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18.725 Algebraic Geometry (MIT) 18.725 Algebraic Geometry (MIT)

Description

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms. This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

Subjects

algebraic geometry | algebraic geometry | Zariski topology | Zariski topology | Product Topology | Product Topology | Affine Varieties | Affine Varieties | Projective Varieties | Projective Varieties | Noether Normalization | Noether Normalization | Affine Morphisms | Affine Morphisms | Finite Morphisms | Finite Morphisms | Sheaves | Sheaves | ?s Theorem | ?s Theorem | Kahler Differentials | Kahler Differentials | Canonical Bundles | Canonical Bundles | Riemann-Hurwitz Formula | Riemann-Hurwitz Formula

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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5.841 Crystal Structure Refinement (MIT) 5.841 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.725 Algebraic Geometry (MIT) 18.725 Algebraic Geometry (MIT)

Description

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms. This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

Subjects

algebraic geometry | algebraic geometry | Zariski topology | Zariski topology | Product Topology | Product Topology | Affine Varieties | Affine Varieties | Projective Varieties | Projective Varieties | Noether Normalization | Noether Normalization | Affine Morphisms | Affine Morphisms | Finite Morphisms | Finite Morphisms | Sheaves | Sheaves | Bezout’s Theorem | Bezout’s Theorem | Kahler Differentials | Kahler Differentials | Canonical Bundles | Canonical Bundles | Riemann-Hurwitz Formula | Riemann-Hurwitz Formula | Chevalley’s Theorem | Chevalley’s Theorem | Bertini’s Theorem | Bertini’s Theorem

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.327 Wavelets, Filter Banks and Applications (MIT) 18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | Multiwavelets

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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21L.015 Introduction to Media Studies (MIT) 21L.015 Introduction to Media Studies (MIT)

Description

Introduction to Media Studies is designed for students who have grown up in a rapidly changing global multimedia environment and want to become more literate and critical consumers and producers of media. Through an interdisciplinary comparative and historical lens, the course defines "media" broadly as including oral, print, performance, photographic, broadcast, cinematic, and digital cultural forms and practices. The course looks at the nature of mediated communication, the functions of media, the history of transformations in media and the institutions that help define media's place in society. This year’s course will focus on issues of network culture and media convergence, addressing such subjects as Intellectual Property, peer2peer authoring, blogging, and game modification. Introduction to Media Studies is designed for students who have grown up in a rapidly changing global multimedia environment and want to become more literate and critical consumers and producers of media. Through an interdisciplinary comparative and historical lens, the course defines "media" broadly as including oral, print, performance, photographic, broadcast, cinematic, and digital cultural forms and practices. The course looks at the nature of mediated communication, the functions of media, the history of transformations in media and the institutions that help define media's place in society. This year’s course will focus on issues of network culture and media convergence, addressing such subjects as Intellectual Property, peer2peer authoring, blogging, and game modification.

Subjects

Comparative Media Studies | Comparative Media Studies | global multimedia environment | global multimedia environment | literate | literate | critical | critical | consumers | consumers | producers | producers | interdisciplinary | interdisciplinary | comparative | comparative | historical | historical | lens | lens | the course defines oral | the course defines oral | print | print | performance | performance | photographic | photographic | broadcast | broadcast | cinematic | cinematic | digital | digital | cultural | cultural | forms | forms | practices | practices | mediated communication | mediated communication | functions | functions | society | society | network culture | network culture | media convergence | media convergence | Intellectual Property | Intellectual Property | peer2peer authoring | peer2peer authoring | blogging | blogging | game modification | game modification | lens | the course defines oral | lens | the course defines oral

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Research Seminar: Michelangelo: A Life on Paper Research Seminar: Michelangelo: A Life on Paper

Description

In this lecture recorded as a part of the University of Oxford History of Art Department's Research Seminar series, Professor Leonard Barkan (Princeton University) discusses the theme "Michelangelo: A Life on Paper". Recording date - 4th November 2010. In this lecture recorded as a part of the University of Oxford History of Art Department's Research Seminar series, Professor Leonard Barkan (Princeton University) discusses the theme "Michelangelo: A Life on Paper". Recording date - 4th November 2010.

Subjects

Michelangelo | Michelangelo | history | history | art | art | History of Art | History of Art | fine art | fine art | Michelangelo | history | art | History of Art | fine art | 2010-11-04 | Michelangelo | history | art | History of Art | fine art | 2010-11-04

License

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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5.841 Crystal Structure Refinement (MIT) 5.841 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.327 Wavelets, Filter Banks and Applications (MIT) 18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | Multiwavelets

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Lillian Tibbs, arrested for stealing a dress Lillian Tibbs, arrested for stealing a dress

Description

Subjects

portrait | portrait | blackandwhite | blackandwhite | woman | woman | blur | blur | eye | eye | face | face | hat | hat | sepia | sepia | hair | hair | nose | nose | chair | chair | dress | dress | fine | fine | grain | grain | custody | custody | blouse | blouse | clothes | clothes | criminal | criminal | crime | crime | photograph | photograph | mysterious | mysterious | mugshot | mugshot | unusual | unusual | ww1 | ww1 | scratch | scratch | theft | theft | seated | seated | policestation | policestation | firstworldwar | firstworldwar | cardigan | cardigan | youngwoman | youngwoman | attentive | attentive | accused | accused | fraud | fraud | arrested | arrested | stealing | stealing | prisoner | prisoner | homefront | homefront | secretlife | secretlife | fascinating | fascinating | digitalimage | digitalimage | blyth | blyth | sixmonths | sixmonths | larceny | larceny | frill | frill | blackborder | blackborder | northshields | northshields | transcription | transcription | socialhistory | socialhistory | £5 | £5 | newsreport | newsreport | courtcase | courtcase | stolenproperty | stolenproperty | criminalrecord | criminalrecord | publicrecords | publicrecords | goodbehaviour | goodbehaviour | neutralbackground | neutralbackground | pettylarceny | pettylarceny | newspaperreport | newspaperreport | 190216 | 190216 | northshieldspolicecourt | northshieldspolicecourt | £5fine | £5fine | northshieldspolicestation | northshieldspolicestation | theshieldsdailynews | theshieldsdailynews | northshieldslocalstudieslibrary | northshieldslocalstudieslibrary | 19ripponterrace | 19ripponterrace | criminalfacesofnorthshieldsfirstworldwar | criminalfacesofnorthshieldsfirstworldwar | microfilmcopies | microfilmcopies | 14september1914 | 14september1914 | mrsagcolledge | mrsagcolledge | detmason | detmason | shieldspolice | shieldspolice | lilliantibbs | lilliantibbs | blythwoman | blythwoman | 12september1914 | 12september1914

License

No known copyright restrictions

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.327 Wavelets, Filter Banks and Applications (MIT) 18.327 Wavelets, Filter Banks and Applications (MIT)

Description

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | Multiwavelets

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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21L.015 Introduction to Media Studies (MIT) 21L.015 Introduction to Media Studies (MIT)

Description

Introduction to Media Studies is designed for students who have grown up in a rapidly changing global multimedia environment and want to become more literate and critical consumers and producers of media. Through an interdisciplinary comparative and historical lens, the course defines "media" broadly as including oral, print, performance, photographic, broadcast, cinematic, and digital cultural forms and practices. The course looks at the nature of mediated communication, the functions of media, the history of transformations in media and the institutions that help define media's place in society. This year’s course will focus on issues of network culture and media convergence, addressing such subjects as Intellectual Property, peer2peer authoring, blogging, and game modification. Introduction to Media Studies is designed for students who have grown up in a rapidly changing global multimedia environment and want to become more literate and critical consumers and producers of media. Through an interdisciplinary comparative and historical lens, the course defines "media" broadly as including oral, print, performance, photographic, broadcast, cinematic, and digital cultural forms and practices. The course looks at the nature of mediated communication, the functions of media, the history of transformations in media and the institutions that help define media's place in society. This year’s course will focus on issues of network culture and media convergence, addressing such subjects as Intellectual Property, peer2peer authoring, blogging, and game modification.

Subjects

Comparative Media Studies | Comparative Media Studies | global multimedia environment | global multimedia environment | literate | literate | critical | critical | consumers | consumers | producers | producers | interdisciplinary | interdisciplinary | comparative | comparative | historical | historical | lens | lens | the course defines oral | the course defines oral | print | print | performance | performance | photographic | photographic | broadcast | broadcast | cinematic | cinematic | digital | digital | cultural | cultural | forms | forms | practices | practices | mediated communication | mediated communication | functions | functions | society | society | network culture | network culture | media convergence | media convergence | Intellectual Property | Intellectual Property | peer2peer authoring | peer2peer authoring | blogging | blogging | game modification | game modification | lens | the course defines oral | lens | the course defines oral

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.... is actually Navan .... is actually Navan

Description

Subjects

eason | eason | easonson | easonson | easoncollection | easoncollection | easonphotographiccollection | easonphotographiccollection | glassnegative | glassnegative | 20thcentury | 20thcentury | nationallibraryofireland | nationallibraryofireland | street | street | horses | horses | carts | carts | mangans | mangans | arch | arch | peterfinegan | peterfinegan | navanmedical | navanmedical | possiblecataloguecorrection | possiblecataloguecorrection | navan | navan | ludlowstreet | ludlowstreet | locationidentified | locationidentified | countymeath | countymeath | navancountymeath | navancountymeath | mangan | mangan | finegan | finegan | farrell | farrell

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

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18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics (MIT) 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics (MIT)

Description

This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.

Subjects

linear algebra | linear algebra | eigensystems for Maxwell's equations | eigensystems for Maxwell's equations | symmetry groups | symmetry groups | representation theory | representation theory | Bloch's theorem | Bloch's theorem | numerical eigensolver methods | numerical eigensolver methods | time and frequency-domain computation | time and frequency-domain computation | perturbation theory | perturbation theory | coupled-mode theories | coupled-mode theories | waveguide theory | waveguide theory | adiabatic transitions | adiabatic transitions | Optical phenomena | Optical phenomena | photonic crystals | photonic crystals | band gaps | band gaps | anomalous diffraction | anomalous diffraction | mechanisms for optical confinement | mechanisms for optical confinement | optical fibers | optical fibers | integrated optical devices | integrated optical devices

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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[Seatrain Louisiana at Refinery Dock, Seatrain Lines]

Description

Subjects

ship | shipping | refinery | loadingdocks | refineries | hoistingmachinery | seatrainlines | railroadtankcars | seatrainlouisiana | ssseatrainlouisiana

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9.675 The Development of Object and Face Recognition (MIT) 9.675 The Development of Object and Face Recognition (MIT)

Description

This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field. This course takes a 'back to the beginning' view that aims to better understand the end result. What might be the developmental processes that lead to the organization of 'booming, buzzing confusions' into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field.

Subjects

computational theories of human cognition | computational theories of human cognition | principles of inductive learning and inference | principles of inductive learning and inference | representation of knowledge | representation of knowledge | computational frameworks | computational frameworks | Bayesian models | Bayesian models | hierarchical Bayesian models | hierarchical Bayesian models | probabilistic graphical models | probabilistic graphical models | nonparametric statistical models | nonparametric statistical models | Bayesian Occam's razor | Bayesian Occam's razor | sampling algorithms for approximate learning and inference | sampling algorithms for approximate learning and inference | probabilistic models defined over structured representations such as first-order logic | probabilistic models defined over structured representations such as first-order logic | grammars | grammars | relational schemas | relational schemas | core aspects of cognition | core aspects of cognition | concept learning | concept learning | concept categorization | concept categorization | causal reasoning | causal reasoning | theory formation | theory formation | language acquisition | language acquisition | social inference | social inference

License

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18.950 Differential Geometry (MIT) 18.950 Differential Geometry (MIT)

Description

This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied. This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied.

Subjects

Metrics | Metrics | Lie bracket | Lie bracket | connections | connections | geodesics | geodesics | tensors | tensors | intrinsic and extrinsic curvature | intrinsic and extrinsic curvature | defined manifolds using coordinate charts | defined manifolds using coordinate charts | Curves and surfaces in three dimensions | Curves and surfaces in three dimensions | Gauss-Bonnet theorem for surfaces | Gauss-Bonnet theorem for surfaces | general relativity | general relativity

License

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5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.

Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scattering

License

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Al, Si 12, Na 0.02 (wt%), eutectic alloy - refined microstructure Al, Si 12, Na 0.02 (wt%), eutectic alloy - refined microstructure

Description

This sample is a casting alloy of eutectic composition. The microstructure has been refined by modification through the addition of a small amount of sodium to the alloy composition. The large silicon plates have been altered to a more favourable fibrous form, leading to an enhancement of the mechanical properties due to the refinement of the microstructure. There is also a change to a planar interface during solidification, which minimises porosity in the casting. This sample is a casting alloy of eutectic composition. The microstructure has been refined by modification through the addition of a small amount of sodium to the alloy composition. The large silicon plates have been altered to a more favourable fibrous form, leading to an enhancement of the mechanical properties due to the refinement of the microstructure. There is also a change to a planar interface during solidification, which minimises porosity in the casting.

Subjects

alloy | alloy | aluminium | aluminium | eutectic | eutectic | metal | metal | modification | modification | refined microstructure | refined microstructure | silicon | silicon | sodium | sodium | DoITPoMS | DoITPoMS | University of Cambridge | University of Cambridge | micrograph | micrograph | corematerials | corematerials | ukoer | ukoer

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Al, Si 12, Na 0.02 (wt%), eutectic alloy - refined microstructure Al, Si 12, Na 0.02 (wt%), eutectic alloy - refined microstructure

Description

This sample is a casting alloy of eutectic composition. The microstructure has been refined by modification through the addition of a small amount of sodium to the alloy composition. The large silicon plates have been altered to a more favourable fibrous form, leading to an enhancement of the mechanical properties due to the refinement of the microstructure. There is also a change to a planar interface during solidification, which minimises porosity in the casting. This sample is a casting alloy of eutectic composition. The microstructure has been refined by modification through the addition of a small amount of sodium to the alloy composition. The large silicon plates have been altered to a more favourable fibrous form, leading to an enhancement of the mechanical properties due to the refinement of the microstructure. There is also a change to a planar interface during solidification, which minimises porosity in the casting.

Subjects

alloy | alloy | aluminium | aluminium | eutectic | eutectic | metal | metal | modification | modification | refined microstructure | refined microstructure | silicon | silicon | sodium | sodium | DoITPoMS | DoITPoMS | University of Cambridge | University of Cambridge | micrograph | micrograph | corematerials | corematerials | ukoer | ukoer

License

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22.611J Introduction to Plasma Physics I (MIT) 22.611J Introduction to Plasma Physics I (MIT)

Description

In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne In this course, students will learn about plasmas, the fourth state of matter. The plasma state dominates the visible universe, and is of increasing economic importance. Plasmas behave in lots of interesting and sometimes unexpected ways. The course is intended only as a first plasma physics course, but includes critical concepts needed for a foundation for further study. A solid undergraduate background in classical physics, electromagnetic theory including Maxwell's equations, and mathematical familiarity with partial differential equations and complex analysis are prerequisites. The course introduces plasma phenomena relevant to energy generation by controlled thermonuclear fusion and to astrophysics, coulomb collisions and transport processes, motion of charged particles in magne

Subjects

plasma phenomena | plasma phenomena | energy generation | energy generation | controlled thermonuclear fusion | controlled thermonuclear fusion | astrophysics | astrophysics | Coulomb collisions | Coulomb collisions | transport processes | transport processes | charged particles | charged particles | magnetic fields | magnetic fields | plasma confinement schemes | plasma confinement schemes | MHD models | MHD models | simple equilibrium | simple equilibrium | stability analysis | stability analysis | Two-fluid hydrodynamic plasma models | Two-fluid hydrodynamic plasma models | wave propagation | wave propagation | kinetic theory | kinetic theory | Vlasov plasma model | Vlasov plasma model | electron plasma waves | electron plasma waves | Landau damping | Landau damping | ion-acoustic waves | ion-acoustic waves | streaming instabilities | streaming instabilities | fourth state of matter | fourth state of matter | plasma state | plasma state | visible universe | visible universe | economics | economics | plasmas | plasmas | motion of charged particles | motion of charged particles | two-fluid hydrodynamic plasma models | two-fluid hydrodynamic plasma models | Debye Shielding | Debye Shielding | collective effects | collective effects | charged particle motion | charged particle motion | EM Fields | EM Fields | cross-sections | cross-sections | relaxation | relaxation | fluid plasma descriptions | fluid plasma descriptions | MHD equilibrium | MHD equilibrium | MHD dynamics | MHD dynamics | dynamics in two-fluid plasmas | dynamics in two-fluid plasmas | cold plasma waves | cold plasma waves | magnetic field | magnetic field | microscopic to fluid plasma descriptions | microscopic to fluid plasma descriptions | Vlasov-Maxwell kinetic theory.linear Landau growth | Vlasov-Maxwell kinetic theory.linear Landau growth | kinetic description of waves | kinetic description of waves | instabilities | instabilities | Vlasov-Maxwell kinetic theory | Vlasov-Maxwell kinetic theory | linear Landau growth | linear Landau growth | 22.611 | 22.611 | 6.651 | 6.651 | 8.613 | 8.613

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