New Boronate Monomers and Polymers By: Robert B. Login (rloginconsulting.com)

Size: px
Start display at page:

Download "New Boronate Monomers and Polymers By: Robert B. Login (rloginconsulting.com)"

Transcription

1 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 valuable whe the alcohol is glucose because its boroate ester ca fuctio as a diabetic idicator of blood glucose or eve as a isuli release mechaism. A recet excellet review goes ito great detail cocerig this iterestig chemistry. rooks, William LA, ad ret S. Sumerli. "Sythesis ad applicatios of boroic acid-cotaiig polymers: From materials to medicie."chemical reviews, (2015): A simple search o Google Scholar retured thousads of boroate refereces, so it is o easy task to comprehed all of its chemistry; therefore, I limited my iterest to polymeric boroate derivatives. Viyl boroate is the first moomer to come to mid, but eve though it will polymerize, it is difficult to polymerize ad ever wet commercial. Mulvaey, J. E.,. A. ttaviai, ad J. J. Laverty. "Preparatio of viyl boroate copolymers ad reactios."joural of Polymer Sciece Part A: Polymer Chemistry, 20.7 (1982): A review of boroate chemistry will help explai my ideas. all, Deis G. "Structure, properties, ad preparatio of boroic acid derivatives. verview of their reactios ad applicatios."oroic acids: preparatio ad applicatios i orgaic sythesis ad medicie, 1 (2006): 1-99 ad d editio. Scheme 1: amig the oxidatio derivatives of borae, while boroxie ad diboroxae are aalogous to ahydrides. ecause of the empty p-orbital o boro, the boroate esters will coordiate a hydroxide to fill that orbital releasig a proto.

2 Scheme 2: (The reverse equilibrium arrow below the - should have a + to reverse the equilibrium.) As show i scheme 2, this reactio is reversible ad p depedet. The reaso is because boro has a free p orbital ad acts as a Lewis acid i water. Li, Meg, et al. "Electrochemical sesig usig boroic acids."chemical Commuicatios, (2015): If you prepare a polymer with boroate esters i ahydrous solvets the add said polymers to aqueous cotaiig solutios i which a sugar has also bee added the because of the equilibria, a trasfer of the more reactive diol will occur(p also plays a roll here as acidic p favors hydrolysis while higher p favors ester formatio). owever, the poit I'm makig is that moomers ad polymers cotaiig boroate esters are stable eough whe ot i aqueous solutio ad their sythesis ca be achieved i such ahydrous solvets without cocer. owever, i water solutio, boroic acids will form boroate esters at the pka of the boroic acid (alkalie). This is very uique because you ca mix i aqueous media, polyboroic acids with polyalcohols to form supermolecular compouds! The reactios occur upo mixig eve at T. Scheme 3: Esterificatio at alkalie p ad egative charge o boro. itroge cotaiig molecules ca replace oe of the groups because it is more ucleophilic.

3 This is just a example as the itroge ca be heterocyclic or o a separate compoud etc. Germacidal oroates A amphoteric-eutral charge Catioic acterial surface C Scheme 4: The geeral idicated quat stads for all types of quats; moomeric, polymeric or surfactats as log as they are capable of killig bacteria. The idea is that i water the catioic charge is balaced by the egative charge o boro rederig the amphoteric harmless. is the idea that the bacteria have a polymeric sugar coat that will form a boroate ester, revealig the germicidal quat where it ca do the most harm. D is the idea that the bacterial polymeric sugar coat will be more attractive ad exchage the boroate ester, freeig the quat ext to the bacterial coatig where it ca disrupt it. D ydrogels: 3,4-dihydroxypyrrolidi-2-oe Scheme 5: Proposed dihydroxy VP( groups must be cis) that ca be cross liked i aqueous solutio with diboroic acids upo mixig! Sythesis of dihydroxy moomers:

4 o, Chi Mig, Wig Yiu Yu, ad Chi Mig Che. "utheium aoparticles Supported o ydroxyapatite as a Efficiet ad ecyclable Catalyst for cis Dihydroxylatio ad xidative eavage of Alkees." Agewadte Chemie, (2004): riksma, Jelle, et al. "omogeeous cis-dihydroxylatio ad epoxidatio of olefis with high 2 2 efficiecy by mixed magaese/activated carboyl catalyst system."tetrahedro letters,43.14 (2002): Saisaha, Pattama, et al. "Magaese catalyzed cis-dihydroxylatio of electro deficiet alkees with 2 2 DI: /c0ob00102c."rgaic & biomolecular chemistry, 8.19 (2010): ataille, Carole J, ad Timothy J. Doohoe. "smium-free direct sy-dihydroxylatio of alkees."chemical Society eviews, 40.1 (2011): (the low yield might be because of steric crowdig) + u Scheme 6: Metathesis route to startig M. With VP copolymers, the 3,4-dihydroxy comoomer would form water soluble copolymers that would form iterestig ad reversible gels with boroic crosslikers suitable for deliverig (poorly soluble) drugs, A ad DA or various proteis that had bee mixed ito the copolymer before crosslikig. elease of said drugs could be accomplished if for example a sugar happeed to be preset. It could eve react through the diol with drugs derivatized with labile baroic acids as pro-drugs that would also be released whe the p was acidic. Similar gels have foud use as sugar idicators ad isuli release systems because sugars will replace the crossliks hece affordig a method to detect them (gel swellig

5 or collapse). Isuli derivatized with releasable diols (the labile diol ca be removed oce outside the gel) that ca be released by glucose. PVP based boroate copolymers would be safe vehicles for such chemistry because PVP has a excellet toxicity profile. Su, Xiaolog, ad Toy D. James. "Glucose sesig i supramolecular chemistry."chemical reviews, (2015): ' ' ' Scheme 7: Dimers of the 3,4 dihydroxy pyrrolidoe ca form liear ad brached polymers examples of which are illustrated i scheme 5. These polymers will form spotaeously i water cotaiig polyboroic acids at basic p's(pka of the boroic acid). They are examples of CF chemistry (covalet orgaic frameworks). ambo, rett M., ad Joh J. Lavige. "Defiig self-assemblig liear oligo (dioxaborole) s."chemistry of materials, (2007): Kubo, Yuji, yuhei ishiyabu, ad Toy D. James. "ierarchical supramolecules ad orgaizatio usig boroic acid buildig blocks."chemical Commuicatios, (2015): rooks, William LA, ad ret S. Sumerli. "Sythesis ad applicatios of boroic acid-cotaiig polymers: From materials to medicie."chemical reviews, (2015): cure cure

6 Scheme 8: Exocyclic acrylate type moomer idea. The five membered rig moomer would be easier to sythesize as it could be prepared from pyruvic acid ad a boroic acid. The resultig polymer could be hydrolyzed i water uder acidic coditios or by oxidatio with hydroge peroxide or with added reactive sugars. The resultig hydroxy carboxylic acid could cure (form polyesters) upo dry dow. ' rp " " Scheme 9: rp boroate moomer possibilities. XS () 2, + Scheme 10: I'm bettig that reactio with boroic acid is very fast ad will grab the desired itermediate? I'm sure there are other sythetic routes, however? ' () A Scheme 11: Polyester or polylamides are possible if the boroate esters would stad up to the catalysts ad coditios required? Moomer A results i the boroate i the

7 polymer backboe where it would be very vulerable to water hydrolysis eve more so tha the commercial polyahydrides. (..see cis-dihydroxylatio refereces) would be more hydrolysis resistat but would easily exchage with more reactive diols(sugars) as a way to expose dihydroxy groups o the polymer backboe. bviously, boro chemistry is much more tha boroic acid derivatives, eve though they are extremely importat for example i Suzuki couplig. The followig book however shows how much more there is to this chemistry. all, D. "oroic Acids Preparatio ad Applicatios i rgaic Sythesis, Medicie ad Materials Secod Completely evised Editio Preface."oroic Acids, 2 (2011). I coclusio, thak you for readig this proposal. I would welcome ay commets or suggestios. Thak you, Dr. obert. Logi (rlogicosultig.com)

Macromolecules 2003, 36,

Macromolecules 2003, 36, 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

More information

Chapter 2. Aromatic Polyketones from α-aminonitriles

Chapter 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 information

Enzymes in Organic Chemistry. Enzymes!

Enzymes in Organic Chemistry. Enzymes! Ezymes i rgaic Chemistry March 17 th, 2015 Ezymes! Ezymes are biological catalysts. They icrease the rate at which equilibrium is reached, but they do ot affect the equilibrium. Ezymes differ from ordiary

More information

Alpha-Amino Ketone based Polymeric Pyrazines By: Robert B. Login (rloginconsulting.com)

Alpha-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 information

Polymerization Lab p. 1 Polymerization Lab

Polymerization 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 information

ALDEHYDES AND KETONES

ALDEHYDES 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 information

6.3 Testing Series With Positive Terms

6.3 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 information

Free Radical Polymerization

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 information

Practice Questions for Exam 3 CH 1020 Spring 2017

Practice Questions for Exam 3 CH 1020 Spring 2017 Practice Questios for Exam 3 C 1020 Sprig 2017 1. Which of the followig ca be cosidered a Brøsted-Lowry base? 5. What is the p of a solutio for which [Ba(O) 2 ] = 0.015 M? 6. The figure below shows three

More information

Chemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics

Chemical 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 information

Precalculus MATH Sections 3.1, 3.2, 3.3. Exponential, Logistic and Logarithmic Functions

Precalculus MATH Sections 3.1, 3.2, 3.3. Exponential, Logistic and Logarithmic Functions Precalculus MATH 2412 Sectios 3.1, 3.2, 3.3 Epoetial, Logistic ad Logarithmic Fuctios Epoetial fuctios are used i umerous applicatios coverig may fields of study. They are probably the most importat group

More information

Kinetics of Complex Reactions

Kinetics 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 information

Miscellaneous Notes. Lecture 19, p 1

Miscellaneous 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 information

Abstracts. p43. p107. M. Tomµs-Gamasa. U. Scholz, W. Dong, J. Feng, and W. Shi. M. B. Hay and J. D. Hicks

Abstracts. p43. p107. M. Tomµs-Gamasa. U. Scholz, W. Dong, J. Feng, and W. Shi. M. B. Hay and J. D. Hicks I 2.1.1.1 Alkylamies with Aryl ad Alkeyl Electrophiles M. Tomµs-Gamasa p9 This review covers selected efficiet sythetic methods for metal-catalyzed cross-couplig reactios that ca directly covert simple

More information

New Structure of Monocyclic Fluoropolymer for 157nm Photoresist

New Structure of Monocyclic Fluoropolymer for 157nm Photoresist New Structure of Moocyclic luoropolymer for 157m Photoresist Masataka Eda, Yoko Takebe, Osamu Yokokoji Research eter, Asahi Glass o., Ltd. Akihiko Otoguro, Shigeo Irie, Toshiro Itai, Kiyoshi ujii Semicoductor

More information

Math 113 Exam 3 Practice

Math 113 Exam 3 Practice Math Exam Practice Exam will cover.-.9. This sheet has three sectios. The first sectio will remid you about techiques ad formulas that you should kow. The secod gives a umber of practice questios for you

More information

Zeros of Polynomials

Zeros of Polynomials Math 160 www.timetodare.com 4.5 4.6 Zeros of Polyomials I these sectios we will study polyomials algebraically. Most of our work will be cocered with fidig the solutios of polyomial equatios of ay degree

More information

CS 270 Algorithms. Oliver Kullmann. Growth of Functions. Divide-and- Conquer Min-Max- Problem. Tutorial. Reading from CLRS for week 2

CS 270 Algorithms. Oliver Kullmann. Growth of Functions. Divide-and- Conquer Min-Max- Problem. Tutorial. Reading from CLRS for week 2 Geeral remarks Week 2 1 Divide ad First we cosider a importat tool for the aalysis of algorithms: Big-Oh. The we itroduce a importat algorithmic paradigm:. We coclude by presetig ad aalysig two examples.

More information

4. Amines, Amides and Amino Acids

4. Amines, Amides and Amino Acids 4. Amies, Amides ad Amio Acids amig Amies These ed i amie. There is, however, rather cofusigly two ways of usig this suffix. The exam board ted to use the propylamie commo versio where the ame r propa-1-amie

More information

2 Synthesis. Scheme 2.1. Retrosynthetic route of the target molecules. p-terphenyl is always (1,1,4,1 )-terphenyl. 2 Synthesis Am/n. Mm/n.

2 Synthesis. Scheme 2.1. Retrosynthetic route of the target molecules. p-terphenyl is always (1,1,4,1 )-terphenyl. 2 Synthesis Am/n. Mm/n. 2 Sythesis - 13-2 Sythesis The sythetic strategy to obtai the T-shaped amphiphiles with a lateral polar chai attached to the cetral bezee rig is outlied i Scheme 2.1. Two sythetic routes were used to sythesize

More information

Polymers. One of the most remarkable and useful polymers known is Teflon, formed via polymerization of tetrafluoroethylene as shown below:

Polymers. 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 information

DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan

DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan Mathematical ad Computatioal Applicatios, Vol. 9, No. 3, pp. 30-40, 04 DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS Muhammad Aslam Noor, Khalida Iayat Noor ad Asif Waheed

More information

4.7 Organic Chemistry

4.7 Organic Chemistry 4.7 rgaic hemistry rude oil rude oil is a fiite resource foud i rocks. rude oil is the remais of a aciet biomass cosistig maily of plakto that was buried i mud. Alkaes Most of the hydrocarbos i crude oil

More information

Synthesis of Ester Acid Hydrazide Pendant Imino Group Copolymers

Synthesis of Ester Acid Hydrazide Pendant Imino Group Copolymers 2011, TextRoad Publicatio ISSN 2090-424X Joural of Basic ad Applied Scietific Research www.textroad.com Sythesis of Ester Acid Hydrazide Pedat Imio Group opolymers Etesar bed.al-tamimi 1 ad Hizoom Mola

More information

POLYMERS

POLYMERS 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 information

Different FRP Resin Chemistries for Different Chemical Environments

Different 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 information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 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 information

Infinite Sequences and Series

Infinite 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 information

Sulfur Trioxide Amine Complexes:

Sulfur Trioxide Amine Complexes: : Versatile Reagets i rgaic Sythesis Dr. Jörg Schrickel Busiess Maager Specialities Cotet Sulfur trioxide chemistry: Itroductio Sulfur trioxide reagets: verview ad Properties Sulfur trioxide amie complexes:

More information

Pell and Lucas primes

Pell and Lucas primes Notes o Number Theory ad Discrete Mathematics ISSN 30 532 Vol. 2, 205, No. 3, 64 69 Pell ad Lucas primes J. V. Leyedekkers ad A. G. Shao 2 Faculty of Sciece, The Uiversity of Sydey NSW 2006, Australia

More information

G. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan

G. R. Pasha Department of Statistics Bahauddin Zakariya University Multan, Pakistan Deviatio of the Variaces of Classical Estimators ad Negative Iteger Momet Estimator from Miimum Variace Boud with Referece to Maxwell Distributio G. R. Pasha Departmet of Statistics Bahauddi Zakariya Uiversity

More information

Copper-catalyzed Electrophilic Polyhydroamination of Internal Alkynes

Copper-catalyzed Electrophilic Polyhydroamination of Internal Alkynes Supportig Iformatio (SI) Copper-catalyzed Electrophilic Polyhydroamiatio of Iteral lkyes ezhao He, Yogwei Wu, ju Qi,, ad e Zhog Tag,, Guagdog Iovative Research Team, State Key Laboratory of Lumiescet Materials

More information

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30. Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8 ad

More information

On the Linear Complexity of Feedback Registers

On 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 information

subject to A 1 x + A 2 y b x j 0, j = 1,,n 1 y j = 0 or 1, j = 1,,n 2

subject to A 1 x + A 2 y b x j 0, j = 1,,n 1 y j = 0 or 1, j = 1,,n 2 Additioal Brach ad Boud Algorithms 0-1 Mixed-Iteger Liear Programmig The brach ad boud algorithm described i the previous sectios ca be used to solve virtually all optimizatio problems cotaiig iteger variables,

More information

Stability Evaluation of Surfactant-Grafted Polyacrylamide Used in Oilfields by Evolution of Ammonia

Stability Evaluation of Surfactant-Grafted Polyacrylamide Used in Oilfields by Evolution of Ammonia Joural of Materials Sciece ad hemical Egieerig, 1,, 15-19 Published lie May 1 i SciRes. http://www.scirp.org/joural/msce http://dx.doi.org/1.3/msce.1.53 Stability Evaluatio of Surfactat-Grafted Polyacrylamide

More information

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Statistics

ACCESS 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

IP Reference guide for integer programming formulations.

IP 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 information

Recursive Algorithm for Generating Partitions of an Integer. 1 Preliminary

Recursive Algorithm for Generating Partitions of an Integer. 1 Preliminary Recursive Algorithm for Geeratig Partitios of a Iteger Sug-Hyuk Cha Computer Sciece Departmet, Pace Uiversity 1 Pace Plaza, New York, NY 10038 USA scha@pace.edu Abstract. This article first reviews the

More information

CHAPTER 11. Practice Questions (a) OH (b) I. (h) NH 3 CH 3 CO 2 (j) C 6 H 5 O - (k) (CH 3 ) 3 N conjugate pair

CHAPTER 11. Practice Questions (a) OH (b) I. (h) NH 3 CH 3 CO 2 (j) C 6 H 5 O - (k) (CH 3 ) 3 N conjugate pair CAPTER 11 Practice Questios 11.1 (a) O (b) I (c) NO 2 (d) 2 PO 4 (e) 2 PO 4 (f) 3 PO 4 (g) SO 4 (h) N 3 (i) C 3 CO 2 (j) C 6 5 O - (k) (C 3 ) 3 N 11.3 cojugate pair PO 3 4 (aq) C 3 COO(aq) PO 2 4 (aq)

More information

C NMR Characteristics and Thermal Properties of Hydroxyethyl Cellulose Grafting Poly(caprolactone) Copolymer

C NMR Characteristics and Thermal Properties of Hydroxyethyl Cellulose Grafting Poly(caprolactone) Copolymer Asia Joural of Chemistry; Vol., No. 8 (0), 0-0 http://dx.doi.org/0./ajchem.0.0 C NMR Characteristics ad Thermal Properties of ydroxyethyl Cellulose Graftig Poly(caprolactoe) Copolymer MING GU, XIN XIN

More information

N Goalby chemrevise.org

N Goalby chemrevise.org 21. olymers There are two types of polymerisatio additio ad codesatio Additio olymerisatio A additio polymer forms whe usaturated moomers react to form a polymer Moomers cotai = bods oly(alkees) are chemically

More information

NICK DUFRESNE. 1 1 p(x). To determine some formulas for the generating function of the Schröder numbers, r(x) = a(x) =

NICK 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 information

Supplementary Information

Supplementary Information Electroic Supplemetary Material (ESI) for Chemical Commuicatios. This joural is The Royal Society of Chemistry 2016 Supplemetary Iformatio Electrical properties of Flexible Multi-chael Si Naowire Field-Effect

More information

Properties and Tests of Zeros of Polynomial Functions

Properties and Tests of Zeros of Polynomial Functions Properties ad Tests of Zeros of Polyomial Fuctios The Remaider ad Factor Theorems: Sythetic divisio ca be used to fid the values of polyomials i a sometimes easier way tha substitutio. This is show by

More information

II. Descriptive Statistics D. Linear Correlation and Regression. 1. Linear Correlation

II. 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 information

Optimization Methods: Linear Programming Applications Assignment Problem 1. Module 4 Lecture Notes 3. Assignment Problem

Optimization 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 information

Estimation for Complete Data

Estimation for Complete Data Estimatio for Complete Data complete data: there is o loss of iformatio durig study. complete idividual complete data= grouped data A complete idividual data is the oe i which the complete iformatio of

More information

Erratum to: An empirical central limit theorem for intermittent maps

Erratum to: An empirical central limit theorem for intermittent maps Probab. Theory Relat. Fields (2013) 155:487 491 DOI 10.1007/s00440-011-0393-0 ERRATUM Erratum to: A empirical cetral limit theorem for itermittet maps J. Dedecker Published olie: 25 October 2011 Spriger-Verlag

More information

Chapter 14: Chemical Equilibrium

Chapter 14: Chemical Equilibrium hapter 14: hemical Equilibrium 46 hapter 14: hemical Equilibrium Sectio 14.1: Itroductio to hemical Equilibrium hemical equilibrium is the state where the cocetratios of all reactats ad products remai

More information

A 2nTH ORDER LINEAR DIFFERENCE EQUATION

A 2nTH ORDER LINEAR DIFFERENCE EQUATION A 2TH ORDER LINEAR DIFFERENCE EQUATION Doug Aderso Departmet of Mathematics ad Computer Sciece, Cocordia College Moorhead, MN 56562, USA ABSTRACT: We give a formulatio of geeralized zeros ad (, )-discojugacy

More information

In-Situ Cyclic Voltammetry and Cyclic Resistometry Analyses of conducting Electroactive polymer membranes

In-Situ Cyclic Voltammetry and Cyclic Resistometry Analyses of conducting Electroactive polymer membranes Iteratioal Joural of ChemTech Research CODEN( USA): IJCRGG ISSN : 0974-4290 Vol.1, No.4, pp 1398-1402, Oct-Dec 2009 I-Situ Cyclic Voltammetry ad Cyclic Resistometry Aalyses of coductig Electroactive polymer

More information

Ring Opening/Fragmentation of Dihydropyrones for the Synthesis of Homopropargyl Alcohols

Ring Opening/Fragmentation of Dihydropyrones for the Synthesis of Homopropargyl Alcohols ig peig/fragmetatio of Dihydropyroes for the Sythesis of Homopropargyl Alcohols ' 1 '-M X 1 '-M 1 H X = C Tf X = Jumreag Tummator ad Gregory B. Dudley J. Am. Chem. Soc. 2008, ASAP Curret Literature Presetatio

More information

Material Balances on Reactive Processes F&R

Material 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 information

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES

OPTIMAL 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 information

Nernst Equation. Nernst Equation. Electric Work and Gibb's Free Energy. Skills to develop. Electric Work. Gibb's Free Energy

Nernst 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 information

9.4.3 Fundamental Parameters. Concentration Factor. Not recommended. See Extraction factor. Decontamination Factor

9.4.3 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 information

Recurrence Relations

Recurrence 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 information

Sigma notation. 2.1 Introduction

Sigma 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 information

Some New Iterative Methods for Solving Nonlinear Equations

Some New Iterative Methods for Solving Nonlinear Equations World Applied Scieces Joural 0 (6): 870-874, 01 ISSN 1818-495 IDOSI Publicatios, 01 DOI: 10.589/idosi.wasj.01.0.06.830 Some New Iterative Methods for Solvig Noliear Equatios Muhammad Aslam Noor, Khalida

More information

Series III. Chapter Alternating Series

Series III. Chapter Alternating Series Chapter 9 Series III With the exceptio of the Null Sequece Test, all the tests for series covergece ad divergece that we have cosidered so far have dealt oly with series of oegative terms. Series with

More information

Problem Cosider the curve give parametrically as x = si t ad y = + cos t for» t» ß: (a) Describe the path this traverses: Where does it start (whe t =

Problem Cosider the curve give parametrically as x = si t ad y = + cos t for» t» ß: (a) Describe the path this traverses: Where does it start (whe t = Mathematics Summer Wilso Fial Exam August 8, ANSWERS Problem 1 (a) Fid the solutio to y +x y = e x x that satisfies y() = 5 : This is already i the form we used for a first order liear differetial equatio,

More information

Bertrand s Postulate

Bertrand 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 information

Matrices and vectors

Matrices 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 information

Research Summary. Scheme 1. General Design. Au(I/III) [Au]

Research Summary. Scheme 1. General Design. Au(I/III) [Au] esearch ummary 1. Goldcatalyzed reactios of fuctioalized allees catalysis has lately attracted icreasig attetio due to ovel reactivities, mild reactio coditios ad sythetic potetials. llees with a heteroatom

More information

ii. O = {x x = 2k + 1 for some integer k} (This set could have been listed O = { -3, -1, 1, 3, 5 }.)

ii. O = {x x = 2k + 1 for some integer k} (This set could have been listed O = { -3, -1, 1, 3, 5 }.) Sets 1 Math 3312 Set Theory Sprig 2008 Itroductio Set theory is a brach of mathematics that deals with the properties of welldefied collectios of objects, which may or may ot be of a mathematical ature,

More information

Chimica Inorganica 3

Chimica Inorganica 3 himica Iorgaica Irreducible Represetatios ad haracter Tables Rather tha usig geometrical operatios, it is ofte much more coveiet to employ a ew set of group elemets which are matrices ad to make the rule

More information

A NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS

A NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS Jural Karya Asli Loreka Ahli Matematik Vol. No. (010) page 6-9. Jural Karya Asli Loreka Ahli Matematik A NEW CLASS OF -STEP RATIONAL MULTISTEP METHODS 1 Nazeeruddi Yaacob Teh Yua Yig Norma Alias 1 Departmet

More information

The "Last Riddle" of Pierre de Fermat, II

The Last Riddle of Pierre de Fermat, II The "Last Riddle" of Pierre de Fermat, II Alexader Mitkovsky mitkovskiy@gmail.com Some time ago, I published a work etitled, "The Last Riddle" of Pierre de Fermat " i which I had writte a proof of the

More information

Sequences of Definite Integrals, Factorials and Double Factorials

Sequences of Definite Integrals, Factorials and Double Factorials 47 6 Joural of Iteger Sequeces, Vol. 8 (5), Article 5.4.6 Sequeces of Defiite Itegrals, Factorials ad Double Factorials Thierry Daa-Picard Departmet of Applied Mathematics Jerusalem College of Techology

More information

Complexation Reactions and Titrations

Complexation 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 information

Linearized Stability and Hopf Bifurcations for a Nonautonomous Delayed Predator-prey System

Linearized Stability and Hopf Bifurcations for a Nonautonomous Delayed Predator-prey System SCIREA Joural of Mathematics http://www.scirea.org/joural/mathematics October 0, 016 Volume 1, Issue1, October 016 Liearized Stability ad Hopf Bifurcatios for a Noautoomous Delayed Predator-prey System

More information

PROPERTIES OF THE POSITIVE INTEGERS

PROPERTIES OF THE POSITIVE INTEGERS PROPERTIES OF THE POSITIVE ITEGERS The first itroductio to mathematics occurs at the pre-school level ad cosists of essetially coutig out the first te itegers with oe s figers. This allows the idividuals

More information

1 Inferential Methods for Correlation and Regression Analysis

1 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 information

Estimation of Backward Perturbation Bounds For Linear Least Squares Problem

Estimation of Backward Perturbation Bounds For Linear Least Squares Problem dvaced Sciece ad Techology Letters Vol.53 (ITS 4), pp.47-476 http://dx.doi.org/.457/astl.4.53.96 Estimatio of Bacward Perturbatio Bouds For Liear Least Squares Problem Xixiu Li School of Natural Scieces,

More information

ChE 471 Lecture 10 Fall 2005 SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS

ChE 471 Lecture 10 Fall 2005 SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS I a exothermic reactio the temperature will cotiue to rise as oe moves alog a plug flow reactor util all of the limitig reactat is exhausted. Schematically

More information

3.2 Properties of Division 3.3 Zeros of Polynomials 3.4 Complex and Rational Zeros of Polynomials

3.2 Properties of Division 3.3 Zeros of Polynomials 3.4 Complex and Rational Zeros of Polynomials Math 60 www.timetodare.com 3. Properties of Divisio 3.3 Zeros of Polyomials 3.4 Complex ad Ratioal Zeros of Polyomials I these sectios we will study polyomials algebraically. Most of our work will be cocered

More information

MA131 - Analysis 1. Workbook 9 Series III

MA131 - Analysis 1. Workbook 9 Series III MA3 - Aalysis Workbook 9 Series III Autum 004 Cotets 4.4 Series with Positive ad Negative Terms.............. 4.5 Alteratig Series.......................... 4.6 Geeral Series.............................

More information

Polygons with concurrent medians

Polygons with concurrent medians Polygos with cocurret medias Joh P. Steiberger epartmet of Mathematics, U avis jpsteib@math.ucdavis.ca November 2, 2003 For Thomas achoff o the occasio of his 65th birthday. bstract The medias of a odd-sided

More information

The Choquet Integral with Respect to Fuzzy-Valued Set Functions

The Choquet Integral with Respect to Fuzzy-Valued Set Functions The Choquet Itegral with Respect to Fuzzy-Valued Set Fuctios Weiwei Zhag Abstract The Choquet itegral with respect to real-valued oadditive set fuctios, such as siged efficiecy measures, has bee used i

More information

CHEE 221: Chemical Processes and Systems

CHEE 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 information

SNAP Centre Workshop. Basic Algebraic Manipulation

SNAP 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 information

On Generalized Fibonacci Numbers

On Generalized Fibonacci Numbers Applied Mathematical Scieces, Vol. 9, 215, o. 73, 3611-3622 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.215.5299 O Geeralized Fiboacci Numbers Jerico B. Bacai ad Julius Fergy T. Rabago Departmet

More information

Math 1030Q Spring Exam #2 Review. (9.2) 8x = log (9.2) 8x = log.32 8x log 9.2 log log log 9.2. x =.06418

Math 1030Q Spring Exam #2 Review. (9.2) 8x = log (9.2) 8x = log.32 8x log 9.2 log log log 9.2. x =.06418 Math 1030Q Sprig 2013 Exam #2 Review 1. Solve for x: 2 + 9.2 8x = 2.32 Solutio: 2 + 9.2 8x = 2.32 9.2 8x = 2.32 2 log 9.2 8x = log.32 8x log 9.2 = log.32 8x log 9.2 log.32 = 8 log 9.2 8 log 9.2 x =.06418

More information

Upper bound for ropelength of pretzel knots

Upper bound for ropelength of pretzel knots Upper boud for ropelegth of pretzel kots Safiya Mora August 25, 2006 Abstract A model of the pretzel kot is described. A method for predictig the ropelegth of pretzel kots is give. A upper boud for the

More information

Principle Of Superposition

Principle Of Superposition ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give

More information

Numerical Integration Formulas

Numerical Integration Formulas Numerical Itegratio Formulas Berli Che Departmet o Computer Sciece & Iormatio Egieerig Natioal Taiwa Normal Uiversity Reerece: 1. Applied Numerical Methods with MATLAB or Egieers, Chapter 19 & Teachig

More information

w (1) ˆx w (1) x (1) /ρ and w (2) ˆx w (2) x (2) /ρ.

w (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 information

The 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.

The 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 information

Massachusetts Institute of Technology

Massachusetts Institute of Technology 6.0/6.3: Probabilistic Systems Aalysis (Fall 00) Problem Set 8: Solutios. (a) We cosider a Markov chai with states 0,,, 3,, 5, where state i idicates that there are i shoes available at the frot door i

More information

Linearly Independent Sets, Bases. Review. Remarks. A set of vectors,,, in a vector space is said to be linearly independent if the vector equation

Linearly Independent Sets, Bases. Review. Remarks. A set of vectors,,, in a vector space is said to be linearly independent if the vector equation Liearly Idepedet Sets Bases p p c c p Review { v v vp} A set of vectors i a vector space is said to be liearly idepedet if the vector equatio cv + c v + + c has oly the trivial solutio = = { v v vp} The

More information

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30. Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PHYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8

More information

Axioms of Measure Theory

Axioms of Measure Theory MATH 532 Axioms of Measure Theory Dr. Neal, WKU I. The Space Throughout the course, we shall let X deote a geeric o-empty set. I geeral, we shall ot assume that ay algebraic structure exists o X so that

More information

The Random Walk For Dummies

The 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 information

NUMERICAL METHODS FOR SOLVING EQUATIONS

NUMERICAL METHODS FOR SOLVING EQUATIONS Mathematics Revisio Guides Numerical Methods for Solvig Equatios Page 1 of 11 M.K. HOME TUITION Mathematics Revisio Guides Level: GCSE Higher Tier NUMERICAL METHODS FOR SOLVING EQUATIONS Versio:. Date:

More information

A.1 Algebra Review: Polynomials/Rationals. Definitions:

A.1 Algebra Review: Polynomials/Rationals. Definitions: MATH 040 Notes: Uit 0 Page 1 A.1 Algera Review: Polyomials/Ratioals Defiitios: A polyomial is a sum of polyomial terms. Polyomial terms are epressios formed y products of costats ad variales with whole

More information

1 Review of Probability & Statistics

1 Review of Probability & Statistics 1 Review of Probability & Statistics a. I a group of 000 people, it has bee reported that there are: 61 smokers 670 over 5 960 people who imbibe (drik alcohol) 86 smokers who imbibe 90 imbibers over 5

More information

BACKMIXING IN SCREW EXTRUDERS

BACKMIXING IN SCREW EXTRUDERS BACKMIXING IN SCREW EXTRUDERS Chris Rauwedaal, Rauwedaal Extrusio Egieerig, Ic. Paul Grama, The Madiso Group Abstract Mixig is a critical fuctio i most extrusio operatios. Oe of the most difficult mixig

More information

IJITE Vol.2 Issue-11, (November 2014) ISSN: Impact Factor

IJITE Vol.2 Issue-11, (November 2014) ISSN: Impact Factor IJITE Vol Issue-, (November 4) ISSN: 3-776 ATTRACTIVITY OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION Guagfeg Liu School of Zhagjiagag Jiagsu Uiversit of Sciece ad Techolog, Zhagjiagag, Jiagsu 56,PR

More information

THE APPEARANCE OF FIBONACCI AND LUCAS NUMBERS IN THE SIMULATION OF ELECTRICAL POWER LINES SUPPLIED BY TWO SIDES

THE APPEARANCE OF FIBONACCI AND LUCAS NUMBERS IN THE SIMULATION OF ELECTRICAL POWER LINES SUPPLIED BY TWO SIDES THE APPEARANCE OF FIBONACCI AND LUCAS NUMBERS IN THE SIMULATION OF ELECTRICAL POWER LINES SUPPLIED BY TWO SIDES Giuseppe Ferri Dipartimeto di Ihgegeria Elettrica-FacoM di Igegeria, Uiversita di L'Aquila

More information