Tabla de Contenidos: “…range - a collection of evenly spaced integers -- Starting value -- Step argument -- Not using range: enumerate() -- list in action -- Negative indexing for lists (and other sequences) -- Slicing lists -- Copying lists -- Shallow copies -- Repeating lists -- Finding list elements with index() -- Membership testing with count() and in -- Removing list elements by index with del -- Removing list elements by value with remove() -- Inserting into a list -- Concatenating lists -- Rearranging list elements -- Out-of-place rearrangement -- Dictionaries -- Copying dictionaries -- Updating dictionaries -- Iterating over dictionary keys -- Iterating over dictionary values -- Iterating over key-value pairs -- Membership testing for dictionary keys -- Removing dictionary items -- Mutability of dictionaries -- Pretty printing -- set - an unordered collection of unique elements -- The set constructor -- Iterating over sets -- Membership testing of sets -- Adding elements to sets -- Removing elements from sets -- Copying sets -- Set algebra operations -- Union -- Intersection -- Difference -- Symmetric difference -- Subset relationships -- Collection protocols -- Container protocol -- Sized protocol -- Iterable protocol -- Sequence protocol -- Other protocols -- Summary -- Chapter 6: Exceptions -- Exceptions and control flow -- Handling exceptions -- Handling multiple exceptions -- Programmer errors -- Empty blocks - the pass statement -- Exception objects -- Imprudent return codes -- Re-raising exceptions -- Exceptions are part of your function's API -- Exceptions raised by Python -- Catching exceptions -- Raising exceptions explicitly -- Guard clauses -- Exceptions, APIs, and protocols -- IndexError -- ValueError -- KeyError -- Choosing not to guard against TypeError -- Pythonic style - EAFP versus LBYL -- Clean-up actions -- Moment of zen…”

“…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: “…PROPIEDADES -- 6.5.1 DEFINICIÓN -- 6.5.2 PROPIEDADES -- 6.6 OPERACIONES GENERALIZADAS -- 6.7 PARTICIÓN Y RECUBRIMIENTO DE UN CONJUNTO -- 6.8 TÉCNICAS DE CONTEO Y ÁLGEBRA DE CONJUNTOS -- RESUMEN DE CONTENIDOS DE LA UNIDAD VI -- ACTIVIDADES DE LA UNIDAD VI -- EJERCICIOS DE AUTOEVALUACIÓN -- BIBLIOGRAFÍA DE LA UNIDAD VI -- UNIDAD VII - RELACIONES Y FUNCIONES…”

Tabla de Contenidos: “…Matrix Operations -- 1.4.1. Algebraic Operations -- 1.4.2. Matrix Indexing -- 1.4.3. …”

Tabla de Contenidos:

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

Tabla de Contenidos: “…Condiciones de segundo orden -- Funciones implícitas -- Derivadas de las funciones implícitas -- Teorema de la función implícita -- El teorema de la envolvente -- Un ejemplo específico -- Un arduo planteamiento directo -- El atajo de la envolvente -- El caso de muchas variables -- Maximización con restricciones -- El método del multiplicador lagrangiano -- El problema formal -- Condiciones de primer orden -- Interpretación del multiplicador lagrangiano -- El multiplicador lagrangiano como proporción de costos a beneficios -- El teorema de la envolvente en problemas de maximización con restricciones -- Restricciones de desigualdad -- Un ejemplo con dos variables -- Variables de holgura -- Solución con el método de Lagrange -- Flexibilidad complementaria -- Condiciones de segundo orden -- Funciones con una variable -- Funciones con dos variables -- Un argumento intuitivo -- Un análisis formal -- Funciones cóncavas -- Maximización con restricciones -- Funciones cuasi cóncavas -- Funciones homogéneas -- Homogeneidad y derivadas -- Teorema de Euler -- Funciones homotéticas -- Resumen -- Problemas -- Lecturas Recomendadas -- Ampliaciones Condiciones de segundo orden y álgebra matricial -- PARTE 2 ELECCIÓN Y DEMANDA -- Capítulo 3 PREFERENCIAS Y UTILIDAD -- Axiomas de la elección racional -- Utilidad -- Ausencia de unicidad en las mediciones de la utilidad -- El supuesto ceteris paribus -- Utilidad derivada del consumo de bienes -- Argumentos de las funciones de utilidad -- DEFINICIÓN Utilidad. -- Bienes económicos -- Intercambios y sustitución -- Curvas de indiferencia y tasa marginal de sustitución -- DEFINICIÓN Curva de indiferencia. -- DEFINICIÓN Tasa marginal de sustitución. -- Mapa de curvas de indiferencia -- Curvas de indiferencia y transitividad -- Convexidad de las curvas de indiferencia -- Convexidad y equilibrio en el consumo…”

Tabla de Contenidos: “…4.6.1 Direction as a Trend -- 4.6.2 Validity of Operations -- 4.6.3 The Meaning of Improper OFNs -- 4.7 Summary and Further Intuitions -- References -- 5 Processing Direction with Ordered Fuzzy Numbers -- 5.1 Introduction -- 5.2 Direction Measurement Tool -- 5.2.1 The PART Function -- 5.2.2 The Direction Determinant -- 5.3 Compatibility Between OFNs -- 5.4 Inference Sensitive to Direction -- 5.4.1 Directed Inference Operation -- 5.4.2 Examples -- 5.5 Aggregation of OFNs -- 5.5.1 The Aggregation's Basic Properties -- 5.5.2 Arithmetic Mean Directed Aggregation -- 5.5.3 Aggregation for Premise Parts of Fuzzy Rules -- 5.6 Summary -- References -- 6 Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes -- 6.1 Introduction -- 6.2 Formal Approach to the Problem -- 6.3 Defuzzification Methods -- 6.3.1 Defuzzification Methods for OFN -- 6.4 Definition of Golden Ratio Defuzzification Operator -- 6.4.1 Golden Ratio for OFN -- 6.5 Golden Ratio -- 6.6 Defuzzification Conditions for GR -- 6.6.1 Normalization -- 6.6.2 Restricted Additivity -- 6.6.3 Homogeneity -- 6.7 Definition of Mandala Factor Defuzzification Operator -- 6.8 Mandala Factor -- 6.9 Defuzzification Conditions for MF -- 6.9.1 Normalization -- 6.9.2 Restricted Additivity -- 6.9.3 Homogeneity -- 6.10 Catalogue of the Shapes of Numbers in OFN Notation -- 6.11 Conclusion -- References -- 7 Two Approaches to Fuzzy Implication -- 7.1 Introduction -- 7.2 Lattice Structure and Implications on SOFNs -- 7.2.1 Step-Ordered Fuzzy Numbers -- 7.2.2 Lattice on mathcalRK -- 7.2.3 Complements and Negation on calN -- 7.2.4 Fuzzy Implication on BSOFN -- 7.2.5 Applications -- 7.3 Metasets -- 7.3.1 The Binary Tree T and the Boolean Algebra mathfrakB -- 7.3.2 General Definition of Metaset -- 7.3.3 Interpretations of Metasets -- 7.3.4 Forcing -- 7.3.5 Set-Theoretic Relations for Metasets…”

Tabla de Contenidos: “…How to make mathematical statements Numbers, equations and functions -- 1.1 Qualitative and quantitative scales -- Habitat classifications -- 1.2 Numbers -- Observations of spatial abundance -- 1.3 Symbols -- Population size and carrying capacity -- 1.4 Logical operations -- 1.5 Algebraic operations -- Size matters in male garter snakes -- 1.6 Manipulating numbers -- 1.7 Manipulating units -- 1.8 Manipulating expressions -- Energy acquisition in voles -- 1.9 Polynomials -- The law of mass action in epidemiology -- 1.10 Equations -- 1.11 First order polynomial equations -- Population size and composition -- 1.12 Proportionality and scaling: a special kind of first order polynomial equation -- Simple mark-recapture -- Converting density to population size -- 1.13 Second and higher order polynomial equations -- Estimating the number of infected animals from the rate of infection -- 1.14 Systems of polynomial equations -- Deriving population structure from data on population size -- 1.15 Inequalities -- Minimum energetic requirements in voles -- 1.16 Coordinate systems -- Non-Cartesian map projections -- 1.17 Complex numbers -- 1.18 Relations and functions -- Food webs…”

Tabla de Contenidos: “…-- Types of temporal tables -- Allen's interval algebra -- Temporal constraints -- Temporal data in SQL Server before 2016 -- Optimizing temporal queries -- Temporal features in SQL:2011 -- System-versioned temporal tables in SQL Server 2017 -- How temporal tables work in SQL Server 2017 -- Creating temporal tables -- Period columns as hidden attributes -- Converting non-temporal tables to temporal tables…”

Tabla de Contenidos: “…-- 2-4 Output, Unemployment, and the Inflation Rate: Okun's Law and the Phillips Curve -- Okun's Law -- The Phillips Curve -- 2-5 The Short Run, the Medium Run, and the Long Run -- 2-6 A Tour of the Book -- The Core -- Extensions -- Back to Policy -- Epilogue -- Appendix: The Construction of Real GDP and Chain-Type Indexes -- The Short Run -- Chapter 3 The Goods Market -- 3-1 The Composition of GDP -- 3-2 The Demand for Goods -- Consumption (C) -- Investment (I) -- Government Spending (G) -- 3-3 The Determination of Equilibrium Output -- Using Algebra -- Using a Graph -- Using Words -- How Long Does It Take for Output to Adjust? …”

Tabla de Contenidos: “…Standard objects -- Custom objects -- Fields -- Standard fields -- Custom fields -- Object relationships -- Apps -- Standard apps -- Custom apps -- Subtab apps -- Tabs -- Hiding and showing tabs -- Standard tabs -- Custom tabs -- Renaming labels for standard tabs, standard objects, and standard fields -- Creating custom objects -- Object Limits -- Object Limits for standard objects -- Object Limits for custom objects -- Creating custom object relationships -- Creating custom fields -- Custom field data types -- Auto Number -- Checkbox -- Currency -- Date -- Date/Time -- Email -- Formula -- Geolocation -- Lookup relationship -- Master-detail relationship -- External lookup relationship -- Hierarchical relationship -- Number -- Percent -- Phone -- Picklist -- Picklist (Multi-select) -- Roll-up summary -- Text -- Text (Encrypted) -- Text Area -- Text Area (Long) -- Text Area (Rich) -- URL -- Dependent picklists -- Building relationship fields -- Lookup relationship options -- Master-detail relationship options -- Allow reparenting option -- Lookup filters -- Building formulas -- Basic formula -- Advanced formula -- Building formulas - best practices -- Formatting with carriage returns and spacing -- Commenting -- Building formula text and compiled character size limits -- Using algebra -- Formula field size limit workarounds -- Custom field governance -- Addressing the issue -- More generic field names -- Field history tracking -- Custom objects to store dated information -- Chatter -- Page layouts -- Creating and modifying a page layout -- Feed-based page layouts -- Feed Tracking -- Creating feed-based page layouts -- Feed View Options -- Enable Full-Width Feed View in the Console -- Enable Compact Feed View in the Console -- Highlight Externally Visible Feed Items -- Publisher options - Automatically Collapse Publisher -- Other Tools and Components…”

Tabla de Contenidos: “…. -- See also -- Chapter 2: Just Enough Linear Algebra for Machine Learning with Spark -- Introduction -- Package imports and initial setup for vectors and matrices -- How to do it... -- There's more... -- See also -- Creating DenseVector and setup with Spark 2.0 -- How to do it... -- How it works... -- There's more... -- See also -- Creating SparseVector and setup with Spark -- How to do it... -- How it works... -- There's more... -- See also -- Creating dense matrix and setup with Spark 2.0 -- Getting ready -- How to do it... -- How it works... -- There's more... -- See also -- Using sparse local matrices with Spark 2.0 -- How to do it... -- How it works... -- There's more... -- See also -- Performing vector arithmetic using Spark 2.0.…”

Tabla de Contenidos: “…Watanabe and the Japanese Yen Carry Trade -- Questions -- Problems -- Appendix: An Algebraic Primer to International Parity Conditions -- Chapter 7. …”

Tabla de Contenidos: “…Traits and Enums -- 6.1 Using a Trait as an Interface -- Problem -- Solution -- Discussion -- See Also -- 6.2 Defining Abstract Fields in Traits -- Problem -- Solution -- Discussion -- See Also -- 6.3 Using a Trait Like an Abstract Class -- Problem -- Solution -- Discussion -- See Also -- 6.4 Using Traits as Mixins -- Problem -- Solution -- Discussion -- See Also -- 6.5 Resolving Method Name Conflicts and Understanding super -- Problem -- Solution -- Discussion -- See Also -- 6.6 Marking Traits So They Can Only Be Used by Subclasses of a Certain Type -- Problem -- Solution -- Discussion -- See Also -- 6.7 Ensuring a Trait Can Only Be Added to a Type That Has a Specific Method -- Problem -- Solution -- Discussion -- 6.8 Limiting Which Classes Can Use a Trait by Inheritance -- Problem -- Solution -- Discussion -- 6.9 Working with Parameterized Traits -- Problem -- Solution -- Discussion -- 6.10 Using Trait Parameters -- Problem -- Solution -- Discussion -- 6.11 Using Traits to Create Modules -- Problem -- Solution -- Discussion -- See Also -- 6.12 How to Create Sets of Named Values with Enums -- Problem -- Solution -- Discussion -- See Also -- 6.13 Modeling Algebraic Data Types with Enums -- Problem -- Solution -- Discussion -- See Also…”

Tabla de Contenidos:

Tabla de Contenidos: “…Computing the largest/smallest value that is less/greater than or equal to the algebraic quotient -- 23. Getting integral and fractional parts from a double -- 24. …”

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…”