Tabla de Contenidos: “…Polynomial and Rational Functions -- 4.1 Polynomial Functions -- Identify Polynomial Functions and Their Degree -- Graph Polynomial Functions Using Transformations -- Identify the Real Zeros of a Polynomial Function and Their Multiplicity -- 4.2 Graphing Polynomial Functions -- Models -- Graph a Polynomial Function -- Graph a Polynomial Function Using a Graphing Utility -- Build Cubic Models from Data -- 4.3 Properties of Rational Functions -- Find the Domain of a Rational Function -- Find the Vertical Asymptotes of a Rational Function -- Find a Horizontal or an Oblique Asymptote of a Rational Function -- 4.4 The Graph of a Rational Function -- Graph a Rational Function -- Solve Applied Problems Involving Rational Functions -- 4.5 Polynomial and Rational Inequalities -- Solve Polynomial Inequalities -- Solve Rational Inequalities -- 4.6 The Real Zeros of a Polynomial Function -- Use the Remainder and Factor Theorems -- Use Descartes' Rule of Signs to Determine the Number of Positive and the Number of Negative Real Zeros of a Polynomial Function -- Use the Rational Zeros Theorem to List the Potential Rational Zeros of a Polynomial Function -- Find the Real Zeros of a Polynomial Function -- Solve Polynomial Equations -- Use the Theorem for Bounds on Zeros -- Use the Intermediate Value Theorem -- 4.7 Complex Zeros -- Fundamental Theorem of Algebra -- Use the Conjugate Pairs Theorem…”

“…This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. …”

“…The work addresses Albert's conjecture and provides insights into nilpotency and solubility of these algebras. It serves as a resource for students and researchers in mathematics, particularly those interested in algebraic structures and their applications…”

“…"The scope of the journal covers algebraic geometry in a broad sense, including complex or arithmetic geometry, algebraic groups and representation theory"--Website, viewed September 12, 2019.…”

Tabla de Contenidos: “….) -- 3.12 IMPLEMENTACIÓN DE CIRCUITOS A PARTIR DE EXPRESIONES BOOLEANAS -- 3.13 CIRCUITOS COMBINACIONALES -- 3. 14 ALGEBRA BOOLEANA -- 3. 15 TEOREMAS DE BOOLE -- 3. 16 TEOREMAS DE DEMORGAN -- DESARROLLO DE COMPETENCIAS -- 3.17 CIRCUITOS LÓGICOS COMBINACIONALES -- 3.17.1 FORMA DE SUMA DE PRODUCTOS -- 3. 17.2 FORMA DE PRODUCTO DE SUMAS -- 3.18 SIMPLIFICACIÓN DE CIRCUITOS LÓGICOS -- 3.18. 1 SIMPLIFICACIÓN ALGEBRAICA -- DESARROLLO DE COMPETENCIAS -- 3. 19 DISEÑO DE CIRCUITOS LÓGICOS COMBINACIONALES -- 3.19.1 MÉTODO DE MAPAS DE KAMAUH (MAPA K) -- 3.19.2 ADYACENCIA -- 3.19.3 AGRUPAMIENTO -- 3.20 PROCESO DE SIMPLIFICACIÓN DE UNA EXPRESIÓN BOOLEANA -- 3.21 PROCESO COMPLETO DE SOLUCIÓN DE UN PROBLEMA, SIMPLIFICACIÓN E (...) -- DESARROLLO DE COMPETENCIAS…”

Tabla de Contenidos: “…Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Table of Contents -- Preface -- Editor -- Contributors -- Chapter 1 Certain Banach-Space Operators Acting on Free Poisson Elements Induced by Orthogonal Projections -- 1.1 Introduction -- 1.2 Preliminaries -- 1.3 Some Banach *-Algebras Induced by Projections -- 1.4 Weighted-Semicircular Elements Induced by Q -- 1.5 Semicircular Elements Induced by Q -- 1.6 The Semicircular Filterization (L[sub(Q)], Ί) -- 1.7 Free Poisson Elements of L[sub(Q)] -- 1.7.1 Free Poisson Elements -- 1.7.2 Certain Free Poisson Elements Induced by S -- 1.7.3 Some Free Poisson Elements Induced by S U X -- 1.8 Free Weighted-Poisson Elements of L[sub(Q)] -- 1.8.1 Free Weighted-Poisson Elements -- 1.8.2 Free Weighted-Poisson Elements Induced by S U X -- 1.8.3 Free Weighted-Poisson Elements Induced by X -- 1.9 Shifts on Z and Integer-Shifts on L[sub(Q)] -- 1.9.1 (±)-Shifts on Z -- 1.9.2 Integer-Shifts on L[sub(Q)] -- 1.9.3 Free Probability on L[sub(Q)] Under the Group-Action of B -- 1.10 Banach-Space Operators on L[sub(Q)] Generated by B -- 1.10.1 Deformed Free Probability of L[sub(Q)] by A -- 1.10.2 Deformed Semicircular Laws on L[sub(Q)] by A -- 1.11 Deformed Free Poisson Distributions on L[sub(Q)] by A -- References -- Chapter 2 Linear Positive Operators Involving Orthogonal Polynomials -- 2.1 Operators Based on Orthogonal Polynomials -- 2.1.1 Notations -- 2.1.2 Definitions -- 2.1.3 Appell Polynomials -- 2.1.4 Boas-Buck-Type Polynomials -- 2.1.5 Charlier Polynomials -- 2.1.6 Approximation by Appell Polynomials -- 2.1.7 Approximation by Operators Including Generalized Appell Polynomials -- 2.1.8 Szász-Type Operators Involving Multiple Appell Polynomials -- 2.1.9 Kantorovich-Type Generalization of K[sub(n)] Operators -- 2.1.10 Kantorovich Variant of Szász Operators Based on Brenke-Type Polynomials…”

Tabla de Contenidos: “…Fundamental Statistical Definitions -- A.1 Random Variables -- A.2 Stochastic Processes -- A.2.1 Convergence in Probability -- A.2.2 Convergence in Distribution -- A.3 Key Theorems Concerning Stochastic Processes -- A.3.1 Law of Large Numbers -- A.3.2 Lindeberg-Lévy's Central Limit Theorem -- B. Matrix Algebra…”

Tabla de Contenidos: “…Intro -- Preface -- Organization -- Invited Talks -- How to Solve Math Problems Without Talent -- Bridging Formal Mathematics and Software Verification -- The Art of SMT Solving -- Contents - Part I -- Contents - Part II -- Contents - Part III -- Decision Procedures -- Split Gröbner Bases for Satisfiability Modulo Finite Fields -- 1 Introduction -- 1.1 Related Work -- 2 Background -- 3 Motivating Example -- 3.1 Verifying the Determinism of Num2Bits -- 3.2 The Challenge of Bit-Splitting -- 3.3 Cooperative Reasoning: A Path Forward -- 4 Approach -- 4.1 Split Gröbner bases -- 4.2 Abstract Procedure: Split -- 4.3 Concrete Procedure: BitSplit -- 5 Experiments -- 5.1 Benchmarks -- 5.2 Comparison to Prior Solvers -- 5.3 Comparison to Variants -- 6 Application -- 6.1 Background on Verifiable Field-Blasting -- 6.2 A New Strategy for Verifying Operator Rules -- 7 Conclusion -- A Additional Background -- B Computing Bitsum Usage in Real World Projects -- C Proof of Theorem 1 -- D Proof of Theorems 2 and 3 -- E Proof of Lemma 1 -- F The Seq Benchmark Family -- G Proof of Theorem 4 -- References -- Arithmetic Solving in Z3 -- 1 Introduction -- 2 Design Goals and Implementation Choices -- 3 Linear Real Arithmetic -- 3.1 Linear Solving -- 3.2 Finding Equal Variables - Cheaply -- 3.3 Bounds Propagation -- 4 Integer Linear Arithmetic -- 4.1 Patching -- 4.2 Cubes -- 4.3 GCD Consistency -- 4.4 Branching -- 4.5 Cuts -- 5 Non-linear Arithmetic -- 5.1 Patch Monomials -- 5.2 Bounds Propagation -- 5.3 Adding Bounds -- 5.4 Gröbner reduction -- 5.5 Incremental Linearization -- 5.6 NLSat -- 6 Shared Equalities -- 7 Evaluation -- 8 Summary and Discussion -- References -- Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic -- 1 Introduction -- 2 Preliminaries -- 3 Classical Automata-Based Decision Procedure for LIA…”

Tabla de Contenidos: “…From Molecules to Mathematics -- 1 Introduction -- 2 Flexible Tiles and New Graph Invariants -- 3 DNA Strand Routing and Topological Graph Theory -- 4 DNA Origami and New Algebraic Structures -- 5 DNA Origami and Origami Knots -- 6 Where Next? …”

Tabla de Contenidos: “…4.5.1 The Case of Standard Vertex Conditions -- 4.5.2 A Counterexample -- 4.5.3 Invariance of the Quadratic Form -- 4.5.4 Positivity of the Ground State for Generalised Delta-Couplings -- 4.6 First Spectral Estimates -- 5 The Characteristic Equation -- 5.1 Characteristic Equation I: Edge Transfer Matrices -- 5.1.1 Transfer Matrix for a Single Interval -- One-Dimensional Schrödinger Equation -- Magnetic Schrödinger Equation -- 5.1.2 The Characteristic Equation -- 5.1.3 The Characteristic Equation, Second Look -- 5.2 Characteristic Equation II: Scattering Approach -- 5.2.1 On the Scattering Matrix Associated with a Compact Interval -- 5.2.2 Positive Spectrum and Scattering Matrices for Finite Compact Graphs -- 5.3 Characteristic Equation III: M-Function Approach -- 5.3.1 M-Function for a Single Interval -- 5.3.2 The Edge M-Function -- 5.3.3 Characteristic Equation via the M-Function: General Vertex Conditions -- 5.3.4 Reduction of the M-Function for Standard Vertex Conditions -- 6 Standard Laplacians and Secular Polynomials -- 6.1 Secular Polynomials -- 6.2 Secular Polynomials for Small Graphs -- 6.3 Zero Sets for Small Graphs -- Appendix 1: Singular Sets on Secular Manifolds, Proof of Lemma 6.3 -- 7 Reducibility of Secular Polynomials -- 7.1 Contraction of Graphs -- 7.2 Extensions of Graphs -- 7.3 Secular Polynomials for the Watermelon Graphand Its Closest Relatives -- 7.4 Secular Polynomials for Flower Graphs and Their Extensions -- 7.5 Reducibility of Secular Polynomials for General Graphs -- 8 The Trace Formula -- 8.1 The Characteristic Equation: Multiplicityof Positive Eigenvalues -- 8.2 Algebraic and Spectral Multiplicities of the Eigenvalue Zero -- 8.3 The Trace Formula for Standard Laplacians -- 8.4 Trace Formula for Laplacians with Scaling-InvariantVertex Conditions -- 9 Trace Formula and Inverse Problems…”

Tabla de Contenidos: “…Change detection technique -- 4.1. Algebra approach -- 4.1.1. Image differencing -- 4.1.2. …”

“…Requiring no background in advanced algebraic geometry, the text serves as a modern introduction to the subject…”

“…In Practical Financial Optimization: A Library of GAMS Models, the authors provide a diverse set of models for portfolio optimization, based on the General Algebraic Modelling System. 'GAMS' consists of a language which allows a high-level, algebraic representation of mathematical models and a set of solvers - numerical algorithms - to solve them. …”

Tabla de Contenidos: “…Ramas de las matemáticas -- Álgebra -- Geometría -- Trigonometría -- Cálculo -- Estadística -- 5.3. …”

Tabla de Contenidos: “…Geometric Mean -- Chapter 2 Linear Algebraic Systems -- 2.1 Problem Definition and Vector Spaces -- 2.1.1 Vector Spaces in Tomographic Radiometric Inversion -- 2.2 Rotations -- 2.3 Projection Matrixes and Data-Filtering -- 2.3.1 Projections and Commercial FM Radio -- 2.4 Singular Value Decomposition (SVD) and Subspaces -- 2.4.1 How to Choose the Rank of A? …”

Tabla de Contenidos: “…Cover -- Title Page -- Copyright Page -- Brief Contents -- Contents -- Examples and Applications -- Preface -- Part I: The Linear Regression Model -- CHAPTER 1 Econometrics -- 1.1 Introduction -- 1.2 The Paradigm of Econometrics -- 1.3 The Practice of Econometrics -- 1.4 Microeconometrics and Macroeconometrics -- 1.5 Econometric Modeling -- 1.6 Plan of the Book -- 1.7 Preliminaries -- 1.7.1 Numerical Examples -- 1.7.2 Software and Replication -- 1.7.3 Notational Conventions -- CHAPTER 2 The Linear Regression Model -- 2.1 Introduction -- 2.2 The Linear Regression Model -- 2.3 Assumptions of the Linear Regression Model -- 2.3.1 Linearity of the Regression Model -- 2.3.2 Full Rank -- 2.3.3 Regression -- 2.3.4 Homoscedastic and Nonautocorrelated Disturbances -- 2.3.5 Data Generating Process for the Regressors -- 2.3.6 Normality -- 2.3.7 Independence and Exogeneity -- 2.4 Summary and Conclusions -- CHAPTER 3 Least Squares Regression -- 3.1 Introduction -- 3.2 Least Squares Regression -- 3.2.1 The Least Squares Coefficient Vector -- 3.2.2 Application: An Investment Equation -- 3.2.3 Algebraic Aspects of the Least Squares Solution -- 3.2.4 Projection -- 3.3 Partitioned Regression and Partial Regression -- 3.4 Partial Regression and Partial Correlation Coefficients -- 3.5 Goodness of Fit and the Analysis of Variance -- 3.5.1 The Adjusted R-Squared and a Measure of Fit -- 3.5.2 R-Squared and the Constant Term in the Model -- 3.5.3 Comparing Models -- 3.6 Linearly Transformed Regression -- 3.7 Summary and Conclusions -- CHAPTER 4 Estimating the Regression Model by Least Squares -- 4.1 Introduction -- 4.2 Motivating Least Squares -- 4.2.1 Population Orthogonality Conditions -- 4.2.2 Minimum Mean Squared Error Predictor -- 4.2.3 Minimum Variance Linear Unbiased Estimation -- 4.3 Statistical Properties of the Least Squares Estimator…”

Tabla de Contenidos: “…4.2 - Maintenance analysis procedures -- 4.2.1 - The MSG Series Procedures -- 4.2.2 - Reliability-Centered Maintenance -- 4.2.3 - MSG-3 Logic -- 4.2.4 - Structures -- 4.2.5 - Fatigue Damage -- 4.2.6 - Environmental Deterioration -- 4.2.7 - Accidental Damage -- 4.2.8 - Systems and Power Plants -- 4.2.9 - Setting Task Frequencies/Intervals -- 4.3 - Statistical reliability assessment -- 4.4 - Logistic support analysis -- 4.4.1 - LSA Tasks -- 4.4.2 - Failure Mode Effect Analysis -- 4.5 - Fault tree analysis -- 4.5.1 - Qualitative Analysis of a Fault Tree -- 4.5.2 - Quantitative Analysis of a Fault Tree -- 4.6 - Level of repair analysis -- 4.7 - Logistic support analysis record -- 4.8 - LSA models -- 4.9 - Elements of ILS -- 4.10 - Support equipment -- 4.11 - Facilities -- 4.12 - Data -- Chapter 5 - Intelligent Structural Rating System Based on Back-Propagation Network -- 5.1 - Introduction -- 5.2 - Artificial neural network -- 5.2.1 - Basic Theory -- 5.2.2 - Back-Propagation Network -- 5.3 - Design BPN for AD -- 5.3.1 - BPN Configuration -- 5.3.2 - Case Study -- 5.4 - Discussion -- 5.4.1 - Selection of Number of Nodes in Hidden Layers and Parameter Ratio -- 5.4.2 - Selection of Training Algorithms -- 5.5 - Conclusions -- Chapter 6 - Fault Tree Analysis for Composite Structural Damage -- 6.1 - Introduction -- 6.2 - Basic principles of fault tree analysis -- 6.2.1 - Elements of FTA -- 6.2.2 - Boolean Algebra Theorems -- 6.3 - FTA for composite damage -- 6.4 - Qualitative analysis -- 6.4.1 - Minimal Cut Sets -- 6.4.2 - Structure Importance Analysis -- 6.4.3 - Probability Importance Analysis -- 6.4.4 - Relative Probability Importance Analysis -- 6.5 - Quantitative analysis -- 6.6 - Discussion -- 6.7 - Potential solutions -- 6.7.1 - Material Design -- 6.7.2 - Fabrication Process -- 6.7.3 - Personnel Training -- 6.7.4 - Surface Protection…”

Tabla de Contenidos: “…Mathematical foundations -- Vectors, matrices, and beyond: a linear algebra primer -- Vectors: one-dimensional data -- Matrices: two-dimensional data -- Rank 3 tensors -- Rank 4 tensors -- Calculus in five minutes: derivatives and finding maxima -- Appendix B. …”

Tabla de Contenidos: “…1 Fractions, Decimals, and Percents -- Self‐Test 14.1 -- 2 Percent Change -- Self‐Test 14.2 -- 3 Fast Percent Change -- Self‐Test 14.3 -- 4 Percent Distribution -- Self‐Test 14.4 -- 5 Tipping -- Self‐Test 14.5 -- Answers to Self‐Test 14.1 -- Answers to Self‐Test 14.2 -- Answers to Self‐Test 14.3 -- Answers to Self‐Test 14.4 -- Answers to Self‐Test 14.5 -- Chapter 15 Solving Simple Equations -- 1 The Care and Treatment of Equations -- 2 Isolating x -- 3 Addition and Subtraction with x -- Self‐Test 15.1 -- 4 Multiplication and Division with x -- Self‐Test 15.2 -- 5 Fractions and Decimals in Equations -- Self‐Test 15.3 -- 6 Negative Numbers -- Self‐Test 15.4 -- 7 Multi‐Step Equations -- Self‐Test 15.5 -- Answers to Self‐Test 15.1 -- Answers to Self‐Test 15.2 -- Answers to Self‐Test 15.3 -- Answers to Self‐Test 15.4 -- Answers to Self‐Test 15.5 -- Chapter 16 Powers and Roots -- 1 Exponents -- Self‐Test 16.1 -- 2 Roots -- Self‐Test 16.2 -- 3 Advanced Problems -- Self‐Test 16.3 -- Answers to Self‐Test 16.1 -- Answers to Self‐Test 16.2 -- Answers to Self‐Test 16.3 -- Chapter 17 Very Large and Very Small Numbers -- 1 Writing Large Numbers -- Self‐Test 17.1 -- 2 Scientific Notation -- Self‐Test 17.2 -- 3 Millions, Billions, Trillions, and Beyond -- Self‐Test 17.3 -- 4 Multiplying Large Numbers -- 5 Dividing Large Numbers -- Self‐Test 17.4 -- 6 Scientific Notation for Very Small Numbers -- Self‐Test 17.5 -- Answers to Self‐Test 17.1 -- Answers to Self‐Text 17.2 -- Answers to Self‐Test 17.3 -- Answers to Self‐Test 17.4 -- Answers to Self‐Test 17.5 -- Chapter 18 Algebra Problems -- 1 Age Problems -- Self‐Test 18.1 -- 2 Finding the Numbers -- Self‐Test 18.2 -- 3 Mixture Problems -- Self‐Test 18.3 -- Answers to Self‐Test 18.1 -- Answers to Self‐Test 18.2 -- Answers to Self‐Test 18.3 -- Chapter 19 Interest Rates -- 1 Simple Interest -- Self‐Test 19.1.…”

Tabla de Contenidos: “…7.2.3.1 Digital Arrays -- 7.2.3.2 Analog Arrays -- 7.2.3.3 Hybrid Arrays -- 7.2.3.4 A Millimeter-Wave Antenna Array System Prototype -- 7.2.4 UE Antennas -- 7.2.5 Antenna Ports and QCL -- 7.2.6 CSI Acquisition -- 7.2.6.1 Reciprocity Based -- 7.2.6.2 Feedback Based -- 7.2.7 Massive MIMO -- 7.3 Multiantenna Techniques in NR -- 7.3.1 CSI Acquisition -- 7.3.1.1 Interference Measurements -- 7.3.2 Downlink MIMO Transmission -- 7.3.3 Uplink MIMO Transmission -- 7.3.4 Beam Management -- 7.3.4.1 Beam Acquisition During Initial Access -- 7.3.4.2 Beam Management Procedures -- 7.3.4.3 Beam Measurement and Reporting -- 7.3.4.4 Beam Indication -- 7.3.4.5 Beam Recovery -- 7.3.4.6 Uplink Beam Management -- 7.4 Experimental Results -- 7.4.1 Beam-Forming Gain -- 7.4.2 Beam Tracking -- 7.4.3 System Simulations -- References -- 8 Channel Coding -- 8.1 Fundamental Limits of Forward Error Correction -- 8.1.1 The Binary AWGN Channel -- 8.1.2 Coding Schemes for the Binary-AWGN Channels -- 8.1.3 Performance Metrics -- 8.2 FEC Schemes for the Bi-AWGN Channel -- 8.2.1 Introduction -- 8.2.2 Some De nitions -- 8.2.3 LDPC Codes -- 8.2.3.1 Fundamentals of LDPC Codes -- 8.2.3.2 The LDPC-Code Solution Chosen for 5G NR -- 8.2.4 Polar Codes -- 8.2.4.1 Fundamentals of Polar Codes -- 8.2.4.2 The Polar-Code Solution Chosen for 5G NR -- Deterministic Reliability Ordering -- Parity-Check Coding -- Rate Adaptation -- 8.2.5 Other Coding Schemes for the Short-Blocklength Regime -- 8.2.5.1 Short Algebraic Linear Block Codes With Ordered-Statistics Decoding -- 8.2.5.2 Linear Block Codes With Tail-Biting Trellises -- 8.2.5.3 Nonbinary LDPC Codes -- 8.2.5.4 Performance -- 8.3 Coding Schemes for Fading Channels -- 8.3.1 The SISO Case -- 8.3.2 The MIMO Case -- References -- 9 Simulator -- 9.1 Simulator Overview -- 9.2 Functional Modules -- 9.2.1 Channel Model -- 9.2.2 Power Ampli er Model…”