A DIRECT RENORMALIZATION GROUP APPROACH FOR THE EXCLUDED VOLUME PROBLEM. S. L. A. de Queiroz and C. M. Chaves DEPARTAMENTO ÜE FÍSICA.


 Elwin Howard Burns
 3 years ago
 Views:
Transcription
1 Nota Científica 24/79 A DIRECT RENORMALIZATION GROUP APPROACH FOR THE EXCLUDED VOLUME PROBLEM S. L. A. de Queiroz and C. M. Chaves DEPARTAMENTO ÜE FÍSICA Outubro 1979
2 Nota Cientifica 24/79 A DIRECT RENORMALIZATION GROUP APPROACH FOR THE EXCLUDED VOLUME PROBLEM* S. L. A. de Queiroz and C. M. Chav.es Departamento de Física, Pontifícia Universidade Católica Cx.P , Rio de Janeiro, RJ, Brasil October 1979 ABSTRACT. l! :. rr'f'' ' We propose 9 direct renormalization group approach/to the excluded volume problem in a square lattice by considering percolating selfavoiding paths in a b x b cell, where b = 2,3. Two ways of counting these paths are presented. In the first one, we get the exponent v *» for b 2 and v for b 3, whereas in the second one v for b 2 and v * for b  3. Comments are made on the extrapolation to b +». RESUMO. Um formalism usando o grupo de renormalização no espaço real e proposto para o problema do volume excluído nuia rede quadrada. Considerate caminhos que percolam numa célula b x b, o*ide b 2,3, e que se; am também caminhos aleatórios sem repetição. Duas maneiras de contagem são apresentadas. Pa primeira obtémse v para b» 2 e v para b 3, enquanto que na segunda maneiva v * para b  2 e v para b 3. Comentase a extrapolação desses resultados para b *».
3 2 Let R denote a site on a lattice and let M ($) be the number of selfavoiding random walks (SAW'S) of n steps beginning at the origin and finishing at site R. The mean square endtoend distance < 2> R n 1.2 by ' of an nstep walk is given < R 2> = 11 I R 2 M.($) n ft I M n<*> a n If we introduce a parameter P, such that to any n step SAW corresponds a weight P n, the mean square endtoend 2 distance is given by +I R 2 P n M (R) ç2 ( p )= Rd2 (!) ín P M «(S) R,n n where now the average is computed over all possible SAW'S. When P approaches a critical value P v diverges as (P~P) from below, Ç(P) The excluded volume problem is related to statistics 13 * of polymers ', and has also been shown to be connected with the n * 0 limit of the ncomponent spin model. Here we propose a positionspace renormalization group approach to this problem, which allows us to calculate directly the exponent v and P. We make use of the relation between percolation and SAW in a lattice 5. An alternative approach has been given recently by Shapiro 2. Consider the cell in a square lattice shown in Fig. 1, for which the scaling factor is b = 2. We count all the vertical (or horizontal, which is equivalent) percolating
4 3 paths 6 through the cell, starting at the origintaken as point 1 in Fig. 1  and ending at points labelled 3 or 6. Paths which are not SAW'S are not counted and a path with n steps has a weight p. Thus the renormalized weight p* is given by p» = p 2 + 2p 3 + p h (2) since we have one twostep walk(123), two threestep walks (1456 and 1256) and one fourstep walk(14523). The recursion relation (2) has two fixed points, the trivial one at p* = 0 and p = At this point A = ^ = and v = ~7 = r *c 3p n> 0.715, in excellent agreement with other results 2 ' 7 * 8. Por a b = 3 cell the same procedure jives p» = 4p9 + 2p 8 + 9p 7 + 5p 6 + 9p 5 + 3P 4 + p 3 (3) from which we get p = and v = c We can also count all the vertical and horizontal SAW'S; clearly, this has the effect of doubling the coefficients of the recursion relations of the first case. We then get p». 2p 2 + 4p 3 + 2P 1 * (b = 2) (4) and analogously for b  3. Our results, for both procedures, are displayed in table 1. The fact that the values of p in column I (the c first definition), are greater than those obtained in II was to be expected, since the definition of an allowed SAW in the former scheme is more restrictive than in the latter one. Although the second procedure seems logically more justified in view of definition (1), it is to be noticed that, for
5 4 b = 3, for example, the two val>*3s obtained for the exponent v differ by less than 4%. Besides, the two series seem to be converging approximately to the same value when b increases. We have extrapolated 6 our results to b > «, by plotting v against 1/b 2 (see table 1). The two series extrapolate practically to the same value, within less than 1%. Of course such extrapolation may be criticized because it is not certain that we are in an asymptotical region neither it is clear that an extrapolation of the results against 1/b 2 in a SAW problem can be supported by the same arguments as in a pure percolation problem 6. Nevertheless, the fact that the values obtained are very close to each other and with the values quoted in the literature 2» 7 / 8 indicates that our definition and our method allows the calculation of the exponent v and p with increasing accuracy when b increases.
6 5 REFERENCES * Work supported by Brazilian agencies FINEP and CNPq. 1. D. S. McKenzie, Polymers and Scaling, Physics Reports 22, 35 (1976). 2. B. Shapiro, J. Phys. Cll, 2829 (1978). 2. T. C. Lubensky, C. Dasgupta and C. M. Chaves, J. Phys. All, 2219 (1978). 4. P. G. de Gennes, Phys. Lett. 38A, 339 (1972). 5. H. E. Stanley, J. Phys. Al, L211 (1977). 6. P. M. C. de Oliveira, S. L. A. de Queiroz, R. Riera and C. M. Chaves, submitted to J. Phys. A. 7. H. J. Hilhorst, Phys. Lett. 56A, 153 (1976). 8. H. J. Hilhorst, Phys. Rev. B16, 1253 (1977).
7 TABLE CAPTION Table 1  Values obtained for p. X and v for b = 2 and b = 3, c for both definitions of percolating paths. Extrapolated values of p and v are also given.
8 TABLE 1 P c (b«2) P c (b«3) P c <b"~> A (b2) X(b3) v(b=2) v(b»3) v(b**») I II
9 FIGURE CAPTION Figure 1  A b x b cell for a square lattice. Here b = 2. The origin is taken at point 1.
10 31 6 * 2 «7 *6 Figure 1
Backbone and elastic backbone of percolation clusters obtained by the new method of burning
J. Phys. A: Math. Gen. 17 (1984) L261L266. Printed in Great Britain LE ITER TO THE EDITOR Backbone and elastic backbone of percolation clusters obtained by the new method of burning H J HerrmanntS, D
More informationTEXTO PARA DISCUSSÃO N 265 ECONOMIC GROWTH, CONVERGENCE AND QUALITY OF HUMAN CAPITAL FORMATION SYSTEM. Luciano Nakabashi Lízia de Figueiredo
TEXTO PARA DISCUSSÃO N 265 ECONOMIC GROWTH, CONVERGENCE AND QUALITY OF HUMAN CAPITAL FORMATION SYSTEM Luciano Nakabashi Lízia de Figueiredo Junho de 2005 Ficha catalográfica 330.34 N63e 2005 Nakabashi,
More informationCurriculum Vitae. 12/1990 M.Sc., PUC/Rio; Supervisor: Rosane Riera Topics: Statistical Physics; phase transitions and critical phenomena
13 September 2007 Curriculum Vitae Fábio Aarão Reis I. Personal data and contact information Full name: Fábio David Alves Aarão Reis Born 30 May 1966 in Rio de Janeiro, Brazil. Married; one daughter, age
More informationMeasurable inhomogeneities in stock trading volume flow
August 2008 EPL, 83 (2008) 30003 doi: 10.1209/02955075/83/30003 www.epljournal.org Measurable inhomogeneities in stock trading volume flow A. A. G. Cortines, R. Riera and C. Anteneodo (a) Departamento
More informationErasmus Mundus External Cooperation Windows. EUBRAZIL STARTUP Call for applications outcome 08/02/2010
L15a0900007 L15a0900027 L15a0900041 L15a0900051 L15a0900057 L15a0900080 L15a0900081 L15a0900084 L15a0900088 L15a0900090 L15a0900093 L15a0900095 L15a0900096 L15a0900099 L15a0900106 L15a0900107 L15a0900115
More informationRandom spin1 Ising model on a Bethe lattice
Revista Brasileira de Física, Vol. 20, no 1, 1990 Rom spin1 Ising model on a Bethe lattice F.A. da Costa S.R. Salinas Instituto de Física, Universidade de São Paulo, Caiza Postal 20516, São Paulo, 01498,
More informationA Simple Observation Concerning Contraction Mappings
Revista Colombiana de Matemáticas Volumen 46202)2, páginas 229233 A Simple Observation Concerning Contraction Mappings Una simple observación acerca de las contracciones German LozadaCruz a Universidade
More informationA model of multilingual digital library
Ana M. B. Pavani LAMBDA Laboratório de Automação de Museus, Bibliotecas Digitais e Arquivos. Departamento de Engenharia Elétrica Pontifícia Universidade Católica do Rio de Janeiro apavani@lambda.ele.pucrio.br
More informationSpecific heat logperiodicity from multifractal energy spectra
Physics Letters A 318 (2003) 452 456 www.elsevier.com/locate/pla Specific heat logperiodicity from multifractal energy spectra Danyel J.B. Soares a, Marcelo L. Lyra b,, Luciano R. da Silva a a Departamento
More informationCritical Phenomena and Percolation Theory: I
Critical Phenomena and Percolation Theory: I Kim Christensen Complexity & Networks Group Imperial College London Joint CRMImperial College School and Workshop Complex Systems Barcelona 813 April 2013
More informationCorrection Between B and H, and the Analysis of the Magnetization Into Uniaxial Superconductor in the Limit at Large Values of B
ISSN 00293865 CBPF CENTRO BRASILEIRO DE PESQUISAS FÍSICAS Rio de Janeiro Notas de Física CBPFNF031/94 April 1994 Correction Between B and H, and the Analysis of the Magnetization Into Uniaxial Superconductor
More informationRegression Clustering
Chapter 449 Introduction This algorithm provides for clustering in the multiple regression setting in which you have a dependent variable Y and one or more independent variables, the X s. The algorithm
More informationQUALITY KNOWLEDGE INTEGRATION: A BRAZILIAN COMPARISON ANALYSIS
QUALITY KNOWLEDGE INTEGRATION: A BRAZILIAN COMPARISON ANALYSIS Úrsula Maruyama maruyama.academic@hotmail.com CEFET/RJ, Departamento de Ensino e Administração (DEPEA) Av. Maracanã 229, Maracanã CEP 20.271110
More informationElementary Statistics. Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination
Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination What is a Scatter Plot? A Scatter Plot is a plot of ordered pairs (x, y) where the horizontal axis is used
More informationAN ANALYSIS OF THE IMPORTANCE OF APPROPRIATE TIE BREAKING RULES IN DISPATCH HEURISTICS
versão impressa ISSN 01017438 / versão online ISSN 16785142 AN ANALYSIS OF THE IMPORTANCE OF APPROPRIATE TIE BREAKING RULES IN DISPATCH HEURISTICS Jorge M. S. Valente Faculdade de Economia Universidade
More informationMcMurry University Pretest Practice Exam. 1. Simplify each expression, and eliminate any negative exponent(s).
1. Simplify each expression, and eliminate any negative exponent(s). a. b. c. 2. Simplify the expression. Assume that a and b denote any real numbers. (Assume that a denotes a positive number.) 3. Find
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationChapter 29 ScaleFree Network Topologies with Clustering Similar to Online Social Networks
Chapter 29 ScaleFree Network Topologies with Clustering Similar to Online Social Networks Imre Varga Abstract In this paper I propose a novel method to model real online social networks where the growing
More informationDyna ISSN: 00127353 dyna@unalmed.edu.co Universidad Nacional de Colombia Colombia
Dyna ISSN: 00127353 dyna@unalmed.edu.co Universidad Nacional de Colombia Colombia VELÁSQUEZ HENAO, JUAN DAVID; RUEDA MEJIA, VIVIANA MARIA; FRANCO CARDONA, CARLOS JAIME ELECTRICITY DEMAND FORECASTING USING
More informationA boxcovering algorithm for fractal scaling in scalefree networks
CHAOS 17, 026116 2007 A boxcovering algorithm for fractal scaling in scalefree networks J. S. Kim CTP & FPRD, School of Physics and Astronomy, Seoul National University, NS50, Seoul 151747, Korea K.I.
More informationarxiv:condmat/0605535v1 [condmat.statmech] 22 May 2006
Virial coefficients and osmotic pressure in polymer solutions in goodsolvent conditions arxiv:condmat/0605535v1 [condmat.statmech] 22 May 2006 Sergio Caracciolo, Bortolo Matteo Mognetti Dipartimento
More informationPlate waves in phononic crystals slabs
Acoustics 8 Paris Plate waves in phononic crystals slabs J.J. Chen and B. Bonello CNRS and Paris VI University, INSP  14 rue de Lourmel, 7515 Paris, France chen99nju@gmail.com 41 Acoustics 8 Paris We
More informationAppendix E: Graphing Data
You will often make scatter diagrams and line graphs to illustrate the data that you collect. Scatter diagrams are often used to show the relationship between two variables. For example, in an absorbance
More informationUnit 7 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationPreCalculus Notes Vertical, Horizontal, and Slant Asymptotes of Rational Functions
PreCalculus Notes Vertical, Horizontal, and Slant Asymptotes of Rational Functions A) Vertical Asymptotes A rational function, in lowest terms, will have vertical asymptotes at the real zeros of the denominator
More informationMonte Carlo Simulation technique. S. B. Santra Department of Physics Indian Institute of Technology Guwahati
Monte Carlo Simulation technique S. B. Santra Department of Physics Indian Institute of Technology Guwahati What is Monte Carlo (MC)? Introduction Monte Carlo method is a common name for a wide variety
More informationTHE SELFAVOIDING WALK
THE SELFAVOIDING WALK A report Submitted to the Department of Mathematics and Statistics In Partial Fulfillment of the Requirements for the Degree of Master of Science In Statistics University of Regina
More informationA signature of power law network dynamics
Classification: BIOLOGICAL SCIENCES: Computational Biology A signature of power law network dynamics Ashish Bhan* and Animesh Ray* Center for Network Studies Keck Graduate Institute 535 Watson Drive Claremont,
More informationAlgebra Graphing an Exponential Function
Graphing an Exponential Function Graphing an exponential or logarithmic function is a process best described by example. Each step of the process is described and illustrated in the examples over the next
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More information3. Examples of discrete probability spaces.. Here α ( j)
3. EXAMPLES OF DISCRETE PROBABILITY SPACES 13 3. Examples of discrete probability spaces Example 17. Toss n coins. We saw this before, but assumed that the coins are fair. Now we do not. The sample space
More informationProblem of the Month: Fair Games
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationChapter 7. Lyapunov Exponents. 7.1 Maps
Chapter 7 Lyapunov Exponents Lyapunov exponents tell us the rate of divergence of nearby trajectories a key component of chaotic dynamics. For one dimensional maps the exponent is simply the average
More informationLesson 18 Student Outcomes Lesson Notes
Lesson 18 Analyzing Residuals Student Outcomes Students use a graphing calculator to construct the residual plot for a given data set. Students use a residual plot as an indication of whether or not the
More informationScience Education in the Americas. Lessons from the experience and the role of the Academies
Science Education in the Americas Lessons from the experience and the role of the Academies The Brazilian experience Programa ABC na Educação Científica Mão na Massa (ABC in Science Education Hands On
More informationHYBRID INTELLIGENT SUITE FOR DECISION SUPPORT IN SUGARCANE HARVEST
HYBRID INTELLIGENT SUITE FOR DECISION SUPPORT IN SUGARCANE HARVEST FLÁVIO ROSENDO DA SILVA OLIVEIRA 1 DIOGO FERREIRA PACHECO 2 FERNANDO BUARQUE DE LIMA NETO 3 ABSTRACT: This paper presents a hybrid approach
More information4. Right click grid ( ) and select New MODFLOW, then select Packages, enabling both the optional Well and Recharge option.
Groundwater Hydrology CE 40460 Example 1  Grid Approach Building a grid is the first step in creating a groundwater model using GMS, and it requires the following components: top and bottom elevations,
More informationEssential Question: What is the relationship among the focus, directrix, and vertex of a parabola?
Name Period Date: Topic: 93 Parabolas Essential Question: What is the relationship among the focus, directrix, and vertex of a parabola? Standard: GGPE.2 Objective: Derive the equation of a parabola
More informationCluster analysis with SPSS: KMeans Cluster Analysis
analysis with SPSS: KMeans Analysis analysis is a type of data classification carried out by separating the data into groups. The aim of cluster analysis is to categorize n objects in k (k>1) groups,
More informationcorrectchoice plot f(x) and draw an approximate tangent line at x = a and use geometry to estimate its slope comment The choices were:
Topic 1 2.1 mode MultipleSelection text How can we approximate the slope of the tangent line to f(x) at a point x = a? This is a Multiple selection question, so you need to check all of the answers that
More informationNotas de Ffsica CBPF CENTRO BRASILEIRO DE PESQUISAS FÍSICAS CBPFNF079/83 THE FALL IN THE RATE OF DEATH FROM HEART DISEASES.
ISSN 002B3865 CBPF CENTRO BRASILEIRO DE PESQUISAS FÍSICAS Notas de Ffsica CBPFNF079/83 THE FALL IN THE RATE OF DEATH FROM HEART DISEASES by George Bemski RIO D JANEIRO 1983 I" NOTAS DE FÍSICA ê uma
More informationAPPLICATIONS OF DIFFERENTIATION
4 APPLICATIONS OF DIFFERENTIATION APPLICATIONS OF DIFFERENTIATION So far, we have been concerned with some particular aspects of curve sketching: Domain, range, and symmetry (Chapter 1) Limits, continuity,
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
More informationPrecalculus A 2016 Graphs of Rational Functions
37 Precalculus A 2016 Graphs of Rational Functions Determine the equations of the vertical and horizontal asymptotes, if any, of each function. Graph each function with the asymptotes labeled. 1. ƒ(x)
More informationCURRICULUM VITAE. Marcos Lima
CURRICULUM VITAE Marcos Lima Current Address Department of Physics & Astronomy Tel: (215) 8980790 University of Pennsylvania Fax: (215) 8982010 209 South 33rd St., DRL 4N4 mlima@sas.upenn.edu Philadelphia,
More informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
More informationPrecise determination of the critical threshold and exponents in a threedimensional continuum percolation model
J. Phys. A: Math. Gen. 30 (1997) L585 L592. Printed in the UK PII: S03054470(97)842801 LETTER TO THE EDITOR Precise determination of the critical threshold and exponents in a threedimensional continuum
More informationMATHEMATICS OF FINANCE AND INVESTMENT
MATHEMATICS OF FINANCE AND INVESTMENT G. I. FALIN Department of Probability Theory Faculty of Mechanics & Mathematics Moscow State Lomonosov University Moscow 119992 g.falin@mail.ru 2 G.I.Falin. Mathematics
More informationPlotting Likert and Other Rating Scales
Plotting Likert and Other Rating Scales Naomi B. Robbins 1, Richard M. Heiberger 2 1 NBR, 11 Christine Court, Wayne, NJ 074706523 2 Temple University, 332 Speakman Hall (00612), Philadelphia, PA 191226083
More informationComputer programming course in the Department of Physics, University of Calcutta
Computer programming course in the Department of Physics, University of Calcutta Parongama Sen with inputs from Prof. S. Dasgupta and Dr. J. Saha and feedback from students Computer programming course
More informationFrom Unknown to Known Impacts of Organizational Changes on Sociotechnical Systems
From Unknown to Known Impacts of Organizational Changes on Sociotechnical Systems Marília Guterres Ferreira 1, 2, Neil Maiden 2, Julio Cesar Sampaio do Prado Leite 1 1 Pontifícia Universidade Católica
More informationThe name of the authors and universities are just an example. Edited with Br.Office 3.2, January 6th 2011.
The name of the authors and universities are just an example. Edited with Br.Office 3.2, January 6 th 2011. For the final version, everything written in blue should be erased TíTULO EM LETRAS MAIÚSCULAS
More informationPerformance of networks containing both MaxNet and SumNet links
Performance of networks containing both MaxNet and SumNet links Lachlan L. H. Andrew and Bartek P. Wydrowski Abstract Both MaxNet and SumNet are distributed congestion control architectures suitable for
More informationStatTools Assignment #1, Winter 2007 This assignment has three parts.
StatTools Assignment #1, Winter 2007 This assignment has three parts. Before beginning this assignment, be sure to carefully read the General Instructions document that is located on the StatTools Assignments
More informationComplexity and Completeness of Finding Another Solution and Its Application to Puzzles
yato@is.s.utokyo.ac.jp seta@is.s.utokyo.ac.jp Π (ASP) Π x s x s ASP Ueda Nagao n nasp parsimonious ASP ASP NP Complexity and Completeness of Finding Another Solution and Its Application to Puzzles Takayuki
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 15 scale to 0100 scores When you look at your report, you will notice that the scores are reported on a 0100 scale, even though respondents
More informationTHE COST OF COLLEGE EDUCATION PROJECT PACKET
THE COST OF COLLEGE EDUCATION PROJECT PACKET Introduction We live in a society where a college education is considered the norm and not the exception. While everyone is expected to attend a college or
More informationISA Guide For Additional and triple Science. By Mr J Kenny
ISA Guide For Additional and triple Science By Mr J Kenny Section 1 There are usually 5 questions. Questions 1, 2, 3 and 5 are generally very similar and examples are given below. Question 1 Write down
More informationBelo Horizonte and Rio de Janeiro, October 15th 2015
Belo Horizonte and Rio de Janeiro, October 15th 2015 Minas Gerais: a large and important state 226,000 square miles (Larger than France or Spain) 20 million people (Comparable to Australia) 2 nd largest
More informationFísica Computacional Conceptos de programación.
Física Computacional Conceptos de programación. F. A. VelázquezMuñoz Departamento de Física CUCEI UdeG 6 de febrero de 2015 Sistemas Operativos msdos windows linux suse; redhat; ubuntu; etc. unix Mac
More informationModel MONTE CARLO SIMULATION OF ADSORPTION OF DIBLOCK COPOLYMERS. Introduction
431 MONTE CARLO SIMULATION OF ADSORPTION OF DIBLOCK COPOLYMERS WAN Y. SHIH, WEIItENG SHill, and ILHAN A. AKSAY Department ofmateria Is Science and Engineering, and Advanced Materials Technology Program,
More informationA Coefficient of Variation for Skewed and HeavyTailed Insurance Losses. Michael R. Powers[ 1 ] Temple University and Tsinghua University
A Coefficient of Variation for Skewed and HeavyTailed Insurance Losses Michael R. Powers[ ] Temple University and Tsinghua University Thomas Y. Powers Yale University [June 2009] Abstract We propose a
More informationALGEBRA I A PLUS COURSE OUTLINE
ALGEBRA I A PLUS COURSE OUTLINE OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines of Best
More informationMultivariate Normal Distribution
Multivariate Normal Distribution Lecture 4 July 21, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #47/21/2011 Slide 1 of 41 Last Time Matrices and vectors Eigenvalues
More informationThe Power (Law) of Indian Markets: Analysing NSE and BSE Trading Statistics
The Power (Law) of Indian Markets: Analysing NSE and BSE Trading Statistics Sitabhra Sinha and Raj Kumar Pan The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai  6 113, India. sitabhra@imsc.res.in
More informationDRAFT. Algebra 1 EOC Item Specifications
DRAFT Algebra 1 EOC Item Specifications The draft Florida Standards Assessment (FSA) Test Item Specifications (Specifications) are based upon the Florida Standards and the Florida Course Descriptions as
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More informationUniform Multicommodity Flow through the Complete Graph with Random Edgecapacities
Combinatorics, Probability and Computing (2005) 00, 000 000. c 2005 Cambridge University Press DOI: 10.1017/S0000000000000000 Printed in the United Kingdom Uniform Multicommodity Flow through the Complete
More informationarxiv: v1 [physics.genph] 10 Jul 2015
Infinite circuits are easy. How about long ones? Mikhail Kagan, Xinzhe Wang Penn State Abington arxiv:507.08v [physics.genph] 0 Jul 05 Abstract We consider a long but finite ladder) circuit with alternating
More informationTutorial 2: Using Excel in Data Analysis
Tutorial 2: Using Excel in Data Analysis This tutorial guide addresses several issues particularly relevant in the context of the level 1 Physics lab sessions at Durham: organising your work sheet neatly,
More informationDrawing a histogram using Excel
Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to
More informationIOWA STATE UNIVERSITY Department of Community and Regional Planning
IOWA STATE UNIVERSITY Department of Community and Regional Planning CRP274 PLANNING ANALYSIS AND TECHNIQUES II INTRODUCTION TO EXCEL FOR WINDOWS 1 Basic Components of Spreadsheet 1.1 Worksheet An Excel
More informationarxiv:condmat/9910374v1 [condmat.statmech] 23 Oct 1999
accepted for publication in Physical Review E. 1 Moment analysis of the probability distributions of different sandpile models arxiv:condmat/9910374v1 [condmat.statmech] 23 Oct 1999 S. Lübeck Theoretische
More informationarxiv:hepth/0507236v1 25 Jul 2005
Non perturbative series for the calculation of one loop integrals at finite temperature Paolo Amore arxiv:hepth/050736v 5 Jul 005 Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo
More informationHigh School Algebra 1 Common Core Standards & Learning Targets
High School Algebra 1 Common Core Standards & Learning Targets Unit 1: Relationships between Quantities and Reasoning with Equations CCS Standards: Quantities NQ.1. Use units as a way to understand problems
More informationResearch on information propagation analyzing odds in horse racing
Challenges for Analysis of the Economy, the Businesses, and Social Progress Péter Kovács, Katalin Szép, Tamás Katona (editors)  Reviewed Articles Research on information propagation analyzing odds in
More informationBorel type bounds for the selfavoiding walk connective constant
Borel type bounds for the selfavoiding walk connective constant B T Graham DMA École Normale Supérieure, 45 rue d Ulm, 75230 Paris Cedex 5, France Email: graham@dma.ens.fr Abstract. Let µ be the selfavoiding
More informationXLVI Pesquisa Operacional na Gestão da Segurança Pública
SIZING AND SCHEDULING RESOURCES: A DECISION SUPPORT SYSTEM APPLIED TO OIL RIGS SCHEDULING Luiza Cavalcanti Marques Pontifícia Universidade Católica (PUCRio) Rua Marquês de São Vicente, 225  Gávea, Rio
More informationBasic Pivot Tables. To begin your pivot table, choose Data, Pivot Table and Pivot Chart Report. 1 of 18
Basic Pivot Tables Pivot tables summarize data in a quick and easy way. In your job, you could use pivot tables to summarize actual expenses by fund type by object or total amounts. Make sure you do not
More informationClassification of Fingerprints. Sarat C. Dass Department of Statistics & Probability
Classification of Fingerprints Sarat C. Dass Department of Statistics & Probability Fingerprint Classification Fingerprint classification is a coarse level partitioning of a fingerprint database into smaller
More informationEXPERIMENT 6 OPTICS: FOCAL LENGTH OF A LENS
EXPERIMENT 6 OPTICS: FOCAL LENGTH OF A LENS The following website should be accessed before coming to class. Text reference: pp189196 Optics Bench a) For convenience of discussion we assume that the light
More informationA simple analysis of the TV game WHO WANTS TO BE A MILLIONAIRE? R
A simple analysis of the TV game WHO WANTS TO BE A MILLIONAIRE? R Federico Perea Justo Puerto MaMaEuSch Management Mathematics for European Schools 94342  CP  12001  DE  COMENIUS  C21 University
More informationPROJETO DE EDUCAÇÃO SUPERIOR A DISTÂNCIA NA ÁREA DA INFORMÁTICA
PROJETO DE EDUCAÇÃO SUPERIOR A DISTÂNCIA NA ÁREA DA INFORMÁTICA 1 04/2005 186TCB3 Mauro Faccioni Filho UNISUL Universidade do Sul de Santa Catarina faccioni@unisul.br Categoria B Conteúdos e Habilidades
More informationReview on Using Packages to Enhance the Teaching of Critical Path Networks
Review on Using Packages to Enhance the Teaching of Critical Path Networks Harry S Ku Abstract The aim of this paper is to review a published paper, Using computer software packages to enhance the teaching
More informationemission process Fundação Universidade Federal do Vale do São Francisco  UNIVASF, C. Postal 309, 48900000, Juazeiro  BA, Brazil;
CBPFNF1/9 1 O resonant structure evaluated by twoproton emission process T. N. Leite 1, N. Teruya, A. Dimarco 3, S. B. Duarte 4, O. A. P. Tavares 4 and M. Gonçalves 5 1 Colegiado de Engenharia Civil,
More informationTranslating WFS Query to SQL/XML Query
Translating WFS Query to SQL/XML Query Vânia Vidal, Fernando Lemos, Fábio Feitosa Departamento de Computação Universidade Federal do Ceará (UFC) Fortaleza CE Brazil {vvidal, fernandocl, fabiofbf}@lia.ufc.br
More information6. LECTURE 6. Objectives
6. LECTURE 6 Objectives I understand how to use vectors to understand displacement. I can find the magnitude of a vector. I can sketch a vector. I can add and subtract vector. I can multiply a vector by
More informationObjectives: To graph exponential functions and to analyze these graphs. None. The number A can be any real constant. ( A R)
CHAPTER 2 LESSON 2 Teacher s Guide Graphing the Eponential Function AW 2.6 MP 2.1 (p. 76) Objectives: To graph eponential functions and to analyze these graphs. Definition An eponential function is a function
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More informationCycle transversals in bounded degree graphs
Electronic Notes in Discrete Mathematics 35 (2009) 189 195 www.elsevier.com/locate/endm Cycle transversals in bounded degree graphs M. Groshaus a,2,3 P. Hell b,3 S. Klein c,1,3 L. T. Nogueira d,1,3 F.
More informationII MiniWorkshop in Partial Differential Equations
Campus de São José do Rio Preto Programa de PósGraduação em Matemática (PPGMATUNESP) II MiniWorkshop in Partial Differential Equations August 162013 Program: 10:0010:30 Fluidos micropolares com dados
More informationCompetitive Analysis of On line Randomized Call Control in Cellular Networks
Competitive Analysis of On line Randomized Call Control in Cellular Networks Ioannis Caragiannis Christos Kaklamanis Evi Papaioannou Abstract In this paper we address an important communication issue arising
More informationGranny s Balloon Trip
Granny s Balloon Trip This problem gives you the chance to: represent data using tables and graphs On her eightieth birthday, Sarah s granny went for a trip in a hot air balloon. This table shows the schedule
More informationdiffy boxes (iterations of the ducci four number game) 1
diffy boxes (iterations of the ducci four number game) 1 Peter Trapa September 27, 2006 Begin at the beginning and go on till you come to the end: then stop. Lewis Carroll Consider the following game.
More informationRational functions are defined for all values of x except those for which the denominator hx ( ) is equal to zero. 1 Function 5 Function
Section 4.6 Rational Functions and Their Graphs Definition Rational Function A rational function is a function of the form that h 0. f g h where g and h are polynomial functions such Objective : Finding
More informationCourse Name: Course Code: ALEKS Course: Instructor: Course Dates: Course Content: Textbook: Dates Objective Prerequisite Topics
Course Name: MATH 1204 Fall 2015 Course Code: N/A ALEKS Course: College Algebra Instructor: Master Templates Course Dates: Begin: 08/22/2015 End: 12/19/2015 Course Content: 271 Topics (261 goal + 10 prerequisite)
More informationFunctional Skills Mathematics Level 1 sample assessment
Functional Skills Mathematics Level 1 sample assessment Marking scheme www.cityandguilds.com September 2011 Version 1.0 Sample paper 1 Task 1 Total marks 1A 3 1B 4 1C 2 1D 2 Marks Functional Maths Level
More informationHow To Run Statistical Tests in Excel
How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting
More information