Fast Integer Division – a Differentiated Offering from C2000 Product Family
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Transmit Processing in MIMO Wireless Systems
IEEE 6th CAS Symp. on Emerging Technologies: Mobile and Wireless Comm Shanghai, China, May 31-June 2,2004 Transmit Processing in MIMO Wireless Systems Josef A. Nossek, Michael Joham, and Wolfgang Utschick Institute for Circuit Theory and Signal Processing, Munich University of Technology, 80333 Munich, Germany Phone: +49 (89) 289-28501, Email: [email protected] Abstract-By restricting the receive filter to he scalar, we weighted by a scalar in Section IV. In Section V, we compare derive the optimizations for linear transmit processing from the linear transmit and receive processing. respective joint optimizations of transmit and receive filters. We A popular nonlinear transmit processing scheme is Tom- can identify three filter types similar to receive processing: the nmamit matched filter (TxMF), the transmit zero-forcing filter linson Harashima precoding (THP) originally proposed for (TxZE), and the transmil Menerfilter (TxWF). The TxW has dispersive single inpur single output (SISO) systems in [IO], similar convergence properties as the receive Wiener filter, i.e. [Ill, but can also be applied to MlMO systems [12], [13]. it converges to the matched filter and the zero-forcing Pter for THP is similar to decision feedback equalization (DFE), hut low and high signal to noise ratio, respectively. Additionally, the contrary to DFE, THP feeds back the already transmitted mean square error (MSE) of the TxWF is a lower hound for the MSEs of the TxMF and the TxZF. symbols to reduce the interference caused by these symbols The optimizations for the linear transmit filters are extended at the receivers. Although THP is based on the application of to obtain the respective Tomlinson-Harashimp precoding (THP) nonlinear modulo operators at the receivers and the transmitter, solutions. -
The Role of the Interval Domain in Modern Exact Real Airthmetic
The Role of the Interval Domain in Modern Exact Real Airthmetic Andrej Bauer Iztok Kavkler Faculty of Mathematics and Physics University of Ljubljana, Slovenia Domains VIII & Computability over Continuous Data Types Novosibirsk, September 2007 Teaching theoreticians a lesson Recently I have been told by an anonymous referee that “Theoreticians do not like to be taught lessons.” and by a friend that “You should stop competing with programmers.” In defiance of this advice, I shall talk about the lessons I learned, as a theoretician, in programming exact real arithmetic. The spectrum of real number computation slow fast Formally verified, Cauchy sequences iRRAM extracted from streams of signed digits RealLib proofs floating point Moebius transformtions continued fractions Mathematica "theoretical" "practical" I Common features: I Reals are represented by successive approximations. I Approximations may be computed to any desired accuracy. I State of the art, as far as speed is concerned: I iRRAM by Norbert Muller,¨ I RealLib by Branimir Lambov. What makes iRRAM and ReaLib fast? I Reals are represented by sequences of dyadic intervals (endpoints are rationals of the form m/2k). I The approximating sequences need not be nested chains of intervals. I No guarantee on speed of converge, but arbitrarily fast convergence is possible. I Previous approximations are not stored and not reused when the next approximation is computed. I Each next approximation roughly doubles the amount of work done. The theory behind iRRAM and RealLib I Theoretical models used to design iRRAM and RealLib: I Type Two Effectivity I a version of Real RAM machines I Type I representations I The authors explicitly reject domain theory as a suitable computational model. -
Download the Basketballplayer.Ngql Fle Here
Nebula Graph Database Manual v1.2.1 Min Wu, Amber Zhang, XiaoDan Huang 2021 Vesoft Inc. Table of contents Table of contents 1. Overview 4 1.1 About This Manual 4 1.2 Welcome to Nebula Graph 1.2.1 Documentation 5 1.3 Concepts 10 1.4 Quick Start 18 1.5 Design and Architecture 32 2. Query Language 43 2.1 Reader 43 2.2 Data Types 44 2.3 Functions and Operators 47 2.4 Language Structure 62 2.5 Statement Syntax 76 3. Build Develop and Administration 128 3.1 Build 128 3.2 Installation 134 3.3 Configuration 141 3.4 Account Management Statement 161 3.5 Batch Data Management 173 3.6 Monitoring and Statistics 192 3.7 Development and API 199 4. Data Migration 200 4.1 Nebula Exchange 200 5. Nebula Graph Studio 224 5.1 Change Log 224 5.2 About Nebula Graph Studio 228 5.3 Deploy and connect 232 5.4 Quick start 237 5.5 Operation guide 248 6. Contributions 272 6.1 Contribute to Documentation 272 6.2 Cpp Coding Style 273 6.3 How to Contribute 274 6.4 Pull Request and Commit Message Guidelines 277 7. Appendix 278 7.1 Comparison Between Cypher and nGQL 278 - 2/304 - 2021 Vesoft Inc. Table of contents 7.2 Comparison Between Gremlin and nGQL 283 7.3 Comparison Between SQL and nGQL 298 7.4 Vertex Identifier and Partition 303 - 3/304 - 2021 Vesoft Inc. 1. Overview 1. Overview 1.1 About This Manual This is the Nebula Graph User Manual. -
Division by Fractions 6.1.1 - 6.1.4
DIVISION BY FRACTIONS 6.1.1 - 6.1.4 Division by fractions introduces three methods to help students understand how dividing by fractions works. In general, think of division for a problem like 8..,.. 2 as, "In 8, how many groups of 2 are there?" Similarly, ½ + ¼ means, "In ½ , how many fourths are there?" For more information, see the Math Notes boxes in Lessons 7.2 .2 and 7 .2 .4 of the Core Connections, Course 1 text. For additional examples and practice, see the Core Connections, Course 1 Checkpoint 8B materials. The first two examples show how to divide fractions using a diagram. Example 1 Use the rectangular model to divide: ½ + ¼ . Step 1: Using the rectangle, we first divide it into 2 equal pieces. Each piece represents ½. Shade ½ of it. - Step 2: Then divide the original rectangle into four equal pieces. Each section represents ¼ . In the shaded section, ½ , there are 2 fourths. 2 Step 3: Write the equation. Example 2 In ¾ , how many ½ s are there? In ¾ there is one full ½ 2 2 I shaded and half of another Thatis,¾+½=? one (that is half of one half). ]_ ..,_ .l 1 .l So. 4 . 2 = 2 Start with ¾ . 3 4 (one and one-half halves) Parent Guide with Extra Practice © 2011, 2013 CPM Educational Program. All rights reserved. 49 Problems Use the rectangular model to divide. .l ...:... J_ 1 ...:... .l 1. ..,_ l 1 . 1 3 . 6 2. 3. 4. 1 4 . 2 5. 2 3 . 9 Answers l. 8 2. 2 3. 4 one thirds rm I I halves - ~I sixths fourths fourths ~I 11 ~'.¿;¡~:;¿~ ffk] 8 sixths 2 three fourths 4. -
Chapter 2. Multiplication and Division of Whole Numbers in the Last Chapter You Saw That Addition and Subtraction Were Inverse Mathematical Operations
Chapter 2. Multiplication and Division of Whole Numbers In the last chapter you saw that addition and subtraction were inverse mathematical operations. For example, a pay raise of 50 cents an hour is the opposite of a 50 cents an hour pay cut. When you have completed this chapter, you’ll understand that multiplication and division are also inverse math- ematical operations. 2.1 Multiplication with Whole Numbers The Multiplication Table Learning the multiplication table shown below is a basic skill that must be mastered. Do you have to memorize this table? Yes! Can’t you just use a calculator? No! You must know this table by heart to be able to multiply numbers, to do division, and to do algebra. To be blunt, until you memorize this entire table, you won’t be able to progress further than this page. MULTIPLICATION TABLE ϫ 012 345 67 89101112 0 000 000LEARNING 00 000 00 1 012 345 67 89101112 2 024 681012Copy14 16 18 20 22 24 3 036 9121518212427303336 4 0481216 20 24 28 32 36 40 44 48 5051015202530354045505560 6061218243036424854606672Distribute 7071421283542495663707784 8081624324048566472808896 90918273HAWKESReview645546372819099108 10 0 10 20 30 40 50 60 70 80 90 100 110 120 ©11 0 11 22 33 44NOT 55 66 77 88 99 110 121 132 12 0 12 24 36 48 60 72 84 96 108 120 132 144 Do Let’s get a couple of things out of the way. First, any number times 0 is 0. When we multiply two numbers, we call our answer the product of those two numbers. -
Three Methods of Finding Remainder on the Operation of Modular
Zin Mar Win, Khin Mar Cho; International Journal of Advance Research and Development (Volume 5, Issue 5) Available online at: www.ijarnd.com Three methods of finding remainder on the operation of modular exponentiation by using calculator 1Zin Mar Win, 2Khin Mar Cho 1University of Computer Studies, Myitkyina, Myanmar 2University of Computer Studies, Pyay, Myanmar ABSTRACT The primary purpose of this paper is that the contents of the paper were to become a learning aid for the learners. Learning aids enhance one's learning abilities and help to increase one's learning potential. They may include books, diagram, computer, recordings, notes, strategies, or any other appropriate items. In this paper we would review the types of modulo operations and represent the knowledge which we have been known with the easiest ways. The modulo operation is finding of the remainder when dividing. The modulus operator abbreviated “mod” or “%” in many programming languages is useful in a variety of circumstances. It is commonly used to take a randomly generated number and reduce that number to a random number on a smaller range, and it can also quickly tell us if one number is a factor of another. If we wanted to know if a number was odd or even, we could use modulus to quickly tell us by asking for the remainder of the number when divided by 2. Modular exponentiation is a type of exponentiation performed over a modulus. The operation of modular exponentiation calculates the remainder c when an integer b rose to the eth power, bᵉ, is divided by a positive integer m such as c = be mod m [1]. -
The Best of Both Worlds?
The Best of Both Worlds? Reimplementing an Object-Oriented System with Functional Programming on the .NET Platform and Comparing the Two Paradigms Erik Bugge Thesis submitted for the degree of Master in Informatics: Programming and Networks 60 credits Department of Informatics Faculty of mathematics and natural sciences UNIVERSITY OF OSLO Autumn 2019 The Best of Both Worlds? Reimplementing an Object-Oriented System with Functional Programming on the .NET Platform and Comparing the Two Paradigms Erik Bugge © 2019 Erik Bugge The Best of Both Worlds? http://www.duo.uio.no/ Printed: Reprosentralen, University of Oslo Abstract Programming paradigms are categories that classify languages based on their features. Each paradigm category contains rules about how the program is built. Comparing programming paradigms and languages is important, because it lets developers make more informed decisions when it comes to choosing the right technology for a system. Making meaningful comparisons between paradigms and languages is challenging, because the subjects of comparison are often so dissimilar that the process is not always straightforward, or does not always yield particularly valuable results. Therefore, multiple avenues of comparison must be explored in order to get meaningful information about the pros and cons of these technologies. This thesis looks at the difference between the object-oriented and functional programming paradigms on a higher level, before delving in detail into a development process that consisted of reimplementing parts of an object- oriented system into functional code. Using results from major comparative studies, exploring high-level differences between the two paradigms’ tools for modular programming and general program decompositions, and looking at the development process described in detail in this thesis in light of the aforementioned findings, a comparison on multiple levels was done. -
Functional C
Functional C Pieter Hartel Henk Muller January 3, 1999 i Functional C Pieter Hartel Henk Muller University of Southampton University of Bristol Revision: 6.7 ii To Marijke Pieter To my family and other sources of inspiration Henk Revision: 6.7 c 1995,1996 Pieter Hartel & Henk Muller, all rights reserved. Preface The Computer Science Departments of many universities teach a functional lan- guage as the first programming language. Using a functional language with its high level of abstraction helps to emphasize the principles of programming. Func- tional programming is only one of the paradigms with which a student should be acquainted. Imperative, Concurrent, Object-Oriented, and Logic programming are also important. Depending on the problem to be solved, one of the paradigms will be chosen as the most natural paradigm for that problem. This book is the course material to teach a second paradigm: imperative pro- gramming, using C as the programming language. The book has been written so that it builds on the knowledge that the students have acquired during their first course on functional programming, using SML. The prerequisite of this book is that the principles of programming are already understood; this book does not specifically aim to teach `problem solving' or `programming'. This book aims to: ¡ Familiarise the reader with imperative programming as another way of imple- menting programs. The aim is to preserve the programming style, that is, the programmer thinks functionally while implementing an imperative pro- gram. ¡ Provide understanding of the differences between functional and imperative pro- gramming. Functional programming is a high level activity. -
Anthyphairesis, the ``Originary'' Core of the Concept of Fraction
Anthyphairesis, the “originary” core of the concept of fraction Paolo Longoni, Gianstefano Riva, Ernesto Rottoli To cite this version: Paolo Longoni, Gianstefano Riva, Ernesto Rottoli. Anthyphairesis, the “originary” core of the concept of fraction. History and Pedagogy of Mathematics, Jul 2016, Montpellier, France. hal-01349271 HAL Id: hal-01349271 https://hal.archives-ouvertes.fr/hal-01349271 Submitted on 27 Jul 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ANTHYPHAIRESIS, THE “ORIGINARY” CORE OF THE CONCEPT OF FRACTION Paolo LONGONI, Gianstefano RIVA, Ernesto ROTTOLI Laboratorio didattico di matematica e filosofia. Presezzo, Bergamo, Italy [email protected] ABSTRACT In spite of efforts over decades, the results of teaching and learning fractions are not satisfactory. In response to this trouble, we have proposed a radical rethinking of the didactics of fractions, that begins with the third grade of primary school. In this presentation, we propose some historical reflections that underline the “originary” meaning of the concept of fraction. Our starting point is to retrace the anthyphairesis, in order to feel, at least partially, the “originary sensibility” that characterized the Pythagorean search. The walking step by step the concrete actions of this procedure of comparison of two homogeneous quantities, results in proposing that a process of mathematisation is the core of didactics of fractions. -
Multiplication and Divisions
Third Grade Math nd 2 Grading Period Power Objectives: Academic Vocabulary: multiplication array Represent and solve problems involving multiplication and divisor commutative division. (P.O. #1) property Understand properties of multiplication and the distributive property relationship between multiplication and divisions. estimation division factor column (P.O. #2) Multiply and divide with 100. (P.O. #3) repeated addition multiple Solve problems involving the four operations, and identify associative property quotient and explain the patterns in arithmetic. (P.O. #4) rounding row product equation Multiplication and Division Enduring Understandings: Essential Questions: Mathematical operations are used in solving problems In what ways can operations affect numbers? in which a new value is produced from one or more How can different strategies be helpful when solving a values. problem? Algebraic thinking involves choosing, combining, and How does knowing and using algorithms help us to be applying effective strategies for answering questions. Numbers enable us to use the four operations to efficient problem solvers? combine and separate quantities. How are multiplication and addition alike? See below for additional enduring understandings. How are subtraction and division related? See below for additional essential questions. Enduring Understandings: Multiplication is repeated addition, related to division, and can be used to solve story problems. For a given set of numbers, there are relationships that -
AUTHOR Multiplication and Division. Mathematics-Methods
DOCUMENT RESUME ED 221 338 SE 035 008, AUTHOR ,LeBlanc, John F.; And Others TITLE Multiplication and Division. Mathematics-Methods 12rogram Unipt. INSTITUTION Indiana ,Univ., Bloomington. Mathematics Education !Development Center. , SPONS AGENCY ,National Science Foundation, Washington, D.C. REPORT NO :ISBN-0-201-14610-x PUB DATE 76 . GRANT. NSF-GY-9293 i 153p.; For related documents, see SE 035 006-018. NOTE . ,. EDRS PRICE 'MF01 Plus Postage. PC Not Available from EDRS. DESCRIPTORS iAlgorithms; College Mathematics; *Division; Elementary Education; *Elementary School Mathematics; 'Elementary School Teachers; Higher Education; 'Instructional1 Materials; Learning Activities; :*Mathematics Instruction; *Multiplication; *Preservice Teacher Education; Problem Solving; :Supplementary Reading Materials; Textbooks; ;Undergraduate Study; Workbooks IDENTIFIERS i*Mathematics Methods Program ABSTRACT This unit is 1 of 12 developed for the university classroom portign_of the Mathematics-Methods Program(MMP), created by the Indiana pniversity Mathematics EducationDevelopment Center (MEDC) as an innovative program for the mathematics training of prospective elenientary school teachers (PSTs). Each unit iswritten in an activity format that involves the PST in doing mathematicswith an eye towardaiplication of that mathematics in the elementary school. This do ument is one of four units that are devoted tothe basic number wo k in the elementary school. In addition to an introduction to the unit, the text has sections on the conceptual development of nultiplication -
Introduction to Abstract Algebra “Rings First”
Introduction to Abstract Algebra \Rings First" Bruno Benedetti University of Miami January 2020 Abstract The main purpose of these notes is to understand what Z; Q; R; C are, as well as their polynomial rings. Contents 0 Preliminaries 4 0.1 Injective and Surjective Functions..........................4 0.2 Natural numbers, induction, and Euclid's theorem.................6 0.3 The Euclidean Algorithm and Diophantine Equations............... 12 0.4 From Z and Q to R: The need for geometry..................... 18 0.5 Modular Arithmetics and Divisibility Criteria.................... 23 0.6 *Fermat's little theorem and decimal representation................ 28 0.7 Exercises........................................ 31 1 C-Rings, Fields and Domains 33 1.1 Invertible elements and Fields............................. 34 1.2 Zerodivisors and Domains............................... 36 1.3 Nilpotent elements and reduced C-rings....................... 39 1.4 *Gaussian Integers................................... 39 1.5 Exercises........................................ 41 2 Polynomials 43 2.1 Degree of a polynomial................................. 44 2.2 Euclidean division................................... 46 2.3 Complex conjugation.................................. 50 2.4 Symmetric Polynomials................................ 52 2.5 Exercises........................................ 56 3 Subrings, Homomorphisms, Ideals 57 3.1 Subrings......................................... 57 3.2 Homomorphisms.................................... 58 3.3 Ideals.........................................