Macro And Micro Mathematics
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Macro And Micro Mathematics
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Author : Roy Hubbert
language : en
Publisher: Createspace Independent Pub
Release Date : 2013-02-28
Macro And Micro Mathematics written by Roy Hubbert and has been published by Createspace Independent Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Mathematics categories.
“Macro and Micro Mathematics: Digital, Relational and Behavioral Mathematics” and its supplemental text, “Macro and Micro Mathematics' Matrix Tables”, are research based texts, targeted at mathematicians, college students, professors, libraries and math enthusiasts in general.Digital Mathematics is the foundation that supports Relational and Behavioral Mathematics, and includes studies of principles, which are fundamentally the embodiment of progression and regression analyses with regard to sequences, arrays and matrices. Digital Mathematics authors, legislates and enforces bylaws that govern the digital microcosm of all numeric expressions. Relational Mathematics governs the formation of internal and external relationships that exist among components of mathematical entities at their differential, sequential, composite and peripheral layers, and is divided between Micro and Macro-Mathematics. Micro Mathematics is limited to the study of internal relationships among components within the same mathematical entity; conversely, Macro Mathematics is limited to the study of external relationships among components of two or more mathematical entities. Behavioral Mathematics is the study of integers' patterns of behavior in mathematical operations.The most outstanding aspect of Digital Mathematics is its comprehension of interrelations among progression and regression, sequences, arrays and matrices. Discussions offered by Digital Mathematics occur within digital arenas where grouping constraints (comparable to associative, distributive, and commutative laws) only permit, numeric expressions with linear, variable or cumulative progression and regression as operants (“operant” is used instead of “operator”), and mathematical operations that produce similar numeric expressions as sums, differences, products and quotients. What distinguish Digital Mathematics from other publications involving matrices are its digital bylaws (i.e. digitization, de-digitization and grouping constraints), equivalences, composite to augment ratios (CARs) and operants' augment ratios (OARs). a) Digitization is the bridge between the digital and conventional domains; through digitization, the integers' digitized multiplication products were discovered, which are arrays that possess the same composite, sequential and differential attributes as their digital predecessors; arrays, in Digital Mathematics are as crucial as integers are in conventional mathematics. A lack of understanding regarding sequences and arrays' interrelationships with matrices has been a major hindrance to progress in the area of Matrix Analysis. b) Disclosures of sequences' intrinsic characteristics and systematic digital structures were provided by the discovery of de-digitization. c) Grouping constraints as digital bylaws enforce the associative, commutative, and distributive properties of integers and progressive numeric expressions, which ensure their predictability in mathematical operations. d) Equivalences, (i.e. differential, sequential and composite) offer disclosures of the functional and structural architecture of progressive numeric expressions, and integers' innate and formed relationships that occur in the formation and production of sequences, arrays and matrices. e) Composite to argument ratios (CARs) disclose the organizational structure of sequences, arrays and matrices within each digital domain. f) Operants' augment ratios (OARs) allow progressive numeric expressions, as operants, to be properly identified so their behavior in mathematical operations can be recognized and observed.
Macro And Micro Mathematics Matrix Tables
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Author : Roy Hubbert
language : en
Publisher: Createspace Independent Pub
Release Date : 2013-02-28
Macro And Micro Mathematics Matrix Tables written by Roy Hubbert and has been published by Createspace Independent Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-28 with Mathematics categories.
“Macro and Micro Mathematics: Digital, Relational and Behavioral Mathematics” and its supplemental text, “Macro and Micro Mathematics' Matrix Tables”, are research based texts, targeted at mathematicians, college students, professors, libraries and math enthusiasts in general.Digital Mathematics is the foundation that supports Relational and Behavioral Mathematics, and includes studies of principles, which are fundamentally the embodiment of progression and regression analyses with regard to sequences, arrays and matrices. Digital Mathematics authors, legislates and enforces bylaws that govern the digital microcosm of all numeric expressions. Relational Mathematics governs the formation of internal and external relationships that exist among components of mathematical entities at their differential, sequential, composite and peripheral layers, and is divided between Micro and Macro-Mathematics. Micro Mathematics is limited to the study of internal relationships among components within the same mathematical entity; conversely, Macro Mathematics is limited to the study of external relationships among components of two or more mathematical entities. Behavioral Mathematics is the study of integers' patterns of behavior in mathematical operations.The most outstanding aspect of Digital Mathematics is its comprehension of interrelations among progression and regression, sequences, arrays and matrices. Discussions offered by Digital Mathematics occur within digital arenas where grouping constraints (comparable to associative, distributive, and commutative laws) only permit, numeric expressions with linear, variable or cumulative progression and regression as operants (“operant” is used instead of “operator”), and mathematical operations that produce similar numeric expressions as sums, differences, products and quotients. What distinguish Digital Mathematics from other publications involving matrices are its digital bylaws (i.e. digitization, de-digitization and grouping constraints), equivalences, composite to augment ratios (CARs) and operants' augment ratios (OARs). a) Digitization is the bridge between the digital and conventional domains; through digitization, the integers' digitized multiplication products were discovered, which are arrays that possess the same composite, sequential and differential attributes as their digital predecessors; arrays, in Digital Mathematics are as crucial as integers are in conventional mathematics. A lack of understanding regarding sequences and arrays' interrelationships with matrices has been a major hindrance to progress in the area of Matrix Analysis. b) Disclosures of sequences' intrinsic characteristics and systematic digital structures were provided by the discovery of de-digitization. c) Grouping constraints as digital bylaws enforce the associative, commutative, and distributive properties of integers and progressive numeric expressions, which ensure their predictability in mathematical operations. d) Equivalences, (i.e. differential, sequential and composite) offer disclosures of the functional and structural architecture of progressive numeric expressions, and integers' innate and formed relationships that occur in the formation and production of sequences, arrays and matrices. e) Composite to argument ratios (CARs) disclose the organizational structure of sequences, arrays and matrices within each digital domain. f) Operants' augment ratios (OARs) allow progressive numeric expressions, as operants, to be properly identified so their behavior in mathematical operations can be recognized and observed.
Micro To Macro Mathematical Modelling In Soil Mechanics
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Author : Pasquale Giovine
language : en
Publisher: Springer
Release Date : 2019-03-25
Micro To Macro Mathematical Modelling In Soil Mechanics written by Pasquale Giovine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-25 with Mathematics categories.
This special issue collects selected contributions (excluding general lectures) of a Symposium on "Micro to MACRO Mathematical Modelling in Soil Mechanics", which took place at the University of Reggio Calabria, Italy, from May 29th to June 1st, 2018. The Symposium provided an opportunity to enhance the scientific debate on the construction of mathematical models for the description of the physical behaviour of soils, as well as on the suggestions provided by the micro-mechanical observation of the matter. The focus was on the comparison between the appropriateness of models and the need of mathematics to obtain rigorous results, which involves know-how from applied mathematical physics, geotechnical engineering and mechanics of solids. The contributions were selected by the Editors and the other Members of the Scientific Committee of the Symposium: Gianfranco Capriz (Pisa, Roma), Claudio di Prisco (Milan), Wolfgang Ehlers (Stuttgart), James T. Jenkins (Cornell), Stefan Luding (Twente), David Muir Wood (Dundee), Kenichi Soga (Berkeley).
Mathematical Descriptions Of Traffic Flow Micro Macro And Kinetic Models
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Author : Gabriella Puppo
language : en
Publisher: Springer Nature
Release Date : 2021-03-31
Mathematical Descriptions Of Traffic Flow Micro Macro And Kinetic Models written by Gabriella Puppo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-31 with Mathematics categories.
The book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.
On Three Levels
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Author : Mark Fannes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
On Three Levels written by Mark Fannes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.
Micro Macro Interactions
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Author : Albrecht Bertram
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-23
Micro Macro Interactions written by Albrecht Bertram and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-23 with Science categories.
Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.
Financial Macro And Micro Econometrics Using R
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Author :
language : en
Publisher: Elsevier
Release Date : 2020-01-25
Financial Macro And Micro Econometrics Using R written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-25 with Mathematics categories.
Financial, Macro and Micro Econometrics Using R, Volume 42, provides state-of-the-art information on important topics in econometrics, including multivariate GARCH, stochastic frontiers, fractional responses, specification testing and model selection, exogeneity testing, causal analysis and forecasting, GMM models, asset bubbles and crises, corporate investments, classification, forecasting, nonstandard problems, cointegration, financial market jumps and co-jumps, among other topics. Presents chapters authored by distinguished, honored researchers who have received awards from the Journal of Econometrics or the Econometric Society Includes descriptions and links to resources and free open source R Gives readers what they need to jumpstart their understanding on the state-of-the-art
Microeconomic Foundations Ii
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Author : David M. Kreps
language : en
Publisher: Princeton University Press
Release Date : 2023-05-23
Microeconomic Foundations Ii written by David M. Kreps and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Business & Economics categories.
A cutting-edge introduction to key topics in modern economic theory for first-year graduate students in economics and related fields Volume II of Microeconomic Foundations introduces models and methods at the center of modern microeconomic theory. In this textbook, David Kreps, a leading economic theorist, emphasizes foundational material, concentrating on seminal work that provides perspective on how and why the theory developed. Because noncooperative game theory is the chief tool of modeling and analyzing microeconomic phenomena, the book stresses the applications of game theory to economics. And throughout, it underscores why theory is most useful when it supports rather than supplants economic intuition. Introduces first-year graduate students to the models and methods at the core of microeconomic theory today Covers an extensive range of topics, including the agency theory, market signaling, relational contracting, bilateral bargaining, auctions, matching markets, and mechanism design Stresses the use—and misuse—of theory in studying economic phenomena and shows why theory should support, not replace, economic intuition Includes extensive appendices reviewing the essential concepts of noncooperative game theory, with guidance about how it should and shouldn’t be used Features free online supplements, including chapter outlines and overviews, solutions to all the problems in the book, and more
Macro Micro Theory On Multifield Coupling Behavior Of Heterogeneous Materials
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Author : Qing-Hua Qin
language : en
Publisher:
Release Date : 2010-10-19
Macro Micro Theory On Multifield Coupling Behavior Of Heterogeneous Materials written by Qing-Hua Qin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-19 with categories.
This book contains a comprehensive treatment of heterogeneous materials under coupled thermal, magnetic, electric, and mechanical loads. The easy-to-understand text clarifies some of the most advanced techniques for analysing and solving multifield problems of heterogeneous materials: micromechanics approach and homogenization method. Readers will benefit from the authors " thorough coverage of the fundamentals followed by detailed mathematical derivation with worked examples.
From Micro To Macro Adventures Of A Wandering Physicist
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Author : Vlatko Vedral
language : en
Publisher: World Scientific
Release Date : 2018-02-08
From Micro To Macro Adventures Of A Wandering Physicist written by Vlatko Vedral and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-08 with Science categories.
This is a popular science book exploring the limits of scientific explanation. In particular, it debates if all sciences will ultimately be reducible to physics. The journey starts with physics itself, where there is a gap between the micro (quantum) and the macro (classical) and moves into chemistry, biology and the social sciences. Written by a practising scientist, this volume offers a personal perspective on various topics and incorporates the latest research.