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Call number: | 9784431558033:ONLINE Show nearby items on shelf |
Title: | From Tracking Code to Analysis : Generalised Courant-Snyder Theory for Any Accelerator Model |
Author(s): |
Etienne Forest |
Date: | 2016 |
Publisher: | Springer Japan |
Size: | 1 online resource (347 p) |
Note: | EBL eBook |
Contents: | Introduction -- The linear transverse normal form: one degree of freedom -- The nonlinear transverse normal form: one degree of freedom -- Classification of linear normal forms -- Nonlinear normal forms -- Spin normal form -- The nonlinear spin-orbi tal phase advance: the mother of all algorithms -- Deprit-Guignard perturbation theory faithful to the code -- Here is the conclusion of this book -- Phasors basis: why do I reject symplectic phasors? -- The logarithm of a map -- Stroboscopic average for the ISF vector n -- Hierarchy of Analytical Methods. |
ISBN: | 9784431558026 |
Series: | eBooks |
Keywords: | Particle accelerators, Design and construction, Computer programs |
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Call number: | 9783319393391:ONLINE Show nearby items on shelf |
Title: | Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014 |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.) |
Contents: | Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic |
vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular | |
varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded | |
topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces | |
ISBN: | 9783319393391 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds |
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Call number: | 9781608077779:ONLINE Show nearby items on shelf |
Title: | Terahertz metrology |
Author(s): |
Mira Naftaly |
Date: | 2015 |
Publisher: | Artech House |
Size: | 1 online resource (386 p.) |
Contents: | Chapter 1 Terahertz Time-Domain Spectrometers -- Photoconductive Emitters and Detectors -- Optical Rectification -- Electro-Optic Detection -- Terahertz Air-Based Coherent Detection -- Cherenkov (Tilted Wavefront) Emitters and Detectors -- Continuou s-Wave Terahertz Time-Domain Spectrometer and Microwave Photonics -- Types of Continuous-Wave Terahertz Emitters and Detectors -- Time-Domain Spectrometer Configurations -- Transmission -- Reflection -- Attenuated Total Reflection -- Asynchronous Optical Sampling -- Substrate Lenses -- Commercial Systems -- Parameter Extraction in Time-Domain . Chapter 2 Spectrometers -- Material Properties and Wave Propagation -- Complex Refractive Index and Complex Permittivity -- Plane Wave Propagation Across an Interf ace.Fresnel Equations -- Plane Wave Propagation Through a Dielectric Slab -- Fabry-Perot Effect -- Extracting Optical Parameters from Terahertz Time-Domain Spectrometers Data -- Transmission-mode Terahertz Time-Domain Spectrometers: Approximation -- Trans mission-Mode Terahertz Time-Domain Spectrometers: Exact Solution -- Reflection-Mode Terahertz Time-Domain Spectrometers: Single Reflection -- Reflection-Mode Terahertz Time-Domain Spectrometers: Double Reflection -- Attenuated Total Reflection -- Preproce ssing and Postprocessing of Data -- Signal Averaging in the Time and Frequency Domains -- Signal Denoising -- Phase Unwrapping -- Sample Requirements -- Sample Thickness -- Lateral Dimensions of Samples -- Loss: Absorption, Scattering, Diffraction |
Chapter 3 Metrology for Time-Domain Spectrometers -- Performance Parameters: Sensitivity, Resolution, Precision, Accuracy, Dynamic Range, and Signal-to-Noise Ratio -- Dynamic Range and Signal-to-Noise Ratio of Terahertz Time-Domain Spectrometers -- System Performance Limits Due to Dynamic Range and Signal-to-Noise Ratio -- Frequency Resolution -- Measurement Bandwidth -- Sources of Random Noise -- Amplitude -- Phase -- Systematic Errors -- Alignment Errors -- Focal Plane Defocusing -- Delay Line Err ors -- Terahertz Beam Profile -- Chapter 4 Evaluation of Uncertainty in Time-Domain Spectroscopy -- Method of Uncertainty Evaluation -- Evaluation of Random and Systematic Errors -- Propagation and Combination of Measurement Uncertainty -- Measurement wit h Resolution Limit -- Sources of Uncertainty in Terahertz Time-Domain Spectroscopy -- Random and Systematic Errors in Amplitude -- Random and Systematic Errors in Sample Thickness -- Random and Systematic Errors in Sample Alignment -- Systematic Error in the Approximated Transfer Function -- Systematic Error Due to Reflections -- Systematic Error in Physical Constants -- Uncertainty in Optical Constants: A Combination of Variances | |
Chapter 5 Metrology for Fourier Transform Spectrometers -- Spectrometer Configurations -- Michelson -- Mach-Zender -- Polarized Fourier Transform Spectrometer (Martin-Pupplett Interferometer) -- Modes of Operation: Step and Integrate or Fast Scannin g -- Moving Stage -- General Fourier Transform Spectrometer Advantages -- Fourier Transform Spectrometer Metrology -- Encoders, Synchronizing, and Time-Stamping -- Instrument Line Function: A Spectral Resolution Limitation -- Apodization -- Cosine and Sin e Terms and Phase Correction Techniques -- Achievable Spectral Resolution -- Sample Measurement Parameter Recovery -- Thin Sample Approximation: Lossless Case -- Dispersive Medium -- Thick Sample Analysis (or Noncollimated Measurement) -- Absorption Coeff icients -- Sources of Noise and Uncertainties -- Time-Domain Errors -- (Software) Noise Reduction Techniques -- Chapter 6 Terahertz Spectrometer Calibration -- Why Calibrate Terahertz Spectrometers -- Frequency Calibration -- Gases -- Solids -- Resonant M esh Filters -- Etalons -- Summary of Frequency Calibration Standards -- Amplitude Linearity Calibration -- Reflection Standards | |
Chapter 7 Terahertz Imaging -- Image Resolution of a Terahertz Imaging System -- Data Analysis in the Far Field -- Imaging Thin Layers -- Spatial Resolution Tests -- Near-Field Imaging -- Chemical Imaging -- Focal Plane Array Microbolometer Cameras -- Chapter 8 Metrology for Vector Network Analyzers -- Vector Network Analyzers -- The Role of a Network Analyzer -- Scattering Parameters -- Vector Network Analyzer Systems -- Extender Heads -- Good Practice Tips -- Metallic Waveguides -- Basic Properti es -- Dispersion -- Standardized Sizes and Frequency Ranges -- Flanges/Interfaces -- Good Practice Tips -- Calibration Standards and Methods -- Calibration: General Principles -- Types of Calibration Standard -- One-Port Calibration Methods -- Two-Port Ca libration Methods -- Connection Repeatability -- System Verification -- Chapter 9 Terahertz Optics -- Terahertz Optical Materials -- Transparency at Terahertz Frequencies -- Inorganic Crystals for Terahertz Optics -- Polymers for Terahertz Optics -- Metal Reflectivities -- Gaussian Optics -- Gaussian Beams -- Parabolic Mirrors -- Dichroic Optical Elements -- Terahertz Transparent/Visible Opaque -- Terahertz Opaque/Visible Transparent -- Terahertz Reflective/Visible Transparent -- Terahertz Transparent/Vis ible Reflective -- Wire-Grid Polarizers -- Antireflection Coatings -- Photonic Crystal Fibers and Terahertz . Waveguides | |
Chapter 10 Terahertz Laser Sources -- Optically Pumped Gas Lasers -- P-Germanium Laser -- Quantum Cascade Lasers -- Pulsed Difference Frequency Generation -- High-Resolution Frequency Measurements Using Continuous-Wave Difference Frequency Generatio n -- Optical Parametric Oscillators -- Free Electron Lasers -- Chapter 11 Electronic Sources of Terahertz Radiation and Terahertz Detectors -- Electronic Sources of Terahertz Radiation: Introduction and Terminology -- Vacuum Electronic Sources -- Backward Wave Oscillators -- Extended Interaction Klystrons -- Solid-State Devices -- Gunn Diodes and IMPATT Oscillators and Amplifiers -- Transistor Amplifiers -- Frequency Multiplied Sources -- Source Characteristics Summary -- Detectors of Terahertz Radiation: Introduction and Terminology . Incoherent Detectors -- Golay Cell -- Pyroelectric Detectors -- Room-Temperature Bolometers -- Cryogenic Bolometers -- Photoconductive Detectors -- Semiconductor Diode Rectifiers -- Thermopiles -- Incoherent Detector Summar y -- Coherent Detectors: Introduction -- Schottky Diode Mixers -- Frequency Measurement | |
ISBN: | 9781608077762 |
Series: | eBooks |
Series: | Artech ebooks |
Keywords: | Terahertz spectroscopy. , Metrology. , Terahertz technology. |
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Call number: | 9781608077113:ONLINE Show nearby items on shelf |
Title: | Control components using Si, GaAs, and GaN technologies |
Author(s): |
I. J. Bahl |
Date: | 2014 |
Publisher: | Artech House |
Size: | 1 online resource (310 p) |
Contents: | Chapter 1 Introduction - History of Components - Types of Control Components - Solid-State Switching Devices - Design of Control Components - Fabrication of Control Components - Chapter 2 Control Devices - PIN Diodes - Operation of PIN Diodes - PIN Diode Models - GaAs MESFETs - Operation of MESFETs - Linear Switch FET Models - Nonlinear Switch FET Models - GaAs HEMTs - GaAs HBTs - GaN HEMTs - CMOS Transistors - Operation of CMOS Switch - Various Body Floating Techniques - CMOS Transistor Models - Schottky Diodes - Varactor Diodes - Transistor Model Scaling - Biasing of Switching Devices - Biasing of PIN Diodes - Biasing of Transistors - Switching Speed of PIN Diodes - Switching Speed of Transistors - Comparison of Switching Devices - Chapter 3 Switches - Switch Parameters - Basic Requirements of a Switch for Wireless Applications - Design of Switches - Switch Configurations - Basic Theory of Switches - Multiport Switches - Matrix Switches - Diversity Switch - High Isolation Switches - Broadband Switches - High-Power Switches - Impedance Transformation Technique - Stacked FETs Method - Resonant Circuit Technique - GaN HEMT Switches - Power Handling of PIN Diode Switches - Low Distortion Switches - Performance of Switch Circuits - PIN D iode Switch Circuits - MESFET Switch Circuits - HEMT Switch Circuits - CMOS Switch Circuits - Comparison of Switch Technologies - Novel Switch Configurations - Filter-Integrated Switch - Redundant Switch - Switched Variable Power Amplifier - Switches with Integrated Control - Intermodulation Analysis of Switches - PIN Diode Switches - MESFET Switches |
Chapter 4 Phase Shifters - Digital Phase Shifters - Analog Phase Shifters - Active Phase Shifters - Theory of Phase Shifters - Reflection-Type Phase Shifter - Switched-Line Phase Shifter - Loaded-Line Phase Shifters - Switched-Network Phase Shifter s - Embedded-Device Phase Shifters - Multibit Phase Shifter Circuits - RMS Errors - PIN Diode Phase Shifters - MESFET/HEMT Phase Shifters - CMOS Phase Shifters - Analog Phase Shifters - Voltage-Controlled Reflection-Type Phase Shifters - Voltage-Controlle d Transmission-Type Phase Shifters - Analog Varactor Diode Phase Shifters - Analog CMOS Phase Shifters - Broadband Phase Shifters - GaAs MESFET/HEMT Broadband Phase Shifters - Broadband CMOS Phase Shifters - Ultrawideband Phase Shifters - Millimeter-Wave Phase Shifters - PIN/Schottky Diode Millimeter-Wave Phase Shifters -MESFET/HEMT Millimeter-Wave Phase Shifters - CMOS Millimeter-Wave Phase Shifters - Active Phase Shifters - Dual-Gate FET Phase Shifters - Switchable-Amplifier Phase Shifters - Vector Modu lator Phase Shifters - Chapter 5 Attenuators - Theory of Attenuators - Fabrication of Attenuators - Fixed Value Attenuators - Attenuator Pad - Temperature Variable Attenuator - Multibit Attenuators - PIN Diode Step Attenuators - GaAs MMIC Step Attenuators - Si CMOS Step Attenuators - Variable Voltage Attenuators - PIN Diode Variable Attenuators - MESFET Variable Attenuators - CMOS Variable Attenuator - GaN HEMT Attenuator - Linear Voltage Variable Attenuators -Reflection-Type Attenuators - Balanced Attenu ators - Frequency Dependent Attenuators - Phase Compensated Attenuators - CMOS Attenuator with Integrated Switch - Distortion in Attenuators - PIN Diode Attenuators - FET Attenuators | |
Chapter 6 Limiters - Limiter Characterization - Limiter Types - PIN Diode Limiters - Analysis of PIN Diode Limiter - Si PIN Diode Limiters in Microstrip Configuration - GaAs PIN Diode Limiters - Matched Limiters - Schottky Diode Limiters - Analysis of Schottky Diode Limiter - Schottky Diode Design and Limiter Configuration - Broadband High Power Limiters - Monolithic GaAs Schottky Diode Limiter Circuits - Limiting Amplifiers - 10-W Limiter with Embedded LNA - BiCMOS Diode Limiter - GaN Schottky Diod e Limiters | |
ISBN: | 9781608077113 |
Series: | Artech House microwave library |
Series: | eBooks |
Series: | Artech eBooks |
Keywords: | Electronic circuits, Mathematical models. , Solid state electronics , Microwave integrated circuits |
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Call number: | 9781608070480:ONLINE Show nearby items on shelf |
Title: | Discrete oscillator design |
Author(s): |
Randall W. Rhea |
Date: | 2010 |
Publisher: | Artech House |
Size: | 1 online resource (450 p.) |
Contents: | Chapter 1 Linear Techniques -- Open-Loop Method -- Match Requirements -- Aligning the Maximum Phase Slope -- Stable Amplifier -- Gain Peak at Phase Zero Intersection -- Moderate Gain -- Random Resonator and Amplifier Combination -- Naming Convention s -- Amplifiers for Sustaining Stages -- Bipolar Amplifier Configurations -- Stabilizing Bipolar Amplifiers -- Stabilized FET Amplifier Configurations -- Basic Common Emitter Amplifier -- Statistical Analysis of the Amplifier -- Amplifier with Resistive F eedback -- General-Purpose Resistive-Feedback Amplifier -- Transformer-Feedback Amplifiers -- Monolythic Microwave Integrated Circuit Amplifiers -- Differential Amplifiers -- Phase-Lead Compensation -- Resonators -- R-C Phase Shift Network -- Delay-Line P hase-Shift Network -- L-C Parallel and Series Resonators -- Loaded Q . Unloaded Q -- Resonator Loss -- Colpitts Resonator -- Resonator Coupling -- Matching with the Resonator -- Measuring the Unloaded Q -- Coupled Resonator Oscillator Example -- Resonator Summary -- One-Port Method -- Negative-Resistance Oscillators -- Negative-Conductance Oscillators -- Analyzing Existing Oscillators -- Optimizing the Design |
Chapter 2 Nonlinear Techniques -- Harmonic Balance -- Nonlinear Amplifiers -- Quiescent Current and Compression -- Impedance Shift -- Phase Shift -- Output Spectrum -- Time Domain Waveform -- Conversion Efficiency -- Operating Class -- Nonlinear Ope n-Loop Cascade -- Nonlinear HB Colpitts -- Closing the Loop and Excitation -- Harmonic Balance Colpitts Output Spectrum -- Excitation Current Versus Oscillator Parameters -- Nonlinear Negative-Resistance Oscillator -- Output Coupling -- Coupling Node -- L oad Pulling -- Loaded Q and Load Pulling -- Degree of Coupling -- Loaded Q and Coupling -- Coupling Reactance and Load Pulling -- Coupling Reactance and Harmonics -- Output Coupling Example 2 -- Passive Level Control -- Supply Pushing -- Spurious Modes -- Unstable Amplifiers -- Multiple Phase Zero Crossings -- Parametric Modes -- Multiple Resonance Modes -- Chapter 3 Transient Techniques -- Starting Modes -- Noise Mode of Starting -- Tansient Mode of Starting -- Time Constant of the Supply Step -- Simulat ion Techniques -- SPICE -- Cayenne -- Triggering -- Simulation Techniques for High Loaded Q -- Steady-State Oscillator Waveforms -- Clapp Oscillator Waveforms -- The Resonator Voltage -- Varactor Coupling -- Waveform Derived Output Spectrum | |
Chapter 4 Noise -- Vector Representation of the Oscillator Output -- Jitter -- The Output in the Frequency Domain -- SSB Phase Noise -- Residual FM and Residual PM -- Two-Port Noise -- Acoustic Disturbances -- Predicting Phase Noise -- Linear Time I nvariant Theory -- Extensions to LTI-Based Theory -- Linear Time Variant Theory -- Measuring Phase Noise -- Direct Method with a Spectrum Analyzer -- Selective Receiver Method -- Heterodyne/Counter Method -- Reference Oscillator Method -- Frequency Discri minator Method -- Example Phase-Noise Measurement System -- Designing for Low Phase Noise -- Estimating the Predominant Noise Source -- Reducing Leeson Noise -- Reducing Pushing Induced Noise -- Reducing Buffer Noise -- Reducing Varactor Modulation Noise -- PLL Noise -- Chapter 5 General-Purpose Oscillators -- Oscillators Without Resonators -- R-C Oscillators -- Wien Bridge -- Multivibrators -- Ring Oscillators -- Twin-T Oscillators -- L-C Oscillators -- Colpitts -- Clapp -- Seiler -- Hartley -- Pierce -- Coupled Series Resonator -- Rhea -- Coupled Parallel Resonator -- Gumm -- Oscillator Topology Selection | |
Chapter 6 Distributed Oscillators -- Resonator Technologies -- Lumped and Distributed Equivalents -- Quarter-Wavelength Resonators -- Ceramic-Loaded Coaxial Resonators -- Capacitor-Loaded Quarter-Wavelength Resonator -- Distributed Oscillator Exampl es -- Negative-Resistance Hybrid Oscillator -- Negative-Resistance High-Power 1 GHz Oscillator -- Quarter-Wavelength Hybrid Oscillator -- Simple Hybrid Coaxial Resonator MMIC -- Probe-Coupled Coaxial Resonator Bipolar -- End-Coupled Hybrid Half-Wavelength Bipolar -- Helical Transmission Line Resonator Bipolar -- DRO Oscillators -- Dielectric Resonator Basic Properties -- Dielectric Resonator Resonant Frequency -- Dielectric Resonator Unloaded Q -- Dielectric Resonator Coupling -- Chapter 7 Tuned Oscillato rs -- Resonator Tuning Bandwidth -- Resonator Voltage -- Permeability Tuning -- Tunable Oscillator Examples -- Permeability Tuned Colpitts JFET -- Vackar JFET VCO -- Hybrid Negative Resistance VCO -- Capacitor-Transformed Negative-Resistance VCO -- Negati ve-Resistance VCO with Transformer -- Negative-Conductance VCO -- Hybrid Coaxial Resonator MMIC -- Loaded Quarter-Wavelength MMIC -- Seiler Coaxial-Resonator CC VCO -- YIG Oscillators | |
Chapter 8 Piezoelectric Oscillators -- Bulk Quartz Resonators -- Quartz Blank Cuts -- Crystal Resonator Model -- Calculating Crystal Resonator Parameters -- Crystal Resonator Frequency Pulling -- Inverted-Mesa Crystal Resonators -- Crystal Oscillato r Operating Mode -- Crystal Oscillator Frequency Accuracy -- Temperature Effects on Crystal Oscillators -- Crystal Resonator Drive Level -- Crystal Resonator Spurious Modes -- Crystal Resonator Aging -- Crystal Resonator Noise -- Crystal Resonator Acceler ation Effects -- Crystal Resonator Standard Holders -- Fundamental Mode Crystal Oscillators -- Miller JFET Crystal -- Colpitts Bipolar Crystal -- Colpitts JFET Crystal -- Pierce Bipolar Crystal -- Pierce MMIC Crystal -- Pierce Inverter TTL Crystal -- Pier ce Inverter CMOS Crystal -- Butler Dual Bipolar Crystal -- Driscoll Bipolar Crystal -- Inverted-Mesa Pierce Bipolar Crystal -- Overtone Mode Crystal Oscillators -- Colpitts Overtone Bipolar Crystal -- CB Butler Overtone Bipolar Crystal -- CC Butler Overt one Bipolar Crystal -- Oscillator with Frequency Multiplier -- Crystal Oscillator Starting -- Surface Acoustic Wave Resonators -- SAW Resonator Models -- SAW Resonator Frequency Stability -- SAW Oscillators -- SAW 1-Port Colpitts Bipolar -- SAW 1-Port But ler Bipolar -- SAW 2-Port Pierce MMIC -- Piezoelectric Ceramic Resonators -- Ceramic Resonator Models -- Ceramic Resonator Accuracy and Stability -- Ceramic Resonator Oscillators -- MEMS and FBAR Resonators | |
ISBN: | 9781608070473 |
Series: | Artech house microwave library |
Series: | eBooks |
Series: | Artech eBooks |
Keywords: | Harmonic oscillators, Design. , Oscillators, Electric, Design. |
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Call number: | 0470148241:ONLINE Show nearby items on shelf |
Title: | Analysis in Vector Spaces |
Author(s): |
Akcoglu |
Date: | 2009 |
Publisher: | Wiley |
Size: | 1 online resource (481 p.) |
ISBN: | 9780470148242 |
Series: | eBooks |
Series: | Wiley Online Library |
Series: | Wiley 2016 package purchase |
Keywords: | Mathematics |
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Call number: | TK7876.P69::2005 Show nearby items on shelf |
Title: | Microwave engineering |
Author(s): |
David M. Pozar |
Date: | 2005 |
Publisher: | J. Wiley |
Contents: | Electromagnetic Theory |
electromagnetic Theory | |
Transmission Line Theory | |
Transmission Lines and Waveguides | |
Microwave Network Analysis | |
Impedance Matching and Tuning | |
Microwave Rsonators | |
Power Dividers and Directional Couplers | |
Microwave Filters | |
Theory and Design of Ferrimagnetic Components | |
Noise and Active RF Components | |
Microwave Amplifier Design | |
Oscillators and Mixers | |
Introduction to Microwave Systems | |
Prefixes | |
Vector Analysis | |
Bessel Functions | |
Other Mathematical Results | |
Physical Constants | |
Conductivities for Some Materials | |
Dielectic Constants and Loss Tangents for Some Materials | |
Properties of Some Microwave Ferrite Materials | |
Standard Rectangular Waveguide Data | |
Standard Coaxial Cable Data | |
ISBN: | 0471448788 |
Keywords: | Microwaves , Microwave devices , Microwave circuits |
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Location: | MAIN |
Call number: | TA350.B35523::1977 Show nearby items on shelf |
Title: | Solutions Manual to Accompany Vector Mechanics for Engineers : Dynamics |
Author(s): |
Ferdinand Pierre Beer 1915- E. Russell (Elwood Russell) Johnston 1925- |
Date: | 1977 |
Publisher: | McGraw - Hill |
Note: | 3rd. ed. |
ISBN: | 0070042829 |
Keywords: | Mechanics, Applied , Vector Analysis , Mechanics, Applied - Problems, Exercises, etc. , Dynamics |
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Call number: | TA350.B3552::1988 Show nearby items on shelf |
Title: | Vector mechanics for engineers: Dynamics |
Author(s): |
Ferdinand P. Beer E. Russell Johnston |
Date: | 1988 |
Edition: | 5th ed. |
Publisher: | New York : McGraw-Hill |
Size: | 459-1047 p |
Note: | part two of Vector mechanics for engineers |
Contents: | Kinematics of particles -- Kinetics of particles: Newton's second law -- Kinetics of particles: energy and momentum methods -- Systems of particles -- Kinematics of rigid bodies -- Plane motion of rigid bodies: forces and accelerations -- Plane moti on of rigid bodies: energy and momentum methods -- Kinetics of rigid bodies in three dimensions -- Mechanical vibrations -- Some useful definitions and properties of Vector algebra -- Moments of inertia of masses. |
ISBN: | 9780070799264 |
Keywords: | Mechanics, Applied. , Vector analysis , Mechanics, Applied, Problems, exercises |
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Call number: | TA350.B3552::1977 Show nearby items on shelf |
Title: | Vector Mechanics for Engineers: Statics and Dynamics |
Author(s): |
Ferdinand Pierre Beer 1915- E. Russell Johnston 1925- |
Date: | 1977 |
Publisher: | McGraw - Hill |
Note: | 3rd. ed. |
ISBN: | 0070042772 |
Keywords: | Mechanics, Applied , Vector Analysis , Mechanics, Applied - Problems, Exercises, etc. |
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Location: | MAIN |
Call number: | TA330.J44::2002 Show nearby items on shelf |
Title: | Advanced engineering mathematics |
Author(s): |
Alan Jeffrey |
Date: | 2002 |
Publisher: | Harcourt Academic Press |
Note: | Volume 2 is the solutions manual |
Contents: | Review of Prerequisites |
Vectors and Matrices | |
Vectors and Vector Spaces | |
Matrices and Systems of Linear Equations | |
Eigenvalues, Eigenvectors and Diagonalization | |
Ordinary Differential Equations | |
First Order Differential Equations | |
Second and Higher Order Linear Differential Equations and Systems | |
The Laplace Transform | |
Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations | |
Fourier Series | |
Fourier Integrals and the Fourier Transform | |
Vector Calculus | |
Vector Differential Calculus | |
Vector Integral Calculus | |
Complex analysis | |
Analytic Functions | |
Complex Integration | |
Laurent Series, Residues, and Contour Integration | |
The Laplace Inversion Integral | |
Particla Differential Equations | |
Numerical Mathematics | |
ISBN: | 012382592X |
Keywords: | Engineering mathematics |
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Call number: | SPRINGER-2016-9789811005190:ONLINE Show nearby items on shelf |
Title: | Recent Advances in Mathematical Sciences Selected Papers from ICREM7 2015 |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (109 p.) |
Note: | 10.1007/978-981-10-0519-0 |
Contents: | Chapter 1: Counting Trees and Rooted Trees with Applications -- Chapter 2: Boundedness and Stability of Leslie-Gower Model with Sokol-Howell Functional Response -- Chapter 3: Fifth order Four Stage Explicit Trigonometrically-fitted Runge–Kutta– Nystrӧm Methods -- Chapter 4: Modified Homotopy Perturbation Method For Fredholm-Volterra Integro-Differential Equation -- Chapter 5: Simultaneous Effects of Soret and Dufour on the Unsteady Stagnation Point Flow of Micropolar Fluid towards a Permeable S tretching Sheet -- Chapter 6: One-Step Implicit Hybrid Method for Solving Semi-Explicit Index-1 Differential Algebraic Equations -- Chapter 7: An Artificial Intelligence Strategy for the Prediction of Wind Speed and Direction in Sarawak for Wind Energy Ma pping -- Chapter 8: Stability Analysis of Dengue Disease Using Host – Vector Model -- Chapter 9: Simple Motion Evasion Differential Game of One Pursuer and One Evader. |
ISBN: | 9789811005190 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Algebra , Mathematical analysis , Analysis (Mathematics) , Game theory , Geometry , Operations research , Management science , Mathematical physics , Mathematics , Analysis , Mathematical Physics , Algebra , Geometry , Operations Research, Management Science , Game Theory, Economics, Social and Behav. Sciences |
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Call number: | SPRINGER-2016-9784431558033:ONLINE Show nearby items on shelf |
Title: | From Tracking Code to Analysis Generalised Courant-Snyder Theory for Any Accelerator Model |
Author(s): |
Etienne Forest |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (347 p.) |
Note: | 10.1007/978-4-431-55803-3 |
Contents: | Introduction -- The linear transverse normal form: one degree of freedom -- The nonlinear transverse normal form: one degree of freedom -- Classification of linear normal forms -- Nonlinear normal forms -- Spin normal form -- The |
nonlinear spin-orbital phase advance: the mother of all algorithms -- Deprit-Guignard perturbation theory faithful to the code -- Here is the conclusion of this book -- Phasors basis: why do I reject symplectic phasors? -- The | |
logarithm of a map -- Stroboscopic average for the ISF vector n -- Hierarchy of Analytical Methods | |
ISBN: | 9784431558033 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Computer programming , Particle acceleration , Physics , Particle Acceleration and Detection, Beam Physics , Numerical and Computational Physics , Programming Techniques |
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Call number: | SPRINGER-2016-9783662489932:ONLINE Show nearby items on shelf |
Title: | Mathematical Analysis II |
Author(s): |
Vladimir A Zorich |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (720 p.) |
Note: | 10.1007/978-3-662-48993-2 |
Contents: | 9 Continuous Mappings (General Theory) -- 10 Differential Calculus from a General Viewpoint -- 11 Multiple Integrals -- 12 Surfaces and Differential Forms in Rn -- 13 Line and Surface Integrals -- 14 Elements of Vector Analysis and Field Theory -- 1 5 Integration of Differential Forms on Manifolds -- 16 Uniform Convergence and Basic Operations of Analysis -- 17 Integrals Depending on a Parameter -- 18 Fourier Series and the Fourier Transform -- 19 Asymptotic Expansions -- Topics and Questions for Mid term Examinations -- Examination Topics -- Examination Problems (Series and Integrals Depending on a Parameter) -- Intermediate Problems (Integral Calculus of Several Variables) -- Appendices: A Series as a Tool (Introductory Lecture) -- B Change of Varia bles in Multiple Integrals -- C Multidimensional Geometry and Functions of a Very Large Number of Variables -- D Operators of Field Theory in Curvilinear Coordinates -- E Modern Formula of Newton–Leibniz -- References -- Index of Basic |
Notation -- Subject Index -- Name Index | |
ISBN: | 9783662489932 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical analysis , Analysis (Mathematics) , Physics , Mathematics , Analysis , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2016-9783319296623:ONLINE Show nearby items on shelf |
Title: | The Parameterization Method for Invariant Manifolds From Rigorous Results to Effective Computations |
Author(s): |
Àlex Haro |
Date: | 2016 |
Size: | 1 online resource (55 p.) |
Note: | 10.1007/978-3-319-29662-3 |
Contents: | An Overview of the Parameterization Method for Invariant Manifolds -- Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points -- The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Va lidated Numerics -- The Parameterization Method in KAM Theory -- A Newton-like Method for Computing Normally Hyperbolic Invariant Tori |
ISBN: | 9783319296623 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Applied Mathematical Sciences: 195 |
Keywords: | Mathematics , Dynamics , Ergodic theory , Partial differential equations , Numerical analysis , Statistical physics , Dynamical systems , Mathematics , Dynamical Systems and Ergodic Theory , Statistical Physics, Dynamical Systems and Complexity , Numerical Analysis , Partial Differential Equations |
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Call number: | SPRINGER-2016-9783319256139:ONLINE Show nearby items on shelf |
Title: | An Introduction to Frames and Riesz Bases |
Author(s): |
Ole Christensen |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (5 p.) |
Note: | 10.1007/978-3-319-25613-9 |
Contents: | Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- Tight Frames and Dual Frame Pairs -- Frames versus Riesz Bases -- Selected Topics in Frame Theory -- Frames of Translates -- Shift-Invariant Systems in l2(R) -- Gabor Frames in L2(R) -- Gabor Frames and Duality -- Selected Topics on Gabor Frames -- Gabor Frames in ℓ2(Z),L2(0,L),CL -- General Wavelet Frames in L2(R) -- Dyadic W avelet Frames for L2(R) -- Frame Multiresolution Analysis -- Wavelet Frames via Extension Principles -- Selected Topics on Wavelet Frames -- Generalized Shift-Invariant Systems in L2(Rd) -- Frames on Locally Compact Abelian Groups -- Perturbation of Frame s -- Approximation of the Inverse Frame Operator -- Expansions in Banach Spaces. Appendix |
ISBN: | 9783319256139 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Functional analysis , Operator theory , Mathematics , Functional Analysis , Abstract Harmonic Analysis , Operator Theory , Signal, Image and Speech Processing |
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Call number: | SPRINGER-2014-9784431549192:ONLINE Show nearby items on shelf |
Title: | Bernoulli Numbers and Zeta Functions [electronic resource] |
Author(s): |
Tsuneo Arakawa Tomoyoshi Ibukiyama Masanobu Kaneko |
Date: | 2014 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powersof consecutive integers . The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advancedtopics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers a formula for Bernoulli numbers by Stirling numbers the Clausenvon Staudttheorem on the denominators of Bernoulli numbers Kummer's congruence betw een Bernoulli numbers and a related theory of p-adic measures the EulerMaclaurin summation formula the functional equation of the Riemann zeta function andthe Dirichlet L functions, and their special values at suitable integers various formulas of exponen tial sums expressed by generalized Bernoulli numbers the relation between ideal classes of orders of quadratic fields and equivalenceclasses of binary quadratic forms class number formula for positive definite binary quadratic forms congruences between so me class numbers and Bernoulli numbers simple zeta functions of prehomogeneous vector spaces Hurwitz numbers |
ISBN: | 9784431549192 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Global analysis (Mathematics) , Number theory |
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Call number: | SPRINGER-2014-9783642543012:ONLINE Show nearby items on shelf |
Title: | Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data [electronic resource] |
Author(s): |
Carl-Fredrik Westin Anna Vilanova Bernhard Burgeth |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emergingfield. Topics covered rang e from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensorfields in engineering, discusses the current sta te of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-orderDescriptors, describes a matrix representation of local phase, outlines ma thematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III,Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to mode l and analyze large and complex diffusion data such as High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging(DKI). A Part entitled Tensor Signal Processing presents new methods for processing tensor-valued data, including a nove l perspective on performing voxel-wise morphometry of diffusion tensor data using kernel-based approach, exploresthe free-water diffusion model, and reviews proposed approaches for computing fabric tensors, emphasizing trabecular bone research. The last P art, Applications of Tensor Processing, discusses metric and curvature tensors, two of themost studied tensors in geometry processing. Also covered is a technique for diagnostic prediction of first-episode schizophrenia patients based on brain diffusion M RI data. The last chapter presents an interactive system integratingthe visual analysis of diffusion MRI tractography with data from electroencephalography |
Contents: | Part I: Tensor Data Visualization: Top Challenges in the Visualization of Engineering Tensor Fields: M Hlawitschka et al |
Tensor Invariants and Glyph Design: A. Kratz et al | |
Part II: Representation and Processing of Higher | |
order Descriptors: Monomial Phase: A Matrix Representation of Local Phase: H. Knutsson et al | |
Order Based Morphology for Colour Images via Matrix Fields: B. Burgeth et al | |
Sharpening Fibers in Diffusion Weighted MRI via Erosion: T.C.J. Dela Haije et al | |
Part III: Higher Order Tensors and Riemannian | |
Finsler Geometry: Higher | |
Order Tensors in Diffusion Imaging: Th | |
ISBN: | 9783642543012 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Visualization, 1612-3786 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Computer graphics , Differential equations, partial , Visualization , Global differential geometry |
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Call number: | SPRINGER-2014-9783319082288:ONLINE Show nearby items on shelf |
Title: | Dynamical Systems Generated by Linear Maps [electronic resource] |
Author(s): |
emal B Dolianin Anatolij B Antonevich |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systemstheory. However, for the d ynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in thecourse of investigation, they confront users with plenty of subtle questions, and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, thebook can be considered as a natural amplification, refinement and supple ment to linear algebra and dynamical systems theory textbooks |
Contents: | From the Contents: Introduction |
Vector trajectory | |
The Jordan basis and special subspaces | |
Representation of the vector trajectory | |
The structures related to the principal term of the vector Trajectory | |
The asymptotic behavior of vector trajectories and trajectories of one | |
dimensional subspaces | |
ISBN: | 9783319082288 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Engineering , Vibration |
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Call number: | SPRINGER-2014-9783319060743:ONLINE Show nearby items on shelf |
Title: | Functional Analysis and Applied Optimization in Banach Spaces [electronic resource] : Applications to Non-Convex Variational Models |
Author(s): |
Fabio Botelho |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physicsand engineering probl ems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation.Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dualapproach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in relatedfields |
Contents: | 1. Topological Vector Spaces |
2. The Hahn | |
Bananch Theorems and Weak Topologies | |
3. Topics on Linear Operators | |
4.Basic Results on Measure and Integration | |
5. The Lebesgue Measure in Rn | |
6. Other Topics in Measure and Integration | |
7. Distributions | |
8. The Lebesque and Sobolev Spaces | |
9. Basic Concepts on the Calculus of Variations | |
10. Basic Concepts on Convex Analysis | |
11. Constrained Variational Analysis | |
12. Duality Applied to Elasticity | |
13. Duality Applied to a Plate Model | |
14. About Ginzburg | |
Landau Type Equations: The Simpler Real Case | |
15. Full Complex Ginzb | |
ISBN: | 9783319060743 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Numerical analysis |
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Call number: | SPRINGER-2014-9783319057231:ONLINE Show nearby items on shelf |
Title: | Invariant Probabilities of Transition Functions [electronic resource] |
Author(s): |
Radu Zaharopol |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transitionfunctions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated usingtransition functions defined by flows, semiflows, a nd one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 areextended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structureof the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizationsof the supports of various types of invariant probability measures and the use of these to obtain criteria for un ique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will beof interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also findthis book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, gen eral topology, measure theory, the Bochner integral and some of itsapplications |
Contents: | Introduction |
1.Transition Probabilities | |
2.Transition Functions | |
3.Vector Integrals and A.E. Convergence | |
4.Special Topics | |
5.The KBBY Ergodic Decomposition, Part I | |
6.The KBBY Ergodic Decomposition, Part II | |
7.Feller Transition Functions | |
Appendices: A.Semiflows and Flows: Introduction | |
B.Measures and Convolutions | |
Bibliography | |
Index | |
ISBN: | 9783319057231 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability and Its Applications, 1431-7028 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Operator theory , Potential theory (Mathematics) , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319057149:ONLINE Show nearby items on shelf |
Title: | Stochastic Differential Equations, Backward SDEs, Partial Differential Equations [electronic resource] |
Author(s): |
Etienne Pardoux Aurel Rcanu |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations(PDEs), and financial mathe matics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. Theauthors present in particular the theory of ref lected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K.It in the 1940s, in order to construct the path of diffusion process es (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had beenstudied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has become an important subject of Mathematics and Applied Mathematics, because of its mathematical richness and its importance forapplications in many areas of Physics, Biology, Economics and Finance, where random processes play an increasingly important role. One important aspect is the connection between diffusion processes and linear partial differentialequations of second order, which is in particular the basis for Monte Carlo numerical methods for linear PDEs. Since the pioneering work of Peng and P ardoux in the early 1990s, a new type of SDEs called backward stochastic differentialequations (BSDEs) has emerged. The two main reasons why this new class of equations is important are the connection between BSDEs and semilinear PDEs, and the fact that B SDEs constitute a natural generalization of the famous Black andScholes model from Mathematical Finance, and thus offer a natural mathematical framework for the formulation of many new models in Finan |
Contents: | Introduction |
Background of Stochastic Analysis | |
Itos Stochastic Calculus | |
Stochastic Differential Equations | |
SDE with Multivalued Drift | |
Backward SDE | |
Annexes | |
Bibliography | |
Index | |
ISBN: | 9783319057149 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Stochastic Modelling and Applied Probability, 0172-4568 : v69 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319040998:ONLINE Show nearby items on shelf |
Title: | Topological Methods in Data Analysis and Visualization III [electronic resource] : Theory, Algorithms, and Applications |
Author(s): |
Peer-Timo Bremer Ingrid Hotz Valerio Pascucci Ronald Peikert |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms andinsights, including fast homo logy computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as therepresentation of large and complex datasets and integrati ng numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made onfinding experimental solutions to open problems in the sector. They provide an i nclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for futureprogress. With papers by some of the worlds leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range fromengineering to medicine |
Contents: | Part I Robust Topological Analysis: 1 Robust Detection of Singularities in Vector Fields: H. Bhatia, A. Gyulassy, H. Wang, P |
T. Bremer and V. Pascucci | |
2 Interpreting Feature Tracking Through the Lens of Robustness: P. Skraba and B. Wang | |
3 Simplification of Morse Decompositions using Morse Set Mergers: L. Sipeki and A. Szymczak | |
4 Toward the Extraction of Saddle Periodic Orbits: J. Kasten, J. Reininghaus, W. Reich and G. Scheuermann | |
Part II Efficient Computation of Topology | |
5 Computational Topology via Functional Programming: A Baseline Analysis: D. Duke and H. Carr | |
6 Distribu | |
ISBN: | 9783319040998 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Visualization, 1612-3786 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Optical pattern recognition , Global analysis (Mathematics) , Visualization , Geometry , Topology |
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Call number: | SPRINGER-2014-9783319022918:ONLINE Show nearby items on shelf |
Title: | Discrete Dynamical Models [electronic resource] |
Author(s): |
Ernesto Salinelli Franco Tomarelli |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several disciplineas Mathematical Analysi s, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems arepresented, paying particular attention to the stabil ity analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to thestudy of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. Thebook is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Eco nomics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations.The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty in the last chapter the detailed solution is given for most of them |
Contents: | 1 Recursive phenomena and difference equations |
2 Linear difference equations | |
3 Discrete dynamical systems: one | |
step scalar equations | |
4 Complex behavior of nonlinear dynamical systems: bifurcations and chaos | |
5 Discrete dynamical systems: vector equations | |
6 Markov chains | |
7 Matrix | |
8 Solutions | |
ISBN: | 9783319022918 |
Series: | eBooks |
Series: | SpringerLink |
Series: | UNITEXT, 2038-5714 : v76 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functional equations , Differentiable dynamical systems |
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Call number: | SPRINGER-2014-9783319020877:ONLINE Show nearby items on shelf |
Title: | An Invitation to Hypoelliptic Operators and Hrmander's Vector Fields [electronic resource] |
Author(s): |
Marco Bramanti |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Hrmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active fieldof research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development |
Contents: | 1 Hrmander's operators: what they are |
2 Hrmander's operators: why they are studied | |
3 A priori estimates in Sobolev spaces | |
4 Geometry of Hrmander's vector fields | |
5 Beyond Hrmander's operators | |
ISBN: | 9783319020877 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Operator theory , Differential equations, partial |
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Call number: | SPRINGER-2014-9783319020457:ONLINE Show nearby items on shelf |
Title: | Locally Convex Spaces [electronic resource] |
Author(s): |
M. Scott Osborne |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convextopological vector spaces, is i ntended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convexspaces, which is why this is an important topic in function al analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varyingdifficulty. Key topics covered include point set topology, topological vector space s, the HahnBanach theorem, seminorms and Frchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach spacetheory typically taught in a beginning graduate real analysis course |
Contents: | 1 Topological Groups |
2 Topological Vector Spaces | |
3 Locally Convex Spaces | |
4 The Classics | |
5 Dual Spaces | |
6 Duals of Fr chet Spaces | |
A Topological Oddities | |
B Closed Graphs in Topological Groups | |
C The Other KreinSmulian Theorem | |
D Further Hints for Selected Exercises | |
Bibliography | |
Index | |
ISBN: | 9783319020457 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Graduate Texts in Mathematics, 0072-5285 : v269 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Functional analysis |
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Call number: | SPRINGER-2013-9789491216862:ONLINE Show nearby items on shelf |
Title: | Single Variable Differential and Integral Calculus [electronic resource] : Mathematical Analysis |
Author(s): |
Elimhan Mahmudov |
Date: | 2013 |
Publisher: | Paris : Atlantis Press : Imprint: Atlantis Press |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book Single variable Differential and Integral Calculus is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book isunique in the field of mathemat ical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important businessfields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequencesof functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems andexamples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Sti eltjes and Lebesque integrals are studied together and compared |
Note: | Springer eBooks |
Contents: | Introduction to Numbers and Set Theory |
Sequences and Series | |
Limits and Continuity of Functions | |
Differential Calculus | |
Some Basic Properties of Differentiable Functions | |
Polynomials and Interpolations | |
Applications of Differential Calculus to Limit Calculations and Extremum Problems | |
The Indefinite Integral | |
The Definite Integral | |
Applications of the Definite Integral | |
ISBN: | 9789491216862 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Differential Equations |
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Call number: | SPRINGER-2013-9789400754102:ONLINE Show nearby items on shelf |
Title: | General Relativity [electronic resource] |
Author(s): |
Norbert Straumann |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book provides a completely revised and expanded version of the previous classic edition General Relativity and Relativistic Astrophysics. In Part I the foundations of general relativity are thoroughly developed, whilePart II is devoted to tests of general relativity and many of its applications. Binary pulsars our best laboratories for general relativity are studied in considerable detail. An introduction to gravitational lensing theory isincluded as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerrsolution, Israels proof of his uniqueness theorem, and a derivation of the b asic laws of black hole physics. Part II ends with Wittens proof of the positive energy theorem, which is presented in detail, together with the requiredtools on spin structures and spinor analysis. In Part III, all of the differential geometric tools req uired are developed in detail. A great deal of effort went into refining and improving the text for the new edition. New material hasbeen added, including a chapter on cosmology. The book addresses undergraduate and graduate students in physics, astrophys ics and mathematics. It utilizes a very well structured approach, which should help it continue to be a standardwork for a modern treatment of gravitational physics. The clear presentation of differential geometry also makes it useful for work on string t heory and other fields of physics, classical as well as quantum |
Note: | Springer eBooks |
Contents: | From the Contents: Part I The General Theory of Relativity |
Introduction | |
Physics in External Gravitational Fields | |
Einsteins Field Equations | |
Part II Applications of General Relativity | |
The Schwarzschild Solution and Classical Tests of General Relativity | |
Weak Gravitational Fields | |
The Post | |
Newtonian Approximation | |
White Dwarfs and Neutron Stars | |
Black Holes | |
The Positive Mass Theorem | |
Essentials of Friedmann | |
Lematre Models | |
Part III Differential Geometry | |
Differentiable Manifolds | |
Tangent Vectors, Vector and Tensor Fields | |
The Lie Derivative | |
Different | |
ISBN: | 9789400754102 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Physics, 1868-4513 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Astronomy |
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Call number: | SPRINGER-2013-9789400753457:ONLINE Show nearby items on shelf |
Title: | Differential Geometry and Mathematical Physics [electronic resource] : Part I. Manifolds, Lie Groups and Hamiltonian Systems |
Author(s): |
Gerd Rudolph Matthias Schmidt |
Date: | 2013 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Starting from an undergraduate level, this book systematically develops the basics of Calculus on manifolds, vector bundles, vector fields and differential forms, Lie groups and Lie group actions, Linear symplecticalgebra and symplectic geometry, Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. Thesecond and third items constitute the link between abstr act calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class andcaustics. The book guides the reader from elementary differential geometry to advan ced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematicaltextbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact |
Note: | Springer eBooks |
Contents: | 1 Differentiable manifolds |
2 Vector bundles | |
3 Vector fields | |
4 Differential forms | |
5 Lie groups | |
6 Lie group actions | |
7 Linear symplectic algebra | |
8 Symplectic geometry | |
9 Hamiltonian systems | |
10 Symmetries | |
11 Integrability | |
12 Hamilton | |
Jacobi theory | |
References | |
ISBN: | 9789400753457 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Theoretical and Mathematical Physics, 1864-5879 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Topological Groups , Global analysis , Global differential geometry , Mathematical physics , Mechanics |
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Call number: | SPRINGER-2013-9784431543183:ONLINE Show nearby items on shelf |
Title: | A Bayesian Analysis of QCD Sum Rules [electronic resource] |
Author(s): |
Philipp Gubler |
Date: | 2013 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The author develops a novel analysis method for QCD sum rules (QCDSR) by applying the maximum entropy method (MEM) to arrive at an analysis with less artificial assumptions than previously held. This is a first-time accomplishmentin the field. In thi s thesis, a reformed MEM for QCDSR is formalized and is applied to the sum rules of several channels: the light-quark meson in the vector channel, the light-quark baryon channel with spin and isospin 1/2, andseveral quarkonium channels at both zero and fi nite temperatures. This novel technique of combining QCDSR with MEM is applied to the study of quarkonium in hot matter, which is an important probe of the quark-gluon plasma currentlybeing created in heavy-ion collision experiments at RHIC and LHC |
Note: | Springer eBooks |
Contents: | Introduction and Review |
Introduction | |
Basic Properties of QCD | |
Basics of QCD Sum Rules | |
The Maximum Entropy Method | |
Applications | |
MEM Analysis of the Meson Sum Rule | |
MEM Analysis of the Nucleon Sum Rule | |
Quarkonium Spectra at finite Temperature from QCD Sum Rules and MEM | |
Concluding Remarks | |
Summary, Conclusion and Outlook | |
Appendix | |
ISBN: | 9784431543183 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5053 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory |
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Call number: | SPRINGER-2013-9783319014487:ONLINE Show nearby items on shelf |
Title: | Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces [electronic resource] |
Author(s): |
Silvestru Sever Dragomir |
Date: | 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators oncomplex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, andquantum computation, to name several. Chapter 1 pr esents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerningnumerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, RyffandClarke as well as some reverse Schwarzinequalities and Grss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapterare elementary butelegant and may be accessible to undergraduate students with a working knowledge of operator theory.A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are alsoemployed in this chapter. All the results presented are completely proved and the original references are mentioned |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2.Inequalities for One Operator | |
3.Inequalities for Two Operators | |
ISBN: | 9783319014487 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Operator theory , Differential Equations |
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Call number: | SPRINGER-2013-9783319011950:ONLINE Show nearby items on shelf |
Title: | Mathematical Physics [electronic resource] : A Modern Introduction to Its Foundations |
Author(s): |
Sadri Hassani |
Date: | 2013 |
Edition: | 2nd ed. 2013 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
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Note: | The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics asdiverse as algebras, cla ssical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups,manifolds, Lie groups and their representations , Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of thefirst one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition,namely the balance between rigor and physical application, has been maintained, as is the abun dance of historical notes and worked out examples that demonstrate the unreasonable effectiveness of mathematics in modern physics.Einstein has famously said, The most incomprehensible thing about nature is that it is comprehensible. What he had in mind w as reiterated in another one of his famous quotes concerning the question of how ... mathematics, beingafter all a product of human thought, is so admirably appropriate to the objects of reality. It is a question that comes to everyone's mind when encoun tering the highly abstract mathematics required for a deep understanding of modernphysics. It is the experience that Eugene Wigner so profoundly described as the unreasonable effectiveness of mathematics in the natural sciences. |
Note: | Springer eBooks |
Contents: | Mathematical Preliminaries |
I Finite | |
Dimensional Vector Spaces | |
1 Vectors and Linear Maps | |
2 Algebras | |
3 Operator Algebra | |
4 Matrices | |
5 Spectral Decomposition | |
II Infinite | |
Dimensional Vector Spaces | |
6 Hilbert Spaces | |
7 Classical Orthogonal Polynomials | |
8 Fourier Analysis | |
III Complex Analysis | |
9 Complex Calculus | |
10 Calculus of Residues | |
11 Advanced Topics | |
IV Differential Equations | |
12 Separation of Variables in Spherical Coordinates | |
13 Second | |
Order Linear Differential Equations | |
14 Complex Analysis of SOLDEs | |
15 Integral Transforms and Differential Equ | |
ISBN: | 9783319011950 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Mathematical physics |
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Call number: | SPRINGER-2013-9783319003573:ONLINE Show nearby items on shelf |
Title: | Green's Kernels and Meso-Scale Approximations in Perforated Domains [electronic resource] |
Author(s): |
Vladimir Maz'ya Alexander Movchan Michael Nieves |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. Theaccurate direct numerical tre atment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Greens function is considered here as the main object of study rather than a tool forgenerating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Greens functions and solutions of boundary valueproblems for meso-scale structures. Such systems involve a large number of small i nclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number ofinclusions. The main focus of the present text is on two topics: (a) asymptotics of Greens kernels in domains w ith singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodicdomains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent varia bles. This book addresses the needs of mathematicians, physicists and engineers, as well asresearch students interested in asymptotic analysis and numerical computations for solutions to partial differential equations |
Note: | Springer eBooks |
Contents: | Part I: Greens functions in singularly perturbed domains: Uniform asymptotic formulae for Greens functions for the Laplacian in domains with small perforations |
Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Greens kernels | |
Greens function for the Dirichlet boundary value problem in a domain with several inclusions | |
Numerical simulations based on the asymptotic approximations | |
Other examples of asymptotic approximations of Greens functions in singularly perturbed domains | |
Part II: Greens tensors for vector e | |
ISBN: | 9783319003573 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2077 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2013-9783319001289:ONLINE Show nearby items on shelf |
Title: | Hypoelliptic Laplacian and BottChern Cohomology [electronic resource] : A Theorem of RiemannRochGrothendieck in Complex Geometry |
Author(s): |
Jean-Michel Bismut |
Date: | 2013 |
Publisher: | Heidelberg : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
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Note: | The book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of RiemannRochGrothendieck for proper submersions. It gives an equality of cohomology classes inBottChern cohomology, which is a refi nement for complex manifolds of de Rham cohomology. When the manifolds are Khler, our main result is known. A proof can be given using the elliptic Hodge theory of the fibres, its deformationvia Quillen's superconnections, and a version in families of the 'fantastic cancellations' of McKeanSinger in local index theory. In the general case, this approach breaks down because the cancellations do not occur any more.Onetool used in the book is a deformation of the Hodge theory of the fibres to a hypoelliptic Hodge theory, in such a way that the relevant cohomological information is preserved, and 'fantastic cancellations' do occur for thedeformation. The deformed hypoelliptic Laplacian acts on the total space of the relative tangent bundle of the fibres. Whil e the original hypoelliptic Laplacian discovered by the author can be described in terms of the harmonicoscillator along the tangent bundle and of the geodesic flow, here, the harmonic oscillator has to be replaced by a quartic oscillator.Another idea dev eloped in the book is that while classical elliptic Hodge theory is based on theHermitian product on forms, the hypoelliptic theory involves a Hermitian pairing which is a mild modification of intersection pairing. Probabilistic considerations play an imp ortant role, either as a motivation of some constructions,or in the proofs themselves |
Note: | Springer eBooks |
Contents: | Introduction |
1 The Riemannian adiabatic limit | |
2 The holomorphic adiabatic limit | |
3 The elliptic superconnections | |
4 The elliptic superconnection forms | |
5 The elliptic superconnections forms | |
6 The hypoelliptic superconnections | |
7 The hypoelliptic superconnection forms | |
8 The hypoelliptic superconnection forms of vector bundles | |
9 The hypoelliptic superconnection forms | |
10 The exotic superconnection forms of a vector bundle | |
11 Exotic superconnections and RiemannRochGrothendieck | |
Bibliography | |
Subject Index | |
Index of Notation. | |
ISBN: | 9783319001289 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v305 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , K-theory , Global analysis , Differential equations, partial |
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Call number: | SPRINGER-2013-9783034806367:ONLINE Show nearby items on shelf |
Title: | Introduction to Mathematical Analysis [electronic resource] |
Author(s): |
Igor Kriz Ale Pultr |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus anddifferential equations. Af ter having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differentialgeometry and even functional analysis. Overall, this t ext provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Part 1. A Rigorous Approach to Advanced Calculus | |
1. Preliminaries | |
2. Metric and Topological Spaces I | |
3. Multivariable Differential Calculus | |
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral | |
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration | |
6. Systems of Ordinary Differential Equations | |
7. System of Linear Differential Equations | |
8. Line Integrals and Green's Theorem | |
Part 2. Analysis and Geometry | |
9. An Introduction to Complex Analysis | |
10. Metric and Top | |
ISBN: | 9783034806367 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functions of complex variables , Differential Equations , Sequences (Mathematics) |
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Call number: | SPRINGER-2013-9783034806039:ONLINE Show nearby items on shelf |
Title: | Quaternion and Clifford Fourier Transforms and Wavelets [electronic resource] |
Author(s): |
Eckhard Hitzer Stephen J Sangwine |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Quaternion andClifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering.This edited volume pres ents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamiltons quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all itssubspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensiveinsights into current developments and applications including their performa nce and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms forhypercomplex algebras, which will help readers to see that software implementations are within our gra sp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms andwavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the con tributions that follow relate to each other and to prior work. The book will be a valuable resource forgraduate students as well as for scientists and engineers |
Note: | Springer eBooks |
Contents: | Preface |
History of Quaternion and Clifford | |
Fourier Transforms and Wavelets | |
Part I: Quaternions | |
1 Quaternion Fourier Transform: Re | |
tooling Image and Signal Processing Analysis | |
2 The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations | |
3 Quaternionic Spectral Analysis of Non | |
Stationary Improper Complex Signals | |
4 Quaternionic Local Phase for Low | |
level Image Processing Using Atomic Functions | |
5 Bochners Theorems in the Framework of Quaternion Analysis | |
6 Bochner | |
Minlos Theorem and Quaternion Fourier Transform | |
Part II: Clifford Algeb | |
ISBN: | 9783034806039 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer vision , Matrix theory , Fourier analysis , Numerical analysis , Number theory |
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Call number: | SPRINGER-2013-9783034804783:ONLINE Show nearby items on shelf |
Title: | Functional Analysis in Asymmetric Normed Spaces [electronic resource] |
Author(s): |
tefan Cobza |
Date: | 2013 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the normimplies that the mult iplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, ismerely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplaybetween the asymmetric norm p and its conjugate. Among the positi ve results one can mention: HahnBanach type theorems and separation results for convex sets, KreinMilman type theorems, analogs of the fundamental principles open mapping, closed graph and uniform boundedness theorems an analog of the Schauders theorem o n the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, oneconsiders normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since t he basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of thebook contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in function al analysis completeness, compactness and Baire category which drasticallydiffer from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analys is, so it may be used for an introduction to thesubject.Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference |
Note: | Springer eBooks |
Contents: | Introduction |
1. Quasi | |
metric and Quasi | |
uniform Spaces. 1.1. Topological properties of quasi | |
metric and quasi | |
uniform spaces | |
1.2. Completeness and compactness in quasi | |
metric and quasi | |
uniform spaces | |
2. Asymmetric Functional Analysis | |
2.1. Continuous linear operators between asymmetric normed spaces | |
2.2. Hahn | |
Banach type theorems and the separation of convex sets | |
2.3. The fundamental principles | |
2.4. Weak topologies | |
2.5. Applications to best approximation | |
2.6. Spaces of semi | |
Lipschitz functions | |
Bibliography | |
Index | |
ISBN: | 9783034804783 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Frontiers in Mathematics, 1660-8046 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory , Topology |
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Call number: | SPRINGER-2013-9781461481454:ONLINE Show nearby items on shelf |
Title: | Mathematics for Econometrics [electronic resource] |
Author(s): |
Phoebus J Dhrymes |
Date: | 2013 |
Edition: | 4th ed. 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The fourth edition of this book continues to deal with a number of mathematical topics that are of great importance in the study of classical econometrics. The major expansion involves a more complete coverage of basic aspects ofmathematics that cont inue to play an increasingly significant role in the literature of econometrics. Thus, the chapter on difference equations has been expanded to include enhanced treatment of lag operators (backward shift operatorsin the statistical literature) that are im portant not only in the context of the dynamic simultaneous equation GLSEM (general linear structural econometric model), but also time series analysis. New features in this edition includechapters on probability theory and the probabilistic basis of clas sical econometrics. There is a lengthy chapter on matrix algebra, which takes the reader from the most elementary aspects to the partitioned inverses, characteristicroots and vectors, symmetric, and orthogonal and positive (semi) definite matrices. The bo ok also covers pseudo-inverses, solutions to systems of linear equations, solutions of vector difference equations with constant coefficients andrandom forcing functions, matrix differentiation, and permutation matrices. Its novel features include an intr oduction to asymptotic expansions, and examples of applications to the general-linear model (regression) and the generallinear structural econometric model (simultaneous equations). Also unique to this edition are two fairly extensive chapters on applicat ions to the GLM (general linear model), GLSEM and time series analysis which treat issues relevantto their underlying theoretical bases, estimation and forecasting. Professor Dhrymes is currently Professor of Economics at Columbia University. Earlier he t aught at Harvard, University of Pennsylvania, University of California at LosAngeles, and Monash University in Australia. He is a fellow of the Econometric Society and the American Statistical Associati |
Note: | Springer eBooks |
Contents: | Preface |
Chapters | |
Bibliography | |
References | |
ISBN: | 9781461481454 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematics , Economics Statistics , Econometrics |
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Call number: | SPRINGER-2013-9781461478676:ONLINE Show nearby items on shelf |
Title: | Introduction to Tensor Analysis and the Calculus of Moving Surfaces [electronic resource] |
Author(s): |
Pavel Grinfeld |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This text is meant to deepen its readers understanding of vector calculus, differential geometry and related subjects in applied mathematics. Designed for advanced undergraduate and graduate students, this text invites itsaudience to take a fresh loo k at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shapeoptimization, boundary perturbation, and dynamic fluid film equations. Tensor calculus is a powerful tool that combines the geometric and analytical perspectives and enables us to take full advantage of the computational utility ofcoordinate systems. The tensor approach can be of benefit to members of all te chnical sciences including mathematics and all engineering disciplines. If calculus and linear algebra are central to the readers scientific endeavors,tensor calculus is indispensable. The language of tensors, originally championed by Einstein, is as fund amental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensortechnique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably v ital and relevant. The authors skilled lecturing capabilities are evident by the inclusion ofinsightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the prop er use of the tensor notation, and the discussion of the interplaybetween algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 when the reader is ready for it. While this text main tains a reasonable level of rigor, it takesgreat care to avoid formalizing the subject. The last part of the textbook is devoted to the calculus of moving surfaces. It is the first textboo |
Note: | Springer eBooks |
Contents: | Preface |
Why Tensor Calculus? | |
1. Rules of the Game | |
2. Coordinate Systems and the Role of Tensor Calculus | |
3. Change of Coordinates | |
4. Tensor Description of Euclidean Spaces | |
5. The Tensor Property | |
6. Covariant Differentiation | |
7. Determinants and the Levi | |
Civita Symbol | |
8. Tensor Description of Surfaces | |
9. Covariant Derivative of Tensors with Surface Indices | |
10. The Curvature Tensor | |
11. Covariant Derivative of Tensors with Spatial Indices | |
12. Integration and Gauss's Theorem | |
13. Intrinsic Features of Embedded Surfaces | |
14. Further Topics in Differential Ge | |
ISBN: | 9781461478676 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Global differential geometry , Mathematical optimization |
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Call number: | SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf |
Title: | Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday |
Author(s): |
Alan Huckleberry Ivan Penkov Gregg Zuckerman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted |
Note: | Springer eBooks |
Contents: | Preface |
Real group orbits on flag manifolds | |
Complex connections with trivial holonomy | |
Indefinite harmonic theory and harmonic spinors | |
Twistor theory and the harmonic hull | |
Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets | |
Propagation of the multiplicity | |
freeness property for holomorphic vector bundles | |
Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains | |
Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf | |
Weakly harmonic Maa forms and the princi | |
ISBN: | 9781461471936 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Progress in Mathematics : v306 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topological Groups , Functional analysis |
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Call number: | SPRINGER-2013-9781461459064:ONLINE Show nearby items on shelf |
Title: | Malliavin Calculus and Stochastic Analysis [electronic resource] : A Festschrift in Honor of David Nualart |
Author(s): |
Frederi Viens Jin Feng Yaozhong Hu Eulalia Nualart |
Date: | 2013 |
Publisher: | Boston, MA : Springer US : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the core mathematical discipline. Stochastic analysis provides a fruitfulinterpretation of th is calculus, particularly as described by David Nualart and the scores of mathematicians he influences and with whom he collaborates. Many of these, including leading stochastic analysts and junior researchers,presented their cutting-edge research at an i nternational conference in honor of David Nualart's career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributedresearch articles for this refereed volume |
Note: | Springer eBooks |
Contents: | An Application of Gaussian Measures to Functional Analysis |
Stochastic Taylor Formulas and Riemannian Geometry | |
Local invertibility of adapted shifts on Wiener Space and related topics | |
Dilation vector field on Wiener space | |
The calculus of differentials for the weak Stratonovich integral | |
Large deviations for Hilbert space valued Wiener processes: a sequence space approach | |
Stationary distributions for jump processes with inert drift | |
An Ornstein | |
Uhlenbeck type process which satisfies sufficient conditions for a simulation based filtering procedure | |
Escape probability for stoc | |
ISBN: | 9781461459064 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v34 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9781461455622:ONLINE Show nearby items on shelf |
Title: | Dihedral Fourier Analysis [electronic resource] : Data-analytic Aspects and Applications |
Author(s): |
Marlos A. G Viana Vasudevan Lakshminarayanan |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Dihedral Fourier Analysis introduces the theory and applications necessary to study experimental data indexed by, or associated with, the points in a dihedral symmetry orbit. This book looks at experimental data and analyticalmodels indexed by certai n dihedral rotations and reversals realized as vector fields. Its particular relevance as a research tool in areas such as optical and molecular biology statisticsappears when formulated within the context ofsymmetry studies, which formally connects algeb raic and statistical reasoning together in one methodology for data summary and inference. Chapter 1 presents an overview of the theory and methods of dihedral analysis. It introduces datasets and examples defining and connecting the algebraic notions of symmetry with those of statistical summaries and inference. Chapter 2 includes the required algebraic aspects and data-analytic results. Chapters 3-6 offer applicationsof the methods presented in the text. This book is intended for data analysts of both t heoretical and applied statistics |
Note: | Springer eBooks |
Contents: | Symmetry and Experimental Data |
Algebraic and Data | |
Analytic Aspects | |
Curvature and Refraction Data | |
Symbolic Sequences | |
Symmetry Preference and Perception | |
Other Applications | |
Glossary | |
Index | |
ISBN: | 9781461455622 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Mathematical statistics |
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Call number: | SPRINGER-2013-9781447148326:ONLINE Show nearby items on shelf |
Title: | Modular Representation Theory of Finite Groups [electronic resource] |
Author(s): |
Peter Schneider |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for exampleover the fieldof complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finitegroups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as wellas Green's direct analysis of indecomposable representations. Ther e is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's workthen establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple acategory a block is by the size and structure of its so-called 'defect group'. All these concepts are made explic it for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentationis strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the read er the group theoretic approach. In particular, in the case of defect groups a detailed proof of theequivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with thesemisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwis |
Note: | Springer eBooks |
Contents: | Prerequisites in module theory |
The Cartan{Brauer triangle | |
The Brauer character | |
Green's theory of indecomposable modules | |
Blocks | |
ISBN: | 9781447148326 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2013-9781441998781:ONLINE Show nearby items on shelf |
Title: | Robust Data Mining [electronic resource] |
Author(s): |
Petros Xanthopoulos Panos M Pardalos Theodore B Trafalis |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Data uncertainty is a concept closely related with most real life applications that involve data collection and interpretation. Examples can be found in data acquired with biomedical instruments or other experimental techniques.Integration of robust optimization in the existing data mining techniques aim to create new algorithms resilient to error and noise. This work encapsulates all the latest applications of robust optimization in data mining. This briefcontains an overview of the rapidly growing field ofrobust data mining research field and presents the most well known machine learning algorithms, their robust counterpart formulations and algorithms for attacking these problems.Thisbrief will appeal to theoreticians and data miners working in thi s field |
Note: | Springer eBooks |
Contents: | 1. Introduction |
2. Least Squares Problems | |
3. Principal Component Analysis | |
4. Linear Discriminant Analysis | |
5.Support Vector Machines | |
6. Conclusion | |
ISBN: | 9781441998781 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Optimization, 2190-8354 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Software engineering , Data mining , Mathematical optimization |
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Call number: | SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf |
Title: | New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number |
Author(s): |
Garret Sobczyk |
Date: | 2013 |
Publisher: | Boston : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s |
Note: | Springer eBooks |
Contents: | 1 Modular Number Systems |
2 Complex and Hyperbolic Numbers | |
3 Geometric Algebra | |
4 Vector Spaces and Matrices | |
5 Outer Product and Determinants | |
6 Systems of Linear Equations | |
7 Linear Transformations on R^n | |
8 Structure of a Linear Operator | |
9 Linear and Bilinear Forms | |
10 Hermitian Inner Product Spaces | |
11 Geometry of Moving Planes | |
12 Representations of the Symmetric Group | |
13 Calculus on m | |
Surfaces | |
14 Differential Geometry of Curves | |
15 Differential Geometry of k | |
Surfaces | |
16 Mappings Between Surfaces | |
17 Non | |
Euclidean and Projective Geometries | |
18 Lie Gr | |
ISBN: | 9780817683856 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics |
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Call number: | SPRINGER-2012-9788876424434:ONLINE Show nearby items on shelf |
Title: | An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs [electronic resource] |
Author(s): |
Mariano Giaquinta Luca Martinazzi |
Date: | 2012 |
Publisher: | Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress ofMathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certainassumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to asregularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of thebasic ideas and techniques introduced in this context, confining ourselves to important but simpl e situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, directmethods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar caseand partial regularity theorems in the vector valued case energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensionalweakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of theLp theory, including the celebrated results of W ente and of Coifman-Lions-Meyer-Semmes |
Note: | Springer eBooks |
Contents: | 1 Harmonic functions |
2 Direct methods | |
3 Hilbert space methods | |
4 L2 | |
regularity: the Caccioppoli inequality | |
5 Schauder estimates | |
6 Some real analysis | |
7 Lp | |
theory | |
8 The regularity problem in the scalar case | |
9 Partial regularity in the vector | |
valued case | |
10 Harmonic maps | |
11 A survey of minimal graphs | |
ISBN: | 9788876424434 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Publications of the Scuola Normale Superiore |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differential equations, partial |
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Call number: | SPRINGER-2012-9783642272257:ONLINE Show nearby items on shelf |
Title: | Bayesian Methods in Structural Bioinformatics [electronic resource] |
Author(s): |
Thomas Hamelryck Kanti Mardia Jesper Ferkinghoff-Borg |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is an edited volume, the goal of which is to provide an overview of the current state-of-the-art in statistical methods applied to problems in structural bioinformatics (and in particular protein structure prediction,simulation, experimenta l structure determination and analysis). It focuses on statistical methods that have a clear interpretation in the framework of statistical physics, rather than ad hoc, black box methods based on neural networksor support vector machines. In addition, the emphasis is on methods that deal with biomolecular structure in atomic detail. The book is highly accessible, and only assumes background knowledge on protein structure, with a minimum ofmathematical knowledge. Therefore, the book includes introductory c hapters that contain a solid introduction to key topics such as Bayesian statistics and concepts in machine learning and statistical physics |
Note: | Springer eBooks |
Contents: | Part I Foundations: An Overview of Bayesian Inference and Graphical Models |
Monte Carlo Methods for Inferences in High | |
dimensional Systems | |
Part II Energy Functions for Protein Structure Prediction: On the Physical Relevance and Statistical Interpretation of Knowledge based Potentials | |
Statistical Machine Learning of Protein Energetics from Experimentally Observed Structures | |
A Statistical View on the Reference Ratio Method | |
Part III Directional Statistics and Shape Theory: Statistical Modelling and Simulation Using the Fisher | |
Bingham Distribution | |
Statistics of Bivariate von Mises | |
ISBN: | 9783642272257 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Statistics for Biology and Health, 1431-8776 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Statistics , Medicine , Bioinformatics |
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Call number: | SPRINGER-2012-9783642231759:ONLINE Show nearby items on shelf |
Title: | Topological Methods in Data Analysis and Visualization II [electronic resource] : Theory, Algorithms, and Applications |
Author(s): |
Ronald Peikert Helwig Hauser Hamish Carr Raphael Fuchs |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods,topological ones stand out due to their solid mathematical foundation. Topologically defined structuresas found in scalar, vector and tensor fieldshave proven their merit in a wide range of scientific domains, and scientists havefound them to be revealing in subjects such as ph ysics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presentedat the fourth Workshop on Topology-Based Methods in Data Analysis and V isualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formalpresentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangiancoherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simpli fication, among other issues of note. The new research results included in this volume relate to all threekey areas in data analysistheory, algorithms and applications |
Note: | Springer eBooks |
Contents: | Part I: Discrete Morse Theory |
Part II: Hierarchical Methods for Extracting and Visualizing Topological Structures | |
Part III: Visualization of Dynamical Systems, Vector and Tensor Fields | |
Part IV: Topological Visualization of Unsteady Flow | |
ISBN: | 9783642231759 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Visualization, 1612-3786 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Electronic data processing , Computer graphics , Algorithms , Visualization |
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Call number: | SPRINGER-2012-9781461438946:ONLINE Show nearby items on shelf |
Title: | Calculus on Normed Vector Spaces [electronic resource] |
Author(s): |
Rodney Coleman |
Date: | 2012 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematicalmaturity. All the important t opology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book isone of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader |
Note: | Springer eBooks |
Contents: | Preface |
1 Normed Vector Spaces | |
2 Differentiation | |
3 Mean value theorems | |
4 Higher derivatives and differentials | |
5 Taylor theorems and applications | |
6 Hilbert spaces | |
7 Convex functions | |
8 The inverse and implicit mapping theorems | |
9 Vector fields | |
10 The flow of a vector field | |
11 The calculus of variations: an introduction | |
Bibliography | |
Index | |
ISBN: | 9781461438946 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Mathematical optimization |
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Call number: | SPRINGER-2012-9781461437611:ONLINE Show nearby items on shelf |
Title: | Solar Flare Magnetic Fields and Plasmas [electronic resource] |
Author(s): |
Yuhong Fan George Fisher |
Date: | 2012 |
Publisher: | New York, NY : Springer US |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is devoted to the dynamics and diagnostics of solar magnetic fields and plasmas in the Suns atmosphere. Five broad areas of current research in Solar Physics are presented: (1) New techniques for incorporatingradiation transfer effects in to three-dimensional magnetohydrodynamic models of the solar interior and atmosphere, (2) The connection between observed radiation processes occurring during flares and the underlying flare energy releaseand transport mechanisms, (3) The global balance o f forces and momenta that occur during flares, (4) The data-analysis and theoretical tools needed to understand and assimilate vector magnetogram observations and (5) Connecting flareand CME phenomena to the topological properties of the magnetic field in the Solar Atmosphere. The role of the Suns magnetic field is a major emphasis of this book, which was inspired by a workshop honoring Richard C. (Dick)Canfield. Dick has been making profound contributions to these areas of research over a long and produc tive scientific career. Many of the articles in this topical issue were first presented as talks during this workshop andrepresent substantial original work. The workshop was held 9 11 August 2010, at the Center Green campus of the National Center for At mospheric Research (NCAR) in Boulder, Colorado. This volume is aimed at researchers and graduatestudents active in solar physics, solar-terrestrial physics and magneto-hydrodynamics. Previously published in Solar Physics journal, Vol. 277/1, 2012 |
Note: | Springer eBooks |
Contents: | Efficient Techniques for Radiation Transfer in Three |
Dimensional MHD Models | |
Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona | |
Understanding Flare Radiation Processes | |
Global Forces and Momenta During Solar Flare Energy Release | |
The Evolution of Sunspot Magnetic Fields Associated with a Solar Flare | |
Global Forces in Eruptive Solar Flares | |
Data Analysis and Theory for Analysis of Vector Magnetogram Data | |
Modeling and Interpreting the Effects of Spatial Resolution on Solar Magnetic Field Maps | |
Magnetic Connectivity Between Active Regions 10987, 10988, 1 | |
ISBN: | 9781461437611 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Astrophysics |
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