Introduction to scientific computing :: for scientists and engineers /
Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these imp...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
[2015]
|
| Schriftenreihe: | De Gruyter textbook.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? |
| Beschreibung: | 1 online resource (xi, 138 pages) : illustrations (some color) |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 3110359421 9783110359428 9783110386806 3110386801 3110359405 9783110359404 |
Internformat
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| 245 | 1 | 0 | |a Introduction to scientific computing : |b for scientists and engineers / |c Timo Heister, Leo G. Rebholz. |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2015] | |
| 300 | |a 1 online resource (xi, 138 pages) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; Contents; 1 Introduction; 1.1 Why study numerical methods?; 1.2 Terminology; 1.3 Convergence terminology; 1.4 Exercises; 2 Computer representation of numbers and roundoff error; 2.1 Examples of the effects of roundoff error; 2.2 Binary numbers; 2.3 64 bit floating point numbers; 2.3.1 Avoid adding large and small numbers; 2.3.2 Subtracting two nearly equal numbers is bad; 2.4 Exercises; 3 Solving linear systems of equations; 3.1 Linear systems of equations and solvability; 3.2 Solving triangular systems; 3.3 Gaussian elimination; 3.4 The backslash operator; 3.5 LU decomposition. | |
| 505 | 8 | |a 3.6 Exercises4 Finite difference methods; 4.1 Approximating the first derivative; 4.1.1 Forward and backward differences; 4.1.2 Centered difference; 4.1.3 Three point difference formulas; 4.1.4 Further notes; 4.2 Approximating the second derivative; 4.3 Application: Initial value ODE's using the forward Euler method; 4.4 Application: Boundary value ODE's; 4.5 Exercises; 5 Solving nonlinear equations; 5.1 The bisection method; 5.2 Newton's method; 5.3 Secant method; 5.4 Comparing bisection, Newton, secant method; 5.5 Combining secant and bisection and the fzero command. | |
| 505 | 8 | |a 5.6 Equation solving in higher dimensions5.7 Exercises; 6 Accuracy in solving linear systems; 6.1 Gauss-Jordan elimination and finding matrix inverses; 6.2 Matrix and vector norms and condition number; 6.3 Sensitivity in linear system solving; 6.4 Exercises; 7 Eigenvalues and eigenvectors; 7.1 Mathematical definition; 7.2 Power method; 7.3 Application: Population dynamics; 7.4 Exercises; 8 Fitting curves to data; 8.1 Interpolation; 8.1.1 Interpolation by a single polynomial; 8.1.2 Piecewise polynomial interpolation; 8.2 Curve fitting; 8.2.1 Line of best fit; 8.2.2 Curve of best fit. | |
| 505 | 8 | |a 8.3 Exercises9 Numerical integration; 9.1 Newton-Cotes methods; 9.2 Composite rules; 9.3 MATLAB's integral function; 9.4 Gauss quadrature; 9.5 Exercises; 10 Initial value ODEs; 10.1 Reduction of higher order ODEs to first order; 10.2 Common methods and derivation from integration rules; 10.2.1 Backward Euler; 10.2.2 Crank-Nicolson; 10.2.3 Runge-Kutta 4; 10.3 Comparison of speed of implicit versus explicit solvers; 10.4 Stability of ODE solvers; 10.4.1 Stability of forward Euler; 10.4.2 Stability of backward Euler; 10.4.3 Stability of Crank-Nicolson; 10.4.4 Stability of Runge-Kutta 4. | |
| 505 | 8 | |a 10.5 Accuracy of ODE solvers10.5.1 Forward Euler; 10.5.2 Backward Euler; 10.5.3 Crank-Nicolson; 10.5.4 Runge-Kutta 4; 10.6 Summary, general strategy, and MATLAB ODE solvers; 10.7 Exercises; A Getting started with Octave and MATLAB; A.1 Basic operations; A.2 Arrays; A.3 Operating on arrays; A.4 Script files; A.5 Function files; A.5.1 Inline functions; A.5.2 Passing functions to other functions; A.6 Outputting information; A.7 Programming in MATLAB; A.8 Plotting; A.9 Exercises. | |
| 520 | |a Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? | ||
| 504 | |a Includes bibliographical references. | ||
| 650 | 0 | |a Engineering |x Data processing. |0 http://id.loc.gov/authorities/subjects/sh85043180 | |
| 650 | 0 | |a Science |x Data processing. |0 http://id.loc.gov/authorities/subjects/sh85118562 | |
| 650 | 0 | |a Numerical analysis. |0 http://id.loc.gov/authorities/subjects/sh85093237 | |
| 650 | 0 | |a Numerical analysis |x Data processing. | |
| 650 | 6 | |a Ingénierie |x Informatique. | |
| 650 | 6 | |a Sciences |x Informatique. | |
| 650 | 6 | |a Analyse numérique. | |
| 650 | 6 | |a Analyse numérique |x Informatique. | |
| 650 | 7 | |a MATHEMATICS |x Numerical Analysis. |2 bisacsh | |
| 650 | 7 | |a Engineering |x Data processing |2 fast | |
| 650 | 7 | |a Numerical analysis |2 fast | |
| 650 | 7 | |a Numerical analysis |x Data processing |2 fast | |
| 650 | 7 | |a Science |x Data processing |2 fast | |
| 650 | 7 | |a Numerische Mathematik |2 gnd |0 http://d-nb.info/gnd/4042805-9 | |
| 650 | 7 | |a MATLAB |2 gnd |0 http://d-nb.info/gnd/4329066-8 | |
| 700 | 1 | |a Rebholz, Leo G., |e author. | |
| 758 | |i has work: |a Introduction to scientific computing (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFRQJpBdTb4bvFWG6CrPBd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn913335694 |
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| _version_ | 1816882317315014656 |
| adam_text | |
| any_adam_object | |
| author | Heister, Timo Rebholz, Leo G. |
| author_GND | http://id.loc.gov/authorities/names/n2015042387 |
| author_facet | Heister, Timo Rebholz, Leo G. |
| author_role | aut aut |
| author_sort | Heister, Timo |
| author_variant | t h th l g r lg lgr |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA297 |
| callnumber-raw | QA297 .H45 2015 |
| callnumber-search | QA297 .H45 2015 |
| callnumber-sort | QA 3297 H45 42015 |
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| contents | Preface; Contents; 1 Introduction; 1.1 Why study numerical methods?; 1.2 Terminology; 1.3 Convergence terminology; 1.4 Exercises; 2 Computer representation of numbers and roundoff error; 2.1 Examples of the effects of roundoff error; 2.2 Binary numbers; 2.3 64 bit floating point numbers; 2.3.1 Avoid adding large and small numbers; 2.3.2 Subtracting two nearly equal numbers is bad; 2.4 Exercises; 3 Solving linear systems of equations; 3.1 Linear systems of equations and solvability; 3.2 Solving triangular systems; 3.3 Gaussian elimination; 3.4 The backslash operator; 3.5 LU decomposition. 3.6 Exercises4 Finite difference methods; 4.1 Approximating the first derivative; 4.1.1 Forward and backward differences; 4.1.2 Centered difference; 4.1.3 Three point difference formulas; 4.1.4 Further notes; 4.2 Approximating the second derivative; 4.3 Application: Initial value ODE's using the forward Euler method; 4.4 Application: Boundary value ODE's; 4.5 Exercises; 5 Solving nonlinear equations; 5.1 The bisection method; 5.2 Newton's method; 5.3 Secant method; 5.4 Comparing bisection, Newton, secant method; 5.5 Combining secant and bisection and the fzero command. 5.6 Equation solving in higher dimensions5.7 Exercises; 6 Accuracy in solving linear systems; 6.1 Gauss-Jordan elimination and finding matrix inverses; 6.2 Matrix and vector norms and condition number; 6.3 Sensitivity in linear system solving; 6.4 Exercises; 7 Eigenvalues and eigenvectors; 7.1 Mathematical definition; 7.2 Power method; 7.3 Application: Population dynamics; 7.4 Exercises; 8 Fitting curves to data; 8.1 Interpolation; 8.1.1 Interpolation by a single polynomial; 8.1.2 Piecewise polynomial interpolation; 8.2 Curve fitting; 8.2.1 Line of best fit; 8.2.2 Curve of best fit. 8.3 Exercises9 Numerical integration; 9.1 Newton-Cotes methods; 9.2 Composite rules; 9.3 MATLAB's integral function; 9.4 Gauss quadrature; 9.5 Exercises; 10 Initial value ODEs; 10.1 Reduction of higher order ODEs to first order; 10.2 Common methods and derivation from integration rules; 10.2.1 Backward Euler; 10.2.2 Crank-Nicolson; 10.2.3 Runge-Kutta 4; 10.3 Comparison of speed of implicit versus explicit solvers; 10.4 Stability of ODE solvers; 10.4.1 Stability of forward Euler; 10.4.2 Stability of backward Euler; 10.4.3 Stability of Crank-Nicolson; 10.4.4 Stability of Runge-Kutta 4. 10.5 Accuracy of ODE solvers10.5.1 Forward Euler; 10.5.2 Backward Euler; 10.5.3 Crank-Nicolson; 10.5.4 Runge-Kutta 4; 10.6 Summary, general strategy, and MATLAB ODE solvers; 10.7 Exercises; A Getting started with Octave and MATLAB; A.1 Basic operations; A.2 Arrays; A.3 Operating on arrays; A.4 Script files; A.5 Function files; A.5.1 Inline functions; A.5.2 Passing functions to other functions; A.6 Outputting information; A.7 Programming in MATLAB; A.8 Plotting; A.9 Exercises. |
| ctrlnum | (OCoLC)913335694 |
| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? 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| id | ZDB-4-EBA-ocn913335694 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:26:41Z |
| institution | BVB |
| isbn | 3110359421 9783110359428 9783110386806 3110386801 3110359405 9783110359404 |
| language | English |
| oclc_num | 913335694 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 138 pages) : illustrations (some color) |
| psigel | ZDB-4-EBA |
| publishDate | 2015 |
| publishDateSearch | 2015 |
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| record_format | marc |
| series | De Gruyter textbook. |
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| spelling | Heister, Timo, author. http://id.loc.gov/authorities/names/n2015042387 Introduction to scientific computing : for scientists and engineers / Timo Heister, Leo G. Rebholz. Berlin ; Boston : De Gruyter, [2015] 1 online resource (xi, 138 pages) : illustrations (some color) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter textbook Print version record. Preface; Contents; 1 Introduction; 1.1 Why study numerical methods?; 1.2 Terminology; 1.3 Convergence terminology; 1.4 Exercises; 2 Computer representation of numbers and roundoff error; 2.1 Examples of the effects of roundoff error; 2.2 Binary numbers; 2.3 64 bit floating point numbers; 2.3.1 Avoid adding large and small numbers; 2.3.2 Subtracting two nearly equal numbers is bad; 2.4 Exercises; 3 Solving linear systems of equations; 3.1 Linear systems of equations and solvability; 3.2 Solving triangular systems; 3.3 Gaussian elimination; 3.4 The backslash operator; 3.5 LU decomposition. 3.6 Exercises4 Finite difference methods; 4.1 Approximating the first derivative; 4.1.1 Forward and backward differences; 4.1.2 Centered difference; 4.1.3 Three point difference formulas; 4.1.4 Further notes; 4.2 Approximating the second derivative; 4.3 Application: Initial value ODE's using the forward Euler method; 4.4 Application: Boundary value ODE's; 4.5 Exercises; 5 Solving nonlinear equations; 5.1 The bisection method; 5.2 Newton's method; 5.3 Secant method; 5.4 Comparing bisection, Newton, secant method; 5.5 Combining secant and bisection and the fzero command. 5.6 Equation solving in higher dimensions5.7 Exercises; 6 Accuracy in solving linear systems; 6.1 Gauss-Jordan elimination and finding matrix inverses; 6.2 Matrix and vector norms and condition number; 6.3 Sensitivity in linear system solving; 6.4 Exercises; 7 Eigenvalues and eigenvectors; 7.1 Mathematical definition; 7.2 Power method; 7.3 Application: Population dynamics; 7.4 Exercises; 8 Fitting curves to data; 8.1 Interpolation; 8.1.1 Interpolation by a single polynomial; 8.1.2 Piecewise polynomial interpolation; 8.2 Curve fitting; 8.2.1 Line of best fit; 8.2.2 Curve of best fit. 8.3 Exercises9 Numerical integration; 9.1 Newton-Cotes methods; 9.2 Composite rules; 9.3 MATLAB's integral function; 9.4 Gauss quadrature; 9.5 Exercises; 10 Initial value ODEs; 10.1 Reduction of higher order ODEs to first order; 10.2 Common methods and derivation from integration rules; 10.2.1 Backward Euler; 10.2.2 Crank-Nicolson; 10.2.3 Runge-Kutta 4; 10.3 Comparison of speed of implicit versus explicit solvers; 10.4 Stability of ODE solvers; 10.4.1 Stability of forward Euler; 10.4.2 Stability of backward Euler; 10.4.3 Stability of Crank-Nicolson; 10.4.4 Stability of Runge-Kutta 4. 10.5 Accuracy of ODE solvers10.5.1 Forward Euler; 10.5.2 Backward Euler; 10.5.3 Crank-Nicolson; 10.5.4 Runge-Kutta 4; 10.6 Summary, general strategy, and MATLAB ODE solvers; 10.7 Exercises; A Getting started with Octave and MATLAB; A.1 Basic operations; A.2 Arrays; A.3 Operating on arrays; A.4 Script files; A.5 Function files; A.5.1 Inline functions; A.5.2 Passing functions to other functions; A.6 Outputting information; A.7 Programming in MATLAB; A.8 Plotting; A.9 Exercises. Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? Includes bibliographical references. Engineering Data processing. http://id.loc.gov/authorities/subjects/sh85043180 Science Data processing. http://id.loc.gov/authorities/subjects/sh85118562 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Numerical analysis Data processing. Ingénierie Informatique. Sciences Informatique. Analyse numérique. Analyse numérique Informatique. MATHEMATICS Numerical Analysis. bisacsh Engineering Data processing fast Numerical analysis fast Numerical analysis Data processing fast Science Data processing fast Numerische Mathematik gnd http://d-nb.info/gnd/4042805-9 MATLAB gnd http://d-nb.info/gnd/4329066-8 Rebholz, Leo G., author. has work: Introduction to scientific computing (Text) https://id.oclc.org/worldcat/entity/E39PCFRQJpBdTb4bvFWG6CrPBd https://id.oclc.org/worldcat/ontology/hasWork Print version: Heister, Timo. Introduction to scientific computing. Berlin ; Boston : De Gruyter, [2015] 9783110359404 (DLC) 2015026895 (OCoLC)913572856 De Gruyter textbook. http://id.loc.gov/authorities/names/n94049545 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=999665 Volltext |
| spellingShingle | Heister, Timo Rebholz, Leo G. Introduction to scientific computing : for scientists and engineers / De Gruyter textbook. Preface; Contents; 1 Introduction; 1.1 Why study numerical methods?; 1.2 Terminology; 1.3 Convergence terminology; 1.4 Exercises; 2 Computer representation of numbers and roundoff error; 2.1 Examples of the effects of roundoff error; 2.2 Binary numbers; 2.3 64 bit floating point numbers; 2.3.1 Avoid adding large and small numbers; 2.3.2 Subtracting two nearly equal numbers is bad; 2.4 Exercises; 3 Solving linear systems of equations; 3.1 Linear systems of equations and solvability; 3.2 Solving triangular systems; 3.3 Gaussian elimination; 3.4 The backslash operator; 3.5 LU decomposition. 3.6 Exercises4 Finite difference methods; 4.1 Approximating the first derivative; 4.1.1 Forward and backward differences; 4.1.2 Centered difference; 4.1.3 Three point difference formulas; 4.1.4 Further notes; 4.2 Approximating the second derivative; 4.3 Application: Initial value ODE's using the forward Euler method; 4.4 Application: Boundary value ODE's; 4.5 Exercises; 5 Solving nonlinear equations; 5.1 The bisection method; 5.2 Newton's method; 5.3 Secant method; 5.4 Comparing bisection, Newton, secant method; 5.5 Combining secant and bisection and the fzero command. 5.6 Equation solving in higher dimensions5.7 Exercises; 6 Accuracy in solving linear systems; 6.1 Gauss-Jordan elimination and finding matrix inverses; 6.2 Matrix and vector norms and condition number; 6.3 Sensitivity in linear system solving; 6.4 Exercises; 7 Eigenvalues and eigenvectors; 7.1 Mathematical definition; 7.2 Power method; 7.3 Application: Population dynamics; 7.4 Exercises; 8 Fitting curves to data; 8.1 Interpolation; 8.1.1 Interpolation by a single polynomial; 8.1.2 Piecewise polynomial interpolation; 8.2 Curve fitting; 8.2.1 Line of best fit; 8.2.2 Curve of best fit. 8.3 Exercises9 Numerical integration; 9.1 Newton-Cotes methods; 9.2 Composite rules; 9.3 MATLAB's integral function; 9.4 Gauss quadrature; 9.5 Exercises; 10 Initial value ODEs; 10.1 Reduction of higher order ODEs to first order; 10.2 Common methods and derivation from integration rules; 10.2.1 Backward Euler; 10.2.2 Crank-Nicolson; 10.2.3 Runge-Kutta 4; 10.3 Comparison of speed of implicit versus explicit solvers; 10.4 Stability of ODE solvers; 10.4.1 Stability of forward Euler; 10.4.2 Stability of backward Euler; 10.4.3 Stability of Crank-Nicolson; 10.4.4 Stability of Runge-Kutta 4. 10.5 Accuracy of ODE solvers10.5.1 Forward Euler; 10.5.2 Backward Euler; 10.5.3 Crank-Nicolson; 10.5.4 Runge-Kutta 4; 10.6 Summary, general strategy, and MATLAB ODE solvers; 10.7 Exercises; A Getting started with Octave and MATLAB; A.1 Basic operations; A.2 Arrays; A.3 Operating on arrays; A.4 Script files; A.5 Function files; A.5.1 Inline functions; A.5.2 Passing functions to other functions; A.6 Outputting information; A.7 Programming in MATLAB; A.8 Plotting; A.9 Exercises. Engineering Data processing. http://id.loc.gov/authorities/subjects/sh85043180 Science Data processing. http://id.loc.gov/authorities/subjects/sh85118562 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Numerical analysis Data processing. Ingénierie Informatique. Sciences Informatique. Analyse numérique. Analyse numérique Informatique. MATHEMATICS Numerical Analysis. bisacsh Engineering Data processing fast Numerical analysis fast Numerical analysis Data processing fast Science Data processing fast Numerische Mathematik gnd http://d-nb.info/gnd/4042805-9 MATLAB gnd http://d-nb.info/gnd/4329066-8 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85043180 http://id.loc.gov/authorities/subjects/sh85118562 http://id.loc.gov/authorities/subjects/sh85093237 http://d-nb.info/gnd/4042805-9 http://d-nb.info/gnd/4329066-8 |
| title | Introduction to scientific computing : for scientists and engineers / |
| title_auth | Introduction to scientific computing : for scientists and engineers / |
| title_exact_search | Introduction to scientific computing : for scientists and engineers / |
| title_full | Introduction to scientific computing : for scientists and engineers / Timo Heister, Leo G. Rebholz. |
| title_fullStr | Introduction to scientific computing : for scientists and engineers / Timo Heister, Leo G. Rebholz. |
| title_full_unstemmed | Introduction to scientific computing : for scientists and engineers / Timo Heister, Leo G. Rebholz. |
| title_short | Introduction to scientific computing : |
| title_sort | introduction to scientific computing for scientists and engineers |
| title_sub | for scientists and engineers / |
| topic | Engineering Data processing. http://id.loc.gov/authorities/subjects/sh85043180 Science Data processing. http://id.loc.gov/authorities/subjects/sh85118562 Numerical analysis. http://id.loc.gov/authorities/subjects/sh85093237 Numerical analysis Data processing. Ingénierie Informatique. Sciences Informatique. Analyse numérique. Analyse numérique Informatique. MATHEMATICS Numerical Analysis. bisacsh Engineering Data processing fast Numerical analysis fast Numerical analysis Data processing fast Science Data processing fast Numerische Mathematik gnd http://d-nb.info/gnd/4042805-9 MATLAB gnd http://d-nb.info/gnd/4329066-8 |
| topic_facet | Engineering Data processing. Science Data processing. Numerical analysis. Numerical analysis Data processing. Ingénierie Informatique. Sciences Informatique. Analyse numérique. Analyse numérique Informatique. MATHEMATICS Numerical Analysis. Engineering Data processing Numerical analysis Numerical analysis Data processing Science Data processing Numerische Mathematik MATLAB |
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