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Salvatore Capozziello, Valerio Faraoni, SpringerLink (Online service)
出版情報: SpringerLink Books - AutoHoldings , Springer Netherlands, 2011
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Extended gravity: a primer / l1:
Why extending gravity? / 1.1:
Cosmological and astrophysical motivation / 1.2:
Mathematical motivation / 1.3:
Quantum gravity motivation / 1.4:
Emergent gravity and thermodynamics of spacetime / 1.4.1:
What a good theory of gravity should do: General Relativity and its extensions / 1.5:
Quantum field theory in curved space / 1.6:
Mach's principle and other fundamental issues / 1.7:
Higher order corrections to Einstein's theory / 1.7.1:
Minimal and non-minimal coupling and the Equivalence Principle / 1.7.2:
Mach's principle and the variation of G / 1.7.3:
Extended gravity from higher dimensions and area metric approach / 1.8:
Conclusions / 1.9:
Mathematical tools / 2:
Conformal transformations / 2.1:
Variational principles in General Relativity / 2.2:
Geodesies / 2.2.1:
Field equations / 2.2.2:
Adding torsion / 2.3:
Noether symmetries / 2.4:
The landscape beyond Einstein gravity / 2.5:
The variational principle and the field equations of Brans-Dicke gravity / 3.1:
The variational principle and the field equations of metric f(R) gravity / 3.2:
Metric f(R) gravity in general / 3.2.1:
A more general class of ETGs / 3.3:
The Palatini formalism / 3.4:
The Palatini approach and the conformal structure of the theory / 3.4.1:
Problems with the Palatini formalism / 3.4.2:
Equivalence between f(R) and scalar-tensor gravity / 3.5:
Equivalence between scalar-tensor and metric f(R) gravity / 3.5.1:
Equivalence between scalar-tensor and Palatini f(R) gravity / 3.5.2:
Conformal transformations applied to extended gravity / 3.6:
Brans-Dicke gravity / 3.6.1:
Scalar-tensor theories / 3.6.2:
Mixed f(R)/scalar-tensor gravity / 3.6.3:
The issue of the conformal frame / 3.6.4:
The initial value problem / 3.7:
The Cauchy problem of scalar-tensor gravity / 3.7.1:
The initial value problem of f(R) gravity in the ADM formulation / 3.7.2:
The Gaussian normal coordinates approach / 3.7.3:
Spherical symmetry / 3.8:
Spherically symmetric solutions of GR and metric f(R) gravity / 4.1:
The Ricci scalar in spherical symmetry / 4.1.1:
Spherical symmetry in metric f(R) gravity / 4.1.3:
Solutions with constant Ricci scalar / 4.1.4:
Solutions with R = R(r) / 4.1.5:
Perturbations / 4.1.6:
Spherical symmetry in f(R) gravity and the Noether approach / 4.1.7:
Noether solutions of spherically symmetric f(R) gravity / 4.1.8:
Non-asymptotically flat and non-static spherical solutions of metric f(R) gravity / 4.1.9:
Spherical symmetry in scalar-tensor gravity / 4.2:
Static solutions of Brans-Dicke theory / 4.2.1:
Dynamical and asymptotically FLRW solutions / 4.2.2:
Collapse to black holes in scalar-tensor theory / 4.2.3:
The Jebsen-Birkhoff theorem / 4.3:
The Jebsen-Birkhoff theorem of GR / 4.3.1:
The non-vacuum case / 4.3.2:
The vacuum case / 4.3.3:
The Jebsen-Birkhoff theorem in scalar-tensor gravity / 4.3.4:
The trivial case ? = constant / 4.3.5:
Static non-constant Brans-Dicke-like field / 4.3.6:
The Jebsen-Birkhoff theorem in Einstein frame scalar-tensor gravity / 4.3.7:
Hawking's theorem and Jebsen-Birkhoff in Brans-Dicke gravity / 4.3.8:
The Jebsen-Birkhoff theorem in f(R) gravity / 4.3.9:
Black hole thermodynamics in extended gravity / 4.4:
Scalar-tensor gravity / 4.4.1:
Metric modified gravity / 4.4.2:
Palatini modified gravity / 4.4.3:
Dilaton gravity / 4.4.4:
From spherical to axial symmetry: an application to f(R) gravity / 4.5:
Weak-field limit / 4.6:
The weak-field limit of extended gravity / 5.1:
The Newtonian and post-Newtonian approximations: general remarks / 5.2:
The Newtonian and post-Newtonian limits of metric f(R) gravity with spherical symmetry / 5.2.1:
Comparison with the standard formalism and the chameleon effect / 5.2.2:
The Post-Minkowskian approximation / 5.3:
The energy-momentum pseudotensor in f(R) gravity and gravitational radiation / 5.3.1:
Gravitational waves / 5.4:
Gravitational waves in scalar-tensor gravity / 5.4.1:
Gravitational waves in higher order gravity / 5.4.2:
Qualitative analysis and exact solutions in cosmology / 5.5:
The Ehlers-Geren-Sachs theorem / 6.1:
The phase space of FLRW cosmology in scalar-tensor and f(R) gravity / 6.2:
The dynamical system / 6.2.1:
Analytical solutions of Brans-Dicke and scalar-tensor cosmology / 6.3:
Analytical solutions of Brans-Dicke cosmology / 6.3.1:
Exact scalar-tensor cosmologies / 6.3.2:
Analytical solutions of metric f(R) cosmology by the Noether approach / 6.4:
Point-like f(R) cosmology / 6.4.1:
Noether symmetries in metric f(R) cosmology / 6.4.2:
Exact cosmologies / 6.4.3:
Higher order point-like Lagrangians for cosmology / 6.4.4:
The Noether symmetry approach for higher order gravities / 6.5.2:
Cosmology / 6.6:
Big Bang, inflationary, and late-time cosmology in GR / 7.1:
The standard Big Bang model / 7.1.1:
Inflation in the early universe / 7.1.2:
The present-day acceleration / 7.1.3:
Using cosmography to map the structure of the universe / 7.2:
The cosmographic apparatus / 7.2.1:
Large scale structure and galaxy clusters / 7.3:
The weak-field limit of f(R) gravity and galaxy clusters / 7.3.1:
Extended systems / 7.3.2:
The cluster mass profiles / 7.3.3:
The galaxy clusters sample / 7.3.4:
The gas density model / 7.3.5:
Temperature profiles / 7.3.6:
The galaxy distribution model / 7.3.7:
Uncertainties in the mass profiles / 7.3.8:
Fitting the mass profiles / 7.3.9:
Results / 7.3.10:
Outlooks / 7.3.11:
Testing cosmological models with observations / 7.4:
Toward a new cosmological standard model / 7.4.1:
Methods to constrain models / 7.4.2:
Data samples for constraining models: large scale structure / 7.4.3:
Testing cosmological models: an example / 7.4.4:
From the early to the present universe / 7.5:
Quantum cosmology / 8.1:
Noether symmetries in quantum cosmology / 8.1.1:
Scalar-tensor quantum cosmology / 8.1.2:
The quantum cosmology of fourth order gravity / 8.1.3:
Quantum cosmology with gravity of order higher than fourth / 8.1.4:
Inflation in ETGs / 8.2:
Scalar-tensor gravity: extended and hyperextended inflation / 8.2.1:
Inflation with quadratic corrections / 8.2.2:
Cosmological perturbations / 8.3:
Scalar perturbations / 8.3.1:
Gravitational wave perturbations / 8.3.2:
Constraints on ETGs from primordial nucleosynthesis / 8.4:
The present universe: f(R) gravity as an alternative to dark energy / 8.5:
Background universe / 8.5.1:
Physical constants and astrophysical and cosmological parameters / 8.5.2:
Physical constants / A.1:
Conversion factors / A.2:
Astrophysical and cosmological.quantities / A.3:
Planck scale quantities / A.4:
The Noether symmetry approach to f(R) gravity / B:
The field equations and the Noether vector for spherically symmetric f(R) gravity / B.1:
The weak-field limit of metric f(R) gravity / B.2:
References
Index
Extended gravity: a primer / l1:
Why extending gravity? / 1.1:
Cosmological and astrophysical motivation / 1.2:
2.

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Krzysztof Bogdan, Tomasz Byczkowski, Piotr Graczyk, Tadeusz Kulczycki, Michal Ryznar, Renming Song, Andrzej Stos, Zoran Vondracek, SpringerLink (Online service)
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2009
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Introduction / 1:
Bases of Potential Theory of Stable Processes / 1.1:
Classical Potential Theory / 1.1.1:
Potential Theory of the Riesz Kernel / 1.1.2:
Green Function and Poisson Kernel of &Deltaα/2 / 1.1.3:
Subordinate Brownian Motions / 1.1.4:
Outline of the Book / 1.2:
Boundary Potential Theory for Schrödinger Operators Based on Fractional Laplacian / K. Bogdan ; T. Byczkowski2:
Boundary Harnack Principle / 2.1:
Approximate Factorization of Green Function / 2.3:
Schrodinger Operator and Conditional Gauge Theorem / 2.4:
Nontangential Convergence for α-harmonic Functions / M. Ryznar3:
Basic Definitions and Properties / 3.1:
Relative Fatou Theorem for α-Harmonic Functions / 3.3:
Extensions to Other Processes / 3.4:
Eigenvalues and Eigenfunctions for Stable Processes / T. Kulczycki4:
Intrinsic Ultracontractivity (IU) / 4.1:
Steklov Problem / 4.3:
Eigenvalue Estimates / 4.4:
Generalized Isoperimetric Inequalities / 4.5:
Potential Theory of Subordinate Brownian Motion / R. Song ; Z. Vondraček5:
Subordinators / 5.1:
Special Subordinators and Complete Bernstein Functions / 5.2.1:
Examples of Subordinators / 5.2.2:
Asymptotic Behavior of the Potential, Lévy and Transition Densities / 5.2.3:
Subordinate Brownian Motion / 5.3:
Definitions and Technical Lemma / 5.3.1:
Asymptotic Behavior of the Green Function / 5.3.2:
Asymptotic Behavior of the Jumping Function / 5.3.3:
Transition Densities of Symmetric Geometric Stable Processes / 5.3.4:
Harnack Inequality for Subordinate Brownian Motion / 5.4:
Capacity and Exit Time Estimates for Some Symmetric Lévy Processes / 5.4.1:
Krylov-Safonov-type Estimate / 5.4.2:
Proof of Harnack Inequality / 5.4.3:
Subordinate Killed Brownian Motion / 5.5:
Definitions / 5.5.1:
Representation of Excessive and Harmonic Functions of Subordinate Process / 5.5.2:
Harnack Inequality for Subordinate Process / 5.5.3:
Martin Boundary of Subordinate Process / 5.5.4:
Boundary Harnack Principle for Subordinate Process / 5.5.5:
Sharp Bounds for the Green Function and the Jumping Function of Subordinate Process / 5.5.6:
Bibliography
Index
Introduction / 1:
Bases of Potential Theory of Stable Processes / 1.1:
Classical Potential Theory / 1.1.1:
3.

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Gitta Kutyniok, J.-M Morel, F. Takens, SpringerLink (Online service)
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2007
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Introduction / 1:
Irregular Wavelet and Gabor Frames / 1.1:
Density for Gabor Systems / 1.2:
Geometry of Time-Scale Indices / 1.3:
Overview of Main Results / 1.4:
Wavelet and Gabor Frames / 2:
Frame Theory / 2.1:
Wavelet Analysis / 2.2:
Time-Frequency Analysis / 2.3:
Amalgam Spaces / 2.4:
Weighted Affine Density / 3:
Definitions / 3.1:
Basic Properties / 3.2:
The Notion of Affine Density by Sun and Zhou / 3.3:
Comparison of Both Notions of Affine Density / 3.4:
Qualitative Density Conditions / 4:
Existence of an Upper Frame Bound / 4.1:
Existence of a Lower Frame Bound / 4.2:
Examples of Wavelet Systems / 4.3:
Density of Sequences in R+ / 4.4:
Affine Density and the Local Integrability Condition / 4.5:
Amalgam Spaces on R \ {0} / 4.5.1:
A Density Version of the Local Integrability Condition / 4.5.2:
A Characterization of Wavelet Parseval Frames / 4.5.3:
Quantitative Density Conditions / 5:
Outline and Comparison with Previous Work / 5.1:
Density of Product Sequences / 5.2:
A Fundamental Relationship / 5.3:
The Nyquist Phenomenon / 5.4:
Sufficient Density Conditions for Wavelet Frames / 5.5:
Existence of Special Weight Functions / 5.6:
Co-Affine Systems / 5.7:
Homogeneous Approximation Property / 6:
Amalgam Spaces and the Continuous Wavelet Transform / 6.1:
The Basic Class B[subscript 0] / 6.2:
The Homogeneous Approximation Property for Wavelet Frames / 6.3:
The Comparison Theorem for Wavelet Frames / 6.4:
Density Results for Wavelet Schauder Bases / 6.5:
Weighted Beurling Density and Shift-Invariant Gabor Systems / 7:
Motivation and Outline of Chapter / 7.1:
Weighted Beurling Density / 7.2:
Littlewood-Paley Type Inequalities / 7.3:
Equivalent Definition of Weighted Beurling Density / 7.4:
Beurling Density, Frame Bounds, and Gabor Generators / 7.5:
Shift-Invariant Gabor Systems / 7.6:
References
Index
Introduction / 1:
Irregular Wavelet and Gabor Frames / 1.1:
Density for Gabor Systems / 1.2:
4.

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edited by Kohei Arai, Supriya Kapoor, Rahul Bhatia
出版情報:   1 online resource (xii, 1015 p.)
シリーズ名: Advances in Intelligent Systems and Computing ; 1289
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herausgegeben von J. Loeckx
出版情報:   619 p.
シリーズ名: Lecture Notes in Computer Science ; 14
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edited by Alain Poli
出版情報:   VIII, 268 p.
シリーズ名: Lecture Notes in Computer Science ; 228
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edited by Marc Gyssens, Jan Paredaens, Dirk Van Gucht
出版情報:   VIII, 412 p.
シリーズ名: Lecture Notes in Computer Science ; 326
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Contents: Invited Lectures.
Logic and Deductive Databases.
Complexity and Optimization.
Object Oriented Databases.
Data Models and Query Languages.
Dynamic Aspects of Databases.
Miscellaneous Topics.
Contents: Invited Lectures.
Logic and Deductive Databases.
Complexity and Optimization.
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edited by Banh Tien Long, Yun-Hae Kim, Kozo Ishizaki, Nguyen Duc Toan, Ivan A. Parinov, Ngoc Pi Vu
出版情報:   1 online resource (xxx, 1065 p.)
シリーズ名: Lecture Notes in Mechanical Engineering ;
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edited by Sebastian Oberst, Benjamin Halkon, Jinchen Ji, Terry Brown
出版情報:   1 online resource (xxvi, 428 p.)
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Hans G. Feichtinger, Bernard Helffer, Michael P. Lamoureux, Nicolas Lerner, Luigi Rodino, F. Takens, Joachim Toft, M. W. Wong, Man Wah Wong, SpringerLink (Online service), Michael Lamoureux
出版情報: SpringerLink Books - AutoHoldings , Springer Berlin Heidelberg, 2008
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Banach Gelfand Triples for Gabor Analysis / H. Feichtinger ; F. Luef ; E. Cordero
Introduction / 1:
Preliminaries / 2:
Gabor Analysis on L[superscript 2] / 3:
Time-Frequency Representations / 4:
The Gelfand Triple (S[subscript 0], L[superscript 2], S[subscript 0]' (R[superscript d]) / 5:
The Spreading Function and Pseudo-Differential Operators / 6:
Gabor Multipliers / 7:
References
Four Lectures in Semiclassical Analysis for Non Self-Adjoint Problems with Applications to Hydrodynamic Instability / B. Helffer
General Introduction
Lecture 1: The Rayleigh-Taylor Model
The Rayleigh-Taylor Model: Physical Origin / 2.1:
Rayleigh-Taylor Mathematically / 2.2:
Elementary Spectral Theory / 2.3:
A Crash Course on h-Pseudodifferential Operators / 2.4:
Application for Rayleigh-Taylor: Semi-Classical Analysis for K(h) / 2.5:
Harmonic Approximation / 2.6:
Instability of Rayleigh-Taylor: An Elementary Approach via WKB Constructions / 2.7:
Lecture 2: Towards Non Self-Adjoint Models
Instability for Kelvin-Helmholtz I: Physical Origin / 3.1:
Around the [epsilon]-Pseudo-Spectrum / 3.2:
Around the h-Family-Pseudospectrum / 3.3:
The Davies Example by Hand / 3.4:
Kelvin-Helmholtz II: Mathematical Analysis / 3.5:
Other Toy Models / 3.6:
Lecture 3: On Semi-Classical Subellipticity
Non Subellipticity: Generic Result / 4.1:
Link with the Standard Non-Hypoellipticity Results for Operators of Principal Type / 4.3:
Elementary Proof for the Non-Subelliptic Model / 4.4:
1/2 Semi-Classical Subellipticity / 4.5:
Lecture 4: Other Non Self-Adjoint Models Coming from Hydrodynamics
Quasi-Isobaric Model (Kull and Anisimov) / 5.1:
Stationary Laminar Solution / 5.3:
From the Physical Parameters to the Relevant Mathematical Parameters / 5.4:
The Convection Velocity Model / 5.5:
The Model for the Ablation Regime / 5.6:
Semi-Classical Regimes for the Ablation Models / 5.7:
Subellipticity II: At the Boundary of [Sigma](a[subscript 0]) / 5.8:
An Introduction to Numerical Methods of Pseudodifferential Operators / M.P. Lamoureux ; G.F. Margrave
Signal Processing and Pseudodifferential Operators
Introduction to Seismic Imaging / 1.1:
Introduction to Pseudodifferential Operators / 1.2:
A Jump in Dimension / 1.3:
Boundedness of the Operators / 1.4:
Manipulating Pseudodifferential Operators
Composition of Operators
Asymptotic Series
Oscillatory Integrals
Other Pseudo-Topics
Numerical Implementations
Sampling and Quantization Error in Signal Processing
The Discrete Fourier Transform and Periodization Errors
Direct Numerical Implementation via the DFT
Operations Count
Numerical Implementation via Product-Convolution Operators
Almost Diagonalization via Wavelet and Gabor Bases
Short Time Fourier Transforms and Their Multipliers
Gabor Transforms and Gabor Multipliers
Gabor Transforms in Practice
Sampled Space
Sampling in the Frequency Domain
Partitions of Unity and Frequency Subsampling
Uniform POUs
Seismic Imaging
Wavefield Extrapolation / 6.1:
Some Facts About the Wick Calculus / N. Lerner
Elementary Fourier Analysis via Wave Packets
The Fourier Transform of Gaussian Functions
Wave Packets and the Poisson Summation Formula
Toeplitz Operators
On the Weyl Calculus of Pseudodifferential Operators
A Few Classical Facts
Symplectic Invariance
Composition Formulas
Definition and First Properties of the Wick Quantization
Definitions
The Garding Inequality with Gain of One Derivative
Variations
Energy Estimates via the Wick Quantization
Subelliptic Operators Satisfying Condition (P)
Polynomial Behaviour of Some Functions
Energy Identities
The Fefferman-Phong Inequality
The Semi-Classical Inequality
The Sjostrand Algebra
Sketching the Proof
A Final Comment
Appendix
Cotlar's Lemma
Schatten Properties for Pseudo-Differential Operators on Modulation Spaces / J. Toft
Schatten-Von Neumann Classes for Operators Acting on Hilbert Spaces
Schatten-Von Neumann Classes for Operators Acting on Modulation Spaces
Continuity and Schatten-Von Neumann Properties for Pseudo-Differential Operators
List of Participants
Banach Gelfand Triples for Gabor Analysis / H. Feichtinger ; F. Luef ; E. Cordero
Introduction / 1:
Preliminaries / 2:
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by Arnold Businger
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シリーズ名: Lecture Notes in Computer Science ; 198
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edited by Akhyar
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Lecture notes in artificial intelligence ;
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Contents: Fundamental Mechanisms for Artificial Intelligence Programming Languages - An Introduction.
Advanced Topics in Automated Deduction.
Qualitative Reasoning.
Knowledge Acquisition for Expert Systems.
Fundamental Mechanisms in Machine Learning and Inductive Inference: Part 2.
Topics in Planning.
Natural Language Systems.
Contents: Fundamental Mechanisms for Artificial Intelligence Programming Languages - An Introduction.
Advanced Topics in Automated Deduction.
Qualitative Reasoning.
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シリーズ名: Lecture Notes in Computer Science ; 70
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edited by Bob F. Caviness
出版情報:   XVIII, 662 p.
シリーズ名: Lecture Notes in Computer Science ; 204
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edited by Gerard Cohen, Jacques Wolfmann
出版情報:   IX, 331 p.
シリーズ名: Lecture Notes in Computer Science ; 388
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edited by H. Ehrig, M. Nagl, G. Rozenberg
シリーズ名: Lecture Notes in Computer Science ; 153
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edited by R. Glowinski, J.L. Lions
出版情報:   X, 434 p.
シリーズ名: Lecture Notes in Computer Science ; 11
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edited by Hartmut Ehrig, Robert A. Kowalski, Giorgio Levi, Ugo Montanari
出版情報:   XIV, 336 p.
シリーズ名: Lecture Notes in Computer Science ; 250
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edited by Jacobus W. de Bakker, A.J. Nijman, Philip C. Treleaven
出版情報:   XVI, 468 p.
シリーズ名: Lecture Notes in Computer Science ; 259
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Puja Dey, Jitendra Nath Roy
出版情報: [Cham] : SpringerLink, [20--]  1 online resource (xx, 273 p.)
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edited by Yi Wang, Kristian Martinsen, Tao Yu, Kesheng Wang
出版情報:   1 online resource (xx, 753 p.)
シリーズ名: Lecture Notes in Electrical Engineering ; 737
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edited by Roberto Conti, Antonio Ruberti
出版情報: Berlin : Springer Berlin Heidelberg, 1973  XVI, 396 p.
シリーズ名: Lecture Notes in Computer Science ; 4
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edited by Josep Diaz, Fernando Orejas
出版情報:   XII, 392 p.
シリーズ名: Lecture Notes in Computer Science ; 352
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Progamming Language Concepts, Language Implementation, Programming Paradigms, Software Development
Progamming Language Concepts, Language Implementation, Programming Paradigms, Software Development
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edited by Bernadette Bouchon, Lorenza Saitta, Ronald R. Yager
出版情報:   VIII, 409 p.
シリーズ名: Lecture Notes in Computer Science ; 313
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Mathematics
Fuzzy Sets and Possibility Theory
Information Theory
Intelligent Data Base
Knowledge Acquisition and Machine Learning
Knowledge Representation
Logics for Artificial Intelligence
Neural Nets
Reasoning Techniques Under Uncertainty
Late Arrivals
Invited Paper
Mathematics
Fuzzy Sets and Possibility Theory
Information Theory
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edited by G.R. Blakely, D. Chaum
出版情報:   XII, 496 p.
シリーズ名: Lecture Notes in Computer Science ; 196
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by Kathleen Jensen, Niklaus Wirth
出版情報:   VI, 169 p. 1 illus.
シリーズ名: Lecture Notes in Computer Science ; 18
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