boundary layer reduced computational time, not compromising on the solution accuracy and appears to be a promising option for complex geometry MHD simulation.
The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers
Zhang, Lin; Ouyang, Jie; Zhang, Xiaohua
2013-04-01
The aim of the paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics (MHD) flow problems with either fully insulating walls or partially insulating and partially conducting walls. Toward this, we first extend the influence domain of the shape function for the element free Galerkin (EFG) method to have arbitrary shape. When the influence factor approaches 1, we find that the EFG shape function almost has the Delta property at the node (i.e. the value of the EFG shape function of the node is nearly equal to 1 at the position of this node) as well as the property of slices in the influence domain of the node (i.e. the EFG shape function in the influence domain of the node is nearly constructed by different functions defined in different slices). Therefore, for MHD flow problems at high Hartmann numbers we follow the idea of the variational multiscale finite element method (VMFEM) to combine the EFG method with the variational multiscale (VM) method, namely the variational multiscale element free Galerkin (VMEFG) method is proposed. Subsequently, in order to validate the proposed method, we compare the obtained approximate solutions with the exact solutions for some problems where such exact solutions are known. Finally, several benchmark problems of MHD flows are simulated and the numerical results indicate that the VMEFG method is stable at moderate and high values of Hartmann number. Another important feature of this method is that the stabilization parameter has appeared naturally via the solution of the fine scale problem. Meanwhile, because this proposed method is a type of meshless method, it can avoid the need for meshing, a very demanding task for complicated geometry problems.
Effects of Hartmann number on combined convection in a channel with cavity using Cu-water nanofluid
Azad, A. K.; Parvin, Salma; Chowdhury, Md. Mustafa Kamal
2017-06-01
Hartmann number effect on combined convective flow in a horizontal channel with a bottom heated open cavity using nanofluid has been studied numerically. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature Th while the other sides of the cavity along with the channel walls are adiabatic. The physical domain is filled with water based nanofluid containing 4% Cu nano particles. The fluid enters from left with initial velocity Ui and temperature Ti and exits from the right. The physical problems are represented mathematically by different sets of governing two-dimensional equations along with the corresponding boundary conditions. Using a class of appropriate transformations, the governing equations along with the boundary conditions are transformed into a non-dimensional form, which are then solved by employing a finite-element method based on Galerkin weighted residuals. The investigations are conducted for different values of Rayleigh number Ra (= 103 - 106) and Hartmann number Ha (= 0 - 20). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number Nuav, and average fluid temperature θav are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity, whereas in the channel these effects are less significant.
Forghani-Tehrani, Pezhman; Karimipour, Arash; Afrand, Masoud; Mousavi, Sayedali
2017-01-01
Nanofluid flow and heat transfer composed of water-silver nanoparticles is investigated numerically inside a microchannel. Finite volume approach (FVM) is applied and the effects of gravity are ignored. The whole length of Microchannel is considered in three sections as l1=l3=0.151 and l2=0.71. The linear variable heat flux affects the microchannel wall in the length of l2 while a magnetic field with strength of B0 is considered over the whole domain of it. The influences of different values of Hartmann number (Ha=0, 10, 20), volume fraction of the nanoparticles (ɸ=0, 0.02, 0.04) and Reynolds number (Re=10, 50, 200) on the hydrodynamic and thermal properties of flow are reported. The investigation of slip velocity variations under the effects of a magnetic field are presented for the first time (to the best knowledge of author) while the non-dimensional slip coefficient are selected as B=0.01, 0.05, 0.1 at different states.
Laparoscopic reversal of Hartmann's procedure
Svenningsen, Peter Olsen; Bulut, Orhan; Jess, Per
2010-01-01
A change in procedure from open to laparoscopic reversal of Hartmann's colostomy was implemented at our department between May 2005 and December 2008. The aim of the study was to investigate if this change was beneficial for the patients.......A change in procedure from open to laparoscopic reversal of Hartmann's colostomy was implemented at our department between May 2005 and December 2008. The aim of the study was to investigate if this change was beneficial for the patients....
Laparoscopic reversal of Hartmann's procedure
Svenningsen, Peter Olsen; Bulut, Orhan; Jess, Per
2010-01-01
INTRODUCTION: A change in procedure from open to laparoscopic reversal of Hartmann's colostomy was implemented at our department between May 2005 and December 2008. The aim of the study was to investigate if this change was beneficial for the patients. MATERIAL AND METHODS: The medical records...... of all patients who underwent reversal of a colostomy after a primary Hartmann's procedure during the period May 2005 to December 2008 were reviewed retrospectively in a case-control study. RESULTS: A total of 43 patients were included. Twenty-one had a laparoscopic and 22 an open procedure. The two...
Reversal of Hartmann's procedure following acute diverticulitis: is timing everything?
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.
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.
A method for the analysis and data reduction from Hartmann and Shack-Hartmann tests
Gantes Nuñez, Fco. Javier; Malacara Hernández, Zacarías; Malacara Hernández, Daniel
2016-08-01
A computer software is proposed in order to determine the centroids of the spots in a Hartmann pattern or Hartmanngrams. The software was developed using algorithms for segmentation of images, which are techniques used in digital image processing. Centroid determination for a Shack-Hartmann pattern is the key point to obtain reliable results. We focus in obtaining good centroid determination for Hartmanngrams under conditions of high noise. The proposed algorithms are the essential part of this work, as they are morphological algorithms, which mainly are modifications of the weighted averaging algorithm. They have several advantages, such as, the adjustment to the shape of every spot of the Hartmanngram and that it is an interactive and automatic software. Although the software is more complete and reliable than other techniques and algorithms, since it can analyze complicated pictures of Hartmanngrams and measure the centroids of the spots.
João Carlos Simões
2000-08-01
main goal of this work was to demonstrate the progressive and adaptive changes in the proximal and distal colon after diverting terminal colostomy (Hartmann's colostomy. These alterations were studied through histologycal examination and the measuring of hydroxyproline content. Forty adult male Wistar rats, weighing 200 g were divided into two groups of 20 rats each (group I and II . Each group was divided in another two sub-groups (A,B,C and D with ten animals each. The rats of A and B sub-groups (group I were submitted to a median laparotomy to perform Hartmann's colostomy in the distal colon. The animals of the control group were only submitted to a laparotomy. All animals were sacrified on the 30th and 60th postoperative days. Hystological examination demonstrated substantial atrophy of mucosal layer, deteriorations in both crypt size and number, and atrophy of all colonic layers. Other changes included acute and chronic inflammatory infiltrate in the lamina propria .These changes were more intense in distal segments of the animals submitted to Hartmann's colostomy (subgroups A and B . Analysis of the colonic hydroxyproline content were normal in all groups. These findings demonstrated morphologic inflammatory and hypotrophic changes in distal colon after Hartmann's colostomy in rats.
Lavastaja, kes ei vasta ootustele : Sebastian Hartmann Saksamaalt / Eero Epner
Epner, Eero, 1978-
2006-01-01
6. apr. NO99 teatris esietendunud NO92 Andrei Tarkovski ja vendade Strugatskite stsenaariumi järgi loodud filmil põhinevast lavastusest "Stalker", lavastaja Sebastian Hartmann ja kunstnik Peter Schubert (mõlemad Saksamaalt)
Lavastaja, kes ei vasta ootustele : Sebastian Hartmann Saksamaalt / Eero Epner
Epner, Eero, 1978-
2006-01-01
6. apr. NO99 teatris esietendunud NO92 Andrei Tarkovski ja vendade Strugatskite stsenaariumi järgi loodud filmil põhinevast lavastusest "Stalker", lavastaja Sebastian Hartmann ja kunstnik Peter Schubert (mõlemad Saksamaalt)
Hartmann test for the James Webb Space Telescope
Knight, J. Scott; Feinberg, Lee; Howard, Joseph; Acton, D. Scott; Whitman, Tony L.; Smith, Koby
2016-07-01
The James Webb Space Telescope's (JWST) end-to-end optical system will be tested in a cryogenic vacuum environment before launch at NASA Johnson Space Center's (JSC) Apollo-era, historic Chamber A thermal vacuum facility. During recent pre-test runs with a prototype "Pathfinder" telescope, the vibration in this environment was found to be challenging for the baseline test approach, which uses phase retrieval of images created by three sub-apertures of the telescope. To address the vibration, an alternate strategy implemented using classic Hartmann test principles combined with precise mirror mechanisms to provide a testing approach that is insensitive to the dynamics environment of the chamber. The measurements and sensitivities of the Hartmann approach are similar to those using phase retrieval over the original sparse aperture test. The Hartmann test concepts have been implemented on the JWST Test Bed Telescope, which provided the rationale and empirical evidence indicating that this Hartmann style approach would be valuable in supplementing the baseline test approach. This paper presents a Hartmann approach implemented during the recent Pathfinder test along with the test approach that is currently being considered for the full optical system test of JWST. Comparisons are made between the baseline phase retrieval approach and the Hartmann approach in addition to demonstrating how the two test methodologies support each other to reduce risk during the JWST full optical system test.
Hartmann-Shack test with random masks for modal wavefront reconstruction.
Soloviev, Oleg; Vdovin, Gleb
2005-11-14
The paper discusses the influence of the geometry of a Hartmann-(Shack) wavefront sensor on the total error of modal wavefront reconstruction. A mathematical model is proposed, which describes the modal wavefront reconstruction in terms of linear operators. The model covers the most general case and is not limited by the orthogonality of decomposition basis or by the method chosen for decomposition. The total reconstruction error is calculated for any given statistics of the wavefront to be measured. Based on this estimate, the total reconstruction error is calculated for regular and randomised Hartmann masks. The calculations demonstrate that random masks with non-regular Fourier spectra provide absolute minimum error and allow to double the number of decomposition modes.
Shack-Hartmann sensor improvement using optical binning
Basden, Alastair; Guzman, Dani; Morris, Tim; Myers, Richard; Saunter, Chris
2007-01-01
We present a design improvement for a recently proposed type of Shack-Hartmann wavefront sensor that uses a cylindrical (lenticular) lenslet array. The improved sensor design uses optical binning and requires significantly fewer detector pixels than the corresponding conventional or cylindrical Shack-Hartmann sensor, and so detector readout noise causes less signal degradation. Additionally, detector readout time is significantly reduced, which reduces the latency for closed loop systems, and data processing requirements. We provide simple analytical noise considerations and Monte-Carlo simulations, and show that the optically binned Shack-Hartmann sensor can offer better performance than the conventional counterpart in most practical situations, and our design is particularly suited for use with astronomical adaptive optics systems.
Synchronous phase demodulation algorithm for conic carrier Hartmann topographer
Gonzalez, Adonai; Rivera, Mariano; Servin, Manuel; Legarda-Saenz, Ricardo; Dalmau, Oscar; Martinez, Amalia
2015-04-01
In this paper, a theoretical analysis of a new algorithm for measuring phase objects (PO) is presented. The algorithm analyses images captured with a modified Hartmann plate. The proposed method demodulates a signal with a conic-wavefront carrier by using synchronous interferometric techniques. Typically a Hartmann plate is a mask with an array of holes, the proposal is to replace those holes with a series of circular concentric rings created by a conic carrier, named Conic Hartmann plate mask (CHM). The proposed algorithm computes a dense correspondence between the pattern source and its interferogram on the PO. This dense correspondence is computed as the phase change of the refracted waveform with respect to the reference one. This approach is more robust than standard techniques that computes the center of each spot in order to estimate its position; which involves pattern recognition and segmentation tasks, something normal in a typical Hartmann test. We show in this work that the new method overcomes different problems such as irregular background illumination, spots overlapping with pupil border and spots matching due to rapid changes on the surface slopes. This work shows a general procedure for radial derivatives integration based on base functions. As far as the authors know, the here presented demonstration has not been reported before. In particular, we show that Zernike polynomials are suitable for PO. Numerical experiments with real and simulated data demonstrate the algorithm performance.
Reversal of Hartmann's procedure: a high-risk operation?
Schmelzer, Thomas M; Mostafa, Gamal; Norton, H James; Newcomb, William L; Hope, William W; Lincourt, Amy E; Kercher, Kent W; Kuwada, Timothy S; Gersin, Keith S; Heniford, B Todd
2007-10-01
Patients who undergo Hartmann's procedure often do not have their colostomy closed based on the perceived risk of the operation. This study evaluated the outcome of reversal of Hartmann's procedure based on preoperative risk factors. We retrospectively reviewed adult patients who underwent reversal of Hartmann's procedure at our tertiary referral institution. Patient outcomes were compared based on identified risk factors (age >60 years, American Society of Anesthesiologists [ASA] score >2, and >2 preoperative comorbidities). One-hundred thirteen patients were included. Forty-four patients (39%) had an ASA score of >or=3. The mean hospital duration of stay was 6.8 days. There were 28 (25%) postoperative complications and no mortality. Patients >60 years old had significantly longer LOS compared with the rest of the group (P = .02). There were no differences in outcomes between groups based on ASA score or the presence of multiple preoperative comorbidities. An albumin level of <3.5 was the only significant predictor of postoperative complications (P = .04). The reversal of Hartmann's operation appears to be a safe operation with acceptable morbidity rates and can be considered in patients, including those with significant operative risk factors.
Hartmann wavefront sensors and their application at FLASH.
Keitel, Barbara; Plönjes, Elke; Kreis, Svea; Kuhlmann, Marion; Tiedtke, Kai; Mey, Tobias; Schäfer, Bernd; Mann, Klaus
2016-01-01
Different types of Hartmann wavefront sensors are presented which are usable for a variety of applications in the soft X-ray spectral region at FLASH, the free-electron laser (FEL) in Hamburg. As a typical application, online measurements of photon beam parameters during mirror alignment are reported on. A compact Hartmann sensor, operating in the wavelength range from 4 to 38 nm, was used to determine the wavefront quality as well as aberrations of individual FEL pulses during the alignment procedure. Beam characterization and alignment of the focusing optics of the FLASH beamline BL3 were performed with λ(13.5 nm)/116 accuracy for wavefront r.m.s. (w(rms)) repeatability, resulting in a reduction of w(rms) by 33% during alignment.
La idea de una philosophia perennis en nicolai hartmann
2011-01-01
A fines del año pasado murió en Alemania, a la edad de 68 años,Nicolai Hartmann, profesor en la Universidad de Gotinga. La noticianos llego sorpresivamente. De sus manos estábamos viendo salir el sistema filosófico más importante de nuestro tiempo y nunca pensamosque la muerte lo alcanzara en medio de su labor.
Experimental implementation of a fast-response Hartmann sensor
Apollonov, V.V.; Vdovin, G.V.; Kiiko, V.V.; Murav' ev, S.V.; Chetkin, S.A. (Inst. Obshchei Fiziki, Moscow (Russian Federation))
1992-07-01
A fast-response automated Hartmann sensor is presented which describes the wavefront as an expansion in terms of the lowest aberrations. This sensor is capable of detecting tilt vectors of the wavefront with a dimensionality of 38 and a cyclicity of 625 Hz, and of expanding the monitored wavefront using a basis of 19 Zernike polynomials with a wavefront reconstruction frequency of 45 Hz. The possibility of using this sensor for determining the dynamic and statistical characteristics of light beams distorted by a turbulent atmosphere is also discussed. 8 refs.
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.
Increasing the sensitivity of a Shack-Hartmann sensor
Kasper, Markus; Hippler, Stefan; Davies, Ric; Glindemann, Andreas
2016-01-01
The Max-Planck institutes for astronomy (MPIA) and for extraterrestrial physics (MPE) run an adaptive optics (AO) system with a laser guide star at the 3.5 m telescope on Calar Alto, Spain. This system, called ALFA, produces now scientific results and works ex- cellent with natural guide stars (NGS) as faint as 13th magnitude in R-band. The ultimate goal however is to achieve similar performances with the laser guide star (LGS) which is faint and extended. We introduce the Shack-Hartmann wavefront sensor implemented in ALFA and present our efforts in increasing its sensitivity by using advanced centroiding and wavefront reconstruction algorithms.
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
Advanced rectal cancer in a long-term Hartmann's pouch: a forgotten organ revisited.
Al Maksoud, Ahmed Mahmoud Abd El Aziz; Ahmed, Iftikhar
2016-01-28
Hartmann's procedure is widely performed as a first-stage operation in cases of left colon emergencies when a one stage management is judged to be unsafe. Forty per cent of patients with Hartmann's procedure never get their stoma reversed, ending with a permanent stoma. The distal excluded Hartmann's pouch is usually forgotten compared to the proximal functioning colon. A 70-year-old man with Hartmann's procedure carried out previously for complicated diverticular disease presented with bleeding per rectum. Invasive adenocarcinoma was confirmed on histology. Subsequent staging revealed a locally advanced rectal cancer. The tumour progressed despite a course of neoadjuvant chemoradiation. The general condition of the patient deteriorated with development of renal failure. The patient died a few weeks later. By reporting this case, we are revisiting the long forgotten Hartmann's pouch to highlight the potential pathologies in the distal stump and to emphasise that a distal stump should not be forgotten even in asymptomatic patients. 2016 BMJ Publishing Group Ltd.
Life Cycle Management at Brødrene Hartmann A/S - strategy,- organisation and implementation
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......Brdr. Hartmann A/S is an international company with subsidiaries and licensed factories worldwide. Hartmann specializes in packaging made of recycled paper. For several years Hartmann has practised life cycle management in order to improve the environmental profile of the products by minimizing...... the total environmental impacts and resource consumptions throughout the full life cycle of the products, with respect to economy and quality.The concept of life cycle management is implemented in Hartmanns environmental strategy and an organisation to take care of the implementation in the every day...
Anti-aliasing optical method for Shack Hartmann WFSs
Herriot, Glen; Véran, Jean-Pierre
2016-07-01
Measurement errors due to aliasing in a Shack-Hartmann WFS are typically 40% larger in variance than the fitting error of an AO system. On bright stars, aliasing is the dominant error within the control radius of the deformable mirror. Wavefront spatial frequencies beyond the WFS' Nyquist frequency corrupt measurements below this frequency. A common misconception is to think that aliasing primarily affects the higher spatial frequency measurements. But in fact aliasing propagates to the lowest order modes, and corrupts even tip/tilt. There are many examples including the observation that the temporal power spectrum of measured tip/tilt from a WFS does not correspond to Kolmogorov theory. We propose a simple optical modification to a SH WFS (borrowed from the digital video camera industry), and present simulation results showing that the aliasing errors are reduced.
Miniaturized Shack-Hartmann Wavefront-Sensors for Starbugs
Goodwin, Michael; Richards, Samuel; Zheng, Jessica; Lawrence, Jon; Leon-Saval, Sergio; Argyros, Alexander
2014-01-01
The ability to position multiple miniaturized wavefront sensors precisely over large focal surfaces are advantageous to multi-object adaptive optics. The Australian Astronomical Observatory (AAO) has prototyped a compact and lightweight Shack-Hartmann wavefront-sensor that fits into a standard Starbug parallel fibre positioning robot. Each device makes use of a polymer coherent fibre imaging bundle to relay an image produced by a microlens array placed at the telescope focal plane to a re-imaging camera mounted elsewhere. The advantages of the polymer fibre bundle are its high-fill factor, high-throughput, low weight, and relatively low cost. Multiple devices can also be multiplexed to a single low-noise camera for cost efficiencies per wavefront sensor. The use of fibre bundles also opens the possibility of applications such as telescope field acquisition, guiding, and seeing monitors to be positioned by Starbugs. We present the design aspects, simulations and laboratory test results.
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...
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
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
Gode resultater efter Hartmanns operation for cancer recti hos højrisikopatienter
Togsverd-Bo, Morten; Gögenur, Ismail; Harvald, Thomas;
2010-01-01
The purpose of this study was to evaluate the incidence of per- and postoperative complications of low anterior resection and Hartmann's operation (HO) for rectal cancer. The study was performed in a department with a high frequency of HO....
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......, Hinchey grade III. The aim of this study was to compare laparoscopic lavage and Hartmann's procedure with health economic evaluation within the framework of the DILALA (DIverticulitis – LAparoscopic LAvage versus resection (Hartmann's procedure) for acute diverticulitis with peritonitis) trial. Methods......), from inclusion in the trial throughout the patient's expected life. Results: The study included 43 patients who underwent laparoscopic lavage and 40 who had Hartmann's procedure in Denmark and Sweden during 2010–2014. In base-case A, the difference in mean cost per patient between laparoscopic lavage...
Nicolai Hartmann: A bibliographical apostille regarding the translation of his Ethics
Vélez León, Paulo,
2012-01-01
International audience; In this work (1) it is specified the central aspects of the structure and content of Nicolai Hartmann´s monumental oeuvre, recently translated into Spanish, Ethics, and (2) in correspondence with the above, it is summarily indicated the purpose of his ethical approach.; En este trabajo [1] se especifican los aspectos centrales de la estructura y contenido de la monumental obra de Nicolai Hartmann, recientemente traducida al castellano, Ética, y [2] en correspondencia c...
Visual Scanning Hartmann Optical Tester (VSHOT) Uncertainty Analysis (Milestone Report)
Gray, A.; Lewandowski, A.; Wendelin, T.
2010-10-01
In 1997, an uncertainty analysis was conducted of the Video Scanning Hartmann Optical Tester (VSHOT). In 2010, we have completed a new analysis, based primarily on the geometric optics of the system, and it shows sensitivities to various design and operational parameters. We discuss sources of error with measuring devices, instrument calibrations, and operator measurements for a parabolic trough mirror panel test. These help to guide the operator in proper setup, and help end-users to understand the data they are provided. We include both the systematic (bias) and random (precision) errors for VSHOT testing and their contributions to the uncertainty. The contributing factors we considered in this study are: target tilt; target face to laser output distance; instrument vertical offset; laser output angle; distance between the tool and the test piece; camera calibration; and laser scanner. These contributing factors were applied to the calculated slope error, focal length, and test article tilt that are generated by the VSHOT data processing. Results show the estimated 2-sigma uncertainty in slope error for a parabolic trough line scan test to be +/-0.2 milliradians; uncertainty in the focal length is +/- 0.1 mm, and the uncertainty in test article tilt is +/- 0.04 milliradians.
More about tunnelling times and superluminal tunnelling (Hartmann effect)
Olkhovsky, V.S. [Ukrainian Akademy of Sciences, Kiev (Ukraine). Inst. for Nuclear Research]|[INFN-Sezione di Catania (Italy); Recami, E. [Bergamo Univ. (Italy). Facolta` di Ingegneria]|[State Univ. at Campinas, Campinas (Brazil); Raciti, F. [Catania Univ. (Italy); Zaichenko, A. [Ukrainian Akademy of Sciences, Kiev (Ukraine). Inst. for Nuclear Reserch
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 <{tau}{sub Pen}>, <{tau}{sub Ret}>, during tunnelling inside a rectangular potential barrier, for various penetration depths x{sub f}; (ii) putting forth and discussing suitable definitions, besides of the mean values, also of the variances (or dispersions) D{sub {tau}T} and D{sub {tau}R} for the time durations of transmission and reflection processes; (iii) mentioning, moreover, that our definition <{tau}{sub 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.
Measurement of corneal topography through Hartmann-Shack wave-front sensor
Yang, Jinsheng; Rao, Xuejun; Rao, Changhui
2008-12-01
A corneal topography based on Hartmann-Shack Sensor is presented in this paper. In the system, the focus of an objective lens is precisely positioned on cornea's curve center. Wave-front of the reflecting beam can be measured by the Hartmann-Shack sensor which is conjugate to the cornea plane. If the corneal surface is a perfect sphere, wave-front detected by the Hartmann-Shack sensor is a plane. As a result, data measured by Hartmann-Shacks sensor is the deviation between the sphere and the real cornea surface. This paper describes a methodology for designing instrument based on Hartmann-Shack sensor. Then, applying this method, an instrument is developed for accurate measurement of corneal topography. In addition, measuring principle of Hartmann-Shack sensor which determined system parameters is also introduced. Repeatability is demonstrated by a series of data. The instrument was able to accurately measure simulative cornea's reflective aberrations, from which corneal topography and corneal refractive aberrations were derived.
陆法林
2005-01-01
By using the usual method of variable separation, bound states of Klein-Gordon equation with equal Hartmann scalar and vector potentials are solved. Properties of the system relate to three quantum numbers and parameters of Hartmann potential. The normalized angle wave function expressed in terms of the universal associated-Legendre polynomial and the normalized radial wave function expressed in terms of the confluent hypergeometric function are presented. The exacl energy spectrum equations are obtained. Bound states of Klein-Gordon equation for Hydrogen potential are special cases for the Hartmann potential in the Letter.%用分离变量方法讨论了在Hartmann标量势和矢量势相等条件下Klein-Gordon方程的束缚态解.体系的性质与三个量子数及Hartmann势的势参数有关.给出了用广义连带勒让得多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数,获得了精确的束缚态能谱方程.氢原子势是本文Hartmann势的特例.
Auto gain control of EMCCD in Shack-Hartmann wavefront sensor for adaptive optics
Zhu, Zhaoyi; Li, Dayu; Hu, Lifa; Mu, QuanQuan; Cao, Zhaoliang; Wang, Yukun; Wang, Shaoxin; Xuan, Li
2016-12-01
Electron multiplying charge-coupled-device (EMCCD) applied in Shack-Hartmann wavefront sensor (S-H WFS) makes the wavefront sensing more efficient for adaptive optics (AO). However when the brightness of the observed target changes in large ranges in a few minutes, a fixed electron multiplying (EM) gain may not be optimum. Thus an auto-gain-control (AGC) method based on the spots image of the S-H WFS is proposed. The designed control value is the average value of the maximum signals of all the light spots in a frame. It has been demonstrated in the experiments that the control value is sensitive to the change of the target brightness, and is stable in the presence of detecting noises and turbulence influence. The goal value for control is predetermined based on the linear relation of the signal with the EM gain and the number of photons collected in sub-apertures. The conditions of the self-protection of the EMCCD are also considered for the goal value. Simulations and experiments indicate that the proposed control method is efficient, and keeps the sensing in a high SNR which reaches the upper SNR limit when sensing with EMCCD. The self-protection of the EMCCD is avoided during the whole sensing process.
Experiments of two pupil lateral motion tracking algorithms using a Shack-Hartmann sensor
Dai, Xiaolin; Hippler, Stefan; Gendron, Eric
2017-01-01
Pupil stability is one of the factors which limit the performance and operational stability of adaptive optics (AO) systems. This paper analyses two pupil-tracking methods to measure the lateral pupil shift: the first one utilizes the fluxes in all outer edge sub-apertures of a Shack-Hartmann sensor and the second one utilizes the real-time interaction matrix used in an AO system. Experiments with 9×9 Shack-Hartmann sensor are conducted to verify both pupil-tracking algorithms. The results show that both algorithms are effective, after two correction steps, the residual pupil shift is reduced to less than 5% of a Shack-Hartmann sub-aperture.
Patterned turbulence in liquid metal flow: computational reconstruction of the Hartmann experiment.
Krasnov, Dmitry; Thess, André; Boeck, Thomas; Zhao, Yurong; Zikanov, Oleg
2013-02-22
We present results of a numerical analysis of Hartmann's historical experiments on flows of mercury in pipes and ducts under the influence of magnetic fields. The computed critical parameters for the laminar-turbulent transition as well as the friction coefficients are in excellent agreement with Hartmann's data. The simulations provide a first detailed view of the flow structures that are experimentally inaccessible. Novel flow regimes with localized turbulent spots near the sidewalls parallel to the magnetic field and otherwise laminar flow are discovered. We finally suggest how these predictions can be tested in a transparent fluid using optical flow measurement.
Evaluation of a scanning Hartmann device for single point turning applications
Miller, A.C. Jr. [Oak Ridge National Lab., TN (United States); Stuhlinger, T.W. [Talandic Research Corp., Tucson, AZ (United States)
1993-08-01
This paper concerns a new, machine mounted aspheric metrology device designed to measure a broad range of figures without the use of auxiliary optics. A prototype device, based on the classical Hartmann test, called a Hartmann Optical Surface Tester (HOST) was evaluated on a single point diamond turning machines. Design, initial testing, and validation data from reference spheres, and two types of aspheres will be discussed. Results of a simulation model for estimating acceptable alignment errors for the HOST on the diamond turning machine will also be presented. Peak-to-valley measurement uncertainty on the test optics was found to be better than 0.08 {mu}m.
Shakeri, S.M.; Hulsken, B.; Van Vliet, L.J.; Stallinga, S.
2015-01-01
Whole Slide Imaging (WSI) systems are used in the emerging field of digital pathology for capturing high-resolution images of tissue slides at high throughput. We present a technique to measure the optical aberrations of WSI systems using a Shack-Hartmann wavefront sensor as a function of field posi
Large-aperture space optical system testing based on the scanning Hartmann.
Wei, Haisong; Yan, Feng; Chen, Xindong; Zhang, Hao; Cheng, Qiang; Xue, Donglin; Zeng, Xuefeng; Zhang, Xuejun
2017-03-10
Based on the Hartmann testing principle, this paper proposes a novel image quality testing technology which applies to a large-aperture space optical system. Compared with the traditional testing method through a large-aperture collimator, the scanning Hartmann testing technology has great advantages due to its simple structure, low cost, and ability to perform wavefront measurement of an optical system. The basic testing principle of the scanning Hartmann testing technology, data processing method, and simulation process are presented in this paper. Certain simulation results are also given to verify the feasibility of this technology. Furthermore, a measuring system is developed to conduct a wavefront measurement experiment for a 200 mm aperture optical system. The small deviation (6.3%) of root mean square (RMS) between experimental results and interferometric results indicates that the testing system can measure low-order aberration correctly, which means that the scanning Hartmann testing technology has the ability to test the imaging quality of a large-aperture space optical system.
Numerical simulation of flow in Hartmann resonance tube and flow in ultrasonic gas atomizer
无
2007-01-01
The gas flow in the Hartmann resonance tube is numerically investigated by the finite volume method based on the Roe solver. The oscillation of the flow is studied with the presence of a needle actuator set along the nozzle axis. Numerical results agree well with the theoretical and experimental results available. Numerical results indicate that the resonance mode of the resonance tube will switch by means of removing or adding the actuator. The gas flow in the ultrasonic gas atomization (USGA) nozzle is also studied by the same numerical methods. Oscillation caused by the Hartmann resonance tube structure, coupled with a secondary resonator, in the USGA nozzle isinvestigated. Effects of the variation of parameters on the iscillation are studied. The mechanism of the transition of subsonic flow to supersonic flow in the USGA nozzle is also discussed based on numerical results.
Reversal of the Hartmann's procedure: A comparative study of laparoscopic versus open surgery
Melkonian, Ernesto; Heine, Claudio; Contreras, David; Rodriguez, Marcelo; Opazo, Patricio; Silva, Andres; Robles, Ignacio; Rebolledo, Rolando
2017-01-01
BACKGROUND: The Hartmann's operation, although less frequently performed today, is still used when initial colonic anastomosis is too risky in the short term. However, the subsequent procedure to restore gastrointestinal continuity is associated with significant morbidity and mortality. PATIENTS AND METHODS: The review of an institutional review board (IRB)-approved prospectively maintained database provided data on the Hartmann's reversal procedure performed by either laparoscopic or open technique at our institution. The data collected included: demographic data, operative approach, conversion for laparoscopic cases and perioperative morbidity and mortality. RESULTS: Over a 14-year period from January 1997 to August 2011, 74 Hartmann's reversal procedures were performed (laparoscopic surgery—49, open surgery—25). The average age was 55 years for the laparoscopic and 57 years for the open surgery group, respectively. Male patients represent 61% of both groups. There was no significant difference in operative time between the two groups (149 min vs 151 min; P = 0.95), and there was a tendency to lower morbidity (3/49—7.3% vs 4/25—16%; P = 0.24) in the laparoscopic surgery group. In the laparoscopic group, eight patients (16.3%) were converted to open surgery, mostly due to severe adhesions. The length of hospital stay was significantly shorter for the laparoscopic group (5 days vs 7 days; P = 0.44). CONCLUSIONS: The Hartmann's reversal procedure can be safely performed in the majority of the cases using a laparoscopic approach with a low morbidity rate and achieving a shorter hospital stay. PMID:27251820
Phase-sensitive two-dimensional neutron shearing interferometer and Hartmann sensor
Baker, Kevin
2015-12-08
A neutron imaging system detects both the phase shift and absorption of neutrons passing through an object. The neutron imaging system is based on either of two different neutron wavefront sensor techniques: 2-D shearing interferometry and Hartmann wavefront sensing. Both approaches measure an entire two-dimensional neutron complex field, including its amplitude and phase. Each measures the full-field, two-dimensional phase gradients and, concomitantly, the two-dimensional amplitude mapping, requiring only a single measurement.
Reversal of the Hartmann's procedure: A comparative study of laparoscopic versus open surgery
Ernesto Melkonian
2017-01-01
Full Text Available Background: The Hartmann's operation, although less frequently performed today, is still used when initial colonic anastomosis is too risky in the short term. However, the subsequent procedure to restore gastrointestinal continuity is associated with significant morbidity and mortality. Patients and Methods: The review of an institutional review board (IRB-approved prospectively maintained database provided data on the Hartmann's reversal procedure performed by either laparoscopic or open technique at our institution. The data collected included: demographic data, operative approach, conversion for laparoscopic cases and perioperative morbidity and mortality. Results: Over a 14-year period from January 1997 to August 2011, 74 Hartmann's reversal procedures were performed (laparoscopic surgery—49, open surgery—25. The average age was 55 years for the laparoscopic and 57 years for the open surgery group, respectively. Male patients represent 61% of both groups. There was no significant difference in operative time between the two groups (149 min vs 151 min; P = 0.95, and there was a tendency to lower morbidity (3/49—7.3% vs 4/25—16%; P = 0.24 in the laparoscopic surgery group. In the laparoscopic group, eight patients (16.3% were converted to open surgery, mostly due to severe adhesions. The length of hospital stay was significantly shorter for the laparoscopic group (5 days vs 7 days; P = 0.44. Conclusions: The Hartmann's reversal procedure can be safely performed in the majority of the cases using a laparoscopic approach with a low morbidity rate and achieving a shorter hospital stay.
On-axis reverse Hartmann test in aspheric optical surface test with the optical flat calibration
Xia, Zhengzheng; Hui, Mei; Zhao, Zhu; Liu, Ming; Dong, Liquan; Liu, Xiaohua; Kong, Lingqin; Zhao, Yuejin
2016-09-01
The Reverse Hartmann test is developed rapidly, robustly, and accurately in measuring precision aspheric surface. The onaxis design provides better control of the astigmatism in the test. We use an on-axis Hartmann test in reverse to measure the aspheric optical mirrors. In the configuration, the LCD with a light pattern on the screen illuminates to the tested surface, and a 2μm-thick pellicle beam splitter is employed to obtain the coaxial light model. An optical flat with 1/20λ surface precision is used to calibrate the rays which pass through the external pinhole and image at the detector, and the data are processed to obtain the direction vectors of arbitrary reflected rays. The surface gradients are determined by the spatial equations of incident and reflected rays which have been calibrated. The shape of surface is finally reconstructed by Zernike polynomial fitting. The experiments include measuring a 76.2mm off-axis parabolic mirror and a 76.2mm spherical mirror. The experimental results show coaxial reverse Hartmann test system may allow for accurate measurements with uncertainties in the micrometer range using cost-effective equipments.
Plantet, C; Meimon, S; Conan, J-M; Fusco, T
2015-11-01
Exoplanet direct imaging with large ground based telescopes requires eXtreme Adaptive Optics that couples high-order adaptive optics and coronagraphy. A key element of such systems is the high-order wavefront sensor. We study here several high-order wavefront sensing approaches, and more precisely compare their sensitivity to noise. Three techniques are considered: the classical Shack-Hartmann sensor, the pyramid sensor and the recently proposed LIFTed Shack-Hartmann sensor. They are compared in a unified framework based on precise diffractive models and on the Fisher information matrix, which conveys the information present in the data whatever the estimation method. The diagonal elements of the inverse of the Fisher information matrix, which we use as a figure of merit, are similar to noise propagation coefficients. With these diagonal elements, so called "Fisher coefficients", we show that the LIFTed Shack-Hartmann and pyramid sensors outperform the classical Shack-Hartmann sensor. In photon noise regime, the LIFTed Shack-Hartmann and modulated pyramid sensors obtain a similar overall noise propagation. The LIFTed Shack-Hartmann sensor however provides attractive noise properties on high orders.
Boland, Elena; Hsu, Allen; Brand, Marc I; Saclarides, Theodore J
2007-07-01
Reversal of a Hartmann's operation can be a morbid undertaking; successful restoration of intestinal continuity cannot be guaranteed. Between June 2001 and July 2006, 35 Hartmann's reversals were undertaken. There were 19 males (54%). Mean age was 54.7 years (range, 14-82 years). Twenty-one (60%) patients had their Hartmann's for diverticular disease, 7 (20%) for anorectal cancer, 4 (11%) for volvulus, and 3 for miscellaneous reasons. Mean length of stay was 7.7 days (range, 3-16 days); 23 per cent required intensive care for a mean 2.3 days (range, 1-4 days). Blood loss was 470 mL, and mean operative time was 4.28 hours (range, 1-8.3 hours). The mean time interval between the original operation and its reversal was 8.9 months (range, 1.4-55 months). Extensive lysis of adhesions was required in 69 per cent, 40 per cent experienced minor complications (urinary tract infections, ileus, and so on), and 38 per cent had major complications (myocardial infarction, leak, hernias, respiratory failure). There was one death (3%). The operation failed because of intraoperative circumstances in three patients (8%). Ten patients (26%) had stomas at the time of discharge of which 3 were intended to be permanent and 7 were temporary. Of the latter, 3 were successfully closed, 3 are awaiting closure, and 1 had complete anastomotic failure requiring permanent diversion. Total failure rate was 10.3 per cent; contributing factors included prior radiation and ultra-low anastomoses.
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.
Veran; Herriot
2000-08-01
In an adaptive optics system with an undersampled Shack-Hartmann wave-front sensor (WFS), variations in seeing, laser guide star quality, and sodium layer thickness and range distance all combine to vary WFS centroid gain across the pupil during an exposure. While using the minimum of 4 pixels per WFS subaperture improves frame rate and read noise, the WFS centroid gain uncertainty may introduce static aberrations and degrade servo loop phase margin. We present a novel method to estimate and compensate WFS gains of each subaperture individually in real time for both natural and laser guide stars.
X-ray active mirror coupled with a Hartmann wavefront sensor
Idir, Mourad, E-mail: mourad.idir@synchrotron-soleil.f [Synchrotron SOLEIL, L' orme des Merisiers, BP 48, 91 192 Gif sur Yvette (France); Mercere, Pascal [Synchrotron SOLEIL, L' orme des Merisiers, BP 48, 91 192 Gif sur Yvette (France); Modi, Mohammed H. [X-ray Optics Section, Raja Ramanna Centre for Advanced Technology, Indore (India); Dovillaire, Guillaume; Levecq, Xavier; Bucourt, Samuel [Imagine Optic, 18 rue Charles de Gaulle, Orsay 91400 (France); Escolano, Lionel; Sauvageot, Paul [ISP System, ZI de la Herray BP 10047, Vic en Bigorre (France)
2010-05-01
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).
Hazem A. Attia
2006-01-01
Full Text Available The unsteady Hartmann flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel nonconducting porous plates is studied with heat transfer taking the ion slip into consideration. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates, while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the ion slip and the uniform suction and injection on both the velocity and temperature distributions is examined.
Analysis of optimal centroid estimation applied to Shack-Hartmann sensing.
Irwan, R; Lane, R G
1999-11-10
The problem of estimating the centroid of an incoherently imaged point with a CCD array is analyzed. An exact analysis is presented that uses the actual short-exposure function at the CCD instead of the traditional Gaussian approximation. The analysis shows that, for Poisson noise, the centroid variance depends on the CCD size and that truncation effects play a significant part in determining the optimum CCD size. The effects of this on a wave-front reconstruction formed by a Shack-Hartmann sensor are described.
Prandtl number of toroidal plasmas
Itoh, Kimitaka (National Inst. for Fusion Science, Nagoya (Japan)); Itoh, Sanae; Fukuyama, Atsushi; Yagi, Masatoshi; Azumi, Masafumi
1993-12-01
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).
Zhu, Zhaoyi; Mu, Quanquan; Li, Dayu; Yang, Chengliang; Cao, Zhaoliang; Hu, Lifa; Xuan, Li
2016-10-17
The centroid-based Shack-Hartmann wavefront sensor (SHWFS) treats the sampled wavefronts in the sub-apertures as planes, and the slopes of the sub-wavefronts are used to reconstruct the whole pupil wavefront. The problem is that the centroid method may fail to sense the high-order modes for strong turbulences, decreasing the precision of the whole pupil wavefront reconstruction. To solve this problem, we propose a sub-wavefront estimation method for SHWFS based on the focal plane sensing technique, by which more Zernike modes than the two slopes can be sensed in each sub-aperture. In this paper, the effects on the sub-wavefront estimation method of the related parameters, such as the spot size, the phase offset with its set amplitude and the pixels number in each sub-aperture, are analyzed and these parameters are optimized to achieve high efficiency. After the optimization, open-loop measurement is realized. For the sub-wavefront sensing, we achieve a large linearity range of 3.0 rad RMS for Zernike modes Z2 and Z3, and 2.0 rad RMS for Zernike modes Z4 to Z6 when the pixel number does not exceed 8 × 8 in each sub-aperture. The whole pupil wavefront reconstruction with the modified SHWFS is realized to analyze the improvements brought by the optimized sub-wavefront estimation method. Sixty-five Zernike modes can be reconstructed with a modified SHWFS containing only 7 × 7 sub-apertures, which could reconstruct only 35 modes by the centroid method, and the mean RMS errors of the residual phases are less than 0.2 rad2, which is lower than the 0.35 rad2 by the centroid method.
Yong Zhang; Gen-Rong Liu; Yue-Fei Wang; Ye-Ping Li; Ya-Jun Zhang; Liang Zhang; Yi-Zhong Zeng; Jie Zhang
2011-01-01
A telescope with a larger primary mirror can collect much more light and resolve objects much better than one with a smaller mirror,and so the larger version is always pursued by astronomers and astronomical technicians.Instead of using a monolithic primary mirror,more and more large telescopes,which are currently being planned or in construction,have adopted a segmented primary mirror design.Therefore,how to sense and phase such a primary mirror is a key issue for the future of extremely large optical/infrared telescopes.The Dispersed Fringe Sensor (DFS),or Dispersed Hartmann Sensor (DHS),is a non-contact method using broadband point light sources and it can estimate the piston by the two-directional spectrum formed by the transmissive grating's dispersion and lenslet array.Thus it can implement the combination of co-focusing by Shack-Hartmann technology and phasing by dispersed fringe sensing technologies such as the template-mapping method and the Hartmann method.We introduce the successful design,construction and alignment of our dispersed Hartmann sensor together with its design principles and simulations.We also conduct many successful real phasing tests and phasing corrections in the visible waveband using our existing indoor segmented mirror optics platform.Finally,some conclusions are reached based on the test and correction of experimental results.
Prime Microlens Arrays for Hartmann-Shack Sensors: An Economical Fabrication Technology
de Lima Monteiro, D. W.; Akhzar-Mehr, O.; Vdovin, G.
A Hartmann-Shack wavefront sensor consists basically of two elements: a microlens array and a photosensitive detector. This paper presents a technique to fabricate close-packed microlens arrays compliant to the sensor requirements. The method is based on bulk-silicon anisotropic etching and requires a single etch mask. We first etch a micromirror array in a KOH solution and use it later as a mold for the replication of microlens arrays. The elements in the fabricated microlens arrays feature excellent fit to a parabolic mirror surface, 100% optical fill factor, excellent parallelism of the optical axes and very high precision of the array pitch. The uniformity of the focal length of the microlenses is high (in the order of 5%) and the surface roughness — expressed in terms of wavefront — is of the order of 8-13 nm. This technology also enables simple single-mask fabrication of arbitrary aspherical optical surfaces.
Artificial neural networks for centroiding elongated spots in Shack-Hartmann wavefront sensors
Mello, A T; Guzman, D; Guesalaga, A
2014-01-01
The use of Adaptive Optics in Extremely Large Telescopes brings new challenges, one of which is the treatment of Shack-Hartmann Wavefront sensors images. When using this type of sensors in conjunction with laser guide stars for sampling the pupil of telescopes with 30+ m in diameter, it is necessary to compute the centroid of elongated spots, whose elongation angle and aspect ratio are changing across the telescope pupil. Existing techniques such as Matched Filter have been considered as the best technique to compute the centroid of elongated spots, however they are not good at coping with the effect of a variation in the Sodium profile. In this work we propose a new technique using artificial neural networks, which take advantage of the neural network's ability to cope with changing conditions, outperforming existing techniques in this context. We have developed comprehensive simulations to explore this technique and compare it with existing algorithms.
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.
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.
Design, validation and application of an ocular Shack-Hartmann aberrometer
Straub, Jochen
The design and testing of an ocular Shack-Hartmann aberrometer is presented. The aberrometer objectively measures optical aberrations in the human eye in vivo. The sensor was successfully tested for measurements of refractive error (sphere and cylinder) and spherical aberration. Vignetting limits the measurement range of the wavefront to a range of -10 D to +15 D. Large refractive errors and decentration of the measurement induce aberrations in the test wavefront. Analytical tools to correct for these systematic errors were developed. A clinical study was conducted assessing visual performance in 158 eyes of 89 subjects before and after LARK refractive surgery. The main results of the study were that refractive surgery corrects refractive errors very accurately. A slight regression in refraction during the 12 months after surgery was noted. Measurements of ocular aberrations using the Shack-Hartmann aberrometer revealed that refractive surgery introduced large amounts of higher order aberrations, mainly spherical aberration and coma. The amount of aberrations changed significantly during the 12 months wound healing period. The dark adapted pupil diameter of the eye increased significantly during the first 6 months after surgery. The changes in ocular aberrations and pupil diameter were correlated to changes in contrast sensitivity in the human eye. The analysis of corneal topography showed that while the anterior corneal curvature changed due to surgery, we also saw a change in the posterior corneal curvature as a biomechanical response to surgery. A Customized Eye Model was designed and tested based on the clinical measurements. The model used conic surfaces and modeled defocus and spherical aberration. This computer eye model was then used in optical lens design software to calculate an optimal Customized Ablation Pattern for individual eyes.
The effect of Hartmann-Hahn mismatching on polarization inversion spin exchange at the magic angle.
Fu, Riqiang; Tian, Changlin; Kim, Hyeongnam; Smith, Scott A; Cross, Timothy A
2002-12-01
The effect of the Hartmann-Hahn mismatch delta = omega(eff)-omega(1S) during polarization inversion spin exchange at the magic angle (PISEMA) has been investigated, where omega(eff) and omega(1S) represent the amplitudes of the 1H effective spin-locking field at the magic angle and the 15N RF spin-locking field, respectively. During the PISEMA evolution period, the exact Hartmann-Hahn match condition (i.e., delta = 0) yields a maximum dipolar scaling factor of 0.816 for PISEMA experiments, while any mismatch results in two different effective fields for the first and second half of each frequency switched Lee-Goldburg (FSLG) cycle. The mismatch effect on the scaling factor depends strongly on the transition angle from one effective field to the other within each FSLG cycle as well as on the cycle time. At low RF spin-lock amplitudes in which the FSLG cycle time is relatively long, the scaling factor rapidly becomes smaller as omega(1S) becomes greater than omega(eff). On the other hand, when omega(1S) lock amplitudes result in a relatively small variation for the scaling factor. Furthermore, ramped amplitude of the 15N RF spin-lock field in synchronization with the flip-flop of the FSLG sequence minimizes the transition angle between the two effective fields within the FSLG cycle. It is shown experimentally that such a ramped amplitude not only gives rise to the same scaling factor but also results in a narrower dipolar line-width in comparison with the rectangular amplitude.
Rodrigo Gomes da Silva
2010-02-01
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.OBJECTIVE: To study was to investigate the associated morbidity and mortality of the restoration of intestinal continuity after Hartmann's procedure. METHODS: Hospital records of 29 patients undergoing surgery to restoration of intestinal
Ontologie della resistenza: note sul concetto di materia in N. Hartmann e G. Lukács
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.
Baranec, Christoph; Dekany, Richard
2008-10-01
We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented.
Unsteady Hartmann Two-Phase Flow: The Riemann-Sum Approximation Approach
Jha, B. K.; Babila, C. T.; Isa, S.
2016-12-01
We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.
Centroids computation and point spread function analysis for reverse Hartmann test
Zhao, Zhu; Hui, Mei; Liu, Ming; Dong, Liquan; Kong, Linqqin; Zhao, Yuejin
2017-03-01
This paper studies the point spread function (PSF) and centroids computation methods to improve the performance of reverse Hartmann test (RHT) in poor conditions, such as defocus, background noise, etc. In the RHT, we evaluate the PSF in terms of Lommel function and classify it as circle of confusion (CoC) instead of Airy disk. Approximation of a CoC spot with Gaussian or super-Gaussian profile to identify its centroid forms the basis of centroids algorithm. It is also effective for fringe pattern while the segmental fringe is served as a 'spot' with an infinite diameter in one direction. RHT experiments are conducted to test the fitting effects and centroiding performances of the methods with Gaussian and super-Gaussian approximations. The fitting results show that the super-Gaussian obtains more reasonable fitting effects. The super-Gauss orders are only slightly larger than 2 means that the CoC has a similar profile with Airy disk in certain conditions. The results of centroids computation demonstrate that when the signal to noise ratio (SNR) is falling, the centroid computed by super-Gaussian method has a less shift and the shift grows at a slower pace. It implies that the super-Gaussian has a better anti-noise capability in centroid computation.
Shakeri, S. M.; Hulsken, Bas; van Vliet, Lucas J.; Stallinga, Sjoerd
2015-03-01
Whole Slide Imaging (WSI) systems are used in the emerging field of digital pathology for capturing high-resolution images of tissue slides at high throughput. We present a technique to measure the optical aberrations of WSI systems using a Shack-Hartmann wavefront sensor as a function of field position. The resulting full-field aberration maps for the lowest order astigmatism and coma are analyzed using nodal aberration theory. According to this theory two coefficients describe the astigmatism and coma inherent to the optical design and another six coefficients are needed to describe the cumulative effects of all possible misalignments on astigmatism and coma. The nodal aberration theory appears to fit well to the experimental data. We have measured and analyzed the full-field aberration maps for two different objective lens-tube lens assemblies and found that only the optical design related astigmatism coefficient differed substantially between the two cases, but in agreement with expectations. We have also studied full-field aberration maps for intentional decenter and tilt and found that these affect the misalignment coefficient for constant coma (decenter) and the misalignment coefficient for linear astigmatism (tilt), while keeping all other nodal aberration theory coefficients constant.
Iteratively Weighted Centroiding for Shack-Hartmann Wave-Front Sensors
Baker, K L; Moallem, M M
2007-02-28
Several techniques have been used with Shack-Hartmann wavefront sensors to determine the local wave-front gradient across each lenslet. In this article we introduce an iterative weighted technique which is specifically targeted for open-loop applications such as aberrometers and metrology. In this article the iterative centroiding technique is compared to existing techniques such as center-of-mass with thresholding, weighted center-of-gravity, matched filter and cross-correlation. Under conditions of low signal-to-noise ratio, the iterative weighted centroiding algorithm is demonstrated to produce a lower variance in the reconstructed phase than existing techniques. The iteratively weighted algorithm was also compared in closed-loop and demonstrated to have the lowest error variance along with the weighted center-of-gravity, however, the iteratively weighted algorithm removes the bulk of the aberration in roughly half the iterations than the weighted center-of-gravity algorithm. This iterative weighted algorithm is also well suited to applications such as guiding on telescopes.
Vargas, Javier; Gonzalez-Fernandez, Luis; Quiroga, Juan Antonio; Belenguer, Tomas
2010-05-01
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.
Speckle Image Enhancement Using Recorded Shack-Hartmann Wavefront Sensor Data
Lobb, Janos
Even today, when many large telescopes have high performance Adaptive Optics systems, speckle imaging is as important as ever to get useful high-spatial-resolution information about important astronomical objects, particularly in the detection of stellar companions of exoplanet host stars. Any methods that can extend the reach of speckle imaging to objects that are fainter or farther away would be welcome additions to the range of techniques for high-resolution imaging. In the first part of the thesis I describe a method to do a selection of frames of an image stack from an astronomical observation done by speckle imaging, using specific Renyi entropy as a classification, that is, a decision-making tool. With this automatic selection process the signal-to-noise ratio can be improved between 15-20% in some cases, although no method could consistently provide improvement in all cases. Another implication of the study is that, by using entropy as a criterion, a sub-stack of 10 to 40% of the "best" frames in a speckle stack can often demonstrate a signal-to-noise ratio comparable to a full stack, which could minimize computation time of the reconstructed image, making it feasible to compute at the telescope. In the second part of the thesis I describe how the data from a Shack-Hartmann sensor, as an a priori information source, can be used to create a better instantaneous Point-Spread-Function (PSF) that can be used to preprocess speckle data, leading to a scientific image with higher S/N and better detection limits for faint companions. This is of some importance in certain science applications of speckle imaging observations, such as the accurate measurement of the radii of exoplanets.
Colostomia tipo hartmann em ratos: alterações morfológicas e dosagem de hidroxiprolina
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.
Nicolai Hartmann: Una apostilla bio-bibliográfica a propósito de la traducción de su Ética
Paulo Vélez León
2012-06-01
Full Text Available [ES] En este trabajo [1] se especifican los aspectos centrales de la estructura y contenido de la monumental obra de Nicolai Hartmann, recientemente traducida al castellano, Ética, y [2] en correspondencia con lo anterior, se indica sumariamente el propósito de su planteamiento ético. [EN] In this work (1 it is specified the central aspects of the structure and content of Nicolai Hartmann´s monumental oeuvre, recently translated into Spanish, Ethics, and (2 in correspondence with the above, it is summarily indicated the purpose of his ethical approach.
Nicolai Hartmann: Una apostilla bio-bibliográfica a propósito de la traducción de su Ética
2012-01-01
[ES] En este trabajo [1] se especifican los aspectos centrales de la estructura y contenido de la monumental obra de Nicolai Hartmann, recientemente traducida al castellano, Ética, y [2] en correspondencia con lo anterior, se indica sumariamente el propósito de su planteamiento ético. [EN] In this work (1) it is specified the central aspects of the structure and content of Nicolai Hartmann´s monumental oeuvre, recently translated into Spanish, Ethics, and (2) in correspondence with the abo...
Antoshkin, L. V.; Goleneva, N. V.; Lavrinov, V. V.; Lavrinova, L. N.
2014-11-01
The results of the correlation analysis of the effectiveness of the algorithm that computes the cross components of wind speed measurements of the wavefront sensor Shack-Hartmann, depending on the intensity of turbulent distortions of the optical parameters of the sensor, the characteristics of the radiation is presented.
Schlawin, E.; Rieke, M.; Leisenring, J.; Walker, L. M.; Fraine, J.; Kelly, D.; Misselt, K.; Greene, T.; Line, M.; Lewis, N.; Stansberry, J.
2017-01-01
The James Webb Space Telescope (JWST) offers unprecedented sensitivity, stability, and wavelength coverage for transiting exoplanet studies, opening up new avenues for measuring atmospheric abundances, structure, and temperature profiles. Taking full advantage of JWST spectroscopy of planets from 0.6 to 28 μm, however, will require many observations with a combination of the NIRISS, NIRCam, NIRSpec, and MIRI instruments. In this white paper, we discuss a new NIRCam mode (not yet approved or implemented) that can reduce the number of necessary observations to cover the 1.0-5.0 μm wavelength range. Even though NIRCam was designed primarily as an imager, it also includes several grisms for phasing and aligning JWST’s 18 hexagonal mirror segments. NIRCam’s long-wavelength channel includes grisms that cover 2.4-5.0 μm with a resolving power of R = 1200-1550 using two separate configurations. The long-wavelength grisms have already been approved for science operations, including wide field and single object (time series) slitless spectroscopy. We propose a new mode that will simultaneously measure spectra for science targets in the 1.0-2.0 μm range using NIRCam’s short-wavelength channel. This mode, if approved, would take advantage of NIRCam’s Dispersed Hartmann Sensor (DHS), which produces 10 spatially separated spectra per source at R ˜ 300. We discuss the added benefit of the DHS in constraining abundances in exoplanet atmospheres as well as its ability to observe the brightest systems. The DHS essentially comes for free (at no time cost) with any NIRCam long-wavelength grism observation, but the detector integration parameters have to be selected to ensure that the long-wavelength grism observations do not saturate and that JWST data volume downlink constraints are not violated. Combining both of NIRCam’s channels will maximize the science potential of JWST, which is a limited life observatory.
Lobato, L.; Márquez, A.; Lizana, A.; Moreno, I.; Iemmi, C.; Campos, J.
2010-08-01
In this paper, the characterization and the optimization of a parallel aligned (PA) liquid crystal on silicon display (LCoS) has been conducted with the aim to apply it to the generation of a microlenses array in a Shack-Hartmann (SH) sensor. The entire sensor setup has been experimentally implemented from scratch. Results obtained for several aberrated wavefront measurements show the suitability of these devices in this particular application. Due to the well-known dynamic properties of LCoS, these devices allow for an easy choice of the parameters of the SH sensor, i.e. the selection of the suitable focal length and aperture of the microlenses of the array, which will definitely determine the dynamic range and the lateral resolution of the SH sensor.
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
Low, R; Pothérat, A
2015-05-01
We investigate aspects of low-magnetic-Reynolds-number flow between two parallel, perfectly insulating walls in the presence of an imposed magnetic field parallel to the bounding walls. We find a functional basis to describe the flow, well adapted to the problem of finding the attractor dimension and which is also used in subsequent direct numerical simulation of these flows. For given Reynolds and Hartmann numbers, we obtain an upper bound for the dimension of the attractor by means of known bounds on the nonlinear inertial term and this functional basis for the flow. Three distinct flow regimes emerge: a quasi-isotropic three-dimensional (3D) flow, a nonisotropic 3D flow, and a 2D flow. We find the transition curves between these regimes in the space parametrized by Hartmann number Ha and attractor dimension d(att). We find how the attractor dimension scales as a function of Reynolds and Hartmann numbers (Re and Ha) in each regime. We also investigate the thickness of the boundary layer along the bounding wall and find that in all regimes this scales as 1/Re, independently of the value of Ha, unlike Hartmann boundary layers found when the field is normal to the channel. The structure of the set of least dissipative modes is indeed quite different between these two cases but the properties of turbulence far from the walls (smallest scales and number of degrees of freedom) are found to be very similar.
QIAN Shang-Wu; HUANG Bo-Wen; WANG De-Yun; GU Zhi-Yu
2002-01-01
This article shows that in spherical polar coordinates, some noncentral separable potentials have super-symmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator astwo important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in ther and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternativemethod to get the required results.
Zhou, Fan; Hong, Xin; Miller, Donald T.; Thibos, Larry N.; Bradley, Arthur
2004-05-01
A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R^2=0.964 to 0.994). The sag error root mean square (RMS) was small, ranging from 0.1 to 0.17 Âµm for four of the five calibrated surfaces with the fifth at 0.36 Âµm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism (0.65-1.2 Âµm) and appreciable levels of trefoil (0.08-0.47 Âµm), coma (0.14-0.19 Âµm), and spherical aberration (0.18-0.25 Âµm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements.
2011-03-01
during our journey through the rigorous AFIT curriculum . Last, but not least, I would like to thank my wife who sacrificed as much as I did to assure...54 36. Transverse magnification...The optical field of the wavefront is typically represented as a complex number in the plane transverse to propagation with amplitude A and a phase
Ning, Yu; Sun, Quan; Wang, Hongyan; Wu, Wuming; Du, Shaojun; Xu, Xiaojun
2015-05-01
In a high-power laser system, a beam splitter refers to the mirror which locates at the cross point of the path of highpower beam and the weak light section. Because of the thermo-optic effect and elasto-optic effect, a beam splitter deforms under intense laser radiation. This deformation adds extra phase on the incident waves and deliveries inaccurate information to the wavefront sensor. Consequently, the output laser focuses at finite distance and gets divergent when arrives at the target. To settle the above problem, this paper presents a new method for real-time correction of the thermal distortion of beam splitter, based on algorithm of the data fusion of two Shack-Hartmann wavefront sensors (SH-WFS). Different from the traditional AO system, which contains a wavefront sensor, a corrector and a servo controller, two extra Shack-Hartmann wavefront detectors are adopted in our AO system, to detect the transmitted and reflected aberrations of beam splitter mirror. And these aberrations are real-timely delivered to the wavefront sensor. Based on coordinate conversion and data fusion algorithm, it makes the wavefront sensor of AO can "see" the aberrations of splitter mirror by itself. Thus, the servo system controls the corrector to compensate these aberrations correctly. In this paper, the theoretical model of data fusion algorithm is carried out. A closed-loop AO system, which consists of a typical AO system and two extra Shack-Hartmann wavefront detectors, is set up to validate the data fusion algorithm. Experimental results show that, the distortion of a CaF2 beam splitter can be real-time corrected when the AO closedloop control is on. The beam quality factor of output laser decreases from 4 to 1.7 times of diffraction limit.
Goleneva, N. V.; Lavrinov, V. V.; Lavrinova, L. N.
2014-11-01
According to data obtained at atmospheric path, was tested an algorithm for calculating the transverse component of the wind speed by correlation analysis of measurements on the Shack-Hartmann wavefront sensor. The correlation method is based on the hypothesis of "frozen" turbulence. Calculated correlation values are the coefficients of the linear correlation between the displacements of the coordinates of the centroids. To automate the algorithm for calculating the transverse component of the wind speed were created the following programming techniques: the moving average method, the gradient descent method, the method of calculation of derivatives.
Reconstrução de trânsito intestinal após confecção de colostomia à Hartmann
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.
Moore, Lori
Plenoptic cameras and Shack-Hartmann wavefront sensors are lenslet-based optical systems that do not form a conventional image. The addition of a lens array into these systems allows for the aberrations generated by the combination of the object and the optical components located prior to the lens array to be measured or corrected with post-processing. This dissertation provides a ray selection method to determine the rays that pass through each lenslet in a lenslet-based system. This first-order, ray trace method is developed for any lenslet-based system with a well-defined fore optic, where in this dissertation the fore optic is all of the optical components located prior to the lens array. For example, in a plenoptic camera the fore optic is a standard camera lens. Because a lens array at any location after the exit pupil of the fore optic is considered in this analysis, it is applicable to both plenoptic cameras and Shack-Hartmann wavefront sensors. Only a generic, unaberrated fore optic is considered, but this dissertation establishes a framework for considering the effect of an aberrated fore optic in lenslet-based systems. The rays from the fore optic that pass through a lenslet placed at any location after the fore optic are determined. This collection of rays is reduced to three rays that describe the entire lenslet ray set. The lenslet ray set is determined at the object, image, and pupil planes of the fore optic. The consideration of the apertures that define the lenslet ray set for an on-axis lenslet leads to three classes of lenslet-based systems. Vignetting of the lenslet rays is considered for off-axis lenslets. Finally, the lenslet ray set is normalized into terms similar to the field and aperture vector used to describe the aberrated wavefront of the fore optic. The analysis in this dissertation is complementary to other first-order models that have been developed for a specific plenoptic camera layout or Shack-Hartmann wavefront sensor application
李中永; 郭建友
2008-01-01
Under the condition of an equal mixing of vector and scalar potentials, we have solved exactly the Klein Gordon equation in an asymmetrical generalized Hartmann potential. With the boundary conditions of bound states, we have obtained the corresponding energy spectrum via an expression and wave functions in terms of hypergeometric functions.%在标量势和矢量势相等的条件下,严格求解了在广义非对称Hartmann势场中粒子运动的Klein Gordon方程;并利用束缚态边界条件,获得了束缚态能谱表达式和由超几何函数表示出的波函数.
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.
Vorob'ev, Nikolai Nikolaevich
2011-01-01
Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the ""golden section"" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval thinkers to base aesthetic and philosophical principles on the beauty of these figures. Recreational readers as well as students and teacher
Number names and number understanding
Ejersbo, Lisser Rye; Misfeldt, Morten
2014-01-01
through using mathematical names for the numbers such as one-ten-one for 11 and five-ten-six for 56. The project combines the renaming of numbers with supporting the teaching with the new number names. Our hypothesis is that Danish children have more difficulties learning and working with numbers, because...... 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....
2016-11-01
the free electron density in USPL-created plasmas are limited in the number of space-time dimensions that can be measured simultaneously. One...profile, and c) parabolic density profile 2.1 Cylindrical Geometry This geometry is a first -order approximation of that created in the...Free Electron Density in Laser-Produced Plasmas by Anthony R Valenzuela Approved for public release; distribution is
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, ...
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.
Oberkofler, Christian Eugen; Rickenbacher, Andreas; Raptis, Dimitri Aristotle; Lehmann, Kuno; Villiger, Peter; Buchli, Christian; Grieder, Felix; Gelpke, Hans; Decurtins, Marco; Tempia-Caliera, Adrien A; Demartines, Nicolas; Hahnloser, Dieter; Clavien, Pierre-Alain; Breitenstein, Stefan
2012-11-01
To evaluate the outcome after Hartmann's procedure (HP) versus primary anastomosis (PA) with diverting ileostomy for perforated left-sided diverticulitis. The surgical management of left-sided colonic perforation with purulent or fecal peritonitis remains controversial. PA with ileostomy seems to be superior to HP; however, results in the literature are affected by a significant selection bias. No randomized clinical trial has yet compared the 2 procedures. Sixty-two patients with acute left-sided colonic perforation (Hinchey III and IV) from 4 centers were randomized to HP (n = 30) and to PA (with diverting ileostomy, n = 32), with a planned stoma reversal operation after 3 months in both groups. Data were analyzed on an intention-to-treat basis. The primary end point was the overall complication rate. The study was discontinued following an interim analysis that found significant differences of relevant secondary end points as well as a decreasing accrual rate (NCT01233713). Patient demographics were equally distributed in both groups (Hinchey III: 76% vs 75% and Hinchey IV: 24% vs 25%, for HP vs PA, respectively). The overall complication rate for both resection and stoma reversal operations was comparable (80% vs 84%, P = 0.813). Although the outcome after the initial colon resection did not show any significant differences (mortality 13% vs 9% and morbidity 67% vs 75% in HP vs PA), the stoma reversal rate after PA with diverting ileostomy was higher (90% vs 57%, P = 0.005) and serious complications (Grades IIIb-IV: 0% vs 20%, P = 0.046), operating time (73 minutes vs 183 minutes, P < 0.001), hospital stay (6 days vs 9 days, P = 0.016), and lower in-hospital costs (US $16,717 vs US $24,014) were significantly reduced in the PA group. This is the first randomized clinical trial favoring PA with diverting ileostomy over HP in patients with perforated diverticulitis.
无
2004-01-01
THE last digit of my home phone number in Beijing is 4. “So what?” European readers might ask.This was my attitude when I first lived in China; I couldn't understand why Chinese friends were so shocked at my indifference to the number 4. But China brings new discoveries every day, and I have since seen the light. I know now that Chinese people have their own ways of preserving their well being, and that they see avoiding the number 4 as a good way to stay safe.
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...
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
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.
Thelin, John R.
2013-01-01
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
Thelin, John R.
2013-01-01
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
Galbraith, Mary J.
1974-01-01
Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)
刘旭泽; 高贵军
2016-01-01
Here,we experimentally addressed the atomization characteristics of the ultrasonic nozzle,modified with a thin rod inserted through the axis of its Hartmann whistle.The impact of the inserted rod and compressed air-pressure on the key variables,including Sauter mean diameter (SMD),atomization angle and water consumption, was investigated with laser particle size analyzer.The results show that the inserted rod and pressure have a major impact on the spraying characteristics.To be specific,as the pressure increased in a range below 0.5 MPa,SMD dramatically decreased and the atomization angle rapidly increased;and a pressure of 0.5 MPa optimized and stabi-lized the atomization,maximized the atomization angle,and minimized SMD and water consumption.The central rod significantly reduced the droplet size.For example,at a pressure higher than 0.4 MPa,the rod decreased SMD by 3μm,with the smallest droplet being 12 μm.%介绍了一种基于Hartmann哨的超声雾化喷嘴.通过激光粒度分析仪对喷嘴的雾化特性进行了实验研究,分析了不同气压对雾滴索特平均直径(SMD)、雾化角和用水量的影响.对喷嘴加装了中心杆,对比了有无中心杆对于雾滴SMD的影响.研究表明:随着气压的增大,雾滴SMD显著减小,雾化角增大,而气压在0.5 MPa时两者达到极值并趋于稳定;喷嘴加入中心杆,并在气压达到一定值后,雾滴SMD有了明显的减小,最小雾滴SMD可以达到12μm;在气压为0.5 MPa,用水量最少,雾化效果最佳.
Number names and number understanding
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...
刘斯语; 白根柱
2015-01-01
In this paper, we are blending of two straight lines in different planes by using the curve with the form of parameters. Discussing the smoothly blending between two non-coplanar straight lines by the improved Hartmann method. We generalize the Hartmann function on the plane to the space curve. And we have deduced the conditions of smoothly blending the straight lines in different planes among this space curve. On the basis of this . We obtain the parameter equation of this transition curve and present a specific example.%利用参数形式的曲线光滑拼接两条异面直线，讨论了对于给定的两条异面直线可用推广的Hart-mann函数光滑拼接的问题，将平面Hartmann函数曲线推广到空间曲线上，推导出该空间曲线光滑拼接异面直线的拼接条件，在此基础上，得到了过渡曲线的参数方程，并给出了具体实例。
Gilles, L; Ellerbroek, B L
2010-11-01
Real-time turbulence profiling is necessary to tune tomographic wavefront reconstruction algorithms for wide-field adaptive optics (AO) systems on large to extremely large telescopes, and to perform a variety of image post-processing tasks involving point-spread function reconstruction. This paper describes a computationally efficient and accurate numerical technique inspired by the slope detection and ranging (SLODAR) method to perform this task in real time from properly selected Shack-Hartmann wavefront sensor measurements accumulated over a few hundred frames from a pair of laser guide stars, thus eliminating the need for an additional instrument. The algorithm is introduced, followed by a theoretical influence function analysis illustrating its impulse response to high-resolution turbulence profiles. Finally, its performance is assessed in the context of the Thirty Meter Telescope multi-conjugate adaptive optics system via end-to-end wave optics Monte Carlo simulations.
Francisco Sérgio P. Regadas
2000-02-01
Full Text Available O objetivo é apresentar a padronização da técnica operatória e os resultados obtidos com a utilização do acesso videolaparoscópico na reconstituição do trânsito intestinal em pacientes previamente submetidos à operação de Hartmann por causas diversas. Foram analisados prospectivamente 32 pacientes, no período de dezembro de 1991 a junho de 1997, com distribuição semelhante com relação ao sexo e com idade média de 42,4 anos. Todos os pacientes foram submetidos ao mesmo preparo pré-operatório e à mesma técnica cirúrgica. Ocorreram três (9,3% complicações transoperatórias. Uma (3,1 % anastomose mecânica incompleta, necessitando de endossutura manual, uma (3,1 % laceração do reto com o grampeador mecânico e uma (3,1 % lesão da artéria epigástrica direita. Ocorreram ainda três (9,3% conversões, sendo uma (3,1 % devido à laceração do reto com o grampeador mecânico, outra (3.1 % pela invasão tumoral na pelve e outra (3,1 % pela presença de excessivas aderências intraperitoneais. O tempo operatório variou de 30 a 240 minutos, na média de 126,2 minutos (2,1 horas. A evolução clínica pós-operatória foi satisfatória. Nove (31,0% pacientes não referiram dor, enquanto 13 (44,8% a referiram em pequena intensidade, e apenas sete (24,0% queixaram-se de dor com maior intensidade. A dieta líquida via oral foi instituída no período médio de 1,6 dias, e a primeira evacuação ocorreu na média de 3,2 dias de pós-operatório. O período médio de hospitalização foi de 4,7 dias. Ocorreram complicações pós-operatórias em oito (27,5% pacientes. Duas (6,8% infecções da ferida do estoma, dois pacientes (6,8% com dor no ombro direito, uma (3,4% deiscência de anastomose, um (3,4% caso de peritonite por provável contaminação do material cirúrgico, uma coleção líquida pélvica e uma hérnia incisional. Em conclusão, a reconstituição do trânsito intestinal por videolaparoscopia apresentou-se segura
Azimuthal Magnetorotational Instability at low and high magnetic Prandtl numbers
Guseva, A; Willis, A P; Avila, M
2016-01-01
The magnetorotational instability (MRI) is considered to be one of the most powerful sources of turbulence in hydrodynamically stable quasi-Keplerian flows, such as those governing accretion disk flows. Although the linear stability of these flows with applied external magnetic field has been studied for decades, the influence of the instability on the outward angular momentum transport, necessary for the accretion of the disk, is still not well known. In this work we model Keplerian rotation with Taylor-Couette flow and imposed azimuthal magnetic field using both linear and nonlinear approaches. We present scalings of instability with Hartmann and Reynolds numbers via linear analysis and direct numerical simulations (DNS) for the two magnetic Prandtl numbers of $1.4 \\cdot 10^{-6}$ and $1$. Inside of the instability domains modes with different axial wavenumbers dominate, resulting in sub-domains of instabilities, which appear different for each $Pm$. The DNS show the emergence of 1- and 2-frequency spatio-te...
Number of Compositions and Convolved Fibonacci numbers
Janjic, Milan
2010-01-01
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved. We also show that numbers of compositions of a natural number with fixed number of ones appear as coefficients of characteristic polynomial of a Hessenberg matrix which determinant is a Fibonacci number. We derive the explicit...
Number of Compositions and Convolved Fibonacci numbers
Janjic, Milan
2010-01-01
We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved. We also show that numbers of compositions of a natural number with fixed number of ones appear as coefficients of characteristic polynomial of a Hessenberg matrix which determinant is a Fibonacci number. We derive the explicit formula for the number of such compositions, in terms of convolutions of Fibonacci numbers.
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.
On Number of Compositions of Natural Numbers
Janjic, Milan
2010-01-01
We first give a combinatorial interpretation of coefficients of Chebyshev polynomials, which allows us to connect them with compositions of natural numbers. Then we describe a relationship between the number of compositions of a natural number in which a certain number of parts are p-1, and other parts are not less than p with compositions in which all parts are not less than p. Then we find a relationship between principal minors of a type of Hessenberg matrices and compositions of natural numbers.
On Multiplying Negative Numbers.
Crowley, Mary L.; Dunn, Kenneth A.
1985-01-01
Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)
All Square Chiliagonal Numbers
A?iru, Muniru A.
2016-01-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…
Numbers Defy the Law of Large Numbers
Falk, Ruma; Lann, Avital Lavie
2015-01-01
As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…
陈榆升; 薄晓波; 高卫东; 盛卫忠; 张波
2014-01-01
目的：探讨 Hartmann 手术治疗结直肠癌的临床效果。方法：回顾分析2006年6月—2013年12月在复旦大学附属中山医院行 Hartmann 手术的63例结直肠癌患者的临床资料。结果：63例患者均顺利完成手术，其中择期手术50例，急诊手术13例。手术时间平均（170．2±44．0）min，术中失血量平均（93．3±38．8）mL，平均住院天数（16．4±10．6）d。术后30 d 内12例出现并发症，其中切口感染6例，造瘘口感染1例，结肠残端感染1例，心衰1例，肾功能不全1例，黏连性肠梗阻2例。42例患者获得随访，随访时间为8～66个月；14例随访5年以上，其中4例生存5年以上，5年生存率为28．6％。结论：Hart-mann 手术仍是治疗结直肠癌的安全有效的术式，可有效改善患者生存质量，延长患者的生存时间。%Objective:To investigate the clinical efficacy of Hartmann′s procedure on colorectal cancer.Methods:The clinical data of 63 patients with colorectal cancer who underwent Hartmann′s procedure from Jun 2006 to Dec 2013 were retrospectively analyzed.Results:All the 63 patients were successfully performed Hartmann′s procedure,of which 50 cases were elective and 13 cases were emergent.The average duration of operation was 170 min.The average volume of intra-operative blood loss was 90 mL.The average duration of hospital stay was 16 d.Postoperative complications within 30 days occurred in 17 patients,of which 6 cases were surgical infection,1 case was stoma infection,1 case was colon stump infection,1 case was heart failure,1 case was renal insufficiency,2 cases were adhesive ileus.Among the 63 cases,42 patients were followed up for 8 to 66 months. Fourteen cases were followed up for more than five years,of which 4 patients survived more than 5 years,and the 5-year sur-vival rate was 28.6%.Conclusions:Hartmann′s procedure is still a safe and effective surgical procedure in the treatment of
Parameterizing by the Number of Numbers
Fellows, Michael R; Rosamond, Frances A
2010-01-01
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for ILPF to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system descripti...
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.
Schlawin, Everett; Leisenring, Jarron; Greene, Tom; Walker, Lisa May; Fraine, Jonathan; Kelly, Doug; Misselt, Karl; Line, Michael; Stansberry, John; Lewis, Nikole
2016-01-01
The James Webb Space Telescope (JWST) offers unprecedented sensitivity, stability, and wavelength coverage for transiting exoplanet studies, opening up new avenues for measuring atmospheric abundances, structure, and temperature profiles. Taking full advantage of JWST spectroscopy of planets from 0.6um to 28um, however, will require many observations with a combination of the NIRISS, NIRCam, NIRSpec, and MIRI instruments. In this white paper, we discuss a new NIRCam mode (not yet approved or implemented) that can reduce the number of necessary observations to cover the 1.0um to 5.0um wavelength range. Even though NIRCam was designed primarily as an imager, it also includes several grisms for phasing and aligning JWST's 18 hexagonal mirror segments. NIRCam's long-wavelength channel includes grisms that cover 2.4um to 5.0um with a resolving power of R = 1200 - 1550 using two separate configurations. The long-wavelength grisms have already been approved for science operations, including wide field and single obj...
On the number of special numbers
KEVSER AKTAS; M RAM MURTY
2017-06-01
For lack of a better word, a number is called special if it has mutually distinct exponents in its canonical prime factorizaton for all exponents. Let $V (x)$ be the number of special numbers $\\leq x$. We will prove that there is a constant $c$ > 1 such that $V (x) \\sim \\frac{cx}{log x}$. We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.
Smith, David Eugene; Ginsburg, Jekuthiel
Counting, naming numbers, numerals, computation, and fractions are the topics covered in this pamphlet. Number lore and interesting number properties are noted; the derivation of some arithmetic terms is briefly discussed. (DT)
Turbulent magnetic Prandtl numbers obtained with MHD Taylor-Couette flow experiments
Gellert, M
2008-01-01
The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B\\_in = B\\_out has been considered. For high enough Hartmann numbers the toroidal field is always unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability. The axial current which drives the instability is reduced by the electromotive force induced by the instability itself. Numerical simulations are presented to probe this effect as a possibility to measure the turbulent conductivity in a laboratory. It is shown numerically that in a sodium experiment (without rotation) an eddy diffusivity 4 times the molecular diffusivity appears resulting in a potential difference of ~34 mV/m. If the cylinders are rotating then also the eddy viscosity can be measured. Nonlinear simulations of the instability lead to a turbulent magnetic Prandtl number of 2.1 for a molecular magnetic Prandtl number of 0.01. The...
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
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.
Damian Slota; Roman Witula
2009-01-01
The scope of the paper is the definition and discussion of the polynomial generalizations of the {sc Fibonacci} numbers called here $delta$-{sc Fibonacci} numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between $delta$-{sc Fibonacci} numbers and {sc Fibonacci} and {sc Lucas} numbersare proven in this paper.
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
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…
Tan, Shanguang
2007-01-01
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the associative and commutative laws of addition and multiplication. So the classic Complex Number is developed from in complex plane with two dimensions to in complex space with N dimensions and the number system is enlarged also.
Rips, Lance J; Thompson, Samantha
2014-03-01
Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).
Simulation of three-dimensional nonideal MHD flow at low magnetic Reynolds number
LU HaoYu; LEE ChunHian
2009-01-01
A numerical procedure based on a five-wave model associated with non-ideal,low magnetic Reynolds number magnetohydrodynamic(MHD)flows was developed.It is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of flow field.To validate the developed procedure,two different test cases were used which included MHD Rayleigh problem and MHD Hartmann problem.The simulations were performed under the assumption of low magnetic Reynolds number.The simulated results were found to be in good agreement with the closed form analytical solutions deduced in the present study,showing that the present algorithm could simulate engineering MHD flow at low magnetic Reynolds number effectively.In the end,a flow field between a pair of segmented electrodes in a three dimensional MHD channel was simulated using the present algorithm with and without including Hall effects.Without the introduction of Hall effects,no distortion was observed in the current and potential lines.By taking the Hall effects into account,the potential lines distorted and clustered at the upstream and downstream edges of the cathode and anode,respectively.
Jarvis, Frazer
2014-01-01
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...
All square chiliagonal numbers
Aṣiru, Muniru A.
2016-10-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square numbers. The study revealed that the determination of square chiliagonal numbers naturally leads to a generalized Pell equation x2 - Dy2 = N with D = 1996 and N = 9962, and has six fundamental solutions out of which only three yielded integer values for use as indices of chiliagonal numbers. The crossing/independent recurrence relations satisfied by each class of indices of the corresponding chiliagonal numbers and square numbers are obtained. Finally, the generating functions serve as a clothesline to hang up the indices of the corresponding chiliagonal numbers and square numbers for easy display and this was used to obtain the first few sequence of square chiliagonal numbers.
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.......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....
Chen, Shi-Chao
2011-01-01
A natural number $n$ is called {\\it multiperfect} or {\\it$k$-perfect} for integer $k\\ge2$ if $\\sigma(n)=kn$, where $\\sigma(n)$ is the sum of the positive divisors of $n$. In this paper, we establish the structure theorem of odd multiperfect numbers analogous as Euler's theorem on odd perfect numbers. We prove the divisibility of the Euler part of odd multiperfect numbers and characterize the forms of odd perfect numbers $n=\\pi^\\alpha M^2$ such that $\\pi\\equiv\\alpha(\\text{mod}8)$. We also present some examples to show the nonexistence of odd perfect numbers as applications.
Matsumoto, Kohji
2002-01-01
The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function Audience Researchers and graduate students interested in recent development of number theory
Xu, Junyan
2012-01-01
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties of fusible numbers. We suggest some possible approaches to the conjecture, and list further problems in the final chapter.
Landy, David; Silbert, Noah; Goldin, Aleah
2013-01-01
Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…
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…
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
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...
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”....
Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert
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...... 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......, 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”....
Cocos, Mihail
2011-01-01
In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm for the construction of a duet of melodic lines given a sequence of numbers and a mode. We attach the .mus files of the counterpoints obtained by using the sequence of primes and several musical modes.
Quantum Random Number Generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2016-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. We discuss the different technologies in quantum random number generation from the early devices based on radioactive decay to the multipl...
1977-05-09
from one of the Moscow institutes. In childhood he played at hypnosis with his sister and hypnotized her. He studies In the 11th grade at night school...O R M I N G OR G. REPORT NUMBER 7. AUTHOR( s ) 8 C O N T R A C T OR GRANT NUMBER(e) Lev Kolodnyy 9. PERFORMING O R G A N I Z A T I O N NAME AND
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 ...
Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl
2016-01-01
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’.......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...
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
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’....
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
Hyperquarks and generation number
Buchmann, Alfons J
2013-01-01
In a model in which quarks and leptons are built up from two spin 1/2 preons as fundamental entities, a new class of fermionic bound states (hyperquarks) arises. It turns out that these hyperquarks are necessary to fulfill the 't Hooft anomaly constraint, which then links the number of fermionic generations to the number of colors and hypercolors.
Multispecies quantum Hurwitz numbers
Harnad, J
2014-01-01
The construction of hypergeometric 2D Toda $\\tau$-functions as generating functions for quantum Hurwitz numbers is extended here to multispecies families. Both the enumerative geometrical significance of these multispecies quantum Hurwitz numbers as weighted enumerations of branched coverings of the Riemann sphere and their combinatorial significance in terms of weighted paths in the Cayley graph of $S_n$ are derived.
Onstad, Torgeir
1991-01-01
After a brief historical account of Leonardo Pisano Fibonacci, some basic results concerning the Fibonacci numbers are developed and proved, and entertaining examples are described. Connections are made between the Fibonacci numbers and the Golden Ratio, biological nature, and other combinatorics examples. (MDH)
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 riboso...
Kolyada, Sergiy; Rybak, Oleksandr
2013-01-01
We introduce and study the Lyapunov numbers -- quantitative measures of the sensitivity of a dynamical system $(X,f)$ given by a compact metric space $X$ and a continuous map $f:X \\to X$. In particular, we prove that for a minimal topologically weakly mixing system all Lyapunov numbers are the same.
Rugani, Rosa; Sartori, Luisa
2016-01-01
Humans show a remarkable tendency to describe and think of numbers as being placed on a mental number line (MNL), with smaller numbers located on the left and larger ones on the right. Faster responses to small numbers are indeed performed on the left side of space, while responses to large numbers are facilitated on the right side of space (spatial-numerical association of response codes, SNARC effect). This phenomenon is considered the experimental demonstration of the MNL and has been extensively replicated throughout a variety of paradigms. Nevertheless, the majority of previous literature has mainly investigated this effect by means of response times and accuracy, whereas studies considering more subtle and automatic measures such as kinematic parameters are rare (e.g., in a reaching-to-grasp movement, the grip aperture is enlarged in responding to larger numbers than in responding to small numbers). In this brief review we suggest that numerical magnitude can also affect the what and how of action execution (i.e., temporal and spatial components of movement). This evidence could have large implications in the strongly debated issue concerning the effect of experience and culture on the orientation of MNL.
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
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
Morrison, Greg
2010-01-01
We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simple analytically tractable networks, and show the utility of our measure to devise a ratings scheme based on the generalized Erdos number that we deploy on the data from the NetFlix prize, and find a significant improvement in our ratings prediction over a baseline.
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,
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
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
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
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
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
Supersymmetric Displaced Number States
Fredy R. Zypman
2015-06-01
Full Text Available We introduce, generate and study a family of supersymmetric displaced number states (SDNS that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.
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
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...
Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik
2006-01-01
highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers, dependent...
Strawn, Candace A.
1998-01-01
Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)
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.
Quantum random number generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2017-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. This review discusses the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. Randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device-independent generation protocols are also discussed.
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...
Brown, Ezra; Brunson, Cornelius
2008-01-01
Fibonacci's forgotten number is the sexagesimal number 1;22,7,42,33,4,40, which he described in 1225 as an approximation to the real root of x[superscript 3] + 2x[superscript 2] + 10x - 20. In decimal notation, this is 1.36880810785...and it is correct to nine decimal digits. Fibonacci did not reveal his method. How did he do it? There is also a…
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.
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...
Chromosome numbers in Bromeliaceae
Cotias-de-Oliveira Ana Lúcia Pires
2000-01-01
Full Text Available The present study reports chromosome numbers of 17 species of Bromeliaceae, belonging to the genera Encholirium, Bromelia, Orthophytum, Hohenbergia, Billbergia, Neoglaziovia, Aechmea, Cryptanthus and Ananas. Most species present 2n = 50, however, Bromelia laciniosa, Orthophytum burle-marxii and O. maracasense are polyploids with 2n = 150, 2n = 100 and 2n = 150, respectively, while for Cryptanthus bahianus, 2n = 34 + 1-4B. B chromosomes were observed in Bromelia plumieri and Hohenbergia aff. utriculosa. The chromosome number of all species was determined for the first time, except for Billbergia chlorosticta and Cryptanthus bahianus. Our data supports the hypothesis of a basic number of x = 25 for the Bromeliaceae family and decreasing aneuploidy in the genus Cryptanthus.
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Qi, Bing; Zhang, Zhen
2016-06-01
Quantum physics can be exploited to generate true random numbers, which have important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness—coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. On the basis of the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modelling the devices. The second category is self-testing QRNG, in which verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category that provides a tradeoff between the trustworthiness on the device and the random number generation speed.
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
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
2007-12-26
265–275. [7] H. G. Grundman, ‘ Sequences of consecutive Niven numbers’, Fibonacci Quart. 32 (1994), 174–175. [8] D. R. Heath-Brown and S. Konyagin...paper, we define a natural sequence in relation to q-Niven numbers. For a fixed but arbitrary k ∈ N and a base q ≥ 2, one may ask whether or not there...other words, ak is the smallest Niven number whose sum of the digits is a given positive integer k. We denote by ck the companion sequence ck = ak/k
Clette, Frédéric; Vaquero, José M; Cliver, Edward W
2014-01-01
Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (1998a,b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in crucial contemporary studies of the solar dynamo or of the solar forcing on the Earth climate. Recently, new efforts have been undertaken to diagnose and correct flaws and biases affecting both sunspot series, in the framework of a series of dedicated Sunspot Number Workshops. Here, we present a global overview of our current understanding of the sunspot number calibration. While the early part of the sunspot record befor...
Babu, K S; Al-Binni, U; Banerjee, S; Baxter, D V; Berezhiani, Z; Bergevin, M; Bhattacharya, S; Brice, S; Brock, R; Burgess, T W; Castellanos, L; Chattopadhyay, S; Chen, M-C; Church, E; Coppola, C E; Cowen, D F; Cowsik, R; Crabtree, J A; Davoudiasl, H; Dermisek, R; Dolgov, A; Dutta, B; Dvali, G; Ferguson, P; Perez, P Fileviez; Gabriel, T; Gal, A; Gallmeier, F; Ganezer, K S; Gogoladze, I; Golubeva, E S; Graves, V B; Greene, G; Handler, T; Hartfiel, B; Hawari, A; Heilbronn, L; Hill, J; Jaffe, D; Johnson, C; Jung, C K; Kamyshkov, Y; Kerbikov, B; Kopeliovich, B Z; Kopeliovich, V B; Korsch, W; Lachenmaier, T; Langacker, P; Liu, C-Y; Marciano, W J; Mocko, M; Mohapatra, R N; Mokhov, N; Muhrer, G; Mumm, P; Nath, P; Obayashi, Y; Okun, L; Pati, J C; Pattie, R W; Phillips, D G; Quigg, C; Raaf, J L; Raby, S; Ramberg, E; Ray, A; Roy, A; Ruggles, A; Sarkar, U; Saunders, A; Serebrov, A; Shafi, Q; Shimizu, H; Shiozawa, M; Shrock, R; Sikdar, A K; Snow, W M; Soha, A; Spanier, S; Stavenga, G C; Striganov, S; Svoboda, R; Tang, Z; Tavartkiladze, Z; Townsend, L; Tulin, S; Vainshtein, A; Van Kooten, R; Wagner, C E M; Wang, Z; Wehring, B; Wilson, R J; Wise, M; Yokoyama, M; Young, A R
2013-01-01
This report, prepared for the Community Planning Study - Snowmass 2013 - summarizes the theoretical motivations and the experimental efforts to search for baryon number violation, focussing on nucleon decay and neutron-antineutron oscillations. Present and future nucleon decay search experiments using large underground detectors, as well as planned neutron-antineutron oscillation search experiments with free neutron beams are highlighted.
Alladi, Krishnaswami
2008-01-01
Contains chapters on number theory and related topics. This title covers topics that focus on multipartitions, congruences and identities, the formulas of Koshliakov and Guinand in Ramanujan's "Lost Notebook", alternating sign matrices and the Weyl character formulas, theta functions in complex analysis, and elliptic functions
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
Schreuder, M.F.
2012-01-01
A low nephron number is, according to Brenner's hyperfiltration hypothesis, associated with hypertension, glomerular damage and proteinuria, and starts a vicious cycle that ends in renal failure over the long term. Nephron endowment is set during foetal life, and there is no formation of nephrons
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…
Haida Numbers and Calculation.
Cogo, Robert
Experienced traders in furs, blankets, and other goods, the Haidas of the 1700's had a well-developed decimal system for counting and calculating. Their units of linear measure included the foot, yard, and fathom, or six feet. This booklet lists the numbers from 1 to 20 in English and Haida; explains the Haida use of ten, hundred, and thousand…
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.
Jorgensen, C.B.; Suetens, S.; Tyran, J.R.
2011-01-01
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
MacCarron, Pádraig; Dunbar, Robin
2016-01-01
The social brain hypothesis predicts that humans have an average of about 150 relationships at any given time. Within this 150, there are layers of friends of an ego, where the number of friends in a layer increases as the emotional closeness decreases. Here we analyse a mobile phone dataset, firstly, to ascertain whether layers of friends can be identified based on call frequency. We then apply different clustering algorithms to break the call frequency of egos into clusters and compare the number of alters in each cluster with the layer size predicted by the social brain hypothesis. In this dataset we find strong evidence for the existence of a layered structure. The clustering yields results that match well with previous studies for the innermost and outermost layers, but for layers in between we observe large variability.
Marco Ruffino
2001-12-01
Full Text Available In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.Neste artigo discuto a intuição subjacente à definição de n∨meros como conjuntos proposta por Frege e Russell, assim como a crítica de Benacerraf a esta definição. Eu tento mostrar que o argumento de Benacerraf não é tão forte como alguns filósofos o tomaram. Adicionalmente, examino uma alternativa à definição de Frege e Russell proposta por Maddy, e indico algumas dificuldades encontrada pela mesma.
Sierpinski and Carmichael Numbers
2013-01-16
appear. 31 [21] E. M. Matveev, ‘An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers. II,’ Izv. Ross. Akad...Math. Comp. 37 (1981), 587–593. [23] C. Pontreau, ‘A Mordell- Lang plus Bogomolov type result for curves in G2m,’ Monatsh. Math. 157 (2009), 267–281. [24
Rocker, Graeme M; Verma, Jennifer Y; Demmons, Jillian; Mittmann, Nicole
2015-02-06
The 'Number Needed to Treat' (NNT) is a useful measure for estimating the number of patients that would need to receive a therapeutic intervention to avoid one of the adverse events that the treatment is designed to prevent. We explored the possibility of an adaption of NNT to estimate the 'Number Needed to $ave' (NN$) as a new, conceptual systems metric to estimate potential cost-savings to the health system from implementation of a treatment, or in this case, a program. We used the outcomes of the INSPIRED COPD Outreach ProgramTM to calculate that 26 patients would need to complete the program to avoid healthcare expenditures of $100,000, based on hospital bed days avoided. The NN$ does not translate into 'cost savings' per se, but redirection of resource expenditures for other purposes. We propose that the NN$ metric, if further developed, could help to inform system-level resource allocation decisions in a manner similar to the way that the NNT metric helps to inform individual-level treatment decisions.
Generalizations of Euler Numbers and Euler Numbers of Higher Order
LUOQiu-ming; QIFeng
2005-01-01
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
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
Thurston, H A
2007-01-01
The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subseq
Pati, Jogesh C.; Salam, Abdus
We suggest that baryon-number conservation may not be absolute and that an integrally charged quark may disintegrate into two leptons and an antilepton with a coupling strength G Bmp2≲ 10-9. On the other hand, if quarks are much heavier than low-lying hadrons, the decay of a three-quark system like the proton is highly forbidden (proton lifetime ≳ 1028 y). Motivation for these ideas appears to arise within a unified theory of hadrons and leptons and their gauge interactions. We emphasize the consequences of such a possibility for real quark searches.
Neukirch, Jürgen; Wingberg, Kay
2013-01-01
The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramificatio
Quantum random number generator
Stipcevic, M
2006-01-01
We report upon a novel principle for realization of a fast nondeterministic random number generator whose randomness relies on intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent detection by the photoelectric effect. Timing information of detected photons is used to generate binary random digits-bits. The bit extraction method based on restartable clock theoretically eliminates both bias and autocorrelation while reaching efficiency of almost 0.5 bits per random event. A prototype has been built and statistically tested.
Beyond natural numbers: negative number representation in parietal cortex.
Blair, Kristen P; Rosenberg-Lee, Miriam; Tsang, Jessica M; Schwartz, Daniel L; Menon, Vinod
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference 6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation.
Lepton family number violation
Herczeg, P.
1999-03-01
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 {tau}, 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.
Beyond Natural Numbers: Negative Number Representation in Parietal Cortex
Blair, Kristen P.; Rosenberg-Lee, Miriam; Tsang, Jessica M.; Schwartz, Daniel L.; Menon, Vinod
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-relate...
On Fibonacci Numbers Which Are Elliptic Korselt Numbers
2014-11-17
On Fibonacci numbers which are elliptic Korselt numbers Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q...SUBTITLE On Fibonacci Numbers Which Are Elliptic Korselt Numbers 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d
Percents Are Not Natural Numbers
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Series of Reciprocal Triangular Numbers
Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin
2013-01-01
Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.
Axiomatic of Fuzzy Complex Numbers
Angel Garrido
2012-01-01
Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead ...
Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers
Whyte, Jemma Catherine; Bull, Rebecca
2008-01-01
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was…
Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers
Horn, Martin Erik
2007-01-01
The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order. And the question is: are Pauli rabbits killer rabbits?
Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers
Whyte, Jemma Catherine; Bull, Rebecca
2008-01-01
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was…
On Types of Distance Fibonacci Numbers Generated by Number Decompositions
Anetta Szynal-Liana
2014-01-01
Full Text Available We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the number n we give a sequence of identities for them. Moreover, we give matrix generators for distance Fibonacci numbers and their direct formulas.
[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.
Axiomatic of Fuzzy Complex Numbers
Angel Garrido
2012-04-01
Full Text Available Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead to very complicated calculi. Moreover, fuzzy numbers with a simpler shape of membership functions often have more intuitive and more natural interpretations. But not only must we apply the concept and the use of fuzzy sets, and its particular case of fuzzy number, but also the new and interesting mathematical construct designed by Fuzzy Complex Numbers, which is much more than a correlate of Complex Numbers in Mathematical Analysis. The selected perspective attempts here that of advancing through axiomatic descriptions.
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
On Bernoulli Numbers and Stirling Numbers%Bernoulli数与Stirling数
高泽图
2001-01-01
In this paper,using the method of formal power series, we study the Bernoulli numbers and the Stirling numbers,and point out the relation between Bernoulli numbers and Stirling numbers,and obtain several identities of including Bernoulli numbers and Stirling numbers.%应用形式幂级数的方法，研究Bernoulli数与Stirling数，指出它们之间的关系，获得几个包含Bernoulli数和Stirling数的恒等式.
Dettlaff, Magda; Yero, Ismael G
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some Cartesian product, strong product or direct product of two paths.
Dettlaff, Magda; Lemanska, Magdalena; Yero, Ismael G.
2012-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
Number sense as the bridge to number understanding
Ejersbo, Lisser Rye
2016-01-01
In this article, I compare number sense, which is understood as an innate capacity to know about the magnitude and relations of numbers, with number understanding, which is understood as the ability to manipulate the symbolic arithmetic developed in a culture. My research focuses on the question...... of how number sense and number understanding can be used in a synergetic process in learning mathematics. Different research results have shown that consistent training in number sense (K-10) influences mathematical competencies in a positive manner, and that young children aged 5-6 years are able...... to solve symbolic problems that involve the approximate addition and subtraction of large two-digit numbers. Our experiment was conducted in a kindergarten class (age 5-6 years) and in a Grade 2 class (age 7-8 years) with students who had difficulties in number reading and symbolic arithmetic. Keywords...
Natural Number Bias in Operations with Missing Numbers
Christou, Konstantinos P.
2015-01-01
This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…
GRAPHS WHOSE CIRCULAR CLIQUE NUMBER EQUAL THE CLIQUE NUMBER
XU Baogang; ZHOU Xinghe
2005-01-01
The circular clique number of a graph G is the maximum fractional k/d such that Gkd admits a homomorphism to G. In this paper, we give some sufficient conditions for graphs whose circular clique number equal the clique number, we also characterize the K1,3-free graphs and planar graphs with the desired property.
Introducing Number and Arithmetic Concepts with Number Sticks.
Baroody, Arthur J.
1993-01-01
This article compares the relative merits of using Cuisenaire rods (unsegmented, unnumbered, and representing continuous quantities) and number sticks (segmented, numbered, and representing discrete quantities) to introduce number and arithmetic concepts to beginning students or students with learning difficulties or mental disabilities. (DB)
Multiple Bracket Function, Stirling Number, and Lah Number Identities
Coskun, Hasan
2012-01-01
The author has constructed multiple analogues of several families of combinatorial numbers in a recent article, including the bracket symbol, and the Stirling numbers of the first and second kind. In the present paper, a multiple analogue of another sequence, the Lah numbers, is developed, and certain associated identities and significant properties of all these sequences are constructed.
A Relation between Prime Numbers and Twin Prime Numbers
2001-01-01
Every mathematician has been concerned with prime numbers, and has metwith mysterious surprises about them. Besides intuition, using empirical methods has an important role to findrelations between prime numbers. A relation between any prime numberand any twin prime number has been obtained.
The concrete theory of numbers: initial numbers and wonderful properties of numbers repunit
Tarasov, Boris V
2007-01-01
In this work initial numbers and repunit numbers have been studied. All numbers have been considered in a decimal notation. The problem of simplicity of initial numbers has been studied. Interesting properties of numbers repunit are proved: $gcd(R_a, R_b) = R_{gcd(a,b)}$; $R_{ab}/(R_aR_b)$ is an integer only if $gcd(a,b) = 1$, where $a\\geq1$, $b\\geq1$ are integers. Dividers of numbers repunit, are researched by a degree of prime number.
THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS
Ejersbo, Lisser Rye; Misfeldt, Morten
2015-01-01
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...... the regularity or irregularity of number naming affects children’s formation of number concepts and arithmetic performance. We investigate this issue by reviewing relevant literature and undertaking a design research project addressing the specific irregularities of the Danish number names. In this project...
Bell Numbers, Determinants and Series
P K Saikia; Deepak Subedi
2013-05-01
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.
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.
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
The Mental Number Line in Dyscalculia: Impaired Number Sense or Access From Symbolic Numbers?
Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël
2016-03-25
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 physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks (number-to-positionandposition-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.
Simple Remarks on Carmichael Numbers
Uchiyama, Shigenori
An odd composite number n for which an-1 ≡ 1 (mod n) for all integers a coprime to n is called a Carmichael number. This paper shows that some class of Carmichael numbers which have relatively large prime factors can be recognized in deterministic polynomial time under the assumption of the Extended Riemann Hypothesis (ERH). Also some related problems are discussed.
Jue, Brian
2010-01-01
Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)
Fletcher, Rodney
2008-01-01
This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…
Betti Numbers of Gaussian Fields
Park, Changbom; Pranav, Pratyush; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A.
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be
Linear or Exponential Number Lines
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…
Goldbach numbers in short intervals
李红泽
1995-01-01
Suppose B is a sufficiently large positive constant, ε is a sufficiently small positive constant, N is a sufficiently large natural number, and A = N7/81+ε. It is proved that all even numbers in (N, N + A) with O(Alog-BN) exceptions are Goldbach numbers.
Kraaikamp, C.; Hartono, Y.
2002-01-01
In this note Hurwitzian numbers are defined for the nearest integer, and backward continued fraction expansions, and Nakada's $\\alpha$-expansions. It is shown that the set of Hurwitzian numbers for these continued fractions coincides with the classical set of such numbers.
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…
Cognitive representation of negative numbers.
Fischer, Martin H
2003-05-01
To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.
Quantum random number generator using photon-number path entanglement
Kwon, Osung; Cho, Young-Wook; Kim, Yoon-Ho
2010-08-01
We report an experimental implementation of quantum random number generator based on the photon-number-path entangled state. The photon-number-path entangled state is prepared by means of two-photon Hong-Ou-Mandel quantum interference at a beam splitter. The randomness in our scheme is of truly quantum mechanical origin as it comes from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.
Pell Numbers, Pell-Lucas Numbers and Modular Group
Q. Mushtaq; U. Hayat
2007-01-01
We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m≥) of the modular group PSL(2,Z)=(x,y:x2=y3=1),where x:z →-1/z and y :z → -1/z, is a 2×2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell-Lucas number. If g fixes elements of Q(√d), where d is a square-free positive number, on the circuit of the coset diagram, then d ＝ 2 and there are only four pairs of ambiguous numbers on the circuit.
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
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.
Nieder, Andreas
2016-06-01
Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions.
Number Comparison and Number Line Estimation Rely on Different Mechanisms
Delphine Sasanguie
2013-12-01
Full Text Available The performance in comparison and number line estimation is assumed to rely on the same underlying representation, similar to a compressed mental number line that becomes more linear with age. We tested this assumption explicitly by examining the relation between the linear/logarithmic fit in a non-symbolic number line estimation task and the size effect (SE in a non-symbolic comparison task in first-, second-, and third graders. In two experiments, a correlation between the estimation pattern in number line estimation and the SE in comparison was absent. An ANOVA showed no difference between the groups of children with a linear or a logarithmic representation considering their SE in comparison. This suggests that different mechanisms underlie both basic number processing tasks.
Iovane, Gerardo
2007-01-01
In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime candidates are obtained in terms of the first perfect number. The asymptotic behaviour is also considered. We obtain for the first time an explicit relation for generating the full set P of prime numbers smaller than n or equal to n.
Number line representations of fractions
Behr, Merlyn J.; Bright, George W.; Wachsmuth, Ipke; Wagner, Sigrid
1982-01-01
The study explored students' interpretations of representations of fractions on number lines and the effect of instruction on those interpretations. Subjects were five fourth-graders, and instruction was a four-day unit on the use of number lines. A 16-item, multiple-choice pre- and posttest was used along with videotaped interviews. Performance improved except when students had to associate a reduced fraction symbol with an equivalent, unreduced fraction representation on a number line. The ...
Brain representations of negative numbers.
Parnes, Michael; Berger, Andrea; Tzelgov, Joseph
2012-12-01
Participants performed a physical comparison task of pairs of positive and pairs of negative one-digit numbers while their electrophysiological brain activity was measured. The numerical value of the presented digits was either congruent or incongruent with the physical size of the digits. Analysis has shown that the earliest event-related potential (ERP) difference between positive and negative numbers was found in the P300 ERP component peak, where there was an inverse effect of congruity in the negative pairs, compared with the positive ones. This pattern of results supports the idea that natural numbers serve as primitives of the human cognitive system, whereas negative numbers are apparently generated if needed.
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.
MARK SHATTUCK
2016-10-01
In this paper, we consider a two-parameter polynomial generalization, denoted by ${\\mathcal G}_{a,b}(n, k; r)$, of the $r$-Lah numbers which reduces to these recently introduced numbers when $a = b = 1$. We present several identities for ${\\mathcal G}_{a,b}(n, k; r)$ that generalize earlier identities given for the $r$-Lah and $r$-Stirling numbers. We also provide combinatorial proofs of some earlier identities involving the $r$-Lah numbers by defining appropriate sign-changing involutions. Generalizing these arguments yields orthogonality-type relations that are satisfied by ${\\mathcal G}_{a,b}(n, k; r)$.
Compendium of Experimental Cetane Numbers
Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.
2014-08-01
This report is an updated version of the 2004 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 March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This Compendium contains cetane values for 389 pure compounds, including 189 hydrocarbons and 201 oxygenates. More than 250 individual measurements are new to this version of the Compendium. For many compounds, numerous measurements are included, often collected by different researchers using different methods. 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 has been expanded and the data has been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.
Mohamed A. Teamah
2011-12-01
Full Text Available Double-diffusive convective flow in an inclined rectangular enclosure with the shortest sides being insulated and impermeable is investigated numerically. Constant temperatures and concentration are imposed along the longest sides of the enclosure. In addition, a uniform magnetic field is applied in a horizontal direction. Laminar regime is considered under steady state condition. The transport equations for continuity, momentum, energy and species transfer are solved using the finite volume technique. The validity of the numerical code used is ascertained and good agreement was found with published results. The numerical results are reported for the effect of thermal Rayleigh number on the contours of streamline, temperature, and concentration. In addition, results for the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for constant Prandtl number, Pr = 0.7, aspect ratio, A = 2, Lewis number, Le = 2, the buoyancy ratio, N = 1, Hartmann number, Ha = 10 and the dimensionless heat generation, Φ = 1. Computations are carried out for RaT ranging from 103 to 5 * 105 and inclination angle range of 0° ⩽ γ ⩽ 180°.
Wave Packets can Factorize Numbers
Mack, H; Haug, F; Freyberger, M; Schleich, W P; Mack, Holger; Bienert, Marc; Haug, Florian; Freyberger, Matthias; Schleich, Wolfgang P.
2002-01-01
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.
Regular Numbers and Mathematical Worlds
Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P.
2016-01-01
Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…
Betti numbers of Gaussian fields
Park, Changbom; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A
2013-01-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; $\\beta_0$ is the number of connected regions, $\\beta_1$ is the number of circular holes, and $\\beta_2$ is the number of three-dimensional voids. Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. $\\beta_0$ dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). $\\beta_1$ dominates the genus near the median thresholds which measures the topology of negatively curved iso-den...
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.
SICs and Algebraic Number Theory
Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon
2017-08-01
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
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…
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…
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…
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 $
Salman, M.; Broersma, Haitze J.
2004-01-01
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 $
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…
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
Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
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.
Urban aerosol number size distributions
T. Hussein
2004-01-01
Full Text Available Aerosol number size distributions have been measured since 5 May 1997 in Helsinki, Finland. The presented aerosol data represents size distributions within the particle diameter size range 8-400nm during the period from May 1997 to March 2003. The daily, monthly and annual patterns of the aerosol particle number concentrations were investigated. The temporal variation of the particle number concentration showed close correlations with traffic activities. The highest total number concentrations were observed during workdays; especially on Fridays, and the lowest concentrations occurred during weekends; especially Sundays. Seasonally, the highest total number concentrations were observed during winter and spring and lower concentrations were observed during June and July. More than 80% of the number size distributions had three modes: nucleation mode (30nm, Aitken mode (20-100nm and accumulation mode (}$'>90nm. Less than 20% of the number size distributions had either two modes or consisted of more than three modes. Two different measurement sites were used; in the first (Siltavuori, 5.5.1997-5.3.2001, the arithmetic means of the particle number concentrations were 7000cm, 6500cm, and 1000cm respectively for nucleation, Aitken, and accumulation modes. In the second site (Kumpula, 6.3.2001-28.2.2003 they were 5500cm, 4000cm, and 1000cm. The total number concentration in nucleation and Aitken modes were usually significantly higher during workdays than during weekends. The temporal variations in the accumulation mode were less pronounced. The lower concentrations at Kumpula were mainly due to building construction and also the slight overall decreasing trend during these years. During the site changing a period of simultaneous measurements over two weeks were performed showing nice correlation at both sites.
Graspable objects shape number processing
Mariagrazia eRanzini
2011-12-01
Full Text Available The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies has demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances, the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1 or with (Experiment 2 a motor action execution (i.e., participants were asked to hold an object in their hands during the task. The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object-number vs. number-object, object type (graspable vs. ungraspable, object size (small vs. large, and Numerical magnitude (small vs. large were manipulated for each experiment. Experiment 1 showed a facilitation – in terms of quicker responses - for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, however interfering with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects communicate with each other, supporting the view that abstract concepts may be grounded in motor experience.
Numbered nasal discs for waterfowl
Bartonek, J.C.; Dane, C.W.
1964-01-01
Numbered nasal discs were successfully used in studies requiring large numbers of individually marked waterfowl. The procedure for constructing these discs is outlined. Blue-winged teal (Anas discors) with 5/8-inch discs, and canvasback (Aythya valisineria) and redhead (A. americana) with 3/4-inch discs can be individually identified up to 50 and 80 yards, respectively, with a gunstock-mounted, 20-power spotting scope. The particular value of these markers is their durability, the number of combinations possible, and the apparent absence of behavioral or mortality influence among such species as the blue-winged teal.
CHANGE OF NUMBERING IN SWITZERLAND
Telephone Service
2002-01-01
Swiss telephone numbers are changing to ten-digit numbers. This means that the 0-022 area code will have to be used for calls to the Geneva region. From 29 March it will no longer be possible to make local calls without the 022 code. There will be no change in the procedure for dialling other destinations from CERN, including Zurich. Don't forget to change the numbers stored in your various memories (fax, telephone, modem, etc.). Please contact the switchboard (111) for any further information. Telephone Service IT/CS/TEL
CHANGE OF NUMBERING IN SWITZERLAND
Telephone Service
2002-01-01
Swiss telephone numbers are changing to ten-digit numbers. This means that the 0-022 area code will have to be used for calls to the Geneva region. From 29 March it will no longer be possible to make local calls without the 022 code. There will be no change in the procedure for dialling other destinations from CERN, including Zürich. Don't forget to change the numbers stored in your various memories (fax, telephone), and modems for ACB users. Please contact the switchboard (111) for any further information. Telephone Service IT/CS/TEL
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.
Fibonacci Numbers and the Spreadsheet.
Verderber, Nadine L.
1991-01-01
Described is a classroom activity incorporating a computer spreadsheet to study number patterns generated by the Fibonacci sequence. Included are examples and suggestions for the use of the spreadsheet in other recursive relationships. (JJK)
Spectral numbers in Floer theories
Usher, Michael
2007-01-01
The chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as the infimum of the filtration levels of chains representing that class. These spectral numbers have been studied extensively in the case of Hamiltonian Floer homology by Oh, Schwarz, and others. We prove that the spectral number associated to any nonzero Floer homology class is always finite, and that the infimum in the definition of the spectral number is always attained. In the Hamiltonian case, this implies that what is known as the "nondegenerate spectrality" axiom holds on all closed symplectic manifolds. Our proofs are entirely algebraic and rather elementary, and apply to any Floer-type theory (including Novikov homology) satisfying certain standard formal properties provided that one works with coefficients in a Novikov ring whose degree-zero part \\Lambda_0 is a field. The key ingredient is a theorem about linear transforma...
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...
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.
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.
Social Security Number (SSN) Verification
U.S. Department of Health & Human Services — This report presents the results of a validation study of Social Security numbers (SSNs) in Medicaid Statistical Information System (MSIS) records for the fourth...
Euclid's Number-Theoretical Work
Zhang, Shaohua
2009-01-01
The object of this paper is to affirm the number-theoretical role of Euclid and the historical significance of Euclid's algorithm. We give a brief introduction about Euclid's number-theoretical work. Our study is the first to show that Euclid's algorithm is essentially equivalent with Division algorithm which is the basis of Theory of Divisibility. Note also that Euclid's algorithm implies Euclid's first theorem and Euclid's second theorem. Thus, in the nature of things, Euclid's algorithm is the most important number-theoretical work of Euclid. For this reason, we further summarize briefly the influence of Euclid's algorithm. It leads to the conclusion that Euclid's algorithm is the greatest number-theoretical achievement of the age.
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 ...
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...
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.
Boolean complexes and boolean numbers
Tenner, Bridget Eileen
2017-01-01
International audience; The Bruhat order gives a poset structure to any Coxeter group. The ideal of elements in this poset having boolean principal order ideals forms a simplicial poset. This simplicial poset defines the boolean complex for the group. In a Coxeter system of rank n, we show that the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres. The number of these spheres is the boolean number, which can be computed inductively from the unlabeled Coxeter syste...
Urban aerosol number size distributions
T. Hussein
2003-10-01
Full Text Available Aerosol number size distributions were measured continuously in Helsinki, Finland from 5 May 1997 to 28 February 2003. The daily, monthly and annual patterns were investigated. The temporal variation of the particle number concentration was seen to follow the traffic density. The highest total particle number concentrations were usually observed during workdays; especially on Fridays, and the lower concentrations occurred during weekends; especially Sundays. Seasonally, the highest total number concentrations were usually observed during winter and spring and the lowest during June and July. More than 80\\% of the particle number size distributions were tri-modal: nucleation mode (Dp < 30 nm, Aitken mode (20–100 nm and accumulation mode (Dp > 90 nm. Less than 20% of the particle number size distributions have either two modes or consisted of more than three modes. Two different measurement sites are used; in the first place (Siltavuori, 5 May 1997–5 March 2001, the overall means of the integrated particle number concentrations were 7100 cm^{−3}, 6320 cm^{−3}, and 960 cm^{−3}, respectively, for nucleation, Aitken, and accumulation modes. In the second site (Kumpula, 6 March 2001–28 February 2003 they were 5670 cm^{−3}, 4050 cm^{−3}, and 900 cm^{−3}. The total number concentration in nucleation and Aitken modes were usually significantly higher during weekdays than during weekends. The variations in accumulation mode were less pronounced. The smaller concentrations in Kumpula were mainly due to building construction and also slight overall decreasing trend during these years. During the site changing a period of simultaneous measurements over two weeks were performed showing nice correlation in both sites.
Numbers for reducible cubic scrolls
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
Shi, Yicheng; Chng, Brenda; Kurtsiefer, Christian
2016-07-01
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.
Entropy estimation and Fibonacci numbers
Timofeev, Evgeniy A.; Kaltchenko, Alexei
2013-05-01
We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.
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
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.
Number matters: control of mammalian mitochondrial DNA copy number.
Clay Montier, Laura L; Deng, Janice J; Bai, Yidong
2009-03-01
Regulation of mitochondrial biogenesis is essential for proper cellular functioning. Mitochondrial DNA (mtDNA) depletion and the resulting mitochondrial malfunction have been implicated in cancer, neurodegeneration, diabetes, aging, and many other human diseases. Although it is known that the dynamics of the mammalian mitochondrial genome are not linked with that of the nuclear genome, very little is known about the mechanism of mtDNA propagation. Nevertheless, our understanding of the mode of mtDNA replication has advanced in recent years, though not without some controversies. This review summarizes our current knowledge of mtDNA copy number control in mammalian cells, while focusing on both mtDNA replication and turnover. Although mtDNA copy number is seemingly in excess, we reason that mtDNA copy number control is an important aspect of mitochondrial genetics and biogenesis and is essential for normal cellular function.
Conversion of Number Systems using Xilinx.
Chinmay V. Deshpande
2015-08-01
Full Text Available There are different types of number systems. Binary number system, octal number system, decimal number system and hexadecimal number system. This paper demonstrates conversion of hexadecimal to binary number using Xilinx software.
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.
Transport numbers in transdermal iontophoresis.
Mudry, Blaise; Guy, Richard H; Delgado-Charro, M Begoña
2006-04-15
Parameters determining ionic transport numbers in transdermal iontophoresis have been characterized. The transport number of an ion (its ability to carry charge) is key to its iontophoretic delivery or extraction across the skin. Using small inorganic ions, the roles of molar fraction and mobility of the co- and counterions present have been demonstrated. A direct, constant current was applied across mammalian skin in vitro. Cations were anodally delivered from either simple M(+)Cl(-) solutions (single-ion case, M(+) = sodium, lithium, ammonium, potassium), or binary and quaternary mixtures thereof. Transport numbers were deduced from ion fluxes. In the single-ion case, maximum cationic fluxes directly related to the corresponding ionic aqueous mobilities were found. Addition of co-ions decreased the transport numbers of all cations relative to the single-ion case, the degree of effect depending upon the molar fraction and mobility of the species involved. With chloride as the principal counterion competing to carry current across the skin (the in vivo situation), a maximum limit on the single or collective cation transport number was 0.6-0.8. Overall, these results demonstrate how current flowing across the skin during transdermal iontophoresis is distributed between competing ions, and establish simple rules with which to optimize transdermal iontophoretic transport.
Hurwitz numbers and BKP hierarchy
Natanzon, S M
2015-01-01
We consider special series in ratios of the Schur functions which are defined by integers $\\textsc{f}\\ge 0$ and $\\textsc{e} \\le 2$, and also by the set of $3k$ parameters $n_i,q_i,t_i,\\,i=1,..., k$. These series may be presented in form of matrix integrals. In case $k=0$ these series generates Hurwitz numbers for the $d$-fold branched covering of connected surfaces with a given Euler characteristic $\\textsc{e}$ and arbitrary profiles at $\\textsc{f}$ ramification points. If $k>0$ they generate weighted sums of the Hurwitz numbers with additional ramification points which are distributed between color groups indexed by $i=1,...,k$, the weights being written in terms of parameters $n_i,q_i,t_i$. By specifying the parameters we get sums of all Hurwitz numbers with $\\textsc{f}$ arbitrary fixed profiles and the additional profiles provided the following condition: both, the sum of profile lengths and the number of ramification points in each color group are given numbers. In case $\\textsc{e}=\\textsc{f}=1,2$ the ser...
Quasiperpendicular high Mach number Shocks
Sulaiman, A H; Dougherty, M K; Burgess, D; Fujimoto, M; Hospodarsky, G B
2015-01-01
Shock waves exist throughout the universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasi-perpendicular shocks across two orders of magnitude in Alfven Mach number (MA) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted timescale of ~0.3 {\\tau}c, where {\\tau}c is the ion gyroperio...
Schellekens, A N
2016-01-01
This paper contains some personal reflections on several computational contributions to what is now known as the "String Theory Landscape". It consists of two parts. The first part concerns the origin of big numbers, and especially the number $10^{1500}$ that appeared in work on the covariant lattice construction (with W. Lerche and D. Luest). This part contains some new results. I correct a huge but inconsequential error, discuss some more accurate estimates, and compare with the counting for free fermion constructions. In particular I prove that the latter only provide an exponentially small fraction of all even self-dual lattices for large lattice dimensions. The second part of the paper concerns dealing with big numbers, and contains some lessons learned from various vacuum scanning projects.
Covering Numbers for Convex Functions
Guntuboyina, Adityanand
2012-01-01
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\\epsilon$-covering number of $\\C([a, b]^d, B)$, in the $L_p$-metric, $1 \\le p 0$, and $\\C([a,b]^d, B)$ denotes the set of all convex functions on $[a, b]^d$ that are uniformly bounded by $B$. We summarize previously known results on covering numbers for convex functions and also provide alternate proofs of some known results. Our results have direct implications in the study of rates of convergence of empirical minimization procedures as well as optimal convergence rates in the numerous convexity constrained function estimation problems.
Negative numbers in simple arithmetic.
Das, Runa; LeFevre, Jo-Anne; Penner-Wilger, Marcie
2010-10-01
Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N = 66) solved standard addition and subtraction problems such as 3 + 4 and 7 - 4 and recasted versions that included explicit negative signs-that is, 3 - (-4), 7 + (-4), and (-4) + 7. Solution times on the recasted problems were slower than those on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problem. Problem size effects were the same or smaller in recasted than in standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.
Put numbers on the sustainability
Hauschild, Michael Zwicky
2014-01-01
exposure of humans, to the local impacts associated with physical transformation of land and extraction of water. Chemicals can cause toxic impacts to humans and ecosystems on all scales. All these impacts need to be quantified if we want to put numbers on sustainability. The life cycle perspective...... on products and systems and the coverage of all relevant environmental impacts are combined in Life cycle assessment (LCA) which is introduced in the talk as the tool to put numbers on environmental sustainability. The basics of LCA are introduced, current applications are presented and a discussion of its...
Newborn infants perceive abstract numbers.
Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S; Streri, Arlette
2009-06-23
Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.
Geometric Number Systems and Spinors
Sobczyk, Garret
2015-01-01
The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The resulting geometric (Clifford) algebra provides a geometric basis for the famous Pauli matrices which, in turn, proves the consistency of the rules of geometric algebra. The flexibility of the concept of geometric numbers opens the door to new understanding of the nature of space-time, and of Pauli and Dirac spinors as points on the Riemann sphere, including Lorentz boosts.
Elementary Number Theory with Applications
Koshy, Thomas
2007-01-01
This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the t
Magic Numbers in Protein Structures
Lindgård, Per-Anker; Bohr, Henrik
1996-01-01
A homology measure for protein fold classes has been constructed by locally projecting consecutive secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multipla of these ......A homology measure for protein fold classes has been constructed by locally projecting consecutive secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multipla...
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
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, M.; Price, C.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 ca...
Surrena, Michelle
2011-01-01
In order to inspire her students to work in mixed media, the author chose to highlight the art of Jasper Johns and Robert Indiana, both of whom used numbers and letters as a main focus in their art. In this article, the author describes a mixed-media printmaking project. (Contains 2 online resources.)
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…
Lenstra theorem in number fields
S Subburam
2014-11-01
In this paper, we present a number field version of the celebrated result of Lenstra (Math. Comp. 42(165) (1984) 331–340) in 1984. Also, this result allows us to improve a result of Wikstrőm (On the -ary GCD-algorithm in rings of integers (2005) pp. 1189–1201).
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...
Questioning Zero and Negative Numbers
Wilcox, Virginia B.
2008-01-01
After experiencing a Developing Mathematical Ideas (DMI) class on the construction of algebraic concepts surrounding zero and negative numbers, the author conducted an interview with a first grader to determine the youngster's existing level of understanding about these topics. Uncovering young students' existing understanding can provide focus…
On badly approximable complex numbers
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...
A generalized sense of number.
Arrighi, Roberto; Togoli, Irene; Burr, David C
2014-12-22
Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.
Covering Numbers for Semicontinuous Functions
2016-04-29
di Matematica pura ed applicata, CLX:303–320, 1991. [3] H. Attouch and R. J-B Wets. A convergence theory for saddle functions. Transactions of the...P. L. Bartlett, J. Shawe-Taylor, and R. C. Williamson. Covering numbers for support vector machines. IEEE Transactions on Information Theory, 48(1
Learning Potentials in Number Blocks
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....
On badly approximable complex numbers
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...
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 discriminant. T
Learning Potentials in Number Blocks
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...
On Fixing number of Functigraphs
Fazil, Muhammad; Javaid, Imran; Murtaza, Muhammad
2016-01-01
The fixing number of a graph $G$ is the order of the smallest subset $S$ of its vertex set $V(G)$ such that stabilizer of $S$ in $G$, $\\Gamma_{S}(G)$ is trivial. Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$, and let $g:V(G_{1})\\rightarrow V(G_{2})$ be a function. A functigraph $F_{G}$ consists of the vertex set $V(G_{1})\\cup V(G_{2})$ and the edge set $E(G_{1})\\cup E(G_{2})\\cup \\{uv:v=g(u)\\}$. In this paper, we study the behavior of the fixing number in passing from $G$ to $F_{G}...
Ufnarovski, Victor; Ahlander, Bo
2003-09-01
We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach's Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.
Bansal, N.; Pendavingh, R.; Pol, J.G. van der
2013-01-01
We consider the problem of determining mn, the number of matroids on n elements. The best known lower bound on mn is due to Knuth (1974) who showed that log log mn is at least n− 3 2 log n−O(1). On the other hand, Piﬀ (1973) showed that log log mn ≤ n − log n + log log n + O(1), and it has been conj
Complex numbers in quantum theory
Maynard, Glenn
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function." This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. (Abstract shortened by ProQuest.).
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.
Brody, T. A.
1984-11-01
A new class of random-number generators is described, based on a combination of the logical exclusive-or operation and the McLaren-Marsaglia mechanism. It is suitable for any word length, requires no multiple-precision arithmetic, and contains no hard-to-determine constants. Though no theory is available, numerical tests have shown it to be very satisfactory. Execution time is less than twice that of standard congruential generators.
Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-03-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.
Quasiperpendicular High Mach Number Shocks
Sulaiman, A. H.; Masters, A.; Dougherty, M. K.; Burgess, D.; Fujimoto, M.; Hospodarsky, G. B.
2015-09-01
Shock waves exist throughout the Universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this Letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasiperpendicular shocks across 2 orders of magnitude in Alfvén Mach number (MA ) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted time scale of ˜0.3 τc , where τc is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and MA and focus on the magnetic structure of such shocks to further show that for the same MA , a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.
A Pseudo-Random Number Generator Based on Normal Numbers
Bailey, David H.
2004-12-31
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.
Video Scanning Hartmann Optical Tester (VSHOT) Uncertainty Analysis: Preprint
Lewandowski, A.; Gray, A.
2010-10-01
This purely analytical work is based primarily on the geometric optics of the system and shows sensitivities to various design and operational parameters. We discuss sources of error with measuring devices, instrument calibrations, and operator measurements for a parabolic trough test. In this paper, we include both the random (precision) and systematic (bias) errors for VSHOT testing and their contributions to the uncertainty. The contributing factors that we considered in this study are target tilt, target face to laser output distance, instrument vertical offset, scanner tilt, distance between the tool and the test piece, camera calibration, and scanner/calibration.
Shack-Hartmann and Interferometric Hybrid Wavefront Sensor
2011-03-24
abstract.cfm?URI=josaa-11-7-2080. 171 24. Flatté, Stanley M. and James S. Gerber . “Irradiance-variance behavior by numerical simulation for plane-wave...www.opticsinfobase.org/abstract.cfm?URI=URI=FiO-2008-FMF2. 23. Flatté, Stanley M., Charles Bracher, and Guang-Yu Wang. “Probability- density functions of...josaa-17-6-1092. 25. Flatté, Stanley M., Guang-Yu Wang, and Jan Martin. “Irradiance variance of optical waves through atmospheric turbulence by
Psychological empowerment in a recruitment company / Suzette Hartmann
Hartmann, Suzette
2003-01-01
People are without a doubt our most important asset. It is imperative that companies develop their people to unleash their full potential, which will in turn be a benefit to the company. The future of successful, competitive companies will depend on the work force of that company. The context that organisations operate within has undergone a change from a hierarchical structure to one of building of human capital. This means that organisations need leadership as a vehicle to ensure successful...
Number Theory, Analysis and Geometry
Goldfeld, Dorian; Jones, Peter
2012-01-01
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th
Number & operations task & drill sheets
Reed, Nat
2011-01-01
For grades 6-8, our State Standards-based combined resource meets the number & operations concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are problems involving place value, fractions, addition, subtraction and using money. The combined task & drill sheets offer spac
Topological Number of Edge States
Hashimoto, Koji
2016-01-01
We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analogue of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a non-commutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.
Propulsion at low Reynolds number
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.
Random number generators and causality
Larrondo, H.A. [Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata (Argentina)]. E-mail: larrondo@fi.mdp.edu.ar; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: mtmartin@venus.unlp.edu.ar; Gonzalez, C.M. [Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata (Argentina)]. E-mail: cmgonzal@fi.mdp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: plastino@venus.unlp.edu.ar; Rosso, O.A. [Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)]. E-mail: oarosso@fibertel.com.ar
2006-04-03
We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.
Random number generators and causality
Larrondo, H. A.; Martín, M. T.; González, C. M.; Plastino, A.; Rosso, O. A.
2006-04-01
We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.
Nielsen number and differential equations
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.
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 ...
The MIXMAX random number generator
Savvidy, Konstantin G
2014-01-01
In this note, we give a practical solution to the problem of determining the maximal period of matrix generators of pseudo-random numbers which are based on an integer-valued unimodular matrix of size NxN known as MIXMAX and arithmetic defined on a Galois field GF[p] with large prime modulus p. The existing theory of Galois finite fields is adapted to the present case, and necessary and sufficient condition to attain the maximum period is formulated. Three efficient algorithms are presented. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute the characteristic polynomial with O(N^2) operations, and third, to apply skips of large number of steps S to the sequence in O(N^2 log(S)) operations. It is demonstrated that the dynamical properties of this generator dramatically improve with the size of the matrix N, as compared to the classes of generators based on sparse matrices and/or sparse characteristic polynomials. Finally, we present the impl...
Formation number for vortex dipoles
Sadri, Vahid; Krueger, Paul S.
2016-11-01
This investigation considers the axisymmetric formation of two opposite sign concentric vortex rings from jet ejection between concentric cylinders. This arrangement is similar to planar flow in that the vortex rings will travel together when the gap between the cylinders is small, similar to a vortex dipole, but it has the advantage that the vortex motion is less constrained than the planar case (vortex stretching and vortex line curvature is allowed). The flow was simulated numerically at a jet Reynolds number of 1,000 (based on ΔR and the jet velocity), jet pulse length-to-gap ratio (L / ΔR) in the range 10-20, and gap-to-outer radius ratio (ΔR /Ro) in the range 0.01-0.1. Small gap ratios were chosen for comparison with 2D results. In contrast with 2D results, the closely paired vortices in this study exhibited pinch-off from the generating flow and finite formation numbers. The more complex flow evolution afforded by the axisymmetric model and its influence on the pinch-off process will be discussed. This material is based on work supported by the National Science Foundation under Grant No. 1133876 and SMU. This supports are gratefully acknowledged.
Banner prints social security numbers
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 ...
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. ...
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...
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...
Nielsen number and differential equations
Jan Andres
2005-06-01
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 PoincarÃƒÂ©'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 RÃŽÂ´-structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Generalized Compositions and Weighted Fibonacci Numbers
Janjic, Milan
2010-01-01
In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted $r$-generalized Fibonacci number. A relationship between these two numbers will be derived. We shall thus obtain a generalization of the well-known formula connecting Fibonacci numbers with the binomial coefficients.
Access to emergency number services.
Harkins, Judith E; Strauss, Karen Peltz
2008-01-01
Access to emergency services is mandated by Title II of the Americans with Disabilities Act (ADA). The Department of Justice oversees the accessibility of public safety answering points (PSAPs), popularly called 9-1-1 centers. The Federal Communications Commission (FCC) has at least two roles in emergency number access: (1) as regulator of the ADA's Title IV on telecommunications access, and (2) as regulator of communications companies with regard to support of and interconnection with PSAPs. The rules of both agencies contributed significantly to the improvement during the 1990s of access to 9-1-1 for people who are deaf, hard of hearing, or speech disabled. However, as new technologies for text wireless communications and relay services have moved quickly to Internet protocol (IP)-based technologies over the past 5-8 years, the use of traditional wireline telephones and text telephones among deaf, hard of hearing, and speech-disabled people has declined. PSAPs cannot be contacted via the newer forms of telecommunications, such as e-mail, instant messaging, and IP-based forms of relay services, including video relay services. The gap between the technology supported by policy and the technologies currently being used by deaf and hard of hearing people has become a serious problem that is difficult to solve because of the separate jurisdictions of the two agencies, the need for coordination within the FCC, technological challenges, and funding issues. In this article, the key policy and technology challenges will be analyzed and recommendations made for short-and long-term solutions to this dilemma.
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.
Arithmetic Algorithms for Hereditarily Binary Natural Numbers
Tarau, Paul
2013-01-01
We study some essential arithmetic properties of a new tree-based number representation, {\\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant numbers like the largest known prime number and its related perfect number as well as the largest known Woodall, Cullen, Proth, Sophie Germain and twin primes as trees of small sizes. More importantly, our number representation supports novel algorithms that...
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
46 CFR Sec. 2 - Voyage numbers.
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Voyage numbers. Sec. 2 Section 2 Shipping MARITIME ADMINISTRATION, DEPARTMENT OF TRANSPORTATION A-NATIONAL SHIPPING AUTHORITY VOYAGE DATA Sec. 2 Voyage numbers. (a... designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change...
Some relations between entropy and approximation numbers
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.
Using Quasigroups for Generating Pseudorandom Numbers
Godavarty, Vinod Kumar
2011-01-01
This paper presents an algorithm for generating pseudorandom numbers using quasigroups. Random numbers have several applications in the area of secure communication. The proposed algorithm uses a matrix of size n x n which is pre-generated and stored. The quality of random numbers generated is compared with other pseudorandom number generator using Marsaglia's Diehard battery of tests.
Mental number space in three dimensions.
Winter, Bodo; Matlock, Teenie; Shaki, Samuel; Fischer, Martin H
2015-10-01
A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated.
A proof of image Euler Number formula
LIN Xiaozhu; SHA Yun; JI Junwei; WANG Yanmin
2006-01-01
Euler Number is one of the most important characteristics in topology. In two- dimension digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved in this paper. It is a new idea to locally compute Euler Number of 2D image.
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
The Bessel Numbers and Bessel Matrices
Sheng Liang YANG; Zhan Ke QIAO
2011-01-01
In this paper,using exponential Riordan arrays,we investigate the Bessel numbers and Bessel matrices.By exploring links between the Bessel matrices,the Stirling matrices and the degenerate Stirling matrices,we show that the Bessel numbers are special case of the degenerate Stirling numbers,and derive explicit formulas for the Bessel numbers in terms of the Stirling numbers and binomial coefficients.
The relational nature of rational numbers
Bruce Brown
2015-06-01
Full Text Available It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of many conceptual properties of the rational number field. Research on rational number learning is divided as to whether children’s difficulties in learning rational numbers arise only from the increased complexity or also include elements of conceptual change. This article argues for a fundamental conceptual difference between whole and rational numbers. It develops the position that rational numbers are fundamentally relational in nature and that the move from absolute counts to relative comparisons leads to a further level of abstraction in our understanding of number and quantity. The argument is based on a number of qualitative, in-depth research projects with children and adults. These research projects indicated the importance of such a relational understanding in both the learning and teaching of rational numbers, as well as in adult representations of rational numbers on the number line. Acknowledgement of such a conceptual change could have important consequences for the teaching and learning of rational numbers.
New families of special numbers for computing negative order Euler numbers
Simsek, Yilmaz
2016-01-01
The main purpose of this paper is to construct new families of special numbers with their generating functions. These numbers are related to the many well-known numbers, which are the Bernoulli numbers, the Fibonacci numbers, the Lucas numbers, the Stirling numbers of the second kind and the central factorial numbers. Our other inspiration of this paper is related to the Golombek's problem \\cite{golombek} \\textquotedblleft Aufgabe 1088, El. Math. 49 (1994) 126-127\\textquotedblright . Our firs...
The Translated Dowling Polynomials and Numbers.
Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S
2014-01-01
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.
A determinant of generalized Fibonacci numbers
Krattenthaler, Christian
2012-01-01
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for Fibonacci numbers.
Negative numbers are generated in the mind.
Ganor-Stern, Dana; Tzelgov, Joseph
2008-01-01
The goal of the present study was to disentangle two possible representations of negative numbers--the holistic representation, where absolute magnitude is integrated with polarity; and the components representation, where absolute magnitude is stored separately from polarity. Participants' performance was examined in two tasks involving numbers from--100 to 100. In the numerical comparison task, participants had to decide which number of a pair was numerically larger/smaller. In the number line task, participants were presented with a spatial number line on which they had to place a number. The results of both tasks support the components representation of negative numbers. The findings suggest that processing of negative numbers does not involve retrieval of their meaning from memory, but rather the integration of the polarity sign with the digits' magnitudes.
The Concept and Operations of Blind Number
PANG Yan-jun; LIU Kai-di; ZHANG Bo-wen
2001-01-01
This paper gives the definition and operations of blind number, and discusses its operationproperties. Blind number is a mathematical tool to express and deal with complex information with severalkinds of uncertainty.
Quantity Cognition: Numbers, Numerosity, Zero and Mathematics.
Harvey, Ben M
2016-05-23
Physical quantities differ from abstract numbers and mathematics, but recent results are revealing the neural representation of both: a new study demonstrates how an absence of quantity is transformed into a representation of zero as a number.
What Do Numbers Do in Transnational Governance?
Krause Hansen, Hans; Porter, Tony
2012-01-01
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...... of numbers and their role in governance. On this basis, we set out the main distinctive ways that numbers are implicated in transnational governance. We conclude that studies of transnational governance would benefit from paying more attention to the much overlooked performative role of numbers in governance...... 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...
The occurrence of prime numbers revisited
Ernesto Tapia Moore; José Tapia Yañez
2016-01-01
Based on an arithmetical and autocatalytic approach, the authors propose a solution for the occurrence of prime numbers. Exact arithmetical calculations are provided for: the closest prime to any given positive integer (or any number of bigger or smaller primes from that integer); the quantity of prime (and composite) numbers between 1 and any positive integer; the quantity of prime (and composite) numbers between any two positive integers.
The occurrence of prime numbers revisited
Ernesto Tapia Moore
2016-03-01
Full Text Available Based on an arithmetical and autocatalytic approach, the authors propose a solution for the occurrence of prime numbers. Exact arithmetical calculations are provided for: the closest prime to any given positive integer (or any number of bigger or smaller primes from that integer; the quantity of prime (and composite numbers between 1 and any positive integer; the quantity of prime (and composite numbers between any two positive integers.
A new definition of Bejan number
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.
Caspar Wessel on representing complex numbers (1799)
Branner, Bodil
1999-01-01
In celebration of the bicentenary of the publication of Wessel's paper on the geometric interpretation of complex numbers it is decsribed how Wessel used complex numbers to represent directions in surveying, at least as early as 1787.......In celebration of the bicentenary of the publication of Wessel's paper on the geometric interpretation of complex numbers it is decsribed how Wessel used complex numbers to represent directions in surveying, at least as early as 1787....
Some inequalities for the Bell numbers
FENG QI
2017-09-01
In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers.
Relativistic theory of tidal Love numbers
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 neut...
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,...
The numbering of Sarawak Forest Department collections
Ashton, P.S.
1966-01-01
Taxonomists working with material collected by the Sarawak Forest Department have often been hard put to decide how to quote numbers. Is the departmental series number preceeded by a letter S, or an F, or would it be best to quote only the collector and the number? I have tried to unravel the histor
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false File numbers. 1.1405 Section 1.1405... Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and...
75 FR 18572 - Facility Control Numbers
2010-04-12
... Internal Revenue Service Facility Control Numbers AGENCY: Internal Revenue Service (IRS), Treasury. ACTION: Notice of planned use of Facility Control Numbers. SUMMARY: The IRS has developed and is publishing in this issue of the Federal Register, Facility Control Numbers to communicate to the motor fuel...
20 CFR 404.1220 - Identification numbers.
2010-04-01
... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that...
2010-07-01
... 32 National Defense 6 2010-07-01 2010-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Developmental Changes in the Whole Number Bias
Braithwaite, David W.; Siegler, Robert S.
2017-01-01
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 integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…
Combinatorial Interpretation of General Eulerian Numbers
Tingyao Xiong
2014-01-01
Full Text Available Since the 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,….
General Eulerian Numbers and Eulerian Polynomials
Tingyao Xiong
2013-01-01
Full Text Available We will generalize the definitions of Eulerian numbers and Eulerian polynomials to general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.
Fascinating Fibonaccis: Mystery and Magic in Numbers.
Garland, Trudi Hammel
This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…
A note on Quarks and numbers theory
Hage-Hassan, Mehdi
2013-01-01
We express the basis vectors of Cartan fundamental representations of unitary groups by binary numbers. We determine the expression of Gel'fand basis of SU (3) based on the usual subatomic quarks notations and we represent it by binary numbers. By analogy with the mesons and quarks we find a new property of prime numbers.
Evaluating Number Sense in Workforce Students
Steinke, Dorothea A.
2015-01-01
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…
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)
The Bezout Number of Piecewise Algebraic Curves
Dian Xuan GONG; Ren Hong WANG
2012-01-01
Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves,a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found.Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.
The Decimal Representation of Real Numbers
Kalapodi, A.
2010-01-01
The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999...equals 1 or not, and if not what number does this…
Reading the World through Very Large Numbers
Greer, Brian; Mukhopadhyay, Swapna
2010-01-01
One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…
CIRCULAR CHROMATIC NUMBER AND MYCIELSKI GRAPHS
Liu Hongmei
2006-01-01
For a general graph G, M(G) denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number xc (M(G))equals to the chromatic number x(M(G)), which have improved some best sufficient conditions published up to date.
Identifying Fractions on a Number Line
Wong, Monica
2013-01-01
Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…
Children's Use of Number Line Estimation Strategies
Peeters, Dominique; Degrande, Tine; Ebersbach, Mirjam; Verschaffel, Lieven; Luwel, Koen
2016-01-01
This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…
Ordinality and the nature of symbolic numbers.
Lyons, Ian M; Beilock, Sian L
2013-10-23
The view that representations of symbolic and nonsymbolic numbers are closely tied to one another is widespread. However, the link between symbolic and nonsymbolic numbers is almost always inferred from cardinal processing tasks. In the current work, we show that considering ordinality instead points to striking differences between symbolic and nonsymbolic numbers. Human behavioral and neural data show that ordinal processing of symbolic numbers (Are three Indo-Arabic numerals in numerical order?) is distinct from symbolic cardinal processing (Which of two numerals represents the greater quantity?) and nonsymbolic number processing (ordinal and cardinal judgments of dot-arrays). Behaviorally, distance-effects were reversed when assessing ordinality in symbolic numbers, but canonical distance-effects were observed for cardinal judgments of symbolic numbers and all nonsymbolic judgments. At the neural level, symbolic number-ordering was the only numerical task that did not show number-specific activity (greater than control) in the intraparietal sulcus. Only activity in left premotor cortex was specifically associated with symbolic number-ordering. For nonsymbolic numbers, activation in cognitive-control areas during ordinal processing and a high degree of overlap between ordinal and cardinal processing networks indicate that nonsymbolic ordinality is assessed via iterative cardinality judgments. This contrasts with a striking lack of neural overlap between ordinal and cardinal judgments anywhere in the brain for symbolic numbers, suggesting that symbolic number processing varies substantially with computational context. Ordinal processing sheds light on key differences between symbolic and nonsymbolic number processing both behaviorally and in the brain. Ordinality may prove important for understanding the power of representing numbers symbolically.
The total bondage number of grid graphs
Hu, Fu-Tao; Xu, Jun-Ming
2011-01-01
The total domination number of a graph $G$ without isolated vertices is the minimum number of vertices that dominate all vertices in $G$. The total bondage number $b_t(G)$ of $G$ is the minimum number of edges whose removal enlarges the total domination number. This paper considers grid graphs. An $(n,m)$-grid graph $G_{n,m}$ is defined as the cartesian product of two paths $P_n$ and $P_m$. This paper determines the exact values of $b_t(G_{n,2})$ and $b_t(G_{n,3})$, and establishes some upper bounds of $b_t(G_{n,4})$.
Sparing of number words in oral production
Carlo Semenza
2014-04-01
In sentences only number words were spared; free standing function words and bound morphemes were as affected as other word categories. Discussion. These findings seem to set cardinal number words apart in the phonological output buffer from other possible building blocks of preassembled phonological units (like function words and bound morphemes. Building blocks constituted by numbers are more cohesive than the blocks constituted by function words and bound morphemes. Bencini et al. (2011 argued that numbers are recursive and consist of basic lexical units which are then combined following syntactic rules. This property would make number words resistant to damage in the phonological buffer.
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
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
Percon8 Algorithm for Random Number Generation
Dr. Mrs. Saylee Gharge
2014-05-01
Full Text Available In today’s technology savvy world, computer security holds a prime importance. Most computer security algorithms require some amount of random data for generating public and private keys, session keys or for other purposes. Random numbers are those numbers that occur in a sequence such that the future value of the sequence cannot be predicted based on present or past values. Random numbers find application in statistical analysis and probability theory. The many applications of randomness have led to the development of random number generating algorithms. These algorithms generate a sequence of random numbers either computationally or physically. In our proposed technique, we have implemented a random number generation algorithm combining two existing random number generation techniques viz. Mid square method and Linear Congruential Generator
Neocortical glial cell numbers in human brains
Pelvig, D.P.; Pakkenberg, H.; Stark, A.K.
2008-01-01
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. (C) 2007 Elsevier Inc. All rights reserved Udgivelsesdato: 2008/11...
Fibonacci number of the tadpole graph
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.
Monotone Hurwitz numbers in genus zero
Goulden, I P; Novak, Jonathan
2012-01-01
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.
Riemann equation for prime number diffusion.
Chen, Wen; Liang, Yingjie
2015-05-01
This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed.
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.
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.
Waring’s Problem for Pyramidal Numbers
邓越凡; 杨振宁
1994-01-01
It has been proved that every positive integer is expressible as a sum of no more than eight pyramidal numbers P(m)=(m-1)m(m+1)/6.This paper reports on a computer calculation of the partition of integers from n=1 to 109 into pyramidal numbers.We find that no integer≤10°needs more than five pyramidal numbers for its partition,and only 241 of them do need five.We define J(n) as the least number of pyramidal numbers to partition n,and Nk(n) as the number of positive integers l less than or equal to n for which J(l)=k.Based on our numerical results we make conjectures about the asymptotic form of Nk(n) for n→∞
Relativistic theory of tidal Love numbers
Binnington, Taylor
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.
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.
On quark number susceptibilities at high temperatures
Bazavov, A; Hegde, P; Karsch, F; Miao, C; Mukherjee, Swagato; Petreczky, P; Schmidt, C; Velytsky, A
2013-01-01
We calculated second and fourth order quark number susceptibilities for 2+1 flavor QCD in the high temperature region using two improved staggered fermion formulations. The calculations are performed at several lattice spacing and we show that in the continuum limit the two formulations give consistent results. We compare our continuum extrapolated results on quark number susceptibilities with recent weak coupling calculations, and find that these cannot simultaneously explain the lattice results for second and fourth order quark number susceptibilities.
Physical tests for random numbers in simulations
Vattulainen, I.; Ala-Nissila, T.; Kankaala, K.
1994-11-01
We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.
A note on generators of number fields
Vaaler, Jeffrey D
2012-01-01
We establish upper bounds for the smallest height of a generator of a number field $k$ over the rational field $\\Q$. Our first bound applies to all number fields $k$ having at least one real embedding. We also give a second conditional result for all number fields $k$ such that the Dedekind zeta-function associated to the Galois closure of $k/\\Q$ satisfies GRH. This provides a partial answer to a question of W. Ruppert.
High Atom Number in Microsized Atom Traps
2015-12-14
Final Performance Report on ONR Grant N00014-12-1-0608 High atom number in microsized atom traps for the period 15 May 2012 through 14 September...TYPE Final Technical Report 3. DATES COVERED (From - To) 05/15/2012-09/14/2012 4. TITLE AND SUBTITLE High atom number in microsized atom traps...forces for implementing a small-footprint, large-number atom -chip instrument. Bichromatic forces rely on absorption and stimulated emission to produce
High speed optical quantum random number generation.
Fürst, Martin; Weier, Henning; Nauerth, Sebastian; Marangon, Davide G; Kurtsiefer, Christian; Weinfurter, Harald
2010-06-07
We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators.
Beyond natural numbers: Representation of negative numbers in the parietal cortex
Kristen Pilner Blair; Miriam eRosenberg-Lee; Tsang, Jessica M.; Schwartz, Daniel L.; Vinod eMenon
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-relate...
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
Caveney, Geoffrey; Sondow, Jonathan
2011-01-01
Gronwall's function $G$ is defined for $n>1$ by $G(n)=\\frac{\\sigma(n)}{n \\log\\log n}$ where $\\sigma(n)$ is the sum of the divisors of $n$. We call an integer $N>1$ a \\emph{GA1 number} if $N$ is composite and $G(N) \\ge G(N/p)$ for all prime factors $p$ of $N$. We say that $N$ is a \\emph{GA2 number} if $G(N) \\ge G(aN)$ for all multiples $aN$ of $N$. In arXiv 1110.5078, we used Robin's and Gronwall's theorems on $G$ to prove that the Riemann Hypothesis (RH) is true if and only if 4 is the only number that is both GA1 and GA2. Here, we study GA1 numbers and GA2 numbers separately. We compare them with superabundant (SA) and colossally abundant (CA) numbers (first studied by Ramanujan). We give algorithms for computing GA1 numbers; the smallest one with more than two prime factors is 183783600, while the smallest odd one is 1058462574572984015114271643676625. We find nineteen GA2 numbers $\\le 5040$, and prove that a GA2 number $N>5040$ exists if and only if RH is false, in which case $N$ is even and $>10^{8576}$.
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...
Pegging Numbers For Various Tree Graphs
Levavi, Ariel
2011-01-01
In the game of pegging, each vertex of a graph is considered a hole into which a peg can be placed. A pegging move is performed by jumping one peg over another peg, and then removing the peg that has been jumped over from the graph. We define the pegging number as the smallest number of pegs needed to reach all the vertices in a graph no matter what the distribution. Similarly, the optimal-pegging number of a graph is defined as the smallest distribution of pegs for which all the vertices in the graph can be reached. We obtain tight bounds on the pegging numbers and optimal-pegging numbers of complete binary trees and compute the optimal-pegging numbers of complete infinitary trees. As a result of these computations, we deduce that there is a tree whose optimal-pegging number is strictly increased by removing a leaf. We also compute the optimal-pegging number of caterpillar graphs and the tightest upper bound on the optimal-pegging numbers of lobster graphs.
On Fibonacci Numbers Which Are Elliptic Carmichael
2014-12-27
On Fibonacci numbers which are elliptic Carmichael Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of...number. 1. REPORT DATE 27 DEC 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE On Fibonacci Numbers Which Are
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2009-01-01
@@ We have to find my friends Alice and Bill,who live in two different houses on Algebra Avenue. Each of the houses on Algebra Avenue is numbered with a two-digit number from 10 to 99. 1 can't remember where Alice and Bill live,but I remember that their house numbers are the reverse of each other (in the sense that "21" is the reverse of"12".) I also remember that the sum of their two house numbers is a perfect square.
Total dominator chromatic number of a graph
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 prior knowledge in sentence comprehension
Pedro Macizo
2013-01-01
Full Text Available We evaluated whether the comprehension of sentences that contained numerical information could benefit from presenting numbers in Arabic format and from using prior knowledge. Participants read sentences including numbers (Arabic digits or number words while the comprehension accuracy was evaluated. In addition, the sentences were biased or unbiased by people's prior knowledge about quantities. The results showed better comprehension for sentences that contained Arabic digits as compared to number words. Moreover, biased sentences were understood more accurately than unbiased sentences. These results indicate that information about magnitude in sentence context is comprehended better when quantities are presented in Arabic format and when they are associated with participants' world knowledge.
Vector perturbations of galaxy number counts
Durrer, Ruth; Tansella, Vittorio
2016-07-01
We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxy number counts.
Vector perturbations of galaxy number counts
Durrer, Ruth
2016-01-01
We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxy number counts.
Generalized Ramsey numbers through adiabatic quantum optimization
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
2013-06-19
... number administration more generally. The memorability, ubiquity, convenience, and universality of... judicious management of telephone numbers and promote further innovation and competition, the NPRM...
Effects of pitch on auditory number comparisons.
Campbell, Jamie I D; Scheepers, Florence
2015-05-01
Three experiments investigated interactions between auditory pitch and the numerical quantities represented by spoken English number words. In Experiment 1, participants heard a pair of sequential auditory numbers in the range zero to ten. They pressed a left-side or right-side key to indicate if the second number was lower or higher in numerical value. The vocal pitches of the two numbers either ascended or descended so that pitch change was congruent or incongruent with number change. The error rate was higher when pitch and number were incongruent relative to congruent trials. The distance effect on RT (i.e., slower responses for numerically near than far number pairs) occurred with pitch ascending but not descending. In Experiment 2, to determine if these effects depended on the left/right spatial mapping of responses, participants responded "yes" if the second number was higher and "no" if it was lower. Again, participants made more number comparison errors when number and pitch were incongruent, but there was no distance × pitch order effect. To pursue the latter, in Experiment 3, participants were tested with response buttons assigned left-smaller and right-larger ("normal" spatial mapping) or the reverse mapping. Participants who received normal mapping first presented a distance effect with pitch ascending but not descending as in Experiment 1, whereas participants who received reverse mapping first presented a distance effect with pitch descending but not ascending. We propose that the number and pitch dimensions of stimuli both activated spatial representations and that strategy shifts from quantity comparison to order processing were induced by spatial incongruities.
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
Kong, Feng; Zhao, Jingjing; You, Xuqun
2012-01-01
Past research suggested that negative numbers could be represented in terms of their components in the visual modality. The present study examined the processing of negative numbers in the auditory modality and whether it is affected by context. Experiment 1 employed a stimuli detection task where only negative numbers were presented binaurally. Experiment 2 employed the same task, but both positive and negative numbers were mixed as cues. A reverse attentional spatial-numerical association of response codes (SNARC) effect for negative numbers was obtained in these two experiments. Experiment 3 employed a number classification task where only negative numbers were presented binaurally. Experiment 4 employed the same task, but both positive and negative numbers were mixed. A reverse SNARC effect for negative numbers was obtained in these two experiments. These findings suggest that negative numbers in the auditory modality are generated from the set of positive numbers, thus supporting a components representation.
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.
Number & operations drill sheets : grades PK-2
Reed, Nat
2010-01-01
For grades PK-2, our Common Core State Standards-based resource meets the number & operations concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. Each drill sheet contains warm-up and timed drill activities for the student to practice number & operations concepts.
A property of algebraic univoque numbers
De Vries, M.
2007-01-01
Consider the set U of real numbers q >= 1 for which only one sequence (c(i)) of integers 0 <= c(i) <= q satisfies the equality Sigma(infinity)(i= 1) ciq(-i) =1. We show that the set of algebraic numbers in U is dense in the closure (U) over bar of U.
Wigner function of the thermo number states
Hu Li-Yun; Fan Hong-Yi
2009-01-01
Based on thermo field dynamics (TFD) and using the thermo Wigner operator in the thermo entangled state representation we derive the Wigner function of number states at finite temperature (named thermo number states). The figure of Wigner function shows that its shape gets smoothed as the temperature rises, implying that the quantum noise becomes larger.
Beyond the Numbers Making Sense of Statistics
Christmann, Edwin
2011-01-01
Statistics is required coursework within most teacher certification programs. Beyond the Numbers presents a nonthreatening, practical approach to statistics, providing step-by-step instructions for understanding and implementing the essential components of the subject.The basic and understandable explanations in Beyond the Numbers break down complex statistical processes to simple arithmetic computations that can be applied with the confidence that accompanies understanding.
Baryon number violation in future accelerators
Tracas, N.D.; Zoupanos, G.
1989-03-30
As a demonstration of the possibility to observe baryon number violation in the next generation of accelerators we present a semirealistic GUT in which proton decay is forbidden and the unification scale is at approx. = 10/sup 3-4/ TeV, leading therefore to observable baryon number violating processes.
A supercongruence for generalized Domb numbers
Osburn, Robert
2012-01-01
Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier's seven "sporadic" solutions to second order Apery-like differential equations.
Motzkin numbers out of Random Domino Automaton
Białecki, Mariusz
2011-01-01
Motzkin numbers are derived from a special case of Random Domino Automaton - recently proposed toy model of earthquakes. An exact 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.
Nonclassicality in phase-number uncertainty relations
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.
Equations with Arithmetic Functions of Pell Numbers
2014-01-01
Postgraduate School in December, 2012. During the preparation of this paper, F. L. was supported in part by Project PAPIIT IN104512 ( UNAM ), VSP...Multiperfect numbers with identical digits, J. Number Theory 131 (2011), 260–284. Received: 10.01.2013 Accepted: 19.04.2014 1 Mathematical Institute, UNAM
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.
Neural correlates of merging number words.
Hung, Yi-Hui; Pallier, Christophe; Dehaene, Stanislas; Lin, Yi-Chen; Chang, Acer; Tzeng, Ovid J-L; Wu, Denise H
2015-11-15
Complex number words (e.g., "twenty two") are formed by merging together several simple number words (e.g., "twenty" and "two"). In the present study, we explored the neural correlates of this operation and investigated to what extent it engages brain areas involved processing numerical quantity and linguistic syntactic structure. Participants speaking two typologically distinct languages, French and Chinese, were required to read aloud sequences of simple number words while their cerebral activity was recorded by functional magnetic resonance imaging. Each number word could either be merged with the previous ones (e.g., 'twenty three') or not (e.g., 'three twenty'), thus forming four levels ranging from lists of number words to complex numerals. When a number word could be merged with the preceding ones, it was named faster than when it could not. Neuroimaging results showed that the number of merges correlated with activation in the left inferior frontal gyrus and in the left inferior parietal lobule. Consistent findings across Chinese and French participants suggest that these regions serve as the neural bases for forming complex number words in different languages.
Keypad Geometry and Divisibility of Numbers
Van Dyke, Frances; Keynes, Michael
2010-01-01
In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…
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…
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.
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.
When Symbolic Spatial Cues Go before Numbers
Herrera, Amparo; Macizo, Pedro
2011-01-01
This work explores the effect of spatial cueing on number processing. Participants performed a parity judgment task. However, shortly before the target number, a cue (arrow pointing to left, arrow pointing to right or a cross) was centrally presented. In Experiment 1, in which responses were lateralized, the cue direction modulated the interaction…
Comments on nonparametric predictions of sunspot numbers
Jensen, J.L.
1993-01-01
Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed.......Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed....
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
From Whole Numbers to Invert and Multiply
Cavey, Laurie O.; Kinzel, Margaret T.
2014-01-01
Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…
Locating Fractions on a Number Line
Wong, Monica
2013-01-01
Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on a…
On Ramsey numbers for paths versus wheels
Salman, M.; Broersma, Haitze J.
2004-01-01
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 $
On Ramsey numbers for paths versus wheels
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 $
Application of Chaotic Number Generators in Econophysics
Pellicer-Lostao, Carmen
2011-01-01
Agent-based models have demonstrated their power and flexibility in Econophysics. However their major challenge is still to devise more realistic simulation scenarios. The complexity of Economy makes appealing the idea of introducing chaotic number generators as simulation engines in these models. Chaos based number generators are easy to use and highly configurable. This makes them just perfect for this application.
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…
Roman Bondage Numbers of Some Graphs
Hu, Fu-Tao
2011-01-01
A Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\to \\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The weight of a Roman dominating function is the value $f(G)=\\sum_{u\\in V} f(u)$. The Roman domination number of $G$ is the minimum weight of a Roman dominating function on $G$. The Roman bondage number of a nonempty graph $G$ is the minimum number of edges whose removal results in a graph with the Roman domination number larger than that of $G$. This paper determines the exact value of the Roman bondage numbers of two classes of graphs, complete $t$-partite graphs and $(n-3)$-regular graphs with order $n$ for any $n\\ge 5$.
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...
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.
Wavelet analysis of sunspot relative numbers
无
2002-01-01
The time series of the monthly smoothed sunspot numbers in 1749-2000 is analyzed with the wavelet.The result shows that besides the known time-variation of the period about 11 years, other main periods of the sunspot numbers, such as the periods of about 100 years and so on,vary with time. We suggest that the time-variation of the main periods is the manifestation of the complex variation of sunspot numbers. It is significant to make a thorough study of the character and mechanism of the time-variation of the periods for proving prediction of sunspot numbers, especially for understanding the variation process of sunspot numbers.
The competition numbers of ternary Hamming graphs
Park, Boram
2010-01-01
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs to characterize a graph by its competition number. In this paper, we give the exact values of the competition numbers of ternary Hamming graphs.
Topological Numbers and the Weyl Semimetal
Elbistan, Mahmut
2016-01-01
Generalized Dirac monopoles in momentum space are constructed in even d+1 dimensions from the Weyl Hamiltonian in terms of Green's functions. In 3+1 spacetime dimensions, the (unit) charge of the monopole is equal to both the winding number and the Chern number, expressed as the integral of the Berry curvature. Based on the equivalence of the Chern and winding numbers, a chirally coupled field theory action is proposed for the Weyl semimetal phase. At the one loop order, the effective action yields both the chiral magnetic effect and the anomalous Hall effect. The Chern number appears as a coefficient in the conductivity, thus emphasizes the role of topology. The anomalous contribution of chiral fermions to transport phenomena is reflected as the gauge anomaly with the topological term $(\\bm{E}\\cdot\\bm{B})$. Relevance of monopoles and Chern numbers for the semiclassical chiral kinetic theory is also discussed.
Compendium of Experimental Cetane Number Data
Murphy, M. J.; Taylor, J. D.; McCormick, R. L.
2004-09-01
In this report, we present a compilation of reported cetane numbers for pure chemical compounds. The compiled database contains cetane values for 299 pure compounds, including 156 hydrocarbons and 143 oxygenates. Cetane number is a relative ranking of fuels based on the amount of time between fuel injection and ignition. The cetane number is typically measured either in a combustion bomb or in a single-cylinder research engine. This report includes cetane values from several different measurement techniques - each of which has associated uncertainties. Additionally, many of the reported values are determined by measuring blending cetane numbers, which introduces significant error. In many cases, the measurement technique is not reported nor is there any discussion about the purity of the compounds. Nonetheless, the data in this report represent the best pure compound cetane number values available from the literature as of August 2004.
True random numbers from amplified quantum vacuum
Jofre, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V; 10.1364/OE.19.020665
2011-01-01
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 t...
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 ...
The lower bound on independence number
LI; Yusheng
2002-01-01
［1］Caro, Y., New Results on the Independence Number, Technical Report, Tel_Aviv: Tel_Aviv University, 1979.［2］Wei, V., A lower bound on the stability number of a simple graph, Bell Laboratories Technical Memorandum, 1981, 81_11217_11219.\\}［3］Alon, N., Spencer, J., The Probabilistic Method, New York: Wiley_Interscience, 1992.［4］Ajtai, M., Komls, J., Szemerédi E., A note on Ramsey numbers, J. Combin. Theory, Ser. A, 1980, 29: 354-360.［5］Shearer, J., A note on the independence number of triangle_free graphs, Discrete Math., 1983, 46: 83-87.［6］Kim, J., The Ramsey number R(3,t)has order of magnitude t\\+2／logt, Random Structures Algorithms, 1995, 7: 174-207.［7］Tardos, E., 1997 Fulkerson Prize, Notices of American Math. Soc., 1998, 45(8): 984.［8］Griggs, J., Lower bounds on the independence number in term of the degrees, J. Combin. Theory, Ser. B, 1983, 34: 22-29.［9］Li, Y., Rousseau, C., Fan_complete graph Ramsey numbers, J. Graph Theory, 1996, 23: 413-420.［10］Shearer, J., A note on the independence number of triangle_free graphs, II, J. Combin. Theory, Ser. B, 1991, 53: 300-307.［11］Li, Y., Rousseau, C., On book_complete Ramsey numbers, J. Combin. Theory, Ser. B, 1996, 68: 36-44.［12］Li, Y., Rousseau, C., Zang, W., Asymptotic upper bounds for Ramsey functions, Graphs Combin., 2001, 17: 123-128.［13］Caro, Y., Li, Y., Rousseau, C. et al., Asymptotic bounds for some bipartite graph: complete graph Ramsey numbers, Discrete Math., 2000, 220: 51-56.
Saxe, Geoffrey B.; Shaughnessy, Meghan M.; Gearhart, Maryl; Haldar, Lina Chopra
2013-01-01
Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…
Saxe, Geoffrey B.; Shaughnessy, Meghan M.; Gearhart, Maryl; Haldar, Lina Chopra
2013-01-01
Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…
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 making the…
Theory of analogous force on number sets
Canessa, Enrique
2003-10-01
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 px 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 px to describe complex phenomena, the theory leads to derive a distinct analogous force fx on number sets proportional to (∂ px/∂ x) T at an analogous system temperature T. In particular, this leads 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.
Effective condition number for finite difference method
Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai
2007-01-01
For solving the linear algebraic equations Ax=b with the symmetric and positive definite matrix A, from elliptic equations, the traditional condition number in the 2-norm is defined by Cond.=[lambda]1/[lambda]n, where [lambda]1 and [lambda]n are the maximal and minimal eigenvalues of the matrix A, respectively. The condition number is used to provide the bounds of the relative errors from the perturbation of both A and b. Such a Cond. can only be reached by the worst situation of all rounding errors and all b. For the given b, the true relative errors may be smaller, or even much smaller than the Cond., which is called the effective condition number in Chan and Foulser [Effectively well-conditioned linear systems, SIAM J. Sci. Statist. Comput. 9 (1988) 963-969] and Christiansen and Hansen [The effective condition number applied to error analysis of certain boundary collocation methods, J. Comput. Appl. Math. 54(1) (1994) 15-36]. In this paper, we propose the new computational formulas for effective condition number Cond_eff, and define the new simplified effective condition number Cond_E. For the latter, we only need the eigenvector corresponding to the minimal eigenvalue of A, which can be easily obtained by the inverse power method. In this paper, we also apply the effective condition number for the finite difference method for Poisson's equation. The difference grids are not supposed to be quasiuniform. Under a non-orthogonality assumption, the effective condition number is proven to be O(1) for the homogeneous boundary conditions. Such a result is extraordinary, compared with the traditional , where hmin is the minimal meshspacing of the difference grids used. For the non-homogeneous Neumann and Dirichlet boundary conditions, the effective condition number is proven to be O(h-1/2) and , respectively, where h is the maximal meshspacing of the difference grids. Numerical experiments are carried out to verify the analysis made.
Low Nephron Number and Its Clinical Consequences
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.
The Bondage Number of Mesh Networks
Hu, Fu-Tao; Xu, Jun-Ming
2011-01-01
The bondage number $b(G)$ of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number greater than that of $G$. Denote $P_n\\times P_m$ be the Cartesian product of two paths $P_n$ and $P_m$. This paper determines that the exact value of $b(P_n\\times P_2)$, $b(P_n\\times P_3)$ and $b(P_n\\times P_4)$ for $n\\ge 2$.
Acceleration Detection of Large (Probably Prime Numbers
Dragan Vidakovic
2013-02-01
Full Text Available In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resortto trial division by a few initial prime numbers, since such a division take less time. How far we should gowith such a division is the that we are trying to answer in this paper?For the theory of the matter is fullyresolved. However, that in practice we do not have much use.Therefore, we present a solution that isprobably irrelevant to theorists, but it is very useful to people who have spent many nights to producelarge (probably prime numbers using its own software.
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.
The covering number of $M_{24}$
Michael Epstein
2016-09-01
Full Text Available A finite cover $\\mathcal{C}$ of a group $G$ is a finite collection of proper subgroups of $G$ such that $G$ is equal to the union of all of the members of $\\mathcal{C}$. Such a cover is called {\\em minimal} if it has the smallest cardinality among all finite covers of $G$. The covering number of $G$, denoted by $\\sigma(G$, is the number of subgroups in a minimal cover of $G$. In this paper the covering number of the Mathieu group $M_{24}$ is shown to be 3336.
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.
Physical tests for random numbers in simulations
Vattulainen, I.; Ala-Nissila, T.; Kankaala, K. (Research Institute for Theoretical Physics, P.O. Box 9 (Siltavuorenpenger 20 C), FIN-00014 University of Helsinki (Finland) Department of Electrical Engineering, Tampere University of Technology, P.O. Box 692, FIN-3310, Tampere (Finland) Center for Scientific Computing, P.O. Box 405, FIN-02101 Espoo (Finland))
1994-11-07
We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of [ital n] successive numbers. We apply the tests to show that recent errors in high precision Ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences.
Modal Wave Number Spectrum for Mesoscale Eddies
KANG Ying; PENG Linhui
2003-01-01
The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the complex sound pressure field in the water containing a mesoscale eddy to examine the variation of local modal wave numbers in such a range-dependent environment. The numerical simulation results show that modal wave number spectra obtained by this method can reflect the location and strength of a mesoscale eddy, therefore it can be used to monitor the strength and spatial scale of ocean mesoscale eddies.
VLSI binary multiplier using residue number systems
Barsi, F.; Di Cola, A.
1982-01-01
The idea of performing multiplication of n-bit binary numbers using a hardware based on residue number systems is considered. This paper develops the design of a VLSI chip deriving area and time upper bounds of a n-bit multiplier. To perform multiplication using residue arithmetic, numbers are converted from binary to residue representation and, after residue multiplication, the result is reconverted to the original notation. It is shown that the proposed design requires an area a=o(n/sup 2/ log n) and an execution time t=o(log/sup 2/n). 7 references.
Baryon Number Violation and String Topologies
Sjöstrand, Torbjörn
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.
On the number of finite topological spaces
Lucio R. Berrone
1993-05-01
Full Text Available In this paper we deal with the problem of enumerating the finite topological spaces, studying the enumeration of a restrictive class of them. By employing simple techniques, we obtain a recursive lower bound for the number of topological spaces on a set of n elements. Besides we prove some collateral results, among which we can bring a new proof (Cor. 1.5 of the fact that p(n – the number of partitions of the integer n – is the number of non-isomorphic Boolean algebras on a set of n elements.
Hyperimmunity and A-computable universal numberings
Issakhov, Assylbek
2016-08-01
Whether there exists a computable universal numbering for a computable family is the key question in theory of numberings. In a very general setting, this problem was explored in [Yu. L. Ershov, Theory of Numberings, Handbook of Computability Theory, North-Holland; Amsterdam: Stud. Log. Found. Math., Vol. 140, pp. 473-503, 1999]. For sets A that are Turing jumps of the empty set, the problem was treated in [S. A. Badaev, S. S. Goncharov, and A. Sorbi, Computability and Models, 11-44 (2003)] and other papers. In this work, we investigate families of total functions computable relative to hyperimmune and hyperimmune-free oracles.
The Modified Negative Decision Number in Graphs
Changping Wang
2011-01-01
Full Text Available A mapping x:V→{-1,1} is called negative if ∑u∈N[v]x(u≤1 for every v∈V. The maximum of the values of ∑v∈Vx(v taken over all negative mappings x, is called the modified negative decision number and is denoted by βD′(G. In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are found.
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
Unpredictability and the transmission of numbers
Myers, John M
2015-01-01
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...
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.
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.
Arabic Alphabet and Numbers Sign Language Recognition
Mahmoud Zaki Abdo
2015-11-01
Full Text Available This paper introduces an Arabic Alphabet and Numbers Sign Language Recognition (ArANSLR. It facilitates the communication between the deaf and normal people by recognizing the alphabet and numbers signs of Arabic sign language to text or speech. To achieve this target, the system able to visually recognize gestures from hand image input. The proposed algorithm uses hand geometry and the different shape of a hand in each sign for classifying letters shape by using Hidden Markov Model (HMM. Experiments on real-world datasets showed that the proposed algorithm for Arabic alphabet and numbers sign language recognition is suitability and reliability compared with other competitive algorithms. The experiment results show that the increasing of the gesture recognition rate depends on the increasing of the number of zones by dividing the rectangle surrounding the hand.
Large Numbers and Calculators: A Classroom Activity.
Arcavi, Abraham; Hadas, Nurit
1989-01-01
Described is an activity demonstrating how a scientific calculator can be used in a mathematics classroom to introduce new content while studying a conventional topic. Examples of reading and writing large numbers, and reading hidden results are provided. (YP)
The disentangling number for phylogenetic mixtures
Sullivant, Seth
2011-01-01
We provide a logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees. This results is useful for analyzing phylogenetic mixture models. The proof depends on interpreting multisets of trees as high dimensional contingency tables.
Multiplex congruence network of natural numbers
Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua
2016-01-01
.... Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers...
Chaotic behaviour of high Mach number flows
Varvoglis, H.; Ghosh, S.
1985-01-01
The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.
Means of Staff Number Reduction and Outplacement
H. Urbancová
2014-01-01
.... The objective is to present the ways of staff number reduction in Czech organizations and outplacement for the laid-off workers and a partial objective is to compare the results with those in the Slovak Republic...
A brief introduction to particle number estimation
Dorph-Petersen, Karl-Anton; Nyengaard, Jens Randel; Gundersen, Hans Jørgen Gottlieb
1998-01-01
The principle of particle number estimation using the disector is described emphasising the practical similarities and differences in the application of the principle in biomedicine and non-biological sciences....
Copy number variation across European populations.
Wanting Chen
Full Text Available Genome analysis provides a powerful approach to test for evidence of genetic variation within and between geographical regions and local populations. Copy number variants which comprise insertions, deletions and duplications of genomic sequence provide one such convenient and informative source. Here, we investigate copy number variants from genome wide scans of single nucleotide polymorphisms in three European population isolates, the island of Vis in Croatia, the islands of Orkney in Scotland and the South Tyrol in Italy. We show that whereas the overall copy number variant frequencies are similar between populations, their distribution is highly specific to the population of origin, a finding which is supported by evidence for increased kinship correlation for specific copy number variants within populations.