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41. A comprehensive course in analysis [2015]
 Simon, Barry, 1946 author.
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — 5 volumes : illustrations (black and white) ; 26 cm + 1 booklet (iii, 68 pages : illustrations ; 25 cm)
 Summary

 * Contents for
 Part 1 (Real Analysis): Preliminaries* Topological spaces* A first look at Hilbert spaces and Fourier series* Measure theory* Convexity and Banach spaces* Tempered distributions and the Fourier transform* Bonus chapter: Probability basics* Bonus chapter: Hausdorff measure and dimension* Bonus chapter: Inductive limits and ordinary distributions* Bibliography* Symbol index* Subject index* Author index* Index of capsule biographies* Contents for Part 2A (Basic Complex Analysis): Preliminaries* The Cauchy integral theorem: Basics Consequences of the Cauchy integral formula* Chains and the ultimate Cauchy integral theorem* More consequences of the CIT* Spaces of analytic functions* Fractional linear transformations* Conformal maps* Zeros of analytic functions and product formulae* Elliptic functions* Selected additional topics* Bibliography* Symbol index* Subject index* Author index* Index of capsule biographies* Contents for Part 2B (Advanced Complex Analysis): Riemannian metrics and complex analysis* Some topics in analytic number theory* Ordinary differential equations in the complex domain* Asymptotic methods* Univalent functions and Loewner evolution* Nevanlinna theory* Bibliography* Symbol index* Subject index* Author index* Index of capsule biographies* Contents for
 Part 3 (Harmonic Analysis): Preliminaries* Pointwise convergence almost everywhere* Harmonic and subharmonic functions* Bonus chapter: Phase space analysis $H^p$ spaces and boundary values of analytic functions on the unit disk* Bonus chapter: More inequalities* Bibliography* Symbol index* Subject index* Author index* Index of capsule biographies* Contents for
 Part 4 (Operator Theory): Preliminaries* Operator basics* Compact operators, mainly on a Hilbert space* Orthogonal polynomials* The spectral theorem* Banach algebras* Bonus chapter: Unbounded selfadjoint operators* Bibliography* Symbol index* Subject index* Author index* Index of capsule biographies.
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QA300 .S536 2015 PT.1  Unknown 
QA300 .S536 2015 PT.2A  Unknown 
QA300 .S536 2015 PT.2B  Unknown 
QA300 .S536 2015 PT.2B  Unknown 
QA300 .S536 2015 PT.3  Unknown 
QA300 .S536 2015 PT.4  Unknown 
QA300 .S536 2015 SUPPL  Unknown 
42. A course in real analysis [2015]
 Junghenn, Hugo D. (Hugo Dietrich), 1939
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xxiii, 589 pages : illustrations ; 24 cm
 Summary

 Functions of One Variable The Real Number System From Natural Numbers to Real Numbers Algebraic Properties of R Order Structure of R Completeness Property of R Mathematical Induction Euclidean Space
 Numerical Sequences Limits of Sequences Monotone Sequences Subsequences. Cauchy Sequences Limit Inferior and Limit Superior
 Limits and Continuity on R Limit of a Function Limits Inferior and Superior Continuous Functions Some Properties of Continuous Functions Uniform Continuity
 Differentiation on R Definition of Derivative. Examples The Mean Value Theorem Convex Functions Inverse Functions L'Hospital's Rule Taylor's Theorem on R Newton's Method
 Riemann Integration on R The RiemannDarboux Integral Properties of the Integral Evaluation of the Integral Stirling's Formula Integral Mean Value Theorems Estimation of the Integral Improper Integrals A Deeper Look at Riemann Integrability Functions of Bounded Variation The RiemannStieltjes Integral
 Numerical Infinite Series Definition and Examples Series with Nonnegative Terms More Refined Convergence Tests Absolute and Conditional Convergence Double Sequences and Series
 Sequences and Series of Functions Convergence of Sequences of Functions Properties of the Limit Function Convergence of Series of Functions Power Series
 Functions of Several Variables Metric Spaces Definitions and Examples Open and Closed Sets Closure, Interior, and Boundary Limits and Continuity Compact Sets The ArzelaAscoli Theorem Connected Sets The StoneWeierstrass Theorem Baire's Theorem
 Differentiation on Rn Definition of the Derivative Properties of the Differential Further Properties of the Derivative The Inverse Function Theorem The Implicit Function Theorem Higher Order Partial Derivatives Higher Order Differentials. Taylor's Theorem on Rn Optimization
 Lebesgue Measure on Rn Some General Measure Theory Lebesgue Outer Measure Lebesgue Measure Borel Sets Measurable Functions
 Lebesgue Integration on Rn Riemann Integration on Rn The Lebesgue Integral Convergence Theorems Connections with Riemann Integration Iterated Integrals Change of Variables
 Curves and Surfaces in Rn Parameterized Curves Integration on Curves Parameterized Surfaces mDimensional Surfaces
 Integration on Surfaces Differential Forms Integrals on Parameterized Surfaces Partitions of Unity Integration on mSurfaces The Fundamental Theorems of Calculus Closed Forms in Rn
 Appendices A Set Theory B Summary of Linear Algebra C Solutions to Selected Problems
 Bibliography Index.
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QA300 .J86 2015  Unknown 
43. Foundations of analysis [2015]
 Krantz, Steven G. (Steven George), 1951 author.
 Boca Raton, FL : CRC Press, 2015.
 Description
 Book — x, 301 pages : ill. ; 24 cm
 Summary

 Number Systems The Real Numbers The Complex Numbers
 Sequences Convergence of Sequences Subsequences Limsup and Liminf Some Special Sequences
 Series of Numbers Convergence of Series Elementary Convergence Tests Advanced Convergence Tests Some Special Series Operations on Series
 Basic Topology Open and Closed Sets Further Properties of Open and Closed Sets Compact Sets The Cantor Set Connected and Disconnected Sets Perfect Sets
 Limits and Continuity of Functions Basic Properties of the Limit of a Function Continuous Functions Topological Properties and Continuity Classifying Discontinuities and Monotonicity
 Differentiation of Functions The Concept of Derivative The Mean Value Theorem and Applications More on the Theory of Differentiation
 The Integral Partitions and the Concept of Integral Properties of the Riemann Integral Sequences and Series of Functions Convergence of a Sequence of Functions More on Uniform Convergence Series of Functions The Weierstrass Approximation Theorem
 Elementary Transcendental Functions Power Series More on Power Series: Convergence Issues The Exponential and Trigonometric Functions Logarithms and Powers of Real Numbers
 Appendix I: Elementary Number Systems
 Appendix II: Logic and Set Theory Table of Notation Glossary Bibliography Index.
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QA300 .K6445 2015  Unknown 
 Agresti, Alan, author.
 Hoboken, New Jersey : Wiley, [2015]
 Description
 Book — xiii, 444 pages : illustrations ; 25 cm.
 Summary

 Preface xi
 1 Introduction to Linear and Generalized Linear Models
 1
 1.1 Components of a Generalized Linear Model
 2
 1.2 Quantitative/Qualitative Explanatory Variables and Interpreting Effects
 6
 1.3 Model Matrices and Model Vector Spaces
 10
 1.4 Identifiability and Estimability
 13
 1.5 Example: Using Software to Fit a GLM
 15
 Chapter Notes
 20
 Exercises
 21
 2 Linear Models: Least Squares Theory
 26
 2.1 Least Squares Model Fitting
 27
 2.2 Projections of Data Onto Model Spaces
 33
 2.3 Linear Model Examples: Projections and SS Decompositions
 41
 2.4 Summarizing Variability in a Linear Model
 49
 2.5 Residuals Leverage and Influence
 56
 2.6 Example: Summarizing the Fit of a Linear Model
 62
 2.7 Optimality of Least Squares and Generalized Least Squares
 67
 Chapter Notes
 71
 Exercises
 71
 3 Normal Linear Models: Statistical Inference
 80
 3.1 Distribution Theory for Normal Variates
 81
 3.2 Significance Tests for Normal Linear Models
 86
 3.3 Confidence Intervals and Prediction Intervals for Normal Linear Models
 95
 3.4 Example: Normal Linear Model Inference
 99
 3.5 Multiple Comparisons: Bonferroni Tukey and FDR Methods
 107
 Chapter Notes
 111
 Exercises
 112
 4 Generalized Linear Models: Model Fitting and Inference
 120
 4.1 Exponential Dispersion Family Distributions for a GLM
 120
 4.2 Likelihood and Asymptotic Distributions for GLMs
 123
 4.3 LikelihoodRatio/Wald/Score Methods of Inference for GLM Parameters
 128
 4.4 Deviance of a GLM Model Comparison and Model Checking
 132
 4.5 Fitting Generalized Linear Models
 138
 4.6 Selecting Explanatory Variables for a GLM
 143
 4.7 Example: Building a GLM
 149
 Appendix: GLM Analogs of Orthogonality Results for Linear Models
 156
 Chapter Notes
 158
 Exercises
 159
 5 Models for Binary Data
 165
 5.1 Link Functions for Binary Data
 165
 5.2 Logistic Regression: Properties and Interpretations
 168
 5.3 Inference About Parameters of Logistic Regression Models
 172
 5.4 Logistic Regression Model Fitting
 176
 5.5 Deviance and Goodness of Fit for Binary GLMs
 179
 5.6 Probit and Complementary Log Log Models
 183
 5.7 Examples: Binary Data Modeling
 186
 Chapter Notes
 193
 Exercises
 194
 6 Multinomial Response Models
 202
 6.1 Nominal Responses: BaselineCategory Logit Models
 203
 6.2 Ordinal Responses: Cumulative Logit and Probit Models
 209
 6.3 Examples: Nominal and Ordinal Responses
 216
 Chapter Notes
 223
 Exercises
 223
 7 Models for Count Data
 228
 7.1 Poisson GLMs for Counts and Rates
 229
 7.2 Poisson/Multinomial Models for Contingency Tables
 235
 7.3 Negative Binomial GLMS
 247
 7.4 Models for ZeroInflated Data
 250
 7.5 Example: Modeling Count Data
 254
 Chapter Notes
 259
 Exercises
 260
 8 QuasiLikelihood Methods
 268
 8.1 Variance Inflation for Overdispersed Poisson and Binomial GLMs
 269
 8.2 BetaBinomial Models and QuasiLikelihood Alternatives
 272
 8.3 QuasiLikelihood and Model Misspecification
 278
 Chapter Notes
 282
 Exercises
 282
 9 Modeling Correlated Responses
 286
 9.1 Marginal Models and Models with Random Effects
 287
 9.2 Normal Linear Mixed Models
 294
 9.3 Fitting and Prediction for Normal Linear Mixed Models
 302
 9.4 Binomial and Poisson GLMMs
 307
 9.5 GLMM Fitting Inference and Prediction
 311
 9.6 Marginal Modeling and Generalized Estimating Equations
 314
 9.7 Example: Modeling Correlated Survey Responses
 319
 Chapter Notes
 322
 Exercises
 324
 10 Bayesian Linear and Generalized Linear Modeling
 333
 10.1 The Bayesian Approach to Statistical Inference
 333
 10.2 Bayesian Linear Models
 340
 10.3 Bayesian Generalized Linear Models
 347
 10.4 Empirical Bayes and Hierarchical Bayes Modeling
 351
 Chapter Notes
 357
 Exercises
 359
 11 Extensions of Generalized Linear Models
 364
 11.1 Robust Regression and Regularization Methods for Fitting Models
 365
 11.2 Modeling With Large p
 375
 11.3 Smoothing Generalized Additive Models and Other GLM Extensions
 378
 Chapter Notes
 386
 Exercises
 388
 Appendix A Supplemental Data Analysis Exercises
 391
 Appendix B Solution Outlines for Selected Exercises
 396
 References
 410
 Author Index
 427
 Example Index
 433
 Subject Index 435.
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QA299.8 .A37 2015  Unknown 
45. Fourier analysis and Hausdorff dimension [2015]
 Mattila, Pertti.
 Cambridge, UK : Cambridge University Press, 2015.
 Description
 Book — xiv, 440 p. : ill. ; 24 cm.
 Summary

 Preface Acknowledgements
 1. Introduction
 2. Measure theoretic preliminaries
 3. Fourier transforms
 4. Hausdorff dimension of projections and distance sets
 5. Exceptional projections and Sobolev dimension
 6. Slices of measures and intersections with planes
 7. Intersections of general sets and measures
 8. Cantor measures
 9. Bernoulli convolutions
 10. Projections of the fourcorner Cantor set
 11. Besicovitch sets
 12. Brownian motion
 13. Riesz products
 14. Oscillatory integrals (stationary phase) and surface measures
 15. Spherical averages and distance sets
 16. Proof of the WolffErdogan Theorem
 17. Sobolev spaces, Schrodinger equation and spherical averages
 18. Generalized projections of Peres and Schlag
 19. Restriction problems
 20. Stationary phase and restriction
 21. Fourier multipliers
 22. Kakeya problems
 23. Dimension of Besicovitch sets and Kakeya maximal inequalities
 24. (n, k) Besicovitch sets
 25. Bilinear restriction References List of basic notation Author index Subject index.
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QA403.5 .M385 2015  Unknown 
 Taheri, Ali, author.
 First edition.  Oxford : Oxford University Press, 2015.
 Description
 Book — 2 volumes (xv, 963 pages) : illustrations ; 25 cm.
 Summary

 1. Harmonic Functions and the MeanValue Property
 2. Poisson Kernels and Green's Representation Formula
 3. AbelPoisson and Fejer Means of Fourier Series
 4. Convergence of Fourier Series: Dini vs. DirichletJordon
 5. HarmonicHardy Spaces hp(D)
 6. Interpolation Theorems of Marcinkiewicz and RieszThorin
 7. The Hilbert Transform on Lp(T) and Riesz's Theorem
 8. HarmonicHardy Spaces hp(Bn)
 9. Convolution Semigroups The Poisson and Heat Kernels on Rn
 10. Perron's Method of SubHarmonic Functions
 11. From AbelPoisson to BochnerRiesz Summability
 12. Fourier Transform on S0(Rn) The HilbertSobolev spaces Hs(Rn).
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 13. Maximal Function Bounding Averages and Pointwise Convergence
 14. HarmonicHardy Spaces hp(H)
 15. Sobolev Spaces A Resolution of the Dirichlet Principle
 16. Singular Integral Operators and VectorValued Inequalities
 17. LittlewoodPaley Theory, LpMultipliers and Function Spaces
 18. Morrey and Campanato vs. Hardy and JohnNirenberg Spaces
 19. Layered Potentials, Jump Relations and Existence Theorems
 20. Second Order Equations in Divergence Form: Continuous Coefficients
 21. Second Order Equations in Divergence Form: Measurable Coefficients
 A. Partition of Unity
 B. Total Boundedness and Compact Subsets of Lp
 C. Gamma and Beta Functions
 D. Volume of the Unit nBall
 E. Integrals Related to Abel and Gauss Kernels
 F. Hausdorff Measures Hs
 G. Evaluation of Some Integrals Over
 H. Sobolev Spaces.
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QA377 .T25 2015 V.1  Unknown 
QA377 .T25 2015 V.2  Unknown 
 Conference on Function Spaces (7th : 2014 : Southern Illinois University at Edwardsville)
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — vii, 301 pages ; 26 cm.
 Summary

 On algebraic properties of the spectrum and spectral radius of elements in a unital algebra by M. Abel Automatic continuity of surjective homomorphisms between topological algebras by M. Abel Characterization of holomorphic and meromorphic functions via maximum principles by J. T. Anderson Hermitian operators on $\mathbf{H}^p_\mathcal{H}(\triangle^n)$ by F. Botelho and J. Jamison Some notions of transitivity for operator spaces by J. A. ChavezDominguez and T. Oikhberg Removability of exceptional sets for differentiable and Lipschitz functions by J. Craig, J. F. Feinstein, and P. Patrick Generalizing trigonometric functions from different points of view by D. E. Edmunds and J. Lang Partial $W^*$dynamical systems and their dilations by G. O. S. Ekhaguere Swiss cheeses and their applications by J. F. Feinstein, S. Morley, and H. Yang Isometries on the special unitary group by O. Hatori Amenability as a hereditary property in some algebras of vectorvalued functions by T. Hoim and D. A. Robbins Weighted norm inequalities for Hardy type operators on monotone functions by P. Jain, M. Singh, and A. P. Singh Norms on normal function algebras by K. Jarosz Maximally modulated singular integral operators and their applications to pseudodifferential operators on Banach function spaces by A. Yu. Karlovich Smoothness to the boundary of biholomorphic mappings: An overview by S. G. Krantz A multiplicative BanachStone theorem by K. Lee Weighted composition operators on weighted sequence spaces by D. M. Luan and L. H. Khoi Spectral isometries into commutative Banach algebras by M. Mathieu and M. Young Eigenvalues and eigenfunctions of the $p(\cdot)$Laplacian. A convergence analysis by O. Mendez Surjective isometries between function spaces by T. Miura Endomorphisms and the Silov representation by D. C. Moore The essential norm of operators on the Bergman space of vectorvalued functions on the unit ball by R. Rahm and B. D. Wick Trigonometric approximation of periodic functions belonging to weighted Lipschitz class $W(L^p, \Psi(t), \beta)$ by S. K. Srivastava and U. Singh Analytic structure of polynomial hulls by J. Wermer.
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QA323 .C66 2014  Unknown 
48. Handbook of enumerative combinatorics [2015]
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xxiii, 1061 pages : illustrations ; 25 cm.
 Summary

 METHODS Algebraic and Geometric Methods in Enumerative Combinatorics Introduction What is a Good Answer? Generating Functions Linear Algebra Methods Posets Polytopes Hyperplane Arrangements Matroids Acknowledgments Analytic Methods Helmut Prodinger Introduction Combinatorial Constructions and Associated Ordinary Generating Functions Combinatorial Constructions and Associated Exponential Generating Functions Partitions and QSeries Some Applications of the Adding a Slice Technique Lagrange Inversion Formula Lattice Path Enumeration: The Continued Fraction Theorem Lattice Path Enumeration: The Kernel Method Gamma and Zeta Function Harmonic Numbers and Their Generating Functions Approximation of Binomial Coefficients Mellin Transform and Asymptotics of Harmonic Sums The MellinPerron Formula MellinPerron Formula: DivideandConquer Recursions Rice's Method Approximate Counting Singularity Analysis of Generating Functions Longest Runs in Words Inversions in Permutations and Pumping Moments Tree Function The Saddle Point Method Hwang's QuasiPower Theorem TOPICS Asymptotic Normality in Enumeration E. Rodney Canfield The Normal Distribution Method
 1: Direct Approach Method
 2: Negative Roots Method
 3: Moments Method
 4: Singularity Analysis Local Limit Theorems Multivariate Asymptotic Normality Normality in Service to Approximate Enumeration Trees Michael Drmota Introduction Basic Notions Generating Functions Unlabeled Trees Labeled Trees Selected Topics on Trees Planar maps Gilles Schaeffer What is a Map? Counting TreeRooted Maps Counting Planar Maps Beyond Planar Maps, an Even Shorter Account Graph Enumeration Marc Noy Introduction Graph Decompositions Connected Graphs with Given Excess Regular Graphs Monotone and Hereditary Classes Planar Graphs Graphs on Surfaces and Graph Minors Digraphs Unlabelled Graphs Unimodality, LogConcavity, RealRootedness and Beyond Petter Branden Introduction Probabilistic Consequences of RealRootedness Unimodality and GNonnegativity LogConcavity and Matroids Infinite LogConcavity The NeggersStanley Conjecture Preserving RealRootedness Common Interleavers Multivariate Techniques Historical Notes Words Dominique Perrin and Antonio Restivo Introduction Preliminaries Conjugacy Lyndon words Eulerian Graphs and De Bruijn Cycles Unavoidable Sets The BurrowsWheeler Transform The GesselReutenauer Bijection Suffix Arrays Tilings James Propp Introduction and Overview The Transfer Matrix Method Other Determinant Methods RepresentationTheoretic Methods Other Combinatorial Methods Related Topics, and an Attempt at History Some Emergent Themes Software Frontiers Lattice Path Enumeration Christian Krattenthaler Introduction Lattice Paths Without Restrictions Linear Boundaries of Slope
 1 Simple Paths with Linear Boundaries of Rational Slope, I Simple Paths with Linear Boundaries with Rational Slope, II Simple Paths with a Piecewise Linear Boundary Simple Paths with General Boundaries Elementary Results on Motzkin and Schroder Paths A continued Fraction for the Weighted Counting of Motzkin Paths Lattice Paths and Orthogonal Polynomials Motzkin Paths in a Strip Further Results for Lattice Paths in the Plane NonIntersecting Lattice Paths Lattice Paths and Their Turns Multidimensional Lattice Paths Multidimensional Lattice Paths Bounded by a Hyperplane Multidimensional Paths With a General Boundary The Reflection Principle in Full Generality QCounting Of Lattice Paths and RogersRamanujan Identities SelfAvoiding Walks Catalan Paths and q tenumeration James Haglund Introduction to qAnalogues and Catalan Numbers The q tCatalan Numbers Parking Functions and the Hilbert Series The q tSchroder Polynomial Rational Catalan Combinatorics Permutation Classes Vincent Vatter Introduction Growth Rates of Principal Classes Notions of Structure The Set of All Growth Rates Parking Functions Catherine H. Yan Introduction Parking Functions and Labeled Trees Many Faces of Parking Functions Generalized Parking Functions Parking Functions Associated with Graphs Final Remarks Standard Young Tableaux Ron Adin and Yuval Roichman Introduction Preliminaries Formulas for Thin Shapes Jeu de taquin and the RS Correspondence Formulas for Classical Shapes More Proofs of the Hook Length Formula Formulas for Skew Strips Truncated and Other NonClassical Shapes Rim Hook and Domino Tableaux qEnumeration Counting Reduced Words
 Appendix 1: Representation Theoretic Aspects
 Appendix 2: Asymptotics and Probabilistic Aspects Computer Algebra Manuel Kauers Introduction Computer Algebra Essentials Counting Algorithms Symbolic Summation The GuessandProve Paradigm Index.
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QA164 .H36 2015  Inlibrary use 
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QA164 .H36 2015  Unknown 
 Cham : Birkhäuser, [2015]
 Description
 Book — xxvii, 717 pages : illustrations (chiefly color) ; 24 cm
 Summary

 Solvability of a Nonstationary Problem of RadiativeConductive Heat Transfer in a System of Semitransparent Bodies. The Nonstationary RadiativeConductive Heat Transfer Problem in a Periodic System of Grey Heat Shields. Semidiscrete and Asymptotic Approximations. A Mixed Impedance Scattering Problem for Partially Coated Obstacles in TwoDimensional Linear Elasticity. HalfLife Distribution Shift of Fission Products by Coupled FissionFusion Processes. DRBEM Simulation on Mixed Convection with Hydromagnetic Effect. Nonlinear Method of Reduction of Dimensionality Based on Artificial Neural Network and Hardware Implementation. On the Eigenvalues of a Biharmonic Steklov Problem. Shape Differentiability of the Eigenvalues of Elliptic Systems. Pollutant Dispersion in the Atmosphere: A Solution Considering Nonlocal Closure of Turbulent Diffusion. The Characteristic Matrix of Nonuniqueness for FirstKind Equations. On the Spectrum of Volume Integral Operators in Acoustic Scattering. Modeling and Implementation of Demand Dispatch Approach in a Smart MicroGrid. Harmonic Functions in a Domain with a Small Hole: A Functional Analytic Approach. Employing Eddy Diffusivities to Simulate the Contaminants Dispersion for a Shear DominatedStable Boundary Layer. Analysis of BoundaryDomain Integral Equations for VariableCoefficient Dirichlet BVP in 2D.Onset of SeparatedWaterLayer in ThreePhase Stratified Flow. An IntegroDifferential Equation for 1D Cell Migration. The MultiGroup Neutron Diffusion Equation in General Geometries Using the Parseval Identity. MultiGroup Neutron Propagation in Transport Theory by Space Asymptotic Methods. Infiltration in Porous Media: On the Construction of a Functional Solution Method for the Richards Equation. A SoftSensor Approach to Probability Density Function Estimation. Two Reasons Why Pollution Dispersion Modeling Needs Sesquilinear Forms. Correcting Terms for Perforated Media by Thin Tubes with Nonlinear Flux and Large Adsorption Parameters. A Finite Element Method For Deblurring Images. MultiParticle Collision Algorithm for Solving an Inverse Radiative Problem.Performance of a HigherOrder Numerical Method for Solving Ordinary Differential Equations by Taylor Series. Retinal Image Quality Assessment Using Shearlet Transform. The RadiativeConductive Transfer Equation in Cylinder Geometry and its Application to Rocket Launch Exhaust Phenomena. A Functional Analytic Approach to Homogenization Problems. Anisotropic Fundamental Solutions for Linear Elasticity and Heat Conduction Problems Based on a Crystalline Class Hierarchy Governed Decomposition Method. On a Model for Pollutant Dispersion in the Atmosphere with Partially Reflective Boundary Conditions. Asymptotic Approximations for Chemical Reactive Flows in Thick Fractal Junctions. BDIE System in the Mixed BVP for the Stokes Equations with Variable Viscosity CalderonZygmund Theory for SecondOrder Elliptic Systems on Riemannian Manifolds. The Regularity Problem in Rough Subdomains of Riemannian Manifolds. A Collocation Method Based on the Central Part Interpolation for Integral Equations. Evolutional Contact with Coulomb Friction on a Periodic Microstructure. Piecewise Polynomial Collocation for a Class of Fractional IntegroDifferential Equations. A Note on Transforming a Plane Strain FirstKind Fredholm Integral Equation into an Equivalent SecondKind Equation. Asymptotic Analysis of the Steklov Spectral Problem in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions. SemiAnalytical Solution for Torsion of a Micropolar Beam of Elliptic Cross Section. L1 Regularized Regression Modeling of Functional Connectivity. Automatic Separation of Retinal Vessels into Arteries and Veins Using Ensemble Learning. Study of Extreme Brazilian Meteorological Events. The Neutron Point Kinetics Equation: Suppression of Fractional Derivative Effects by Temperature Feedback. Comparison of Analytical and Numerical Solution Methods for the Point Kinetics Equation with Temperature Feedback Free of Stiffness. The Wind Meandering Phenomenon in an Eulerian Three Dimensional Model to Simulate the Pollutants Dispersion. Semilinear SecondOrder Ordinary Differential Equations: Distances Between Consecutive Zeros of Oscillatory Solutions. Oscillation Criteria for some ThirdOrder Linear Ordinary Differential Equations. Oscillation Criteria for some SemiLinear EmdenFowler ODE. Analytic Representation of the Solution of Neutron Kinetic Transport Equation in SlabGeometry Discrete Ordinates Formulation. New Constructions in the Theory of Elliptic Boundary Value Problems. Optimal Control of Partial Differential Equations by Means of Stackelberg Strategies: An Environmental Application. An Overview of the Modified BuckleyLeverett Equation. Influence of Stochastic Moments on the Solution of the Neutron Point Kinetics Equation. The Hamilton Principle for Mechanical Systems with Impacts and Unilateral Constraints. Numerical Solutions and Their Error Bounds for Oscillatory Neural Networks..
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QA431 .I49 2015  Unknown 
50. Introduction to the calculus of variations [2015]
 Introduction au calcul des variations. English
 Dacorogna, Bernard, 1953 author.
 3rd edition.  London : Imperial College Press, [2015] Hackensack, NJ : World Scientific Publishing Co., Pte. Ltd., [date of distribution not identified]
 Description
 Book — x, 311 pages ; 24 cm
 Summary

 Introduction Preliminaries Classical Methods Direct Methods: Existence Direct Methods: Regularity Minimal Surfaces Isoperimetric Inequality Solutions to the Exercises Bibliography Index.
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QA315 .D34313 2015  Unknown 
51. An invitation to real analysis [2015]
 Moreno, Luis F., author.
 Washington, DC : The Mathematical Association of America, [2015]
 Description
 Book — xviii, 661 pages : illustrations ; 26 cm.
 Online
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QA331.5 .M66 2015  Unknown 
 Grindrod, Peter, author.
 Oxford : Oxford University Press, 2015.
 Description
 Book — xiii, 261 pages : ill. ; 24 cm
 Summary

 Introduction: The Underpinnings of Analytics
 1. Similarity, Graphs and Networks, Random Matrices and SVD
 2. Dynamically Evolving Networks
 3. Structure and Responsiveness
 4. Clustering and Unsupervised Classication
 5. Multiple Hypothesis Testing Over Live Data
 6. Adaptive Forecasting
 7. Customer Journeys and Markov Chains
 Appendix: Uncertainty, Probability and Reasoning.
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QA76.9 .D343 G758 2015  Unknown 
53. Numbers and functions : steps into analysis [2015]
 Burn, R. P., author.
 Third edition.  Cambridge, United Kingdom : Cambridge University Press, [2015]
 Description
 Book — xxv, 347 pages ; 23 cm
 Summary

 Preface to first edition Preface to second edition Preface to third edition Glossary Part I. Numbers:
 1 Mathematical induction
 2. Inequalities
 3. Sequences: a first bite at infinity
 4. Completeness: what the rational numbers lack
 5. Series: infinite sums Part II. Functions:
 6. Functions and continuity: neighbourhoods, limits of functions
 7. Continuity and completeness: functions on intervals
 8. Derivatives: tangents
 9. Differentiation and completeness: mean value theorems, Taylor's Theorem
 10. Integration: the fundamental theorem of calculus
 11. Indices and circle functions
 12. Sequences of functions
 Appendix 1. Properties of the real numbers
 Appendix 2. Geometry and intuition
 Appendix 3. Questions for student investigation and discussion Bibliography Index.
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QA300 .B88 2015  Unknown 
54. A primer on real analysis [2015]
 Sultan, Alan, author.
 [United States] : [publisher not identified], [2015?]
 Description
 Book — vi, 272 pages : illustrations ; 26 cm
 Online
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QA300 .S963 2015  Unknown 
55. Problems in real and functional analysis [2015]
 Torchinsky, Alberto, author.
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — x, 467 pages ; 27 cm.
 Summary

 * Problems: Set theory and metric spaces* Measures Lebesgue measure* Measurable and integrable functions $L^p$ spaces* Sequences of functions* Product measures* Normed linear spaces* Functionals Normed linear spaces* Linear operators* Hilbert spaces* Index.
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QA300 .T65 2015  Unknown 
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — ix, 258 pages ; 26 cm.
 Summary

 S. G. Dani as I have known him by M. S. Raghunathan Cubic averages and large intersections by V. Bergelson and A. Leibman Liouville property on $G$spaces by C. R. E. Raja A new connection between metric theory of Diophantine approximations and distribution of algebraic numbers by V. Bernik and F. Gotze The gap distribution of slopes on the golden L by J. S. Athreya, J. Chaika, and S. Lelievre Uniformly recurrent subgroups by E. Glasner and B. Weiss Values of binary quadratic forms at integer points and Schmidt games by D. Kleinbock and B. Weiss Conformal families of measures for general iterated function systems by M. Denker and M. Yuri Dani's work on probability measures on groups by F. Ledrappier and R. Shah On the homogeneity at infinity of the stationary probability for an affine random walk by Y. Guivarc'h and E. Le Page Dani's work on dynamical systems on homogeneous spaces by D. W. Morris Calculus of generalized Riesz products by e. H. el Abdalaoui and M. G. Nadkarni Diophantine approximation exponents on homogeneous varieties by A. Ghosh, A. Gorodnik, and A. Nevo Ergodicity of principal algebraic group actions by H. Li, J. Peterson, and K. Schmidt A note on three problems in metric Diophantine approximation by V. Beresnevich and S. Velani Dynamical invariants for group automorphisms by R. Miles, M. Staines, and T. Ward.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA614.8 .R45 2015  Unknown 
57. Single digits : in praise of small numbers [2015]
 Chamberland, Marc, 1964 author.
 Princeton, New Jersey : Princeton University Press, [2015]
 Description
 Book — xii, 226 pages : illustrations ; 25 cm
 Summary

The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan's conjecture, and so much more. The book's short sections can be read independently and digested in bitesized chunksespecially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA300 .C4412 2015  Unknown 
 Analyse mathématique. English
 Choimet, Denis, author.
 Cambridge, United Kingdom : Cambridge University Press, 2015.
 Description
 Book — xv, 508 pages : illustrations ; 24 cm
 Summary

 Foreword Gilles Godefroy Preface
 1. The Littlewood Tauberian theorem
 2. The Wiener Tauberian theorem
 3. The Newman Tauberian theorem
 4. Generic properties of derivative functions
 5. Probability theory and existence theorems
 6. The HausdorffBanachTarski paradoxes
 7. Riemann's 'other' function
 8. Partitio Numerorum
 9. The approximate functional equation of theta0
 10. The Littlewood conjecture
 11. Banach algebras
 12. The Carleson corona theorem
 13. The problem of complementation in Banach spaces
 14. Hints for solutions References Notations Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA300 .C45413 2015  Unknown 
59. Understanding analysis [2015]
 Abbott, Stephen, 1964 author.
 Second edition.  New York ; Heidelberg : Springer, [2015]
 Description
 Book — xii, 312 pages : illustrations ; 25 cm.
 Summary

 Preface.
 1 The Real Numbers.
 2 Sequences and Series.
 3 Basic Topology of R.
 4 Functional Limits and Continuity.
 5 The Derivative.
 6 Sequences and Series of Functions.
 7 The Riemann Integral.
 8 Additional Topics. Bibliography. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

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QA300 .A18 2015  Unknown 
 Roe, John, 1959 author.
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — xiii, 269 pages : illustrations ; 22 cm.
 Summary

 Prelude: Love, hate, and exponentials Paths and homotopies The winding number Topology of the plane Integrals and the winding number Vector fields and the rotation number The winding number in functional analysis Coverings and the fundamental group Coda: The Bott periodicity theorem Linear algebra Metric spaces Extension and approximation theorems Measure zero Calculus on normed spaces Hilbert space Groups and graphs Bibliography Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA299.8 .R64 2015  Unknown 