scholarly journals Almost Exact Computation of Eigenvalues in Approximate Differential Problems

2019 ◽  
Vol 24 (4) ◽  
pp. 96 ◽  
Author(s):  
José M. A. Matos ◽  
Maria João Rodrigues
Keyword(s):  
Eigenvalue Problems ◽  
High Accuracy ◽  
Second Step ◽  
Matlab Toolbox ◽  
Differential Problem ◽  
Algebraic Problem ◽  
Polynomial Expression ◽  
Computation Of Eigenvalues ◽  
Potential Use ◽  
Mathematics And Physics

Differential eigenvalue problems arise in many fields of Mathematics and Physics, often arriving, as auxiliary problems, when solving partial differential equations. In this work, we present a method for eigenvalues computation following the Tau method philosophy and using Tau Toolbox tools. This Matlab toolbox was recently presented and here we explore its potential use and suitability for this problem. The first step is to translate the eigenvalue differential problem into an algebraic approximated eigenvalues problem. In a second step, making use of symbolic computations, we arrive at the exact polynomial expression of the determinant of the algebraic problem matrix, allowing us to get high accuracy approximations of differential eigenvalues.

Utilisation d'éléments structuraux en aluminium dans les ponts routiers : Étude économique et structurale

2001 ◽  
Vol 28 (6) ◽  
pp. 1029-1040 ◽  
Author(s):  
Carol Roy ◽  
Denis Beaulieu ◽  
Josée Bastien
Keyword(s):  
Cost Analysis ◽  
Bridge Deck ◽  
Concrete Slab ◽  
Second Step ◽  
Structural System ◽  
Analysis Study ◽  
Simple Repair ◽  
Potential Use ◽  
Economic Standpoint ◽  
Made In

The study presented in this paper is part of a project aiming at evaluating the potential use of aluminum in structures. The types of intervention could range from a simple repair or a reinforcement involving structural aluminum, the replacement of a used bridge deck by an aluminum deck, to the construction of a new bridge made in full or in part of aluminum. It is this latter type of intervention that justified a research project, the results of which are presented in this article. The first step involves identifying the most advantageous type of aluminum structural system from a structural standpoint as well as an economic standpoint. This step includes the analysis and partial design of 40 girder- or truss-type road bridges, spanning 15 and 35 m, supporting either an active concrete slab or an aluminum deck. These studies have shown that bridges built using a Pratt-type truss and an active concrete slab provided the best results. It is also shown that some calculation criteria, such as vibration, deflection, and fatigue criteria limited the extensive use of aluminum in bridges. In the second step, nine bridges are more comprehensively analysed and designed, based on the standards used in North America, and three are fully designed, including the connexions, in order to realize a cost analysis study that is as accurate as possible. Special attention is given to vibration and fatigue problems as well as to the details related to connexions calculation. The study concludes that the development of an aluminum-only medium span road bridge system is a non-viable project in the short to mid term from a structural standpoint as well as an economic standpoint, and it makes recommendations on the use of aluminum decks and on the continuation of the work.Key words: aluminum, analysis, bridges, connexions, design, fatigue, standards, vibration.[Journal translation]

Effects of Heat Treatment on the Magnetic Properties and Dimension Accuracy of Fe-12%Al Soft-Magnetism Alloy

2011 ◽  
Vol 217-218 ◽  
pp. 572-577
Author(s):  
Jun Yan Sun ◽  
Jian Ming Tang
Keyword(s):  
Heat Treatment ◽  
Magnetic Property ◽  
Treatment Process ◽  
High Accuracy ◽  
Second Step ◽  
Property A ◽  
Finish Machining ◽  
Passing Rate ◽  
Alloy Material ◽  
Soft Magnetism

Theoretical analysis and experiment all show that heat stress has effect on the accuracy of Fe-12%Al soft-magnetism alloy’s dimension after heat treatment and also heat treatment process has effect on magnetic property and also the stress caused by machining has effect on magnetic property. A kind of new method is proposed to improve the magnetic property and accuracy of dimension of soft-magnetism alloy after heat treatment, in which the first step is to perform half-finish machining on soft-magnetism alloy material and leave a one-side margin 0.05mm, and the second step is to perform heat treatment and then finish machining during which some degree of tolerance margin is required to be set if the requirement of magnetic property is satisfied and last step is to the renewing magnetism treatment. This method can guarantee the high accuracy of soft magnetism alloy’s dimension as well as can renew the lost of magnetic property by 75%-91% which will improve the passing rate by almost double.

scholarly journals New Approaches to OCR for Early Printed Books

DigItalia ◽  
2020 ◽  
Vol 15 (2) ◽  
pp. 74-87
Author(s):  
Nikolaus Weichselbaumer ◽  
Mathias Seuret ◽  
Saskia Limbach ◽  
Rui Dong ◽  
Manuel Burghardt ◽  
...  
Keyword(s):  
Online Training ◽  
High Accuracy ◽  
Historical Research ◽  
Training Data ◽  
16Th Century ◽  
Second Step ◽  
Printed Books ◽  
Accuracy Level ◽  
Computer Scientists ◽  
Data Book

Books printed before 1800 present major problems for OCR. One of the main obstacles is the lack of diversity of historical fonts in training data. The OCR-D project, consisting of book historians and computer scientists, aims to address this deficiency by focussing on three major issues. Our first target was to create a tool that identifies font groups automatically in images of historical documents. We concentrated on Gothic font groups that were commonly used in German texts printed in the 15th and 16th century: the well-known Fraktur and the lesser known Bastarda, Rotunda, Textura und Schwabacher. The tool was trained with 35,000 images and reaches an accuracy level of 98%. It can not only differentiate between the above-mentioned font groups but also Hebrew, Greek, Antiqua and Italic. It can also identify woodcut images and irrelevant data (book covers, empty pages, etc.). In a second step, we created an online training infrastructure (okralact), which allows for the use of various open source OCR engines such as Tesseract, OCRopus, Kraken and Calamari. At the same time, it facilitates training for specific models of font groups. The high accuracy of the recognition tool paves the way for the unprecedented opportunity to differentiate between the fonts used by individual printers. With more training data and further adjustments, the tool could help to fill a major gap in historical research.

scholarly journals An Intra-Subject Approach Based on the Application of HMM to Predict Concentration in Educational Contexts from Nonintrusive Physiological Signals in Real-World Situations

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1777
Author(s):  
Ana Serrano-Mamolar ◽  
Miguel Arevalillo-Herráez ◽  
Guillermo Chicote-Huete ◽  
Jesus G. G. Boticario
Keyword(s):  
Real World ◽  
Markov Models ◽  
Low Cost ◽  
High Accuracy ◽  
Physiological Signals ◽  
Detection Accuracy ◽  
Related Information ◽  
Additional Control ◽  
Affect Detection ◽  
Potential Use

Previous research has proven the strong influence of emotions on student engagement and motivation. Therefore, emotion recognition is becoming very relevant in educational scenarios, but there is no standard method for predicting students’ affects. However, physiological signals have been widely used in educational contexts. Some physiological signals have shown a high accuracy in detecting emotions because they reflect spontaneous affect-related information, which is fresh and does not require additional control or interpretation. Most proposed works use measuring equipment for which applicability in real-world scenarios is limited because of its high cost and intrusiveness. To tackle this problem, in this work, we analyse the feasibility of developing low-cost and nonintrusive devices to obtain a high detection accuracy from easy-to-capture signals. By using both inter-subject and intra-subject models, we present an experimental study that aims to explore the potential application of Hidden Markov Models (HMM) to predict the concentration state from 4 commonly used physiological signals, namely heart rate, breath rate, skin conductance and skin temperature. We also study the effect of combining these four signals and analyse their potential use in an educational context in terms of intrusiveness, cost and accuracy. The results show that a high accuracy can be achieved with three of the signals when using HMM-based intra-subject models. However, inter-subject models, which are meant to obtain subject-independent approaches for affect detection, fail at the same task.

The calculation of the latent roots and vectors of matrices on the pilot model of the A.C.E.

1954 ◽  
Vol 50 (4) ◽  
pp. 536-566 ◽  
Author(s):  
J. H. Wilkinson
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Storage Capacity ◽  
Eigenvalue Problems ◽  
High Accuracy ◽  
Point Of View ◽  
Aircraft Industry ◽  
Pilot Model ◽  
Very High ◽  
Latent Roots

ABSTRACTThe problem of finding the latent roots and vectors of matrices has been treated in a number of papers ((2)–(7)) mainly from the point of view of desk computers. In this paper the problem is treated from the standpoint of users of high-speed automatic computers. In the first section a number of iterative processes are described and, in the second, the techniques developed for using these processes on the Pilot Model of the Automatic Computing Engine. It is shown that the methods give very high accuracy and can be used to deal with matrices of high orders even on a machine of very limited storage capacity. They have been used on numerous matrices of orders up to 60 mainly on problems arising in the aircraft industry and on eigenvalue problems for systems of ordinary differential equations.

scholarly journals Lanczos Bidiagonalization With Partial Reorthogonalization

1998 ◽  
Vol 27 (537) ◽  
Author(s):  
Rasmus Munk Larsen
Keyword(s):  
Eigenvalue Problems ◽  
Sparse Matrix ◽  
Singular Values ◽  
High Accuracy ◽  
Symmetric System ◽  
Lanczos Algorithm ◽  
Lanczos Bidiagonalization ◽  
Left And Right ◽  
Test Matrices ◽  
Matlab Package

A partial reorthogonalization procedure (BPRO) for maintaining semi-orthogonality among the left and right Lanczos vectors in the Lanczos bidiagonalization (LBD) is presented. The resulting algorithm is mathematically equivalent to the symmetric Lanczos algorithm with partial reorthogonalization (PRO) developed by Simon but works directly on the Lanczos bidiagonalization of A. For computing the singular values and vectors of a large sparse matrix with high accuracy, the BPRO algorithm uses only half the amount of storage and a factor of 3-4 less work compared to methods based on PRO applied to an equivalent symmetric system. Like PRO the algorithm presented here is based on simple recurrences which enable it to monitor the loss of orthogonality among the Lanczos vectors directly without forming inner products. These recurrences are used to develop a Lanczos bidiagonalization algorithm with partial reorthogonalization which has been implemented in a MATLAB package for sparse SVD and eigenvalue problems called PROPACK. Numerical experiments with the routines from PROPACK are conducted using a test problem from inverse helioseismology to illustrate the properties of the method. In addition a number of test matrices from the Harwell-Boeing collection are used to compare the accuracy and efficiency of the MATLAB implementations of BPRO and PRO with the svds routine in MATLAB 5.1, which uses an implicitly restarted Lanczos algorithm.

scholarly journals A Novel Un-differenced PPP-RTK Concept

2011 ◽  
Vol 64 (S1) ◽  
pp. S180-S191 ◽  
Author(s):  
Baocheng Zhang ◽  
Peter J.G. Teunissen ◽  
Dennis Odijk
Keyword(s):  
Low Cost ◽  
Northern China ◽  
High Accuracy ◽  
Single Frequency ◽  
Second Step ◽  
Reference Network ◽  
Dual Frequency ◽  
Atmospheric Delays ◽  
Gnss Observations ◽  
Regional Reference

In this contribution, a novel un-differenced (UD) (PPP-RTK) concept, i.e. a synthesis of Precise Point Positioning and Network-based Real-Time Kinematic concept, is introduced. In the first step of our PPP-RTK approach, the UD GNSS observations from a regional reference network are processed based upon re-parameterised observation equations, corrections for satellite clocks, phase biases and (interpolated) atmospheric delays are calculated and provided to users. In the second step, these network-based corrections are used at the user site to restore the integer nature of his UD phase ambiguities, which makes rapid and high accuracy user positioning possible. The proposed PPP-RTK approach was tested using two GPS CORS networks with inter-station distances ranging from 60 to 100 km. The first test network is the northern China CORS network and the second is the Australian Perth CORS network. In the test of the first network, a dual-frequency PPP-RTK user receiver was used, while in the test of the second network, a low-cost, single-frequency PPP-RTK user receiver was used. The performance of fast ambiguity resolution and the high accuracy positioning of the PPP-RTK results are demonstrated.

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