Macromolecules 2003, 36,
|
|
- Hugh Burke
- 5 years ago
- Views:
Transcription
1 Cyclic AFT/MADIX CT Agets by obert B. Logi rlogicosultig.com Cyclic AFT CTA's ca polymerize viyl moomers ito cyclic polymers. Cyclic polymers because of their uique properties compared to their liear couterparts iclude reduced hydrodyamic volume, lower itrisic viscosity ad distictive fluorescece ehacemet, higher Tg, higher refractive idex. Cyclic polymers exhibit edless topologically with more striget restrictios o the backboe coformatio ad the absece of chai eds (JUNAL F PLYME CIENCE, PAT A: PLYME CHEMITY 2016, 54, ). Macromolecules 2003, 36,
2
3 Moad et. al. Aust. J. Chem. 2009, 62, The above were really the few refereces I foud for AFT rig expasio polymerizatio(ep). They appear to require a macrocycle CTA so that rig strai is ot
4 a factor or ca rig strai ehace the polymerizatio? To explai my ideas the followig figures are referred to: ythesis of the 4,5-Dipheyl-1,3-oxathiolae-2-thioe moomer i 86% yield: I. Yavari - Me C 2 " Base + + Pheyl derivatives are show but other derivatives are possible X Y
5 et. al. ylett 2008(6), The facile reactio of C2 with epoxides is the reaso I'm iterested i this xathate's MADIX potetial. The reaso for the 1,2 epoxy derivative is that the reactio affords the uwated isomer (5 positio) if a moo-substituted epoxide is employed (ther sythesis routes could be proposed that would afford the moo derivative attached to the 4-carbo ext to sulfur). This 4 substituet however must be capable of stabilizig radicals that are reactive eough to start the MADIX polymerizatio. The bezyl group is kow to do this. The iitial small amout of added iitiator adds to the 2-thioe group, the geerates the carbo radical stabilized by the bezyl group(hog et. al. show above is a example). More detailed explaatio of AFT/MADIX ca be foud i several reviews such as D.J. Kiddie et. al. Macromol. 2012, 45, efereces for Xathate sythesis: N. Kihara et. al. JC 1995, 60, Maggi et. al. ythesis 2008(1), W. Clegg et. al. JC 2010, 75, Y. Taguchi et. al. Bull. oc. Jp., 61, (1988). W. Choi et. al. Macromolecules, 1998, 31, My idea is to use this type of cyclic xathates i AFT/MADIX CTA polymerizatio. With the above CTA's, the polymerizatio could possibly go two ways; cyclic formatio of a macrocyclic or a cyclicpolymer cotaiig multiple xathate moieties. X ad Y are attached i a very large macrocycle. ca be from the various moomers such as NVP, Vac, MA, MMA etc. that could be employed i this polymerizatio. What follows is what should be a example of this idea.
6 Macromolecular apid Commuicatios; oriao-moro et. al. I do't uderstad why the bezyl group does't stabilize the carbo radical? ly 4 refereces cited this referece, idicatig to me that the above iterpretatio of the reactio was ot of iterest or valid. If their iterpretatio is correct the they would have to idicate what's at the other ed of the polystyree? The termial of the polymer would be hard to distiguish with all the styree pheyls if ideed it was a bezyl i possibly a cyclic motif? ice o attempt to try this CTA with MMA etc. which would clearly show the termial moiety if it was bezyl; therefore, I believe my iterpretatio is valid. However their sythesis of the dithiolactoe itself is useful. Here's what the experts say! Aust. J. Chem. 2009, 62, The thiolactoe 19 was proposed to cotrol the polymerizatio of t by a similar additio fragmetatio process (cheme 2).[83] The mechaism as show seems ulikely sice, for cotrol, most of the propagatig species would eed to be preset as
7 the dormat species 21. E experimets showed that a high cocetratio of radicals were ot preset durig polymerizatio. The mechaism would suggest that the fial product should also have structure 21. Clearly this is ot the case. Numerous refereces clearly show the geeratio ad stability of the bezyl's group's iteractio with the carbo radical ad its ability to start the MADIX polymerizatio, the same mechaism should be at play here also. Livig Catioic Cyclic Polymerizatio ecetly several very iterestig papers have appeared cocerig the applicatio of AFT CTA's that work with catioic CLP. With the AFT aget, block polymers of viyl ethers are easily sythesized, ot oly that but catioic followed by CP polymerizatio is possible.
8 Although these papers illustrate how selected AFT CTA's ca be used, I could ot fid ay example of their use to form cyclic polymers of viyl ethers. Cosiderig my previous paper cocerig cyclic AFT CTA's, it would seem obvious that or similar AFT CTA's would result i well cotrolled catioic cyclic polymerizatio. I ca visualize several iterestig applicatios for cyclic catioic polymerizatio. I aalogy with the crow ethers, cyclic methyl viyl ether or other VE's or mixtures or CP followig catioic ca all be accomplished with AFT/MADIX CTA's. uch large macrocycles havig ether groups, for example, projectig i or out of the cyclic chai would have uusual complexig behavior. Coductig said catioic polymerizatio i the presece of a complexig aget should cotrol orietatio of the ether groups much like a catio cotrols the preparatio of crow ethers. VE VE H + H H ather tha draw all AFT/MADIX CTA possibilities, the above are suggested.
9 Cyclic catioic polymerizatio followed by CP would afford copolymers of MVE ad NVP for example (may moomer combiatios are obviously possible), that would lead to cyclics exhibitig uique complexig ability. Fluorie derivatives might eve have use as blood substitutes. I hope you foud these proposals iterestig. Thaks for readig! Dr. obert B. Logi, rlogicosultig.com
Free Radical Polymerization
Free Radical Polymerizatio Referece: Aspe Polymers: Uit Operatios ad Reactio Models, Aspe Techology, Ic., 2013. 1. Itroductio The free-radical bulk/solutio polymerizatio model is applicable to bulk ad
More informationPolymerization Lab p. 1 Polymerization Lab
Polymerizatio Lab p. 1 Polymerizatio Lab Itroductio: Polymers (Greek-PLY...may ad MES...parts) have existed sice the begiig of life. Both "atural" ad "sythetic" polymers are a itegral part of our life.
More informationRecurrence Relations
Recurrece Relatios Aalysis of recursive algorithms, such as: it factorial (it ) { if (==0) retur ; else retur ( * factorial(-)); } Let t be the umber of multiplicatios eeded to calculate factorial(). The
More informationPOLYMERS
POLYMERS Short Aswer Questios: **1.What is PHBV? How is it useful to ma? As. PHBV is Poly β-hydroxy butyrate-co- β-hydroxy valerate.it is a biodegradable polymer. It is used i speciality packig, orthopaedic
More informationPolymerization of Glycidyl Nitrate via Catalysis with BF3 THF : Compatibility with the Activated Monomer (AM) Mechanism
ATK THIKL INC Polymerizatio of Glycidyl Nitrate via Catalysis with BF3 THF : Compatibility with the Activated Moomer (AM) Mechaism Prepared For 2004 IM/EM Techical Symposium November 15-17, 2004 Sa Fracisco,
More informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationKinetics of Complex Reactions
Kietics of Complex Reactios by Flick Colema Departmet of Chemistry Wellesley College Wellesley MA 28 wcolema@wellesley.edu Copyright Flick Colema 996. All rights reserved. You are welcome to use this documet
More informationBertrand s Postulate
Bertrad s Postulate Lola Thompso Ross Program July 3, 2009 Lola Thompso (Ross Program Bertrad s Postulate July 3, 2009 1 / 33 Bertrad s Postulate I ve said it oce ad I ll say it agai: There s always a
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationCALCULATION OF FIBONACCI VECTORS
CALCULATION OF FIBONACCI VECTORS Stuart D. Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithaca.edu ad Dai Novak Departmet of Mathematics, Ithaca College
More information1 Generating functions for balls in boxes
Math 566 Fall 05 Some otes o geeratig fuctios Give a sequece a 0, a, a,..., a,..., a geeratig fuctio some way of represetig the sequece as a fuctio. There are may ways to do this, with the most commo ways
More information6.3 Testing Series With Positive Terms
6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial
More informationChemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics
Chemical Kietics CHAPTER 14 Chemistry: The Molecular Nature of Matter, 6 th editio By Jesperso, Brady, & Hyslop CHAPTER 14 Chemical Kietics Learig Objectives: Factors Affectig Reactio Rate: o Cocetratio
More informationSamples questions on Polymer Chemistry
Samples questios o Polymer Chemistry Symbols carry usual meaigs Module 1: Lecture 1-3 1. For a polydisperse polymer sample rak the M, M w, M z, ad M v accordig to their values. I 10 g of a polystyree sample
More informationNew Boronate Monomers and Polymers By: Robert B. Login (rloginconsulting.com)
ew oroate Moomers ad Polymers y: obert. Logi (rlogicosultig.com) oroate ester techology is of great iterest because esterificatio of boroic acid is spotaeous but is readily reversible ad this is especially
More information9.4.3 Fundamental Parameters. Concentration Factor. Not recommended. See Extraction factor. Decontamination Factor
9.4.3 Fudametal Parameters Cocetratio Factor Not recommeded. See Extractio factor. Decotamiatio Factor The ratio of the proportio of cotamiat to product before treatmet to the proportio after treatmet.
More informationCHEE 221: Chemical Processes and Systems
CHEE 221: Chemical Processes ad Systems Module 3. Material Balaces with Reactio Part a: Stoichiometry ad Methodologies (Felder & Rousseau Ch 4.6 4.8 ot 4.6c ) Material Balaces o Reactive Processes What
More informationTowards the Development of a High-spin Organic Polymer
Appedix II: Towards the Developmet of a High-spi rgaic Polymer 194 II.1 Itroductio The developmet of pure orgaic materials with ferromagetic properties is of log stadig theoretical ad experimetal iterest.
More informationMaterial Balances on Reactive Processes F&R
Material Balaces o Reactive Processes F&R 4.6-4.8 What does a reactio do to the geeral balace equatio? Accumulatio = I Out + Geeratio Cosumptio For a reactive process at steady-state, the geeral balace
More informationNernst Equation. Nernst Equation. Electric Work and Gibb's Free Energy. Skills to develop. Electric Work. Gibb's Free Energy
Nerst Equatio Skills to develop Eplai ad distiguish the cell potetial ad stadard cell potetial. Calculate cell potetials from kow coditios (Nerst Equatio). Calculate the equilibrium costat from cell potetials.
More informationChapter 6 Part 5. Confidence Intervals t distribution chi square distribution. October 23, 2008
Chapter 6 Part 5 Cofidece Itervals t distributio chi square distributio October 23, 2008 The will be o help sessio o Moday, October 27. Goal: To clearly uderstad the lik betwee probability ad cofidece
More informationSNAP Centre Workshop. Basic Algebraic Manipulation
SNAP Cetre Workshop Basic Algebraic Maipulatio 8 Simplifyig Algebraic Expressios Whe a expressio is writte i the most compact maer possible, it is cosidered to be simplified. Not Simplified: x(x + 4x)
More informationOptimization Methods: Linear Programming Applications Assignment Problem 1. Module 4 Lecture Notes 3. Assignment Problem
Optimizatio Methods: Liear Programmig Applicatios Assigmet Problem Itroductio Module 4 Lecture Notes 3 Assigmet Problem I the previous lecture, we discussed about oe of the bech mark problems called trasportatio
More informationChapter 2. Aromatic Polyketones from α-aminonitriles
hapter 2 Aromatic Polyketoes from α-amioitriles 2.1 ythesis of α-amioitriles α-amioitriles 1 are a class of compouds which cotai the amie ad itrile fuctioal groups o the same carbo. The geeral structure
More information11 Hidden Markov Models
Hidde Markov Models Hidde Markov Models are a popular machie learig approach i bioiformatics. Machie learig algorithms are preseted with traiig data, which are used to derive importat isights about the
More informationSEMICONDUCTING POLYMERS WITH ROTAXANE ARCHITECTURE
Joural of Optoelectroics ad Advaced Materials Vol. 2, No. 5, 2000, p. 525-530 Sectio 2: Orgaic materials SEMICONDUCTING POLYMERS WITH ROTAXANE ARCHITECTURE "P. Poi" Istitute of Macromolecular Chemistry,
More informationWhat Is Required? You need to determine the hydronium ion concentration in an aqueous solution. K w = [H 3 O + ][OH ] =
Calculatig the [H3O + ] or [OH ] i Aqueous Solutio (Studet textbook page 500) 11. The cocetratio of hydroxide ios, OH (aq), i a solutio at 5C is 0.150 /. Determie the cocetratio of hydroium ios, H 3 O
More informationCHAPTER I: Vector Spaces
CHAPTER I: Vector Spaces Sectio 1: Itroductio ad Examples This first chapter is largely a review of topics you probably saw i your liear algebra course. So why cover it? (1) Not everyoe remembers everythig
More informationBeurling Integers: Part 2
Beurlig Itegers: Part 2 Isomorphisms Devi Platt July 11, 2015 1 Prime Factorizatio Sequeces I the last article we itroduced the Beurlig geeralized itegers, which ca be represeted as a sequece of real umbers
More informationFacile Chain-End Modification of RAFT Polymers
Facile Chai-Ed Modificatio of RAFT Polymers helby hakel CC Chemistry, UCB Emre Discekici Read de Alaiz Group, Chemistry ad Biochemistry MARC U-TAR, NIH Importace of Modificatio Importace of Modificatio
More information4.3 Growth Rates of Solutions to Recurrences
4.3. GROWTH RATES OF SOLUTIONS TO RECURRENCES 81 4.3 Growth Rates of Solutios to Recurreces 4.3.1 Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer.
More informationRADICAL EXPRESSION. If a and x are real numbers and n is a positive integer, then x is an. n th root theorems: Example 1 Simplify
Example 1 Simplify 1.2A Radical Operatios a) 4 2 b) 16 1 2 c) 16 d) 2 e) 8 1 f) 8 What is the relatioship betwee a, b, c? What is the relatioship betwee d, e, f? If x = a, the x = = th root theorems: RADICAL
More informationComplexation Reactions and Titrations
Chapter 17 Complexatio Reactios ad Titratios Lewis acid-base cocept Lewis acid electro pair acceptor [metal catios, M + ] Lewis base electro pair door [ligad, molecules or ios] Coordiate covalet bod a
More informationPolynomials with Rational Roots that Differ by a Non-zero Constant. Generalities
Polyomials with Ratioal Roots that Differ by a No-zero Costat Philip Gibbs The problem of fidig two polyomials P(x) ad Q(x) of a give degree i a sigle variable x that have all ratioal roots ad differ by
More information11. FINITE FIELDS. Example 1: The following tables define addition and multiplication for a field of order 4.
11. FINITE FIELDS 11.1. A Field With 4 Elemets Probably the oly fiite fields which you ll kow about at this stage are the fields of itegers modulo a prime p, deoted by Z p. But there are others. Now although
More informationSILICA NANOPARTICLES PRODUCED BY THERMAL ARC PLASMA. MODELLING
Joural of Optoelectroics ad Advaced Materials Vol. 5, No. 3, September 003, p. 679-686 SILICA NANOPARTICLES PRODUCED BY THERMAL ARC PLASMA. MODELLING E. Balabaova * Istitute of Electroics, Bulgaria Academy
More informationOptimization Methods MIT 2.098/6.255/ Final exam
Optimizatio Methods MIT 2.098/6.255/15.093 Fial exam Date Give: December 19th, 2006 P1. [30 pts] Classify the followig statemets as true or false. All aswers must be well-justified, either through a short
More informationCALCULATING FIBONACCI VECTORS
THE GENERALIZED BINET FORMULA FOR CALCULATING FIBONACCI VECTORS Stuart D Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithacaedu ad Dai Novak Departmet
More informationThe axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c.
5.4 Applicatio of Perturbatio Methods to the Dispersio Model for Tubular Reactors The axial dispersio model for tubular reactors at steady state ca be described by the followig equatios: d c Pe dz z =
More information11.6 Absolute Convergence and the Ratio and Root Tests
.6 Absolute Covergece ad the Ratio ad Root Tests The most commo way to test for covergece is to igore ay positive or egative sigs i a series, ad simply test the correspodig series of positive terms. Does
More informationA representation approach to the tower of Hanoi problem
Uiversity of Wollogog Research Olie Departmet of Computig Sciece Workig Paper Series Faculty of Egieerig ad Iformatio Scieces 98 A represetatio approach to the tower of Haoi problem M. C. Er Uiversity
More informationMOTION. The easy stuff; The gaseous state - Translational motion. The crystalline state - Oscillations about a Mean position.
The easy stuff; MOTION The gaseous state - Traslatioal motio The crystallie state - Oscillatios about a Mea positio The hard stuff; The liquid state - Coupled motios MOTION IN POLYMERS LARGE SCALE MOTION
More informationHomework 3. = k 1. Let S be a set of n elements, and let a, b, c be distinct elements of S. The number of k-subsets of S is
Homewor 3 Chapter 5 pp53: 3 40 45 Chapter 6 p85: 4 6 4 30 Use combiatorial reasoig to prove the idetity 3 3 Proof Let S be a set of elemets ad let a b c be distict elemets of S The umber of -subsets of
More informationALDEHYDES AND KETONES
ALDEHYDES AND KETONES Itroductio The group C=O is kow as carboyl group. This group is foud i aldehydes, ketoes, carboxylic acids, esters ad acid derivatives. I this group carbo atom makes sp hybridizatio.
More informationDiels-Alder Reactions of Furan By: Robert B. Login rloginconsulting.com
Diels-Alder eactios of Fura By: obert B. Logi rlogicosultig.com eversible DA eactios: DA reversible reactios of furas ad maleimides are a type of click reactio that ca proceed at some lower temperature
More informationStochastic Matrices in a Finite Field
Stochastic Matrices i a Fiite Field Abstract: I this project we will explore the properties of stochastic matrices i both the real ad the fiite fields. We first explore what properties 2 2 stochastic matrices
More informationA New Recursion for Space-Filling Geometric Fractals
A New Recursio for Space-Fillig Geometric Fractals Joh Shier Abstract. A recursive two-dimesioal geometric fractal costructio based upo area ad perimeter is described. For circles the radius of the ext
More informationAME 513. " Lecture 3 Chemical thermodynamics I 2 nd Law
AME 513 Priciples of Combustio " Lecture 3 Chemical thermodyamics I 2 d Law Outlie" Why do we eed to ivoke chemical equilibrium? Degrees Of Reactio Freedom (DORFs) Coservatio of atoms Secod Law of Thermodyamics
More informationRoberto s Notes on Infinite Series Chapter 1: Sequences and series Section 3. Geometric series
Roberto s Notes o Ifiite Series Chapter 1: Sequeces ad series Sectio Geometric series What you eed to kow already: What a ifiite series is. The divergece test. What you ca le here: Everythig there is to
More informationELE B7 Power Systems Engineering. Symmetrical Components
ELE B7 Power Systems Egieerig Symmetrical Compoets Aalysis of Ubalaced Systems Except for the balaced three-phase fault, faults result i a ubalaced system. The most commo types of faults are sigle liegroud
More informationMiscellaneous Notes. Lecture 19, p 1
Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before oo, Thur, Apr. 25. The PHYS 213 fial exam times are * 8-10 AM, Moday, May 6 * 1:30-3:30 PM, Wed, May 8 The
More informationNICK DUFRESNE. 1 1 p(x). To determine some formulas for the generating function of the Schröder numbers, r(x) = a(x) =
AN INTRODUCTION TO SCHRÖDER AND UNKNOWN NUMBERS NICK DUFRESNE Abstract. I this article we will itroduce two types of lattice paths, Schröder paths ad Ukow paths. We will examie differet properties of each,
More informationChapter 6. Advanced Counting Techniques
Chapter 6 Advaced Coutig Techiques 6.: Recurrece Relatios Defiitio: A recurrece relatio for the sequece {a } is a equatio expressig a i terms of oe or more of the previous terms of the sequece: a,a2,a3,,a
More informationMAT 271 Project: Partial Fractions for certain rational functions
MAT 7 Project: Partial Fractios for certai ratioal fuctios Prerequisite kowledge: partial fractios from MAT 7, a very good commad of factorig ad complex umbers from Precalculus. To complete this project,
More informationn outcome is (+1,+1, 1,..., 1). Let the r.v. X denote our position (relative to our starting point 0) after n moves. Thus X = X 1 + X 2 + +X n,
CS 70 Discrete Mathematics for CS Sprig 2008 David Wager Note 9 Variace Questio: At each time step, I flip a fair coi. If it comes up Heads, I walk oe step to the right; if it comes up Tails, I walk oe
More informationRegression, Part I. A) Correlation describes the relationship between two variables, where neither is independent or a predictor.
Regressio, Part I I. Differece from correlatio. II. Basic idea: A) Correlatio describes the relatioship betwee two variables, where either is idepedet or a predictor. - I correlatio, it would be irrelevat
More informationACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Statistics
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER 1 018/019 DR. ANTHONY BROWN 8. Statistics 8.1. Measures of Cetre: Mea, Media ad Mode. If we have a series of umbers the
More information~W I F
A FIBONACCI PROPERTY OF WYTHOFF PAIRS ROBERT SILBER North Carolia State Uiversity, Raleigh, North Carolia 27607 I this paper we poit out aother of those fasciatig "coicideces" which are so characteristically
More informationChapter Vectors
Chapter 4. Vectors fter readig this chapter you should be able to:. defie a vector. add ad subtract vectors. fid liear combiatios of vectors ad their relatioship to a set of equatios 4. explai what it
More informationPolymers. One of the most remarkable and useful polymers known is Teflon, formed via polymerization of tetrafluoroethylene as shown below:
Experimet 8 Chem 276 Fall Semester 2010 Page 1 of 5 Polymers Itroductio A polymer is a gigatic chailike molecule made by coectig may small molecules, kow as moomers. The process by which polymers are formed
More informationStructural Confirmation of Polymeric Material Using MS/MS and Fragmentation Mechanisms
Structural Cofirmatio of Polymeric Material Usig MS/MS ad Fragmetatio Mechaisms Kirste Crave, 1 Michael McCullagh, 1 Pascal Gerbaux, 2 ad Julie De Witer 2 1 Waters Corporatio, Machester, UK 2 Uiversity
More informationAlpha-Amino Ketone based Polymeric Pyrazines By: Robert B. Login (rloginconsulting.com)
Alpha-Amio Ketoe based Polymeric Pyrazies y: obert. Logi (rlogicosultig.com) Pyrazie chemistry had its start log ago i the 19 th cetury. It is a vast chemical techology as witess by the followig books.
More informationA Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata
A Simple Optimum-Time FSSP Algorithm for Multi-Dimesioal Cellular Automata HIROSHI UMEO Uiversity of Osaka Electro-Commuicatio umeo@cyt.osakac.ac.jp KINUO NISHIDE Uiversity of Osaka Electro-Commuicatio
More informationSigma notation. 2.1 Introduction
Sigma otatio. Itroductio We use sigma otatio to idicate the summatio process whe we have several (or ifiitely may) terms to add up. You may have see sigma otatio i earlier courses. It is used to idicate
More informationEXPERIMENTAL AND MODELLING INVESTIGATION OF A NOVEL TETRAFUNCTIONAL INITIATOR IN FREE RADICAL POLYMERIZATION. by Matthew Justin Scorah
EXPEIMENTAL AND MODELLING INVESTIGATION OF A NOVEL TETAFUNCTIONAL INITIATO IN FEE ADICAL POLYMEIZATION by Matthew Justi Scorah A thesis preseted to the Uiversity of Waterloo i fulfillmet of the thesis
More informationTriatomics-in-molecules method applied to helium cluster cations
- 1 - Triatomics-i-molecules method applied to helium cluster catios Reé KALUS Departmet of hysics, Uiversity of Ostrava, 30. duba 22, 701 03 Ostrava 1 e-mail: Ree.Kalus@osu.cz ABSTRACT The triatomics-i-molecules
More informationActivity 3: Length Measurements with the Four-Sided Meter Stick
Activity 3: Legth Measuremets with the Four-Sided Meter Stick OBJECTIVE: The purpose of this experimet is to study errors ad the propagatio of errors whe experimetal data derived usig a four-sided meter
More informationInverse Matrix. A meaning that matrix B is an inverse of matrix A.
Iverse Matrix Two square matrices A ad B of dimesios are called iverses to oe aother if the followig holds, AB BA I (11) The otio is dual but we ofte write 1 B A meaig that matrix B is a iverse of matrix
More informationThe Random Walk For Dummies
The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli
More informationLoad Dependent Ritz Vector Algorithm and Error Analysis
Load Depedet Ritz Vector Algorithm ad Error Aalysis Writte by Ed Wilso i 006. he Complete eigealue subspace I the aalysis of structures subected to three base acceleratios there is a requiremet that oe
More informationOn the Linear Complexity of Feedback Registers
O the Liear Complexity of Feedback Registers A. H. Cha M. Goresky A. Klapper Northeaster Uiversity Abstract I this paper, we study sequeces geerated by arbitrary feedback registers (ot ecessarily feedback
More informationMatrices and vectors
Oe Matrices ad vectors This book takes for grated that readers have some previous kowledge of the calculus of real fuctios of oe real variable It would be helpful to also have some kowledge of liear algebra
More informationChapter 22. Comparing Two Proportions. Copyright 2010, 2007, 2004 Pearson Education, Inc.
Chapter 22 Comparig Two Proportios Copyright 2010, 2007, 2004 Pearso Educatio, Ic. Comparig Two Proportios Read the first two paragraphs of pg 504. Comparisos betwee two percetages are much more commo
More informationSize, shape and temperature effect on nanomaterials
Idia Joural of Pure & Applied Physics Vol. 53, November 2015, pp. 768-775 Size, shape ad temperature effect o aomaterials G Sharma, S Bhatt, R Kumar & M Kumar* Departmet of Physics, G.B. Pat Uiversity
More informationA widely used display of protein shapes is based on the coordinates of the alpha carbons - - C α
Nice plottig of proteis: I A widely used display of protei shapes is based o the coordiates of the alpha carbos - - C α -s. The coordiates of the C α -s are coected by a cotiuous curve that roughly follows
More informationPYRIDINE AND AMINE FUNCTIONALIZED POLYMERS BY ANIONIC AND CONTROLLED FREE RADICAL POLYMERIZATION METHODS MZIKAYISE PATRICK NDAWUNI
PYRIDINE AND AMINE FUNCTINALIZED PLYMERS BY ANINIC AND CNTRLLED FREE RADICAL PLYMERIZATIN METDS by MZIKAYISE PATRICK NDAWUNI Submitted i fulfillmet of the requiremets for the DCTR F PILSPY i the subject
More informationCurve Sketching Handout #5 Topic Interpretation Rational Functions
Curve Sketchig Hadout #5 Topic Iterpretatio Ratioal Fuctios A ratioal fuctio is a fuctio f that is a quotiet of two polyomials. I other words, p ( ) ( ) f is a ratioal fuctio if p ( ) ad q ( ) are polyomials
More informationDifferent FRP Resin Chemistries for Different Chemical Environments
Differet FRP Resi Chemistries for Differet Chemical Eviromets Do Kelley, Jim Graham, Thom Johso Ashlad Performace Materials ABSTRACT The corrosio challeges posed by differet chemical eviromets madate the
More informationMath 116 Practice for Exam 3
Math 6 Practice for Exam Geerated October 0, 207 Name: SOLUTIONS Istructor: Sectio Number:. This exam has 7 questios. Note that the problems are ot of equal difficulty, so you may wat to skip over ad retur
More informationDiscrete-Time Systems, LTI Systems, and Discrete-Time Convolution
EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [
More informationCS284A: Representations and Algorithms in Molecular Biology
CS284A: Represetatios ad Algorithms i Molecular Biology Scribe Notes o Lectures 3 & 4: Motif Discovery via Eumeratio & Motif Represetatio Usig Positio Weight Matrix Joshua Gervi Based o presetatios by
More informationEnd-of-Year Contest. ERHS Math Club. May 5, 2009
Ed-of-Year Cotest ERHS Math Club May 5, 009 Problem 1: There are 9 cois. Oe is fake ad weighs a little less tha the others. Fid the fake coi by weighigs. Solutio: Separate the 9 cois ito 3 groups (A, B,
More informationw (1) ˆx w (1) x (1) /ρ and w (2) ˆx w (2) x (2) /ρ.
2 5. Weighted umber of late jobs 5.1. Release dates ad due dates: maximimizig the weight of o-time jobs Oce we add release dates, miimizig the umber of late jobs becomes a sigificatly harder problem. For
More informationTheorem: Let A n n. In this case that A does reduce to I, we search for A 1 as the solution matrix X to the matrix equation A X = I i.e.
Theorem: Let A be a square matrix The A has a iverse matrix if ad oly if its reduced row echelo form is the idetity I this case the algorithm illustrated o the previous page will always yield the iverse
More informationIP Reference guide for integer programming formulations.
IP Referece guide for iteger programmig formulatios. by James B. Orli for 15.053 ad 15.058 This documet is iteded as a compact (or relatively compact) guide to the formulatio of iteger programs. For more
More informationIncreasing timing capacity using packet coloring
003 Coferece o Iformatio Scieces ad Systems, The Johs Hopkis Uiversity, March 4, 003 Icreasig timig capacity usig packet colorig Xi Liu ad R Srikat[] Coordiated Sciece Laboratory Uiversity of Illiois e-mail:
More information5 3B Numerical Methods for estimating the area of an enclosed region. The Trapezoidal Rule for Approximating the Area Under a Closed Curve
5 3B Numerical Methods for estimatig the area of a eclosed regio The Trapezoidal Rule for Approximatig the Area Uder a Closed Curve The trapezoidal rule requires a closed o a iterval from x = a to x =
More informationThe Binomial Theorem
The Biomial Theorem Robert Marti Itroductio The Biomial Theorem is used to expad biomials, that is, brackets cosistig of two distict terms The formula for the Biomial Theorem is as follows: (a + b ( k
More informationDS 100: Principles and Techniques of Data Science Date: April 13, Discussion #10
DS 00: Priciples ad Techiques of Data Sciece Date: April 3, 208 Name: Hypothesis Testig Discussio #0. Defie these terms below as they relate to hypothesis testig. a) Data Geeratio Model: Solutio: A set
More information(A sequence also can be thought of as the list of function values attained for a function f :ℵ X, where f (n) = x n for n 1.) x 1 x N +k x N +4 x 3
MATH 337 Sequeces Dr. Neal, WKU Let X be a metric space with distace fuctio d. We shall defie the geeral cocept of sequece ad limit i a metric space, the apply the results i particular to some special
More informationORTHOGONAL MATRIX IN CRYPTOGRAPHY
Orthogoal Matrix i Cryptography ORTHOGONAL MATRIX IN CRYPTOGRAPHY Yeray Cachó Sataa Member of CriptoRed (U.P.M.) ABSTRACT I this work is proposed a method usig orthogoal matrix trasform properties to ecrypt
More informationRecall the study where we estimated the difference between mean systolic blood pressure levels of users of oral contraceptives and non-users, x - y.
Testig Statistical Hypotheses Recall the study where we estimated the differece betwee mea systolic blood pressure levels of users of oral cotraceptives ad o-users, x - y. Such studies are sometimes viewed
More informationOPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES
OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES Peter M. Maurer Why Hashig is θ(). As i biary search, hashig assumes that keys are stored i a array which is idexed by a iteger. However, hashig attempts to bypass
More informationAn Interesting Class of Polynomial Vector Fields
A Iterestig Class of Polyomial Vector Fields Gerik Scheuerma, Has Hage ad Heiz Krüger Abstract. The visualizatio of vector fields is oe of the most importat topics i visualizatio. Of special iterest over
More informationII. Descriptive Statistics D. Linear Correlation and Regression. 1. Linear Correlation
II. Descriptive Statistics D. Liear Correlatio ad Regressio I this sectio Liear Correlatio Cause ad Effect Liear Regressio 1. Liear Correlatio Quatifyig Liear Correlatio The Pearso product-momet correlatio
More informationTEACHER CERTIFICATION STUDY GUIDE
COMPETENCY 1. ALGEBRA SKILL 1.1 1.1a. ALGEBRAIC STRUCTURES Kow why the real ad complex umbers are each a field, ad that particular rigs are ot fields (e.g., itegers, polyomial rigs, matrix rigs) Algebra
More informationChapter 22. Comparing Two Proportions. Copyright 2010 Pearson Education, Inc.
Chapter 22 Comparig Two Proportios Copyright 2010 Pearso Educatio, Ic. Comparig Two Proportios Comparisos betwee two percetages are much more commo tha questios about isolated percetages. Ad they are more
More information1 Inferential Methods for Correlation and Regression Analysis
1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet
More informationFeedback in Iterative Algorithms
Feedback i Iterative Algorithms Charles Byre (Charles Byre@uml.edu), Departmet of Mathematical Scieces, Uiversity of Massachusetts Lowell, Lowell, MA 01854 October 17, 2005 Abstract Whe the oegative system
More informationChapter 6: Numerical Series
Chapter 6: Numerical Series 327 Chapter 6 Overview: Sequeces ad Numerical Series I most texts, the topic of sequeces ad series appears, at first, to be a side topic. There are almost o derivatives or itegrals
More information