SYNERESIS OF SODIUM OLEATE GELS IN ORGANIC SOLVENTS

Size: px
Start display at page:

Download "SYNERESIS OF SODIUM OLEATE GELS IN ORGANIC SOLVENTS"

Transcription

1 SYNERESIS OF SODIUM OLEATE GELS IN ORGANIC SOLVENTS Part V. Syneress of Sodum Oleate Gels n Mxtures of Organc Solvents BY MATh, PRASAD, F.A.Sc. AND V. SUNDA.M (From the Chemcal Laboratores, The Insttute of Scence, Bombay) Receved September 23, 1950 VARIOUS nvestgators have ponted out the mportance of the nature of the dsperson medum on the syr..ercss of gels. Usually the dsperson medum has been changed by the addton of other substances, such as acds, alcohols and others. Very few nvestgators have studed the syneress of the same gel-formng substance n dfferent meda. Hard/observed that the syneress of azomethne gels starts n a fcw mnutes n an ether gel, n a few hours n an alcohol or an aldehyde gel and n a few days n a carbon tetrachlorde gel. Le Blanc and Kroger 2 have notced that the syneress of caoutchouc gels n benzene starts earler than n carbon tetrachlorde; the velocty of the man amount exuded n both the solvents s the same but the fnal amount exuded by the gel n carbon tetrachlorde s somewhat greater. It has been observed n a prevous communcaton 3 that gels of sodum oleate n xylene synerse more rapdly than those n pnene. In the present nx, estgaton, an attempt has been made to study the syneress of sodum oleate gels n mxtures of (a) xylene and toluene and (b) xylene and pnene. EXPERIMENTAL (a) g. of sodum oleate was weghed out nto fve dfferent testtubes of the same nternal dameter (1.65 cm.) whch were flled wth several mxtures of xytene (A) and toluene (B). It was observed that f the mxtures contaned more than 70% by volume of toluene, the soap does not dssolve completely and the gels obtaned are not homogeneous. Hence mxtures contanng more than 70 toluene were not used. (b) g. of sodum oleate was weghed out nto seven dfferent testtubes of the same nternal dameter (1.65 cm.) whch were flled wth several mxtures of xylene (A) and pnene (C). The test-tubes were placed n an ol-bath, the temperature of whch was mantaned at C. n the case of mxtures of xylene and toluene and at C. n the case of mxtures of xylene and pnene, and the 344

2 Synertss of Sodum Oleate Gels n Organc Solvenls--V 345 contents of the test-tubes strred tll all the soap had dssolved. Then a long condensng tube was attached to each test-tube and the test-tubes were allowed to stand n the bath tll all the bubbles had dsappeared. The testtubes were then tghtly corked and transferred to a thermostat or a thermos flask dependng on the temperature at whch readngs were taken. At defnte ntervals of tme (t) after the gels had set, the amount of syneretcum (X) n each test-tube was measured by the method followed n Part II. n The temperatures used were 30 C. and 40 C. n the thermostat and 20 C. n the thermos flask. Sodum oleate used was of the B.D.H. qualty and the xylene used was obtaned from S. B. Penck & Co., New York. Toluene was obtaned from May & Baker, Ltd., and pnene from the Cty Chemcal Corporaton, New York. The results obtaned are gven n Tables I and II. DISCUSSION OF RESULTS It s seen from Table I that n the case of gels n mxtures of xylene and toluene the syneress ncreases wth an ncrease n the amount of toluene n the mxture. Ths fact s seen at all the temperatures. Also, the amount of syrteress at any one composton of the mxture s greatest at 20 C. and decreases as the temperature s ncreased. The effect of temperature on gels n mxtures of solvents s therefore smlar to that on gels n these pure solvents (cf. Part III of ths seres'). The graphs of syneress aganst composton of the mxture are more or less straght lnes for all the tme ntervals TABLE I Values of X for gels n mxtures of xylene and toluene at varous ntervals Composton Temperature '20 C. Temperature 30* C. Temperature 40 C. o[ the mxtare f A ] B 15 ran.; ' 30 ran, 1 hr I 2 hr. 15ran. 30 mm.l " ' I hr. 2 hrs. 15 ran. 30 mn.[ I hr. 2 hr ]0c.c. 8c. fc.c 4c.c. 3c.c. 0cc: 2c.c. 4c.c. 6c.c. 7c. I ! I o J [ , l , t I *

3 346 Mata Prasad and V. S u n d a r a m TABLE II Values of J( for gels n mxtures of xylene and pnene at varous ntervals omposton of the mxture A C Temperature 20 C. 15 mn.] 30 ran Temperature 30* C. 1 hr. ] 2 h r s. 15 ran 30mn. hr. F 0 c.c cc. I e,c c.c. 2c.c. 2" c. 4c.c c.c0 6c.c. 2 e x. 8c.c. I0 c. 0c.c.l 10c.c.! I Temperature40* C. 2 hrs, 15 mn. 30 ran. I hr. 2 hrs I " ! " O , ' J Oo studed, ndcatng the possblty of an addtvty law. The graphs of syneress aganst composton at 20 C. are shown n Fg. 1. Snce no gels are formed n pure toluene wth 0.10 g. of the soap, the valdty of the addtvty law cannot be tested n any case. It s seen from Table II that on ncreasng the percentage of pnene n the mxture of xylene and pnene, the amount of syneress of gels at frst ncreases, reaches a maxmum n a mxture contanng 80 xylene and 20 pnene, and then gradually falls off. The graphs of syneress aganst composton of the mxture are S-shaped for all the tme ntervals and temperatures studed; those n the case of syneress at 20 C. are shown n Fg. 2. The amount of syneretcum gven out by a gel n pure xylene s greater than that gven out by the same gel n pure pnene. Hence, t would be expected that on ncreasng the amount of pnene n the mxture the amount of syneretcum should contnually decrease. Palt and co-workers have shown that n the case of organc mxtures contanng a glycol as one component, the solublty of soap reaches a maxmum value at ntermedate compostons of the mxture. Probably n the mxtures of pnene and xyene me solu0lty has an optmum value n the mxture contanng 80 xylene and 20% pnene. Snce the same amount of soap s used n all the mxtures the amount of supersaturaton wll be teast n the mxture of 80 o xylene and 2 0 pnene and hence the gel formed wll be weaker (cf Part IV"). Therefore the syneress of the gel n the

4 Syneress ot; Sodum Oleage Gels n Organc Solvents--V 347 3") Z.*70 ' -,)o -Z,4O X X Z.-IO..Io ao 2.,4. 6 FIo. oe 1 L'I)O,-4o 2-40 I)... -_ j,, r A j. g 6 l F I G. = ) mxture of 80% ylene and 20 pnene would be maxmum. Such an effect s not observed n the mxtures of toluene and xylene, probably because both these solvents belong to the same homologous seres and the solublty n these solvents probabi fouows the addtvt law,

5 348 Mata Prasad and V. Sundaram It s also observed, as n the case of gels n mxtures of xylen and toluene, that syneress at a lower temperature s greater than at hgher ones. Further work for the examnaton of the behavour of soap gels n mxtures of organc lquds s n progress. One of the authors (V. S.) s grateful to the authortes of the Unversty of Bombay for the award of a Research Studentshp whch enabled hm to carry out ths nvestgaton. SUMMARY The rates of syneress n mxtures of (1)xylcnc and toluene and (2) xylenc and pnenc have becn nvestgated. In the case of xylene-toluene mxtures, syneress seems to be addtve whcreas n the case of xylenepnene mxtures, synercss shows a maxmum value n a mxture of 80 xylene and 20 pnene. REFERENCES 1. Hardy.. Proe. Roy. Soe., 1912, 87 A, Le Blanc and Kroger.. Z Elektrochem., 1921, 27, Prasad and Sundaram.. Part II, Communcated for publcaton Part Ill,,,,, 5. PaIR and Co-workers..... Indan Chem. Sac., 1942, 19, 271 ; 1949, 26, 12; jr Am. Chem. Soc., 1947, 69, 3120 ; 3". Am. Ol Chem. Sot., 1947, 24, Prasad and Sundaram.. Part IV, Communcated for publcaton.

Prediction of Ultrasonic Velocity in Binary Mixtures of a Nuclear Extractant and Monocarboxylic Acids using Several Theoretical Models

Prediction of Ultrasonic Velocity in Binary Mixtures of a Nuclear Extractant and Monocarboxylic Acids using Several Theoretical Models Predcton of ltrasonc Velocty n Bnary Mxtures of a Nuclear Extractant and Monocarboxylc Acds usng Several Theoretcal Models R. K. Mshra 1, B. Dala 1*, N. Swan 2 and S.K. Dash 3 1 BSH, Gandh Insttute of

More information

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:

Introduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law: CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and

More information

Mass Transfer Processes

Mass Transfer Processes Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.

More information

Adsorption: A gas or gases from a mixture of gases or a liquid (or liquids) from a mixture of liquids is bound physically to the surface of a solid.

Adsorption: A gas or gases from a mixture of gases or a liquid (or liquids) from a mixture of liquids is bound physically to the surface of a solid. Searatons n Chemcal Engneerng Searatons (gas from a mxture of gases, lquds from a mxture of lquds, solds from a soluton of solds n lquds, dssolved gases from lquds, solvents from gases artally/comletely

More information

A novel mathematical model of formulation design of emulsion explosive

A novel mathematical model of formulation design of emulsion explosive J. Iran. Chem. Res. 1 (008) 33-40 Journal of the Iranan Chemcal Research IAU-ARAK www.au-jcr.com A novel mathematcal model of formulaton desgn of emulson explosve Mng Lu *, Qfa Lu Chemcal Engneerng College,

More information

Gasometric Determination of NaHCO 3 in a Mixture

Gasometric Determination of NaHCO 3 in a Mixture 60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)

More information

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential

Open Systems: Chemical Potential and Partial Molar Quantities Chemical Potential Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,

More information

Using Spectrophotometric Methods to Determine an Equilibrium Constant Prelab

Using Spectrophotometric Methods to Determine an Equilibrium Constant Prelab Usng Spectrophotometrc Methods to Determne an Equlbrum Constant Prelab 1. What s the purpose of ths experment? 2. Wll the absorbance of the ulbrum mxture (at 447 nm) ncrease or decrease as Fe soluton s

More information

CHEMICAL ENGINEERING

CHEMICAL ENGINEERING Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton

More information

Volume 18 Figure 1. Notation 1. Notation 2. Observation 1. Remark 1. Remark 2. Remark 3. Remark 4. Remark 5. Remark 6. Theorem A [2]. Theorem B [2].

Volume 18 Figure 1. Notation 1. Notation 2. Observation 1. Remark 1. Remark 2. Remark 3. Remark 4. Remark 5. Remark 6. Theorem A [2]. Theorem B [2]. Bulletn of Mathematcal Scences and Applcatons Submtted: 016-04-07 ISSN: 78-9634, Vol. 18, pp 1-10 Revsed: 016-09-08 do:10.1805/www.scpress.com/bmsa.18.1 Accepted: 016-10-13 017 ScPress Ltd., Swtzerland

More information

One-sided finite-difference approximations suitable for use with Richardson extrapolation

One-sided finite-difference approximations suitable for use with Richardson extrapolation Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,

More information

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth

More information

Ttle Cs-trans somerzaton of malec a pressure Author(s) Kyama, Ryo; Mnomura, Shgeru Ctaton The Revew of Physcal Chemstry of ssue Date 1952 URL http://hdl.handle.net/2433/46672 Rght Type Departmental Bulletn

More information

Solutions Review Worksheet

Solutions Review Worksheet Solutons Revew Worksheet NOTE: Namng acds s ntroduced on pages 163-4 and agan on pages 208-9.. You learned ths and were quzzed on t, but snce acd names are n the Data Booklet you wll not be tested on ths

More information

A study on the effect of ball diameter on breakage properties of clinker and limestone

A study on the effect of ball diameter on breakage properties of clinker and limestone Indan Journal of Chemcal Technology Vol. 9, May 202, pp. 80-84 A study on the effect of ball dameter on breakage propertes of clnker and lmestone Vedat Denz* Department of Chemcal Engneerng, Htt Unversty,

More information

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W] Secton 1.3: Acceleraton Tutoral 1 Practce, page 24 1. Gven: 0 m/s; 15.0 m/s [S]; t 12.5 s Requred: Analyss: a av v t v f v t a v av f v t 15.0 m/s [S] 0 m/s 12.5 s 15.0 m/s [S] 12.5 s 1.20 m/s 2 [S] Statement:

More information

On Tiling for Some Types of Manifolds. and their Folding

On Tiling for Some Types of Manifolds. and their Folding Appled Mathematcal Scences, Vol. 3, 009, no. 6, 75-84 On Tlng for Some Types of Manfolds and ther Foldng H. Rafat Mathematcs Department, Faculty of Scence Tanta Unversty, Tanta Egypt hshamrafat005@yahoo.com

More information

Managing Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration

Managing Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration Managng Caacty Through eward Programs on-lne comanon age Byung-Do Km Seoul Natonal Unversty College of Busness Admnstraton Mengze Sh Unversty of Toronto otman School of Management Toronto ON M5S E6 Canada

More information

Mathematics Intersection of Lines

Mathematics Intersection of Lines a place of mnd F A C U L T Y O F E D U C A T I O N Department of Currculum and Pedagog Mathematcs Intersecton of Lnes Scence and Mathematcs Educaton Research Group Supported b UBC Teachng and Learnng Enhancement

More information

A study of ethoxymethylation in the 3-position of chroman-4-ones

A study of ethoxymethylation in the 3-position of chroman-4-ones Proc. Indan Acad. Sc. {Chem. Sc.), Vol. 13, No. 1, January 1991, pp. 25-31. 9 Prnted n Inda. A study of ethoxymethylaton n the 3-poston of chroman-4-ones AMOLAK C JAIN* and RENE SAKSENA Department of Chemstry,

More information

The L(2, 1)-Labeling on -Product of Graphs

The L(2, 1)-Labeling on -Product of Graphs Annals of Pure and Appled Mathematcs Vol 0, No, 05, 9-39 ISSN: 79-087X (P, 79-0888(onlne Publshed on 7 Aprl 05 wwwresearchmathscorg Annals of The L(, -Labelng on -Product of Graphs P Pradhan and Kamesh

More information

Influence Of Operating Conditions To The Effectiveness Of Extractive Distillation Columns

Influence Of Operating Conditions To The Effectiveness Of Extractive Distillation Columns Influence Of Operatng Condtons To The Effectveness Of Extractve Dstllaton Columns N.A. Vyazmna Moscov State Unversty Of Envrnmental Engneerng, Department Of Chemcal Engneerng Ul. Staraya Basmannaya 21/4,

More information

Remarks on the Properties of a Quasi-Fibonacci-like Polynomial Sequence

Remarks on the Properties of a Quasi-Fibonacci-like Polynomial Sequence Remarks on the Propertes of a Quas-Fbonacc-lke Polynomal Sequence Brce Merwne LIU Brooklyn Ilan Wenschelbaum Wesleyan Unversty Abstract Consder the Quas-Fbonacc-lke Polynomal Sequence gven by F 0 = 1,

More information

NUMERICAL DIFFERENTIATION

NUMERICAL DIFFERENTIATION NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the

More information

Negative Binomial Regression

Negative Binomial Regression STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...

More information

18. SIMPLE LINEAR REGRESSION III

18. SIMPLE LINEAR REGRESSION III 8. SIMPLE LINEAR REGRESSION III US Domestc Beers: Calores vs. % Alcohol Ftted Values and Resduals To each observed x, there corresponds a y-value on the ftted lne, y ˆ ˆ = α + x. The are called ftted values.

More information

Module 14: THE INTEGRAL Exploring Calculus

Module 14: THE INTEGRAL Exploring Calculus Module 14: THE INTEGRAL Explorng Calculus Part I Approxmatons and the Defnte Integral It was known n the 1600s before the calculus was developed that the area of an rregularly shaped regon could be approxmated

More information

28. SIMPLE LINEAR REGRESSION III

28. SIMPLE LINEAR REGRESSION III 8. SIMPLE LINEAR REGRESSION III Ftted Values and Resduals US Domestc Beers: Calores vs. % Alcohol To each observed x, there corresponds a y-value on the ftted lne, y ˆ = βˆ + βˆ x. The are called ftted

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

Lecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES

Lecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES COMPUTATIONAL FLUID DYNAMICS: FDM: Appromaton of Second Order Dervatves Lecture APPROXIMATION OF SECOMD ORDER DERIVATIVES. APPROXIMATION OF SECOND ORDER DERIVATIVES Second order dervatves appear n dffusve

More information

ME 300 Exam 2 November 18, :30 p.m. to 7:30 p.m.

ME 300 Exam 2 November 18, :30 p.m. to 7:30 p.m. CICLE YOU LECTUE BELOW: Frst Name Last Name 1:3 a.m. 1:3 p.m. Nak Gore ME 3 Exam November 18, 14 6:3 p.m. to 7:3 p.m. INSTUCTIONS 1. Ths s a closed book and closed notes examnaton. You are provded wth

More information

AP Physics 1 & 2 Summer Assignment

AP Physics 1 & 2 Summer Assignment AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers

More information

First Law of Thermodynamics

First Law of Thermodynamics Frst Law of Thermodynamcs Readng: Chapter 18, Sectons 18-7 to 18-11 Heat and Work When the pston s dsplaced by ds, force exerted by the gas = F = pa, work done by the gas: dw Fds ( pa)( ds) p( Ads) p d.

More information

Statistics Chapter 4

Statistics Chapter 4 Statstcs Chapter 4 "There are three knds of les: les, damned les, and statstcs." Benjamn Dsrael, 1895 (Brtsh statesman) Gaussan Dstrbuton, 4-1 If a measurement s repeated many tmes a statstcal treatment

More information

Name ID # For relatively dilute aqueous solutions the molality and molarity are approximately equal.

Name ID # For relatively dilute aqueous solutions the molality and molarity are approximately equal. Name ID # 1 CHEMISTRY 212, Lect. Sect. 002 Dr. G. L. Roberts Exam #1/Sprng 2000 Thursday, February 24, 2000 CLOSED BOOK EXM No notes or books allowed. Calculators may be used. tomc masses of nterest are

More information

TitleSynthesis of melamine from urea, II.

TitleSynthesis of melamine from urea, II. TtleSynthess of melamne from urea, II Author(s) Knoshta, Hdeo Ctaton The Revew of Physcal Chemstry of 7 Issue Date 9-0- URL http://hdl.handle.net//7 Rght Type Departmental Bulletn Paper Textverson publsher

More information

find (x): given element x, return the canonical element of the set containing x;

find (x): given element x, return the canonical element of the set containing x; COS 43 Sprng, 009 Dsjont Set Unon Problem: Mantan a collecton of dsjont sets. Two operatons: fnd the set contanng a gven element; unte two sets nto one (destructvely). Approach: Canoncal element method:

More information

CCO Commun. Comb. Optim.

CCO Commun. Comb. Optim. Communcatons n Combnatorcs and Optmzaton Vol. 2 No. 2, 2017 pp.87-98 DOI: 10.22049/CCO.2017.13630 CCO Commun. Comb. Optm. Reformulated F-ndex of graph operatons Hamdeh Aram 1 and Nasrn Dehgard 2 1 Department

More information

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity

LINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have

More information

The internal structure of natural numbers and one method for the definition of large prime numbers

The internal structure of natural numbers and one method for the definition of large prime numbers The nternal structure of natural numbers and one method for the defnton of large prme numbers Emmanul Manousos APM Insttute for the Advancement of Physcs and Mathematcs 3 Poulou str. 53 Athens Greece Abstract

More information

On the number of regions in an m-dimensional space cut by n hyperplanes

On the number of regions in an m-dimensional space cut by n hyperplanes 6 On the nuber of regons n an -densonal space cut by n hyperplanes Chungwu Ho and Seth Zeran Abstract In ths note we provde a unfor approach for the nuber of bounded regons cut by n hyperplanes n general

More information

DIELECTRIC MEASUREMENTS OF THE TERNARY MIXTURES OF ALCOHOLS WITH ANILINE IN CARBON TETRACHLORIDE AT 301K

DIELECTRIC MEASUREMENTS OF THE TERNARY MIXTURES OF ALCOHOLS WITH ANILINE IN CARBON TETRACHLORIDE AT 301K Vol. 1 No. 4 147-15 Octoer - Decemer 17 ISSN: 974-1496 e-issn: 976-83 CODEN: RJCAP http://www.rasayanjournal.com http://www.rasayanjournal.co.n DIELECTRIC MEASUREMENTS OF THE TERNARY MIXTURES OF ALCOHOLS

More information

Anti-van der Waerden numbers of 3-term arithmetic progressions.

Anti-van der Waerden numbers of 3-term arithmetic progressions. Ant-van der Waerden numbers of 3-term arthmetc progressons. Zhanar Berkkyzy, Alex Schulte, and Mchael Young Aprl 24, 2016 Abstract The ant-van der Waerden number, denoted by aw([n], k), s the smallest

More information

Title solubility of compressed acetylene.

Title solubility of compressed acetylene. Ttle The solubltes of compressed acet solublty of compressed acetylene Author(s) Hraoka, Hroyuk Ctaton The Revew of Physcal Chemstry of 18 ssue Date 1954-09-10 URL http://hdl.handle.net/2433/46704 Rght

More information

Computational Fluid Dynamics. Smoothed Particle Hydrodynamics. Simulations. Smoothing Kernels and Basis of SPH

Computational Fluid Dynamics. Smoothed Particle Hydrodynamics. Simulations. Smoothing Kernels and Basis of SPH Computatonal Flud Dynamcs If you want to learn a bt more of the math behnd flud dynamcs, read my prevous post about the Naver- Stokes equatons and Newtonan fluds. The equatons derved n the post are the

More information

Math1110 (Spring 2009) Prelim 3 - Solutions

Math1110 (Spring 2009) Prelim 3 - Solutions Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.

More information

MATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018

MATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018 MATH 5630: Dscrete Tme-Space Model Hung Phan, UMass Lowell March, 08 Newton s Law of Coolng Consder the coolng of a well strred coffee so that the temperature does not depend on space Newton s law of collng

More information

The optimal delay of the second test is therefore approximately 210 hours earlier than =2.

The optimal delay of the second test is therefore approximately 210 hours earlier than =2. THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple

More information

Susceptibility and Inverted Hysteresis Loop of Prussian Blue Analogs with Orthorhombic Structure

Susceptibility and Inverted Hysteresis Loop of Prussian Blue Analogs with Orthorhombic Structure Commun. Theor. Phys. 58 (202) 772 776 Vol. 58, No. 5, November 5, 202 Susceptblty and Inverted Hysteress Loop of Prussan Blue Analogs wth Orthorhombc Structure GUO An-Bang (ÁËǑ) and JIANG We ( å) School

More information

Assortment Optimization under MNL

Assortment Optimization under MNL Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.

More information

modeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products

modeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory

More information

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

Lecture 4: November 17, Part 1 Single Buffer Management

Lecture 4: November 17, Part 1 Single Buffer Management Lecturer: Ad Rosén Algorthms for the anagement of Networs Fall 2003-2004 Lecture 4: November 7, 2003 Scrbe: Guy Grebla Part Sngle Buffer anagement In the prevous lecture we taled about the Combned Input

More information

Supporting Materials

Supporting Materials Chrstopher Lockhart and Dmtr K. Klmov Molecular nteractons of Alzhemer's bomarker FDDNP wth A peptde Supportng Materals Parameterzaton of FDDNP molecule: CHARMM General Force Feld (CGenFF verson 2b6) was

More information

CHEM 112 Exam 3 Practice Test Solutions

CHEM 112 Exam 3 Practice Test Solutions CHEM 11 Exam 3 Practce Test Solutons 1A No matter what temperature the reacton takes place, the product of [OH-] x [H+] wll always equal the value of w. Therefore, f you take the square root of the gven

More information

Chapter 18, Part 1. Fundamentals of Atmospheric Modeling

Chapter 18, Part 1. Fundamentals of Atmospheric Modeling Overhead Sldes for Chapter 18, Part 1 of Fundamentals of Atmospherc Modelng by Mark Z. Jacobson Department of Cvl & Envronmental Engneerng Stanford Unversty Stanford, CA 94305-4020 January 30, 2002 Types

More information

SIMPLE REACTION TIME AS A FUNCTION OF TIME UNCERTAINTY 1

SIMPLE REACTION TIME AS A FUNCTION OF TIME UNCERTAINTY 1 Journal of Expermental Vol. 5, No. 3, 1957 Psychology SIMPLE REACTION TIME AS A FUNCTION OF TIME UNCERTAINTY 1 EDMUND T. KLEMMER Operatonal Applcatons Laboratory, Ar Force Cambrdge Research Center An earler

More information

Problem Set 9 - Solutions Due: April 27, 2005

Problem Set 9 - Solutions Due: April 27, 2005 Problem Set - Solutons Due: Aprl 27, 2005. (a) Frst note that spam messages, nvtatons and other e-mal are all ndependent Posson processes, at rates pλ, qλ, and ( p q)λ. The event of the tme T at whch you

More information

Why? Chemistry Crunch #4.1 : Name: KEY Phase Changes. Success Criteria: Prerequisites: Vocabulary:

Why? Chemistry Crunch #4.1 : Name: KEY Phase Changes. Success Criteria: Prerequisites: Vocabulary: Chemstry Crunch #4.1 : Name: KEY Phase Changes Why? Most substances wll eventually go through a phase change when heated or cooled (sometmes they chemcally react nstead). Molecules of a substance are held

More information

PART I: MULTIPLE CHOICE (32 questions, each multiple choice question has a 2-point value, 64 points total).

PART I: MULTIPLE CHOICE (32 questions, each multiple choice question has a 2-point value, 64 points total). CHEMISTRY 123-07 Mdterm #2 answer key November 04, 2010 Statstcs: Average: 68 p (68%); Hghest: 91 p (91%); Lowest: 37 p (37%) Number of students performng at or above average: 58 (53%) Number of students

More information

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department

More information

Prediction of the flash point of ternary ideal mixtures

Prediction of the flash point of ternary ideal mixtures Electronc Journal of New Materals, Energy and Envronment Volume No. (25), -5 url: http://ejnmee.eu/ eissn: 2367-6868 redcton of the flash pont of ternary deal mxtures M. Hrstova Unversty of Chemcal Technology

More information

NEW GENERAL FORMULAS FOR PYTHAGOREAN TRIPLES

NEW GENERAL FORMULAS FOR PYTHAGOREAN TRIPLES NEW GENERAL FORMULAS FOR PYTHAGOREAN TRIPLES EDUARDO CALOOY ROQUE Abstract. Ths paper shows the General Formulas for Pythagorean trples that were derved from the dfferences of the sdes of a rght trangle.

More information

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng

More information

Module 9. Lecture 6. Duality in Assignment Problems

Module 9. Lecture 6. Duality in Assignment Problems Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept

More information

ERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY

ERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY Proceedngs: Indoor Ar 2005 ERROR RESEARCH ON A HEPA FILTER MEDIA TESTING SYSTEM OF MPPS(MOST PENETRATION PARTICLE SIZE) EFFICIENCY S Lu, J Lu *, N Zhu School of Envronmental Scence and Technology, Tanjn

More information

Ttle The state dagrams of formaldehyde acetylene mxtures Author(s) Kyama, Ryo; Teransh, Hrosh Ctaton The Revew of Physcal Chemstry of 17 Issue Date 1952 URL http://hdl.handle.net/2433/46674 Rght Type Departmental

More information

y i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem

y i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem SOLUTION TO HOMEWORK #7 #roblem 1 10.1-1 a. In order to solve ths problem, we need to know what happens at the bubble pont; at ths pont, the frst bubble s formed, so we can assume that all of the number

More information

Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 10 - Phase Equilibria and Polymer Blends February 7, 2001

Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 10 - Phase Equilibria and Polymer Blends February 7, 2001 Checal Engneerng 60/60 Polyer Scence and Engneerng Lecture 0 - Phase Equlbra and Polyer Blends February 7, 00 Therodynacs of Polyer Blends: Part Objectves! To develop the classcal Flory-Huggns theory for

More information

Example: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41,

Example: (13320, 22140) =? Solution #1: The divisors of are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 41, The greatest common dvsor of two ntegers a and b (not both zero) s the largest nteger whch s a common factor of both a and b. We denote ths number by gcd(a, b), or smply (a, b) when there s no confuson

More information

System in Weibull Distribution

System in Weibull Distribution Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co

More information

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9. 9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson

More information

Grand canonical Monte Carlo simulations of bulk electrolytes and calcium channels

Grand canonical Monte Carlo simulations of bulk electrolytes and calcium channels Grand canoncal Monte Carlo smulatons of bulk electrolytes and calcum channels Thess of Ph.D. dssertaton Prepared by: Attla Malascs M.Sc. n Chemstry Supervsor: Dr. Dezső Boda Unversty of Pannona Insttute

More information

Lecture 12. Transport in Membranes (2)

Lecture 12. Transport in Membranes (2) Lecture 12. Transport n embranes (2) odule Flow Patterns - Perfect mxng - Countercurrent flow - Cocurrent flow - Crossflow embrane Cascades External ass-transfer Resstances Concentraton Polarzaton and

More information

A new Approach for Solving Linear Ordinary Differential Equations

A new Approach for Solving Linear Ordinary Differential Equations , ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of

More information

This model contains two bonds per unit cell (one along the x-direction and the other along y). So we can rewrite the Hamiltonian as:

This model contains two bonds per unit cell (one along the x-direction and the other along y). So we can rewrite the Hamiltonian as: 1 Problem set #1 1.1. A one-band model on a square lattce Fg. 1 Consder a square lattce wth only nearest-neghbor hoppngs (as shown n the fgure above): H t, j a a j (1.1) where,j stands for nearest neghbors

More information

Q e E i /k B. i i i i

Q e E i /k B. i i i i Water and Aqueous Solutons 3. Lattce Model of a Flud Lattce Models Lattce models provde a mnmalst, or coarse-graned, framework for descrbng the translatonal, rotatonal, and conformatonal degrees of freedom

More information

An Interactive Optimisation Tool for Allocation Problems

An Interactive Optimisation Tool for Allocation Problems An Interactve Optmsaton ool for Allocaton Problems Fredr Bonäs, Joam Westerlund and apo Westerlund Process Desgn Laboratory, Faculty of echnology, Åbo Aadem Unversty, uru 20500, Fnland hs paper presents

More information

Graph Reconstruction by Permutations

Graph Reconstruction by Permutations Graph Reconstructon by Permutatons Perre Ille and Wllam Kocay* Insttut de Mathémathques de Lumny CNRS UMR 6206 163 avenue de Lumny, Case 907 13288 Marselle Cedex 9, France e-mal: lle@ml.unv-mrs.fr Computer

More information

Nice plotting of proteins II

Nice plotting of proteins II Nce plottng of protens II Fnal remark regardng effcency: It s possble to wrte the Newton representaton n a way that can be computed effcently, usng smlar bracketng that we made for the frst representaton

More information

Estimation of the composition of the liquid and vapor streams exiting a flash unit with a supercritical component

Estimation of the composition of the liquid and vapor streams exiting a flash unit with a supercritical component Department of Energ oltecnco d Mlano Va Lambruschn - 05 MILANO Eercses of Fundamentals of Chemcal rocesses rof. Ganpero Gropp Eercse 8 Estmaton of the composton of the lqud and vapor streams etng a unt

More information

Non-Mixture Cure Model for Interval Censored Data: Simulation Study ABSTRACT

Non-Mixture Cure Model for Interval Censored Data: Simulation Study ABSTRACT Malaysan Journal of Mathematcal Scences 8(S): 37-44 (2014) Specal Issue: Internatonal Conference on Mathematcal Scences and Statstcs 2013 (ICMSS2013) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Journal

More information

Thermodynamics General

Thermodynamics General Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,

More information

FREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced,

FREQUENCY DISTRIBUTIONS Page 1 of The idea of a frequency distribution for sets of observations will be introduced, FREQUENCY DISTRIBUTIONS Page 1 of 6 I. Introducton 1. The dea of a frequency dstrbuton for sets of observatons wll be ntroduced, together wth some of the mechancs for constructng dstrbutons of data. Then

More information

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution

Department of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable

More information

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours

UNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x

More information

P exp(tx) = 1 + t 2k M 2k. k N

P exp(tx) = 1 + t 2k M 2k. k N 1. Subgaussan tals Defnton. Say that a random varable X has a subgaussan dstrbuton wth scale factor σ< f P exp(tx) exp(σ 2 t 2 /2) for all real t. For example, f X s dstrbuted N(,σ 2 ) then t s subgaussan.

More information

Chapter Newton s Method

Chapter Newton s Method Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve

More information

CS-433: Simulation and Modeling Modeling and Probability Review

CS-433: Simulation and Modeling Modeling and Probability Review CS-433: Smulaton and Modelng Modelng and Probablty Revew Exercse 1. (Probablty of Smple Events) Exercse 1.1 The owner of a camera shop receves a shpment of fve cameras from a camera manufacturer. Unknown

More information

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol

Using the estimated penetrances to determine the range of the underlying genetic model in casecontrol Georgetown Unversty From the SelectedWorks of Mark J Meyer 8 Usng the estmated penetrances to determne the range of the underlyng genetc model n casecontrol desgn Mark J Meyer Neal Jeffres Gang Zheng Avalable

More information

A Hybrid Variational Iteration Method for Blasius Equation

A Hybrid Variational Iteration Method for Blasius Equation Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method

More information

Problem Set 6: Trees Spring 2018

Problem Set 6: Trees Spring 2018 Problem Set 6: Trees 1-29 Sprng 2018 A Average dstance Gven a tree, calculate the average dstance between two vertces n the tree. For example, the average dstance between two vertces n the followng tree

More information

KINETICS OF GAS HYDRATE FORMATION FROM PYROLYSIS GAS IN WATER-IN-OIL EMULSION SYSTEM

KINETICS OF GAS HYDRATE FORMATION FROM PYROLYSIS GAS IN WATER-IN-OIL EMULSION SYSTEM Proceedngs of the 7th Internatonal Conference on Gas Hydrates (ICGH 211), Ednburgh, Scotland, Unted Kngdom, July 17-21, 211. KINETICS OF GAS HYDRATE FORMATION FROM PYROLYSIS GAS IN WATER-IN-OIL EMULSION

More information

METHOD OF NETWORK RELIABILITY ANALYSIS BASED ON ACCURACY CHARACTERISTICS

METHOD OF NETWORK RELIABILITY ANALYSIS BASED ON ACCURACY CHARACTERISTICS METHOD OF NETWOK ELIABILITY ANALYI BAED ON ACCUACY CHAACTEITIC ławomr Łapńsk hd tudent Faculty of Geodesy and Cartography Warsaw Unversty of Technology ABTACT Measurements of structures must be precse

More information

THE CURRENT BALANCE Physics 258/259

THE CURRENT BALANCE Physics 258/259 DSH 1988, 005 THE CURRENT BALANCE Physcs 58/59 The tme average force between two parallel conductors carryng an alternatng current s measured by balancng ths force aganst the gravtatonal force on a set

More information

On the correction of the h-index for career length

On the correction of the h-index for career length 1 On the correcton of the h-ndex for career length by L. Egghe Unverstet Hasselt (UHasselt), Campus Depenbeek, Agoralaan, B-3590 Depenbeek, Belgum 1 and Unverstet Antwerpen (UA), IBW, Stadscampus, Venusstraat

More information

Maximizing the number of nonnegative subsets

Maximizing the number of nonnegative subsets Maxmzng the number of nonnegatve subsets Noga Alon Hao Huang December 1, 213 Abstract Gven a set of n real numbers, f the sum of elements of every subset of sze larger than k s negatve, what s the maxmum

More information

Ttle The reacton between urea and phtha pressure Author(s) Yanagmoto, Takao Ctaton The Revew of Physcal Chemstry of 77 Issue Date 1956-02-20 URL http://hdl.handle.net/2433/46732 Rght Type Departmental

More information

SOLUTION/EXAMPLES. Contact during the exam: phone: , EXAM TBT4135 BIOPOLYMERS. 14 December Time:

SOLUTION/EXAMPLES. Contact during the exam: phone: , EXAM TBT4135 BIOPOLYMERS. 14 December Time: 1 NRWEGIN UNIVERSITY F SCIENCE ND TECHNLGY DEPRTMENT F BITECHNLGY Professor Bjørn E. Chrstensen, Department of Botechnology Contact durng the exam: phone: 73593327, 92634016 EXM TBT4135 BIPLYMERS 14 December

More information