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Call number: | 9783319517537:ONLINE Show nearby items on shelf |
Title: | Extended Abstracts Summer 2015 Strategic Behavior in Combinatorial Structures Quantitative Finance |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (VI, 139 p. 5 illus., 3 illus. in color p.) |
Contents: | Part-I -- Foreword -- On the Push & Pull Protocol for Rumour Spreading -- Random Walks that Find Perfect Objects and the Lovasz Local Lemma -- Logit Dynamics with Concurrent Updates for Local Interaction Games -- Logit Dynamics with |
Concurrent Updates for Local Interaction Games -- Carpooling in Social Networks -- Who to Trust for Truthful Facility Location? -- Metric and Spectral Properties of Dense Inhomogeneous Random Graphs -- On-Line List Colouring of Random | |
Graphs -- Approximation Algorithms for Computing Maximin Share Allocations -- An Alternate Proof of the Algorithmic Lovász Local Lemma -- Learning Game-Theoretic Equilibria via Query Protocols -- The Lower Tail: Poisson Approximation | |
Revisited -- Population Protocols for Majority in Arbitrary Networks -- The Asymptotic Value in Finite Stochastic Games -- Almost All 5-Regular Graphs Have a 3-Flow -- Part-II -- Foreword -- On the Short-Time Behaviour of the Implied | |
Volatility Skew for Spread Options and Applications -- An Alternative to CARMA Models via Iterations of Ornstein-Uhlenbeck Processes -- Euler-Poisson Schemes for Levy Processes -- On Time-Consistent Portfolios with Time-Inconsistent | |
Preferences -- A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models -- A Highly Efficient Pricing Method for European-Style Options Based on Shannon Wavelets -- A New Pricing Measure in the | |
Barndor-Nielsen-Shephard Model for Commodity Markets | |
ISBN: | 9783319517537 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Dynamics , Ergodic theory , Differential equations , Actuarial science , Convex geometry , Discrete geometry , Probabilities , Combinatorics , Mathematics , Combinatorics , Ordinary Differential Equations , Dynamical Systems and Ergodic Theory , Convex and Discrete Geometry , Probability Theory and Stochastic Processes , Actuarial Sciences |
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Call number: | 9783319500386:ONLINE Show nearby items on shelf |
Title: | Stochastic Modeling |
Author(s): |
Nicolas Lanchier |
Date: | 2017 |
Size: | 1 online resource (XIII, 303 p. 63 illus., 6 illus. in color p.) |
Contents: | 1. Basics of Measure and Probability Theory -- 2. Distribution and Conditional Expectation -- 3. Limit Theorems -- 4. Stochastic Processes: General Definition -- 5. Martingales -- 6. Branching Processes -- 7. Discrete-time Markov |
Chains -- 8. Symmetric Simple Random Walks -- 9. Poisson Point and Poisson Processes -- 10. Continuous-time Markov Chains -- 11. Logistic Growth Process -- 12. Wright-Fisher and Moran Models -- 13. Percolation Models -- 14. Interacting | |
Particle Systems -- 15. The Contact Process -- 16. The Voter Model -- 17. Numerical Simulations in C and Matlab | |
ISBN: | 9783319500386 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Mathematical models , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Mathematical Modeling and Industrial Mathematics |
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Call number: | 9783319441658:ONLINE Show nearby items on shelf |
Title: | New Horizons in Fundamental Physics |
Author(s): | |
Date: | 2017 |
Size: | 1 online resource (IX, 389 p. 134 illus., 95 illus. in color p.) |
Contents: | Part I Nuclear Structure and Superheavy Elements: Intertwining of Greiner's Theoretical Works and our Experimental Studies (J.H. Hamilton et al.) -- Eighty years of research on super-heavy nuclei (S. Hofmann) -- Perspectives of heavy |
and superheavy nuclei research (A.V. Karpov et al.) -- Superheavy Element Chemistry - New experimental results challenge theoretical understanding (R. Eichler) -- 25 Years of FRS Experiments and New Horizons (H. Geissel et al.) -- SHE | |
Research with Rare-Isotope Beams, Challenges and Perspectives, and the new Generation of SHE Factories (G. Münzenberg et al.) -- Multi-modal Collinear Ternary Fission (W. von Oertzen et al.) -- From the stable to the exotic: clustering | |
in light nuclei (C. Beck) -- Towards Laser Spectroscopy of Superheavy Elements (H. Backe) -- Part II Physics of Heavy-Ion Collisions: Chemical freeze-out conditions in hadron resonance gas (V. Vovchenko et al.) -- The QCD Phase Diagram | |
and Hadron Formation in Relativistic Nuclear Collisions (F. Becattini et al.) -- Degrees of Freedom of the Quark Gluon Plasma, tested by Heavy Mesons (H. Berrehrah et al.) -- Electromagnetic emissivity of hot and dense matter (E.L. | |
Bratkovskaya at al.) -- Heavy-Ion Collisions: Status of Chemical Equilibrium (J. Cleymans) -- Novel developments of HYDJET++ model for ultra-relativistic heavy-ion collisions (L. Bravina et al.) -- Jet tomography in heavy-ion | |
collisions-Challenges, Results, and Open Problems (B. Betz) -- Part III QED - Strong Fields and High Precision: Probing QED Vacuum with Heavy Ions (J. Rafelski et al.) -- Laser assisted Breit-Wheeler and Schwinger processes (T. Nousch | |
et al.) -- A method to measure vacuum birefringence at FCC-ee (U.I. Uggerhoj et al.) -- Unifying Quantum Electro-Dynamics and Many-Body Perturbation Theory (I. Lindgren et al.) -- Part IV Astrophysics: Simulations of accretion disks | |
around massive stars (M. Algalán et al.).-Neutron Stars-Possibilities and Limits for Exotic Phases (S. Schramm et al.) -- The Case for an Underground Neutrino Facility in South Africa (Z.Z. Vilakazia et al.) -- Part IV Special topics: | |
Covariant Hamiltonian representation of Noether's theorem and its application to SU(N) gauge theories (J. Struckmeier et al.) -- Infrastructure Estimates for a Highly Renewable Global Electricity Grid (M. Dahl et al.) -- Power flow | |
tracing in complex networks (M. Schäfer et al.) -- Patent protection of high-level research results (T. J. Bürvenich) | |
ISBN: | 9783319441658 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Physics , Astrophysics , Nuclear physics , Heavy ions , Hadrons , Atoms , Matter , Physics , Nuclear Physics, Heavy Ions, Hadrons , Atoms and Molecules in Strong Fields, Laser Matter Interaction , Applications of Graph Theory and Complex Networks , Astrophysics and Astroparticles |
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Call number: | SPRINGER-2016-9789462392014:ONLINE Show nearby items on shelf |
Title: | Spaces of Continuous Functions |
Author(s): |
G.L.M Groenewegen |
Date: | 2016 |
Size: | 1 online resource (173 p.) |
Note: | 10.2991/978-94-6239-201-4 |
Contents: | Topological Preliminaries -- Metrizable Compact Spaces -- The Stone-Weierstrass Theorem -- Weak Topologies. The Alaoglu Theorem -- Riesz Spaces -- Yosida’s Representation Theorem -- The Stone-Čech compactification -- Evaluations -- C(X) determin es X -- The Riesz Representation Theorem -- Banach Algebras -- Other Scalars |
ISBN: | 9789462392014 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Atlantis Studies in Mathematics: 4 |
Keywords: | Mathematics , Functional analysis , Measure theory , Mathematics , Functional Analysis , Measure and Integration |
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Call number: | SPRINGER-2016-9789462391154:ONLINE Show nearby items on shelf |
Title: | Lectures on the Mathematics of Quantum Mechanics II: Selected Topics |
Author(s): |
Gianfausto Dell'Antonio |
Date: | 2016 |
Size: | 1 online resource (381 p.) |
Note: | 10.2991/978-94-6239-115-4 |
Contents: | Wigner functions Husimi distribution Semiclassical -- Pseudodiffential operators Calderon-Vaillantcourt -- Compact, Shatten-class Carleman operators -- Periodic potentials Theory of Bloch-Floquet-Zak -- Connection with the properties |
of a crystal -- Lie-Trotter-Kato formula Wiener process -- Elements of probability theory Sigma algebras -- Ornstein-Uhlenbeck process -- Modular Operator Tomita-Takesaki theory -- Scattering theory Time-dependent formalism -- Time | |
independent formalisms Flux-across surfaces -- The method of Enss Propagation estimates -- The N-body Quantum System -- Positivity preserving maps -- Hypercontractivity. Logarithmic Sobolev inequalities -- Measure (gage) spaces. | |
Cliﬀord algebra, C.A.R. relations | |
ISBN: | 9789462391154 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Atlantis Studies in Mathematical Physics: Theory and Applications: 2 |
Keywords: | Physics , Mathematical physics , Quantum physics , Mechanics , Physics , Quantum Physics , Mathematical Physics , Mechanics |
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Call number: | SPRINGER-2016-9783319335728:ONLINE Show nearby items on shelf |
Title: | Open Problems in the Geometry and Analysis of Banach Spaces |
Author(s): |
Antonio J Guirao |
Date: | 2016 |
Size: | 1 online resource (169 p.) |
Note: | 10.1007/978-3-319-33572-8 |
Contents: | Preface -- Basic linear structure -- Basic linear geometry -- Biorthogonal systems -- Smoothness, smooth approximation -- Nonlinear geometry -- Some more nonseparable problems -- Some applications -- Bibliography -- List of concepts and problems -- Symbol index -- Subject index. |
ISBN: | 9783319335728 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Approximation theory , Functional analysis , Measure theory , Convex geometry , Discrete geometry , Algebraic topology , Mathematics , Functional Analysis , Approximations and Expansions , Measure and Integration , Convex and Discrete Geometry , Algebraic Topology |
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Call number: | SPRINGER-2016-9783319310893:ONLINE Show nearby items on shelf |
Title: | Brownian Motion, Martingales, and Stochastic Calculus |
Author(s): |
Jean-François Le Gall |
Date: | 2016 |
Size: | 1 online resource (1 p.) |
Note: | 10.1007/978-3-319-31089-3 |
Contents: | Gaussian variables and Gaussian processes -- Brownian motion -- Filtrations and martingales -- Continuous semimartingales -- Stochastic integration -- General theory of Markov processes -- Brownian motion and partial differential equations -- Stoch astic differential equations -- Local times -- The monotone class lemma -- Discrete martingales -- References |
ISBN: | 9783319310893 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Graduate Texts in Mathematics: 274 |
Keywords: | Mathematics , Measure theory , Economics, Mathematical , System theory , Mathematical models , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Quantitative Finance , Measure and Integration , Mathematical Modeling and Industrial Mathematics , Systems Theory, Control |
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Call number: | SPRINGER-2016-9783319307442:ONLINE Show nearby items on shelf |
Title: | Real Analysis |
Author(s): |
Peter A Loeb |
Date: | 2016 |
Size: | 1 online resource (274 p.) |
Note: | 10.1007/978-3-319-30744-2 |
Contents: | Preface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References. |
ISBN: | 9783319307442 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Measure theory , Functions of real variables , Mathematics , Real Functions , Functional Analysis , Measure and Integration |
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Call number: | SPRINGER-2016-9783319306209:ONLINE Show nearby items on shelf |
Title: | Introduction to Probability with Statistical Applications |
Author(s): |
Géza Schay |
Date: | 2016 |
Edition: | 2nd ed. 2016 |
Size: | 1 online resource (385 p.) |
Note: | 10.1007/978-3-319-30620-9 |
Contents: | Introduction -- The Algebra of Events -- Combinatorial Problems -- Probabilities -- Random Variables -- Expectation, Variance, Moments -- Some Special Distributions -- The Elements of Mathematical Statistics |
ISBN: | 9783319306209 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Mathematical statistics , Measure theory , Applied mathematics , Engineering mathematics , Probabilities , Statistics , Mathematics , Probability Theory and Stochastic Processes , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Scien , Probability and Statistics in Computer Science , Measure and Integration , Applications of Mathematics |
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Call number: | SPRINGER-2016-9783319295350:ONLINE Show nearby items on shelf |
Title: | The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators |
Author(s): |
Volodymyr Koshmanenko |
Date: | 2016 |
Size: | 1 online resource (237 p.) |
Note: | 10.1007/978-3-319-29535-0 |
Contents: | Preface -- Introduction -- 1.Preliminaries -- 2.Symmetric Operators and Closable Quadratic Forms -- 3.Self-adjoint Extensions of Symmetric Operators -- 4.Rigged Hilbert Spaces -- 5.Singular Quadratic Forms -- 6.Dense Subspaces in Scales of Hilbert Spaces -- 7.Singular Perturbations of Self-adjoint Operators -- 8.Super-singular Perturbations -- 9.Some Aspects of the Spectral Theory -- References -- Subject Index -- Notation Index |
ISBN: | 9783319295350 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 253 |
Keywords: | Mathematics , Measure theory , Operator theory , Mathematical physics , Mathematics , Operator Theory , Measure and Integration , Mathematical Applications in the Physical Sciences |
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Call number: | SPRINGER-2016-9783319290461:ONLINE Show nearby items on shelf |
Title: | Measure and Integration |
Author(s): |
Hari Bercovici |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (300 p.) |
Note: | 10.1007/978-3-319-29046-1 |
Contents: | Rings of sets -- Measurability -- Integrals and Measures -- Convergence Theorems for Lebesgue Integrals -- Existence and Uniqueness of Measures -- Signed Measures, Complex Measures and Absolute Continuity -- Measure and Topology -- Product Measures -- The Lp Spaces -- Fourier Analysis -- Standard Measure Spaces. |
ISBN: | 9783319290461 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Measure theory , Functions of real variables , Mathematics , Measure and Integration , Real Functions |
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Call number: | SPRINGER-2016-9783319278735:ONLINE Show nearby items on shelf |
Title: | New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing, and Multifractal Analysis |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (19 p.) |
Note: | 10.1007/978-3-319-27873-5 |
Contents: | Multifractal Analysis of Cantor-like Measures -- Multifractal Analysis and Wavelets -- An Introduction to Mandelbrot Cascades -- Lebesgue-type Inequalities for Greedy Approximation -- Results on Non-linear Approximation for Wavelet Bases in Weighte d Function Spaces -- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem -- Model Sets and New Versions pf Shannon Sampling Theorem -- Stylometry and Mathematical Study of Authorship -- Thoughts on Numerical and Conceptua l Harmonic Analysis |
ISBN: | 9783319278735 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Harmonic analysis , Fourier analysis , Measure theory , Computer science , Computer mathematics , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Signal, Image and Speech Processing , Measure and Integration , Mathematical Applications in Computer Science |
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Call number: | SPRINGER-2016-9783319278179:ONLINE Show nearby items on shelf |
Title: | Exercises in Analysis Part 2: Nonlinear Analysis |
Author(s): |
Leszek Gasiński |
Date: | 2016 |
Size: | 1 online resource (1062 p.) |
Note: | 10.1007/978-3-319-27817-9 |
Contents: | 1. Function Spaces -- 2. Nonlinear and Multivalued Maps -- 3. Smooth and Nonsmooth Calculus -- 4. Degree Theory. Fixed Point Theory -- 5. Variational and Topological Methods -- Index |
ISBN: | 9783319278179 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Functional analysis , Measure theory , Probabilities , Topology , Mathematics , Functional Analysis , Measure and Integration , Probability Theory and Stochastic Processes , Topology |
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Call number: | SPRINGER-2016-9783319252742:ONLINE Show nearby items on shelf |
Title: | The Special Theory of Relativity Foundations, Theory, Verification, Applications |
Author(s): |
Costas Christodoulides |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (480 p.) |
Note: | 10.1007/978-3-319-25274-2 |
Contents: | Historical Introduction -- The Main Landmarks in the Development of the Special Theory of Relativity -- The Principle of Relativity of Galileo. Galileo’s Invariance Hypothesis. The Law of Inertia. Inertial Frames of Reference |
Relativity -- Rømer and the Speed of Light -- Newton’s Laws of Motion. Inertia and Inertial Frames of Reference -- The Aberration of Light -- Arago’s Measurements Concerning the Constancy of the Speed of Light from Stars -- | |
Measurements of the Speed of Light in the Laboratory -- Attempts to Measure the Dragging of Aether by Moving Media -- Maxwell’s Equations and the Wave Equation -- The Experiment of Michelson and Morley -- The Lorentz-Fitzgerald | |
Contraction Hypothesis -- The Increase of the Mass of the Electron with Speed -- The Invariance of Maxwell’s Equations and the Lorentz Transformation -- The Formulation of the Special Theory of Relativity -- Prolegomena -- Inertial | |
Frames of Reference -- The Calibration of a Frame of Reference and the Synchronization of its Clocks -- The Relativity of Simultaneity -- The Relativity of Time and Length -- The Inevitability of the Special Theory of Relativity -- | |
Relativistic Kinematics -- The Lorentz Transformation for the Coordinates of an Event -- The Transformation of Velocity -- The Transformation of Acceleration -- Applications of Relativistic Kinematics -- The ‘Meson’ Paradox -- The | |
apparent focusing of fast charged particle beams due to the dilation of time -- The Sagnac Effect -- Clocks Moving Around the Earth -- The Experiment of Hafele and Keating -- Einstein’s Train -- The Twin Paradox -- Motion with a | |
Constant Proper Acceleration. Hyperbolic Motion -- Two Successive Lorentz Transformations. The Wigner Rotation -- Optical Phenomena -- The Aberration of Light -- Fizeau’s Experiment. Fresnel’s Aether Dragging Theory -- The Doppler | |
Effect -- Relativistic Beaming or the Headlight Effect -- The Pressure Exerted by Light -- Relativistic Dynamics -- The Dfinition of Relativistic Momentum. Relativistic Mass -- Relativistic Energy -- The Relationship Between Momentum | |
and Energy -- Classical Approximations -- Particles with Zero Rest Mass -- The Conservation of Momentum and of Energy -- The Equivalence of Mass and Energy -- The Transformation of Momentum and Energy -- The Zero-Momentum Frame of | |
Reference -- The Transformation of the Total Momentum and the Total Energy of a System of Particles -- The Collision of two Identical Particles -- The Transformation of Force -- Motion Under the Influence of a Constant Force. The | |
Motion of a Charged Particle in a Constant Uniform Electric Field -- The Motion of a Charged Particle in a Constant Homogeneous Magnetic Field -- Applications of Relativistic Dynamics -- The Compton Effect -- The Inverse Compton Effect | |
-- The Consequences of the Special Theory of Relativity on the Design of Particle Accelerators -- Mass Defect and Binding Energy of the Atomic Nucleus -- Threshold Energy -- The General Equations for the Motion of a Relativistic Rocket | |
-- Minkowski’s Spacetime and Four-Vectors -- The ‘World’ of Minkowski -- Four-Vectors -- Electromagnetism -- Introduction -- The Invariance of Electric Charge -- The Transformations of the Electric Field and the Magnetic Field -- The | |
Fields of a Moving Electric Charge -- The Derivation of the Differential form of the Biot-Savart Law from Coulomb’s Law -- The Force Exerted on a Moving Charge by an Electric Current -- Experiments -- The Speed of Light -- The Aether | |
-- The Dilation of Time -- The Relativistic Doppler Effect -- The Contraction of Length -- The Test of the Predictions of Relativistic Kinematics -- The Sagnac Effect -- The Relativistic Mass -- The Equivalence of Mass and Energy -- | |
The Test of the Predictions of Relativistic Dynamics -- The Invariance of Electric Charge -- Appendix 1. The Paradox of the Room and the Rod -- Appendix 2. The Appearance of Moving Bodies -- Appendix 3. The Derivation of the Expression | |
for the Relativistic Mass in General -- Appendix .4. The Invariance of the Equations of Maxwell and the Wave Equation Under the Lorentz Transformation -- Appendix 5. Tachyons -- Appendix 6. The Lorentz Transformation in Matrix Form -- | |
Appendix 7. Table of Some Functions of the Speed -- Solutions of the Problem | |
ISBN: | 9783319252742 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Gravitation , Observations, Astronomical , Astronomy , Physics , Classical and Quantum Gravitation, Relativity Theory , Astronomy, Observations and Techniques |
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Call number: | SPRINGER-2016-9783319210186:ONLINE Show nearby items on shelf |
Title: | Integral Operators in Non-Standard Function Spaces Volume 2: Variable Exponent Hölder, Morrey–Campanato and Grand Spaces |
Author(s): |
Vakhtang Kokilashvili |
Date: | 2016 |
Size: | 1 online resource (1003 p.) |
Note: | 10.1007/978-3-319-21018-6 |
Contents: | IV: Grand Lebesgue Spaces -- 14 Maximal Functions and Potentials -- 15 Grand Lebesgue Spaces on Sets with Infinite Measure -- V: Grand Morrey Spaces -- 16 Maximal Functions, Fractional and Singular Integrals -- 17 Multiple Operators on the Cone of Decreasing Functions -- A: Grand Bochner Spaces -- Bibliography -- Symbol Index -- Subject Index.IV: Grand Lebesgue Spaces -- 14 Maximal Functions and Potentials -- 15 Grand Lebesgue Spaces on Sets with Infinite Measure -- V: Grand Morrey Spaces -- 16 Max imal Functions, Fractional and Singular Integrals -- 17 Multiple Operators on the Cone of Decreasing Functions -- A: Grand Bochner Spaces -- Bibliography -- Symbol Index -- Subject Index |
ISBN: | 9783319210186 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Operator Theory: Advances and Applications: 249 |
Keywords: | Mathematics , Functional analysis , Operator theory , Mathematics , Operator Theory , Functional Analysis |
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Call number: | SPRINGER-2016-9783319202242:ONLINE Show nearby items on shelf |
Title: | Gravity: Where Do We Stand? |
Author(s): | |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (103 p.) |
Note: | 10.1007/978-3-319-20224-2 |
Contents: | Introduction -- Gravity: Newtonian, post-Newtonian and General Relativistic -- Newtonian Gravity and its classical tests (Equivalence Principle, Measure of G, 1/r2 dependence) -- Gravitational Tests with Interplanetary Probes -- |
Probing gravity with second generation lunar laser ranging -- Fundamental physics with the LAGEOS satellites -- The role of binary pulsars in testing Gravity Theories -- Gravitational waves: theory, sources, detectors -- Possible low | |
energy manifestations of strings and gravity -- Effective Field Theories with Lorentz Violations and their observational constraints -- Search for generic violations of Lorentz invariance in the Standard Model Extension formalism -- | |
The MOND-TeVeS theory and the lensing results from the Bullet Cluster | |
ISBN: | 9783319202242 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Physics , Quantum field theory , String theory , Gravitation , Astrophysics , Cosmology , Physics , Classical and Quantum Gravitation, Relativity Theory , Cosmology , Astrophysics and Astroparticles , Quantum Field Theories, String Theory |
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Call number: | SPRINGER-2016-9781447168119:ONLINE Show nearby items on shelf |
Title: | Lectures on Functional Analysis and the Lebesgue Integral |
Author(s): |
Vilmos Komornik |
Date: | 2016 |
Size: | 1 online resource (403 p.) |
Note: | 10.1007/978-1-4471-6811-9 |
Contents: | Some papers of general interest -- Topological prerequisites -- Part 1 Functional analysis -- Hilbert spaces -- Banach spaces -- Locally convex spaces -- Part 2 The Lebesgue integral -- Monotone functions -- The Lebesgue integral in R -- Generalize d Newton-Leibniz formula -- Integrals on measure spaces -- Part 3 Function spaces -- Spaces of continuous functions -- Spaces of integrable functions -- Almost everywhere convergence -- Hints and solutions to some exercises -- Bibliography -- Teaching rem arks -- Subject index -- Name index |
ISBN: | 9781447168119 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Keywords: | Mathematics , Approximation theory , Functional analysis , Measure theory , Mathematics , Functional Analysis , Measure and Integration , Approximations and Expansions |
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Call number: | SPRINGER-2014-9789401788250:ONLINE Show nearby items on shelf |
Title: | Measurement and Probability [electronic resource] : A Probabilistic Theory of Measurement with Applications |
Author(s): |
Giovanni Battista Rossi |
Date: | 2014 |
Publisher: | Dordrecht : Springer Netherlands : Imprint: Springer |
Size: | 1 online resource |
Note: | Measurement plays a fundamental role both in physical and behavioral sciences, as well as in engineering and technology: it is the link between abstract models and empirical reality and is a privileged method of gatheringinformation from the real wor ld. Is it possible to develop a single theory of measurement for the various domains of science and technology in which measurement is involved? This book takes the challenge by addressing the followingmain issues: What is the meaning of measurement? How do we measure? What can be measured? A theoretical framework that could truly be shared by scientists in different fields, ranging from physics and engineering to psychology isdeveloped. The future in fact will require greater collaboration between scienc e and technology and between different sciences. Measurement, which played a key role in the birth of modern science, can act as an essentialinterdisciplinary tool and language for this new scenario. A sound theoretical basis for addressing key problems i n measurement is provided. These include perceptual measurement, the evaluation of uncertainty, the evaluation ofinter-comparisons, the analysis of risks in decision-making and the characterization of dynamical measurement. Currently, increasing attention is paid to these issues due to their scientific, technical, economic and social impact. Thebook proposes a unified probabilistic approach to them which may allow more rational and effective solutions to be reached. Great care was taken to make the text a s accessible as possible in several ways. Firstly, by giving preferenceto as interdisciplinary a terminology as possible secondly, by carefully defining and discussing all key terms. This ensures that a wide readership, including people from different mat hematical backgrounds and different understandingsof measurement can all benefit from this work. Concerning mathematics, all the main results are preceded by intuitive discussions and illustrated by si |
Contents: | Part I: General Problems |
1 Measurability | |
2 Uncertainty | |
Part II: Theory | |
3 The Measurement Scale: Deterministic Framework | |
4 The Measurement Scale: Probabilistic Approach | |
5 The Measurement Process | |
6 Inference in Measurement | |
7 Multidimensional Measurements | |
Part III: Applications | |
8 Perceptual Measurement | |
9 The Evaluation of Measurement Uncertainty | |
10 Evaluating Inter | |
Comparisons | |
11 Measurement | |
Based Decisions | |
12 Dynamic Measurement | |
Appendix | |
Bibliography | |
ISBN: | 9789401788250 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Series in Measurement Science and Technology, 2198-7807 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Mathematics , Engineering , Psychometrics |
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Title: | Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations [electronic resource] |
Author(s): |
Jzef Bana Mohammad Mursaleen |
Date: | 2014 |
Publisher: | New Delhi : Springer India : Imprint: Springer |
Size: | 1 online resource |
Note: | This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has manyapplications. Thebookdi scusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness in particular, the Hausdorff measure of noncompactness has beenapplied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators. Thebookconsists of eight self-contained chapters. Chapter 1 discussesthe theory of FK spaces andChapter2various duals of sequence spaces, which are used to characterize the matrix classes be tween these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties.The techniques associated with measures of noncompactness are applied to characterize the compact matrix ope rators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential andintegral equations, which are obtained with the help of argumentations based on compactness conditions |
Contents: | Chapter 1. Introduction to FK spaces |
Chapter 2. Matrix Transformations | |
Chapter 3. Some new sequence spaces of non | |
absolute type | |
Chapter 4. Some non | |
classical sequence spaces | |
Chapter 5. Measures of noncompactness | |
Chapter 6. Application to compact matrix operators | |
Chapter 7. Applications to infinite systems of differential equations | |
Chapter 8. Applications to integral equations | |
ISBN: | 9788132218869 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Integral equations , Operator theory , Differential Equations , Differential equations, partial , Sequences (Mathematics) |
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Call number: | SPRINGER-2014-9784431551089:ONLINE Show nearby items on shelf |
Title: | Weakly Wandering Sequences in Ergodic Theory [electronic resource] |
Author(s): |
Stanley Eigen Arshag Hajian Yuji Ito Vidhu Prasad |
Date: | 2014 |
Publisher: | Tokyo : Springer Japan : Imprint: Springer |
Size: | 1 online resource |
Note: | The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant anddeep properties of ergo dic transformations that preserve an infinite measure. This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinitemeasure. Connections of these sequences to additi ve number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory isadequate for the reader |
ISBN: | 9784431551089 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Number theory |
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Call number: | SPRINGER-2014-9783662439203:ONLINE Show nearby items on shelf |
Title: | Geometry and Analysis of Fractals [electronic resource] : Hong Kong, December 2012 |
Author(s): |
De-Jun Feng Ka-Sing Lau |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written bythe leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong.The volume offers insights into a number o f exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematicalphysics. |
Contents: | Mandelbrot cascades and related topics |
Law of pure types and some exotic spectra of fractal spectral measures | |
The role of transfer operators and shifts in the study of fractals: encoding | |
models, analysis and geometry, commutative and non | |
commutative | |
Generalized energy inequalities and higher multifractal moments | |
Some Aspects of Multifractal analysis | |
Heat kernels on metric measure spaces | |
Stochastic completeness of jump processes on metric measure spaces | |
Self similar sets, entropy and additive combinatorics | |
Quasisymmetric modification of metrics on self | |
similar sets | |
Re | |
ISBN: | 9783662439203 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v88 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783642450822:ONLINE Show nearby items on shelf |
Title: | A Measure Theoretical Approach to Quantum Stochastic Processes [electronic resource] |
Author(s): |
Wilhelm Waldenfels |
Date: | 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as powerseries of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), ineach case the Hamiltonian of the associated o ne-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theoryof the Hudson-Parthasarathy equation and the amplified oscillator pro blem. To that end, a chapter on white noise calculus has also been included |
Contents: | Weyl Algebras |
Continuous Sets of Creation and Annihilation Operators | |
One | |
Parameter Groups | |
Four Explicitly Calculable One | |
Excitation Processes | |
White Noise Calculus | |
Circled Integrals | |
White Noise Integration | |
The Hudson | |
Parthasarathy Differential Equation | |
The Amplifies Oscillator | |
Approximation by Coloured Noise | |
Index | |
ISBN: | 9783642450822 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Physics, 0075-8450 : v878 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory , Mathematical physics |
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Call number: | SPRINGER-2014-9783642405235:ONLINE Show nearby items on shelf |
Title: | An Introduction to Markov Processes [electronic resource] |
Author(s): |
Daniel W Stroock |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including studentsfrom engineering, econ omics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes.Applications are dispersed throughout the book. In addition, a whole chapter isdevoted to reversible processes and the use of thei r associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm.The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing isthe section with a new technique for computing stationarymeasures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for span ning trees in a connected graph |
Contents: | Preface |
Random Walks, a Good Place to Begin | |
Doeblin's Theory for Markov Chains | |
Stationary Probabilities | |
More about the Ergodic Theory of Markov Chains | |
Markov Processes in Continuous Time | |
Reversible Markov Processes | |
A minimal Introduction to Measure Theory | |
Notation | |
References | |
Index | |
ISBN: | 9783642405235 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Graduate Texts in Mathematics, 0072-5285 : v230 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319095318:ONLINE Show nearby items on shelf |
Title: | Translational Recurrences [electronic resource] : From Mathematical Theory to Real-World Applications |
Author(s): |
Norbert Marwan Michael Riley Alessandro Giuliani Jr. Webber Charles L |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantifi cationanalysis (RQA) with s pecial emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods. Readers will discover new applications and insights into a range of systems provided byrecurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, ofany statistical distribution, free of any particular model type, and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes, or classifi cation of system states. Th ebook will be of interest to an interdisciplinary audience of recurrence plot users and re searchers interested in time series analysis of complex systems in general |
Contents: | 1 A Recurrence Plot |
based Distance Measure: S. Spiegel et al | |
2 Fast computation of recurrences in long time series: T. Rawald et al | |
3 Unthresholded recurrence plots for complex | |
valued representations of narrow band signals: A. Sipers et al | |
4 Quantifying redundancy and information content of lines in recurrence plots using the theory of framework rigidity: A. Sipers et al | |
5 Recent advances in non | |
stationary signal processing based on Recurrence Plot Analysis concept: C. Ioana et al | |
6 A Recurrence | |
Based Approach for Feature Extraction in Brain | |
Computer Interface Systems: L.F.S | |
ISBN: | 9783319095318 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v103 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Visualization , Mathematical statistics |
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Call number: | SPRINGER-2014-9783319081298:ONLINE Show nearby items on shelf |
Title: | Tychastic Measure of Viability Risk [electronic resource] |
Author(s): |
Jean-Pierre Aubin Luxi Chen Olivier Dordan |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand, and measuring the risk by computing the hedgingexit time function assoc iating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term tychastic viability measure of risk is anevolutionary alternative to statistical measures, whe n dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners |
Contents: | Part I Description, Illustration and Comments of the Results |
The Viabilist Portfolio Performance and Insurance Approach | |
Technical and Quantitative Analysis of Tubes | |
Uncertainty on Uncertainties | |
Part II Mathematical Proofs | |
Why Viability Theory? A Survival Kit | |
General Viabilist Portfolio Performance and Insurance Problem | |
ISBN: | 9783319081298 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf |
Title: | Probability on Compact Lie Groups [electronic resource] |
Author(s): |
David Applebaum |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects |
Contents: | Introduction |
1.Lie Groups | |
2.Representations, Peter | |
Weyl Theory and Weights | |
3.Analysis on Compact Lie Groups | |
4.Probability Measures on Compact Lie Groups | |
5.Convolution Semigroups of Measures | |
6.Deconvolution Density Estimation | |
Appendices | |
Index | |
Bibliography | |
ISBN: | 9783319078427 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Probability Theory and Stochastic Modelling, 2199-3130 : v70 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319067612:ONLINE Show nearby items on shelf |
Title: | Relativity and Gravitation [electronic resource] : 100 Years after Einstein in Prague |
Author(s): |
Ji Bik Tom Ledvinka |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem ofgravitation. Before he l eft Prague in July 1912 he had submitted the paper Relativitt und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham in which he remarkably anticipated what a future theory of gravity should looklike. At the occasion of the Einstein-in-Prague cente nary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: Relativity and Gravitation, 100 Years after Einstein inPrague. The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation, and conceptual and historical issues. Theconference attracted over 200 scientists from 31 countries, among them a number of leading experts in the f ield of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts ofcontributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors . Full texts of the plenary talks are included in the volume General Relativity, Cosmology andAstrophysics--Perspectives 100 Years after Einstein in Prague, eds. J. Bik and T. Ledvinka, published also by Springer Verlag |
Contents: | Abstracts of Plenary Talks |
Part I Classical General Relativity | |
Exact Hairy Black Holes | |
Black Hole Formation from a Complete Past for the Einstein | |
Vlasov System | |
How to Measure Deviation from the Kerr Initial Data Recent Progress | |
Hidden Symmetries of the Dirac Equation in Curved Space | |
time | |
Geometrostatics: the Geometry of Static Space | |
times | |
The Gravitational Equation in Higher Dimensions | |
Geometric Inequalities for Black Holes | |
Scalar Fields on anti | |
de Sitter Background | |
Canonical Super energy Tensors in General Relativity: a Reappraisal | |
Einsteins Prague F | |
ISBN: | 9783319067612 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Physics, 0930-8989 : v157 |
Series: | Physics and Astronomy (Springer-11651) |
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Call number: | SPRINGER-2014-9783319062662:ONLINE Show nearby items on shelf |
Title: | Operator Theory in Harmonic and Non-commutative Analysis [electronic resource] : 23rd International Workshop in Operator Theory and its Applications, Sydney, July 2012 |
Author(s): |
Joseph A Ball Michael A Dritschel A.F.M Elst Pierre Portal Denis Potapov |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This book comprisesthe proceedings of the XXIII International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012.It includes twelve artic les presenting both surveys of current research in operator theory and original results. The contributors are A. Amenta P. Auscher and S. Stahlhut W. Bauer C. Herrera Yaez and N. Vasilevski C.C. Cowen, S. Jungand E. Ko R.E. Curto, I.S. Hwang and W.Y. Lee S. Dey and K.J. Haria F. Gesztesy and R. Weikard G. Godefroy B. Jefferies S. Patnaik and G. Weiss W.J. Ricker A. Skripka |
Contents: | Introduction |
Tent Spaces over Metric Measure Spaces under Doubling and Related Assumptions | |
Remarks on Functional Calculus for Perturbed First | |
order Dirac Operators | |
(m, ) | |
Berezin Transform and Approximation of Operators on Weighted Bergman Spaces over the Unit Ball | |
Normal and Cohyponormal Weighted Composition Operators on H2 | |
A Subnormal Toeplitz Completion Problem | |
Generalized Repeated Interaction Model and Transfer Functions | |
Some Remarks on the Spectral Problem Underlying the CamassaHolm Hierarchy | |
Remarks on Spaces of Compact Operators between Reflexive Banach Space | |
ISBN: | 9783319062662 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Operator Theory: Advances and Applications, 0255-0156 : v240 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Operator theory |
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Call number: | SPRINGER-2014-9783319061764:ONLINE Show nearby items on shelf |
Title: | Exercises in Analysis [electronic resource] : Part 1 |
Author(s): |
Leszek Gasiksi Nikolaos S Papageorgiou |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces topological spaces measure, integration, and Martingales measure andtopology and functional analysis . Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for betterunderstanding of the material. At least 170 exercises/problems ar e presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for theapplication surrounding each topic. This nearly encyclopedic coverage of exercises in mathemat ical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problemsvaluable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all ofthe above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume |
Contents: | 1. Metric Spaces |
2. Topological Spaces | |
3. Measure, Integral, and Martingales | |
4. Measures and Topology | |
5. Functional Analysis | |
Other Problem Books | |
List of Symbols | |
Index | |
ISBN: | 9783319061764 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Problem Books in Mathematics, 0941-3502 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Distribution (Probability theory) , Topology |
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Call number: | SPRINGER-2014-9783319058528:ONLINE Show nearby items on shelf |
Title: | An Introduction to Random Interlacements [electronic resource] |
Author(s): |
Alexander Drewitz Balzs Rth Artm Sapozhnikov |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Thisbook gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental resultsand methods of this rap idly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to timesproportional to the volume of the torus. Random inter lacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on thetorus to random interlacements and the full proof of the percolation phase t ransition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with theunderlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of randominterlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature |
Contents: | Random Walk, Green Function, Equilibrium Measure |
Random Interlacements: First Definition and Basic Properties | |
Random Walk on the Torus and Random Interlacements | |
Poisson Point Processes | |
Random Interlacements Point Process | |
Percolation of the Vacant Set | |
Source of Correlations and Decorrelation via Coupling | |
Decoupling Inequalities | |
Phase Transition of Vu | |
Coupling of Point Measures of Excursions | |
ISBN: | 9783319058528 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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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-2014-9783319048079:ONLINE Show nearby items on shelf |
Title: | Analytic and Probabilistic Approaches to Dynamics in Negative Curvature [electronic resource] |
Author(s): |
Franoise Dal'Bo Marc Peign Andrea Sambusetti |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | The work of E. Hopf and G.A. Hedlund, in the 1930s, on transitivity and ergodicity of the geodesic flow for hyperbolic surfaces, marked the beginning of the investigation of the statistical properties and stochastic behavior ofthe flow. The first cen tral limit theorem for the geodesic flow was proved in the 1960s by Y. Sinai for compact hyperbolic manifolds. Since then, strong relationships have been found between the fields of ergodic theory, analysis, andgeometry. Different approaches and new tools have been developed to study the geodesic flow, including measure theory, thermodynamic formalism, transfer operators, Laplace operators, and Brownian motion. All these different points ofview have led to a deep understanding of more general dynamical sy stems, in particular the so-called Anosov systems, with applications to geometric problems such as counting, equirepartition, mixing, and recurrence properties of theorbits. This book comprises two independent texts that provide a self-contained introduct ion to two different approaches to the investigation of hyperbolic dynamics. The first text, by S. Le Borgne, explains the method of martingalesfor the central limit theorem. This approach can be used in several situations, even for weakly hyperbolic flow s, and the author presents a good number of examples and applications to equirepartition and mixing. The second text, by F.Faure and M. Tsujii, concerns the semiclassical approach, by operator theory: chaotic dynamics is described through the spectrum of the associated transfer operator, with applications to the asymptotic counting of periodic orbits. Thebook will be of interest for a broad audience, from PhD and Post-Doc students to experts working on geometry and dynamics |
ISBN: | 9783319048079 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer INdAM Series, 2281-518X : v9 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Operator theory , Global differential geometry , Distribution (Probability theory) |
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Title: | Superconcentration and Related Topics [electronic resource] |
Author(s): |
Sourav Chatterjee |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | A certain curious feature of random objects, introduced by the author as super concentration, and two related topics, chaos and multiple valleys, are highlighted in this book. Although super concentration hasestablished itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiplevalleys. He achieves a substantial degree of simplification and clarit y in the presentation of these findings by using the spectral approach. Understanding the fluctuations of random objects is one of the major goals of probabilitytheory and a whole subfield of probability and analysis, called concentration of measure, is d evoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations ofvery complicated random variables. Usually,concentration of measure is useful when more direct problem-specific ap proaches fail as a result, it has massively gained acceptance over the last forty years. And yet, there is a largeclass of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substant ial contribution of this book, which developed from a set of six lectures the author firstheld at the Cornell Probability Summer School in July 2012. The book is interspersed with a sizable number of open problems for professional mathematicians as well a s exercises for graduate students working in the fields of probabilitytheory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability |
Contents: | Preface |
1.Introduction | |
2.Markov semigroups | |
3.Super concentration and chaos | |
4.Multiple valleys | |
5.Talagrands method for proving super concentration | |
6.The spectral method for proving super concentration | |
7.Independent flips | |
8.Extremal fields | |
9.Further applications of hypercontractivity | |
10.The interpolation method for proving chaos | |
11.Variance lower bounds | |
12.Dimensions of level sets | |
Appendix A. Gaussian random variables | |
Appendix B. Hypercontractivity | |
Bibliography | |
Indices | |
ISBN: | 9783319038865 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Title: | A Course on Integration Theory [electronic resource] : including more than 150 exercises with detailed answers |
Author(s): |
Nicolas Lerner |
Date: | 2014 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathodory Theorem. It also includes some elementary properties ofHausdorff measures as we ll as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change-of-variables formulas as well as the constructionand study of classical Cantor sets are treate d in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym theorem, notions ofharmonic analysis, classical inequalities and interpolation theore ms including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercisesand detailed solutions. A comprehensive appendix provides the reader with various eleme nts of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advancedmaterial such as some basic properties of cardinals and ordinals which are useful for the study of measurabi lity |
Contents: | 1 Introduction |
2 General theory of integration | |
3 Construction of the Lebesgue measure on R^d | |
4 Spaces of integrable functions | |
5 Integration on a product space | |
6 Diffeomorphisms of open subsets of R^d and integration | |
7 Convolution | |
8 Complex measures | |
9 Harmonic analysis | |
10 Classical inequalities | |
ISBN: | 9783034806947 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics |
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Call number: | SPRINGER-2014-9781461496380:ONLINE Show nearby items on shelf |
Title: | Real Analysis for the Undergraduate [electronic resource] : With an Invitation to Functional Analysis |
Author(s): |
Matthew A Pons |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis.While these advanced t opics are not typically encountered until graduate study, the text is designed for the beginner. The authors engaging style makes advanced topics approachable without sacrificing rigor. The text alsoconsistently encourages the reader to pick up a pencil a nd take an active part in the learning process. Key features include: - examples to reinforce theory - thorough explanations preceding definitions, theorems and formal proofs -illustrations to support intuition - over 450 exercises designed to develop con nections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delvedeeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate cu rriculum |
Contents: | The Real Numbers |
Sequences in R | |
Numerical Series | |
Continuity | |
The Derivative | |
Sequence and Series of Functions | |
The Riemann Integral | |
Lebesgue Measure on R | |
Lebesgue Integration | |
ISBN: | 9781461496380 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Functional analysis |
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Call number: | SPRINGER-2014-9781461495871:ONLINE Show nearby items on shelf |
Title: | Introduction to Stochastic Integration [electronic resource] |
Author(s): |
K.L Chung R.J Williams |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduatecourse in stochastic ca lculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales then Its change of variable formula is developedfor continuous martingales. Applications include a c haracterization of Brownian motion, Hermite polynomials of martingales, the FeynmanKac functional and theSchrdinger equation. For Brownian motion, the topics of local time,reflected Brownian motion, and time change are discussed. New to the second editio n are a discussion of the CameronMartinGirsanov transformation and a final chapter which provides an introduction to stochastic differentialequations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematician s, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also provesthat stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has be come one of the most powerful tools in modern probability theory. Journal of the AmericanStatistical Association An attractive textwritten in [a] lean and precise styleeminently readable. Especially pleasant are the care and attention devoted to details A very fine book. Mathematical Reviews |
Contents: | 1 Preliminaries |
2 Definition of the Stochastic Integral | |
3 Extension of the Predictable Integrands | |
4 Quadratic Variation Process | |
5 The Ito Formula | |
6 Applications of the Ito Formula | |
7 Local Time and Tanaka's Formula | |
8 Reflected Brownian Motions | |
9 Generalization Ito Formula, Change of Time and Measure | |
10 Stochastic Differential Equations | |
References | |
Index | |
ISBN: | 9781461495871 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Modern Birkhuser Classics, 2197-1803 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9781447153610:ONLINE Show nearby items on shelf |
Title: | Probability Theory [electronic resource] : A Comprehensive Course |
Author(s): |
Achim Klenke |
Date: | 2014 |
Edition: | 2nd ed. 2014 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineeringand computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To addressthese concepts, the title covers a wide variet y of topics, many of which are not usually found in introductory textbooks, such as: limit theorems for sums of random variables martingales percolation Markov chains andelectrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integral and stochasticdifferential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts inprobability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulat ions and some difficult proofs have been made more accessible. A wealth ofexamples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathe matics and statistics in physics, computer science,economics and biology |
Contents: | Basic Measure Theory |
Independence | |
Generating Functions | |
The Integral | |
Moments and Laws of Large Numbers | |
Convergence Theorems | |
Lp | |
Spaces and the RadonNikodym Theorem | |
Conditional Expectations | |
Martingales | |
Optional Sampling Theorems | |
Martingale Convergence Theorems and Their Applications | |
Backwards Martingales and Exchangeability | |
Convergence of Measures | |
Probability Measures on Product Spaces | |
Characteristic Functions and the Central Limit Theorem | |
Infinitely Divisible Distributions | |
Markov Chains | |
Convergence of Markov Chains | |
Markov Chains and Electr | |
ISBN: | 9781447153610 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Differentiable dynamical systems , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9780817684099:ONLINE Show nearby items on shelf |
Title: | A Probability Path [electronic resource] |
Author(s): |
Sidney I Resnick |
Date: | 2014 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate studentsfrom a variety of disci plines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research instatistics, applied probability, biology, operations research, mathematical finance, and engineering. Aone-semester course is laid out in an efficient and readable manner covering the core material. The first three chaptersprovide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applicationsto statistics (quantile and distribution function estimation), and applied probability. Two subsequent cha pters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treatsconditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance. Like Adventures in Stochastic Processes, Resnicks related and very successful textbook, A Probability Path isrich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study. The present uncorrected, softcover reprintis designed to make this classic textbookavailable to a wider audience. This book is different from the classical textbooks on probability theory in that it treats the measure theoreticbackground not as a prerequisite but as an integral part of probability theory. Th e result is that the reader gets a thorough and well-structured framewo |
ISBN: | 9780817684099 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Modern Birkhuser Classics, 2197-1803 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) , Mathematical statistics |
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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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Title: | Regularity of Optimal Transport Maps and Applications [electronic resource] |
Author(s): |
Guido Philippis |
Date: | 2013 |
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: | In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Breniertheorem on existence of opt imal transport maps and of Caffarellis Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5we show how the above mentioned results allows to p rove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is wellknown that in this case global regularity can not be expected). More pre cisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero |
Note: | Springer eBooks |
ISBN: | 9788876424588 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Publications of the Scuola Normale Superiore : v17 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematical optimization |
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Title: | Spectral Theory and Quantum Mechanics [electronic resource] : With an Introduction to the Algebraic Formulation |
Author(s): |
Valter Moretti |
Date: | 2013 |
Publisher: | Milano : Springer Milan : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given tospectral theory features t hat are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in oneplace a number of useful rigorous statements on t he mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out toMaster's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. Thebook should benefit established researchers to organise and present the profusion of advanced ma terial disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly |
Note: | Springer eBooks |
Contents: | Introduction and mathematical backgrounds |
Normed and Banach spaces, examples and applications | |
Hilbert spaces and bounded operators | |
Families of compact operators on Hilbert spaces and fundamental properties | |
Densely | |
defined unbounded operators on Hilbert spaces | |
Phenomenology of quantum systems and Wave Mechanics: an overview | |
The first 4 axioms of QM: propositions, quantum states and observables | |
Spectral Theory I: generalities, abstract C | |
algebras and operators in B(H) | |
Spectral theory II: unbounded operators on Hilbert spaces | |
Spectral Theory III: applications | |
Mathem | |
ISBN: | 9788847028357 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | UNITEXT, 2038-5714 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Mathematical physics |
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Title: | Condition [electronic resource] : The Geometry of Numerical Algorithms |
Author(s): |
Peter Brgisser Felipe Cucker |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability andcomplexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis onthe probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching inits third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between thecurrent elementary expositions of the subject based on the simplex method and those focusing on convex programming |
Note: | Springer eBooks |
Contents: | Preface |
Overture: On the Condition of Numerical Problems and the Numbers that Measure It | |
I Condition in Linear Algebra (Adagio): 1 Normwise Condition of Linear Equation Solving | |
2 Probabilistic Analysis | |
3 Error Analysis of Triangular Linear Systems | |
4 Probabilistic Analysis of Rectangular Matrices | |
5 Condition Numbers and Iterative Algorithms | |
Intermezzo I: Condition of Structured Data | |
II Condition in Linear Optimization (Andante): 6 A Condition Number for Polyhedral Conic Systems | |
7 The Ellipsoid Method | |
8 Linear Programs and their Solution Sets | |
9 Interior | |
point Met | |
ISBN: | 9783642388965 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v349 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Computer science , Computer science Mathematics , Algorithms , Mathematical optimization , Distribution (Probability theory) |
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Title: | Random Matrices and Iterated Random Functions [electronic resource] : Mnster, October 2011 |
Author(s): |
Gerold Alsmeyer Matthias Lwe |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Random Matrices are one of the major research areas in modern probability theory, due to their prominence in many different fields such as nuclear physics, statistics, telecommunication, free probability, non-commutative geometry,and dynamical system s. A great deal of recent work has focused on the study of spectra of large random matrices on the one hand and on iterated random functions, especially random difference equations, on the other. However, themethods applied in these two research areas are fairly dissimilar. Motivated by the idea that tools from one area could potentially also be helpful in the other, the volume editors have selected contributions that present results andmethods from random matrix theory as well as from the theory of itera ted random functions. This work resulted from a workshop that was held in Mnster, Germany in 2011. The aim of the workshop was to bring together researchers fromtwo fields of probability theory: random matrix theory and the theory of iterated random funct ions. Random matrices play fundamental, yet very different roles in the two fields. Accordingly, leading figures and young researchers gavetalks on their field of interest that were also accessible to a broad audience |
Note: | Springer eBooks |
Contents: | E. Le Page: Tails of a stationary probability measure for an affine stochastic recursion on the line |
Yv. Guivarch: On homogeneity at infinity of stationary measures for affine stochastic recursions | |
M. Stolz: Limit theorems for random elements of the compact classical groups | |
T. Kriecherbauer: Universality of local eigenvalue statistics | |
R. Speicher: Asymptotic eigenvalue distribution of random matrices and free stochastic analysis | |
M. Peign: Conditioned random walk in Weyl chambers and renewal theory in a cone | |
D. Buraczewski: The linear stochastic equation R =_d \sum_{ i=1} | |
ISBN: | 9783642388064 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v53 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642376177:ONLINE Show nearby items on shelf |
Title: | On the Estimation of Multiple Random Integrals and U-Statistics [electronic resource] |
Author(s): |
Pter Major |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version issimpler. But in order to a pply such a method we have to show that the linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work istheir investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of suchquantities. The proofs apply a number of useful techniques of modern p robability that enable us to investigate the non-linear functionals of independent random variables. This lecture note yields insights into these methods, and mayalso be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Motivation of the investigation. Discussion of some problems | |
3 Some estimates about sums of independent random variables | |
4 On the supremum of a nice class of partial sums | |
5 Vapnik ervonenkis classes and L2 | |
dense classes of functions | |
6 The proof of Theorems 4.1 and 4.2 on the supremum of random sums | |
7 The completion of the proof of Theorem 4.1 | |
8 Formulation of the main results of this work | |
9 Some results about U | |
statistics | |
10 MultipleWienerIt integrals and their properties | |
11 The diagram formula for products of degenerate U | |
statistics | |
ISBN: | 9783642376177 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2079 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783642333026:ONLINE Show nearby items on shelf |
Title: | Guts of Surfaces and the Colored Jones Polynomial [electronic resource] |
Author(s): |
David Futer Efstratia Kalfagianni Jessica Purcell |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that thegrowth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for theknot in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternatingknots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of thecomplement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Decomposition into 3balls | |
3 Ideal Polyhedra | |
4 Ibundles and essential product disks | |
5 Guts and fibers | |
6 Recognizing essential product disks | |
7 Diagrams without non | |
prime arcs | |
8 Montesinos links | |
9 Applications | |
10 Discussion and questions | |
ISBN: | 9783642333026 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2069 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Cell aggregation Mathematics |
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Call number: | SPRINGER-2013-9783642326660:ONLINE Show nearby items on shelf |
Title: | Multi-Layer Potentials and Boundary Problems [electronic resource] : for Higher-Order Elliptic Systems in Lipschitz Domains |
Author(s): |
Irina Mitrea Marius Mitrea |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is ofsecond order a variety of t ools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When thedifferential operator is of higher-order (as is the case, e .g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Caldern, one ofthe founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatmentbased on this approach. This research monograph lays, for the first time, the mathematical foundation ai med at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential methodand addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including l ayer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions,boundary value problems with data in WhitneyLebesque spaces, WhitneyBesov spaces, WhitneySobolev- based Lebesgue spaces, WhitneyTriebelLizorkin spaces, WhitneySobolev-based Hardy spaces, WhitneyBMO and WhitneyVMOspaces |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Smoothness scales and Calden | |
Zygmund theory in the scalar | |
valued case | |
3 Function spaces of Whitney arrays | |
4 The double multi | |
layer potential operator | |
5 The single multi | |
layer potential operator | |
6 Functional analytic properties of multi | |
layer potentials and boundary value problems | |
ISBN: | 9783642326660 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2063 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Integral equations , Differential equations, partial , Potential theory (Mathematics) |
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Call number: | SPRINGER-2013-9783642313929:ONLINE Show nearby items on shelf |
Title: | Financial Modeling, Actuarial Valuation and Solvency in Insurance [electronic resource] |
Author(s): |
Mario V Wthrich Michael Merz |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Risk management for financial institutions is one of the key topics the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling. Currently, there are many new developments inthis area in the fina ncial and insurance industry (Basel III and Solvency II), but none of these developments provides a fully consistent and comprehensive framework for the analysis of solvency questions. Merz and Wthrich combineideas from financial mathematics (no-arbitrage theory, equivalent martingale measure), actuarial sciences (insurance claims modeling, cash flow valuation) and economic theory (risk aversion, probability distortion) to provide a fullyconsistent framework. Within this framework they then study solvency questions in incomplete markets, analyze hedging risks, and study asset-and-liability management questions, as well as issues like the limited liability options,dividend to shareholder questions, the role of re-insurance, etc. This work embeds the solven cy discussion (and long-term liabilities) into a scientific framework and is intended for researchers as well as practitioners in thefinancial and actuarial industry, especially those in charge of internal risk management systems. Readers should have a go od background in probability theoryand statistics, and should be familiar with popular distributions,stochastic processes, martingales, etc |
Note: | Springer eBooks |
Contents: | 1.Introduction |
Part I: Financial Valuation Principles | |
2.State price deflators and stochastic discounting | |
3.spot rate models | |
4.Stochastic forward rate and yield curve modeling | |
5.Pricing of financial assets | |
Part II: Actuarial Valuation and Solvency | |
6.Actuarial and financial modeling | |
7.Valuation portfolio | |
8.Protected valuation portfolio | |
9.Solvency | |
10.Selected topics and examples | |
Part III: Appendix | |
11.Auxiliary considerations | |
References | |
Index | |
ISBN: | 9783642313929 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Finance, 1616-0533 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Finance , Economics Statistics |
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Call number: | SPRINGER-2013-9783642307096:ONLINE Show nearby items on shelf |
Title: | Variational, Topological, and Partial Order Methods with Their Applications [electronic resource] |
Author(s): |
Zhitao Zhang |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry,measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been usedextensively to solve existence of solutions for ellipt ic equations, wave equations, Schrdinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This bookis useful for researchers and graduate students in the field of nonlinear fu nctional analysis. Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, andmixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the auth or uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with aclass of MongeAmpre equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications i s studied. Chapter 7 is devoted to the DancerFucik spectrum. In Chapter 8, some results on sign-changingsolutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, thefocus is on free boundary problems, Schrdinger systems from BoseEinstein condensate and competing systems with many species |
Note: | Springer eBooks |
Contents: | 1 Preliminaries |
Sobolev spaces and embedding theorems | |
Critical point | |
Cone and partial order | |
Brouwer Degree | |
Compact map and Leray | |
Schauder Degree | |
Fredholm operators | |
Fixed point index | |
Banach's Contract Theorem, Implicit Functions Theorem | |
Krein | |
Rutman theorem | |
Bifurcation theory | |
Rearrangements of sets and functions | |
Genus and Category | |
Maximum principles and symmetry of solution | |
Comparison theorems | |
2 Cone and Partial Order Methods | |
Increasing operators | |
Decreasing operators | |
Mixed monotone operators | |
Applications of mixed monotone operators | |
Fur | |
ISBN: | 9783642307096 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, 1389-2177 : v29 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis |
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Call number: | SPRINGER-2013-9783319023038:ONLINE Show nearby items on shelf |
Title: | GerberShiu Risk Theory [electronic resource] |
Author(s): |
Andreas E Kyprianou |
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: | Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical CramrLundberg model and the surplus of an insurance company. Thebook studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are alsoconsidered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chaptercorresponds to approximately two hours of lectures |
Note: | Springer eBooks |
Contents: | Introduction |
The Wald martingale and the maximum | |
The Kella | |
Whitt martingale and the minimum | |
Scale functions and ruin probabilities | |
The GerberShiu measure | |
Reflection strategies | |
Perturbation | |
at | |
maximum strategies | |
Refraction strategies | |
Concluding discussion | |
References | |
ISBN: | 9783319023038 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | EAA Series, 1869-6929 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Distribution (Probability theory) |
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Call number: | SPRINGER-2013-9783319015774:ONLINE Show nearby items on shelf |
Title: | The Real Numbers [electronic resource] An Introduction to Set Theory and Analysis |
Author(s): |
John Stillwell |
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: | While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbersto model the line, an d to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theoryuncountability, the axiom of choice, and large cardinals. In fact, virtually all theconcepts of infinite set theory are needed fo r a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines adown-to-earth introduction to set theory with an exposition of the essen ce of analysisthe study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate studentsand professional mathematicians who, until now, have been content to assume the real numbers. I ts prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of realnumber and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich pr esentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will helpmotivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncoun table sets, countable ordinals, the continuum problem, the CantorSchrderBernsteintheorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions |
Note: | Springer eBooks |
Contents: | The Fundamental Questions |
From Discrete to Continuous | |
Infinite Sets | |
Functions and Limits | |
Open Sets and Continuity | |
Ordinals | |
The Axiom of Choice | |
Borel Sets | |
Measure Theory | |
Reflections | |
Bibliography | |
Index | |
ISBN: | 9783319015774 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Logic, Symbolic and mathematical |
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