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The Simplex, Duplex and Pascal's Triangles

The Simplex, Duplex and Pascal's Triangles
Author: Thomas M. Green
Publisher: CreateSpace
Total Pages: 176
Release: 2015-07-25
Genre:
ISBN: 9781514677094
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Prepare to be intrigued by the many facets of the properties of the amazing array of numbers known as Pascal's Triangle and its many relatives. Some of the topics you will find: Polytopes Simplexes and the Simplex Triangle Tetrahedral, and higher dimensional figurate numbers Duplexes and The Duplex Triangle Geometric Duplication - Cubes and Hypercubes Vandermonde's Identity for the Duplex Triangle and the Triplex Triangle Euler's formula for Simplexes and Duplexes Recurrent Sequences in Pascal's Triangle and its Relatives Including the Fibonacci, Pell and Jacobsthal Sequences Pythagorean Triples - Related to the Sequences Listed Above Properties Involving String Products and more. There is a comprehensive index that will allow readers to easily search for topics of their interest. One goal is to provide a vehicle to the discovery of some higher mathematics related to higher dimensional geometric figures, at an entry level for the young beginning researcher by including many exercises that ask for verification of a pattern by testing specific cases and conjecturing a generalization of the pattern. Another major goal was to make available source materials for mathematics teachers to use in their classes. Included are many topics suitable for introducing students, at the pre-college level, to the sense of satisfaction one receives while exploring and discovering significant parts of advanced mathematics. I hope you will enjoy exploring this amazing Arithmetic Triangle and its relatives as much as I have. There is still much more to be discovered, of that I am certain. Teachers and students are eligible for special discounts for purchases of this book. Send an email to [email protected] for information on qualifying for a discount code to use before ordering.

Pascal's Arithmetical Triangle

Pascal's Arithmetical Triangle
Author: Anthony William Fairbank Edwards
Publisher: Oxford University Press, USA
Total Pages: 200
Release: 1987
Genre: Language Arts & Disciplines
ISBN:
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A history of Pascal's Arithmetical Triangle, tracing its roots in Pythagorean arithmetic, Hindu combinatorics and Arabic algebra, and giving an account of the progressive solution of combinatorial problems from the earliest recorded examples through the Renaissance and later mathematicians. The author shows how Pascal's work in establishing the peroperties of the numbers and their application in various fields let to Newton's discovery of the binomial theorem for fractional and negative indices and to Leibniz's discovery of calculus.

Pascal's Triangle

Pascal's Triangle
Author: Thomas M. Green
Publisher: Dale Seymour Publication
Total Pages: 278
Release: 1986-01
Genre: Mathematics
ISBN: 9780866513067
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Pascal's triangle and where to find it - Number patterns within Pascal's triangle - Figurate numbers and Pascal's triangle - Higher dimensional figurate numbers - Counting problems.

Gnuplot in Action

Gnuplot in Action
Author: Philipp K. Janert
Publisher: Simon and Schuster
Total Pages: 779
Release: 2016-03-08
Genre: Computers
ISBN: 1638352771
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Summary Gnuplot in Action, Second Edition is a major revision of this popular and authoritative guide for developers, engineers, and scientists who want to learn and use gnuplot effectively. Fully updated for gnuplot version 5, the book includes four pages of color illustrations and four bonus appendixes available in the eBook. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology Gnuplot is an open-source graphics program that helps you analyze, interpret, and present numerical data. Available for Unix, Mac, and Windows, it is well-maintained, mature, and totally free. About the Book Gnuplot in Action, Second Edition is a major revision of this authoritative guide for developers, engineers, and scientists. The book starts with a tutorial introduction, followed by a systematic overview of gnuplot's core features and full coverage of gnuplot's advanced capabilities. Experienced readers will appreciate the discussion of gnuplot 5's features, including new plot types, improved text and color handling, and support for interactive, web-based display formats. The book concludes with chapters on graphical effects and general techniques for understanding data with graphs. It includes four pages of color illustrations. 3D graphics, false-color plots, heatmaps, and multivariate visualizations are covered in chapter-length appendixes available in the eBook. What's Inside Creating different types of graphs in detail Animations, scripting, batch operations Extensive discussion of terminals Updated to cover gnuplot version 5 About the Reader No prior experience with gnuplot is required. This book concentrates on practical applications of gnuplot relevant to users of all levels. About the Author Philipp K. Janert, PhD, is a programmer and scientist. He is the author of several books on data analysis and applied math and has been a gnuplot power user and developer for over 20 years. Table of Contents PART 1 GETTING STARTED Prelude: understanding data with gnuplot Tutorial: essential gnuplot The heart of the matter: the plot command PART 2 CREATING GRAPHS Managing data sets and files Practical matters: strings, loops, and history A catalog of styles Decorations: labels, arrows, and explanations All about axes PART 3 MASTERING TECHNICALITIES Color, style, and appearance Terminals and output formats Automation, scripting, and animation Beyond the defaults: workflow and styles PART 4 UNDERSTANDING DATA Basic techniques of graphical analysis Topics in graphical analysis Coda: understanding data with graphs

Rules of Thumb for Mechanical Engineers

Rules of Thumb for Mechanical Engineers
Author: J. Edward Pope
Publisher: Gulf Professional Publishing
Total Pages: 417
Release: 1997
Genre: Technology & Engineering
ISBN: 0884157903
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Fluids -- Heat transfer -- Thermodynamics -- Mechanical seals -- Pumps and compressors -- Drivers -- Gears -- Bearings -- Piping and pressure vessels -- Tribology -- Vibration -- Materials -- Stress and strain -- Fatigue -- Instrumentation -- Engineering economics.

Algorithms for Communications Systems and their Applications

Algorithms for Communications Systems and their Applications
Author: Nevio Benvenuto
Publisher: John Wiley & Sons
Total Pages: 960
Release: 2020-12-29
Genre: Technology & Engineering
ISBN: 1119567971
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This welcome second edition to the 2002 original presents the logical arithmetical or computational procedures within communications systems that will ensure the solution to various problems. The authors comprehensively introduce the theoretical elements which are at the basis of the field of algorithms for communications systems. Various applications of these algorithms are then illustrated with a focus on wired and wireless network access technologies. The updated applications will focus on 5G standards, and new material will include MIMO systems (Space-time block coding / Spatial multiplexing / Beamforming and interference management / Channel Estimation /mmWave Model); OFDM and SC-FDMA (Synchronization / Resource allocation (bit and power loading) / Filtered OFDM); Full Duplex Systems (Digital interference cancellation techniques).

Instrument Engineers' Handbook, Volume 3

Instrument Engineers' Handbook, Volume 3
Author: Bela G. Liptak
Publisher: CRC Press
Total Pages: 1140
Release: 2018-10-08
Genre: Technology & Engineering
ISBN: 1439863431
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Instrument Engineers' Handbook – Volume 3: Process Software and Digital Networks, Fourth Edition is the latest addition to an enduring collection that industrial automation (AT) professionals often refer to as the "bible." First published in 1970, the entire handbook is approximately 5,000 pages, designed as standalone volumes that cover the measurement (Volume 1), control (Volume 2), and software (Volume 3) aspects of automation. This fourth edition of the third volume provides an in-depth, state-of-the-art review of control software packages used in plant optimization, control, maintenance, and safety. Each updated volume of this renowned reference requires about ten years to prepare, so revised installments have been issued every decade, taking into account the numerous developments that occur from one publication to the next. Assessing the rapid evolution of automation and optimization in control systems used in all types of industrial plants, this book details the wired/wireless communications and software used. This includes the ever-increasing number of applications for intelligent instruments, enhanced networks, Internet use, virtual private networks, and integration of control systems with the main networks used by management, all of which operate in a linked global environment. Topics covered include: Advances in new displays, which help operators to more quickly assess and respond to plant conditions Software and networks that help monitor, control, and optimize industrial processes, to determine the efficiency, energy consumption, and profitability of operations Strategies to counteract changes in market conditions and energy and raw material costs Techniques to fortify the safety of plant operations and the security of digital communications systems This volume explores why the holistic approach to integrating process and enterprise networks is convenient and efficient, despite associated problems involving cyber and local network security, energy conservation, and other issues. It shows how firewalls must separate the business (IT) and the operation (automation technology, or AT) domains to guarantee the safe function of all industrial plants. This book illustrates how these concerns must be addressed using effective technical solutions and proper management policies and practices. Reinforcing the fact that all industrial control systems are, in general, critically interdependent, this handbook provides a wide range of software application examples from industries including: automotive, mining, renewable energy, steel, dairy, pharmaceutical, mineral processing, oil, gas, electric power, utility, and nuclear power.

Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics

Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics
Author: Stéphane Avril
Publisher: Springer
Total Pages: 161
Release: 2016-10-12
Genre: Technology & Engineering
ISBN: 3319450719
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The articles in this book review hybrid experimental-computational methods applied to soft tissues which have been developed by worldwide specialists in the field. People developing computational models of soft tissues and organs will find solutions for calibrating the material parameters of their models; people performing tests on soft tissues will learn what to extract from the data and how to use these data for their models and people worried about the complexity of the biomechanical behavior of soft tissues will find relevant approaches to address this complexity.