REFRACTIVE INDEX IN BINARY AND TERNARY MIXTURES WITH DIETHYLENE GLYCOL, 1,4-DIOXANE AND WATER BETWEEN K

Size: px
Start display at page:

Download "REFRACTIVE INDEX IN BINARY AND TERNARY MIXTURES WITH DIETHYLENE GLYCOL, 1,4-DIOXANE AND WATER BETWEEN K"

Transcription

1 U.P.B. Sc. Bull., Seres B, Vol. 7, Iss. 4, 00 ISSN REFRACTIVE INDEX IN BINARY AND TERNARY MIXTURES WITH DIETHYLENE GLYCOL,,4-DIOXANE AND WATER BETWEEN K Olga IULIAN, Amala ŞTEFANIU, Oaa CIOCIRLAN 3, Aca FEDELEŞ 4 S-au determat expermetal ş s-au corelat dc de refracţe petru amestecurle bare ş terare cu apă,,4-doxa ş detleglcol la 93.5 K, K ş 33.5 K pe îtreaga gamă de compozţ. Petru a calcula dc de refracţe s-au utlzat ecuaţle predctve Loretz Lorez, Weer, Heller, Gladstoe Dale, Arago Bot s Edwards; s-a aalzat acurateţea de calcul a acestora. Valorle măsurate expermetal pot f utlzate petru a obţe depedeţa propretate - compozţe petru amestecurle cu glcol studate.ecuaţa Loretz- Loretz, cu u suport teoretc avasat, poate f utlzată cu succes petru toate sstemele. Refractve dces for bary ad terary mxtures cotag water,,4- doxae ad dethylee glycol were expermetally measured ad correlated at 93.5 K, K ad 33.5 K over the etre rage of compostos. Loretz Lorez, Weer, Heller, Gladstoe Dale, Arago Bot ad Edwards predctve equatos were used to calculate the refractve dex; ther accuracy was aalyzed. The expermetal values ca be used to obta the property - composto depedeces for the studed mxtures wth glycols. The Loretz Lorez equato havg a advaced theoretcal support ca be used successfully for all systems. Keywords: refractve dex, predcto, dethylee glycol. Itroducto The kowledge of refractve dex of lqud mxtures at dfferet temperatures s a mportat step for ther structural characterzato. Alog wth other thermodyamc data, refractve dex values are also useful for practcal purposes egeerg calculatos. Refractve dex s useful to assess purty of substaces, to calculate the molecular electroc polarzablty [], to estmate the Prof., Dept. of Appled Physcal Chemstry ad Electrochemstry, Uversty POLITEHNICA of Bucharest, Romaa, e-mal: olgaula@yahoo.com PhD studet, Dept. of Appled Physcal Chemstry ad Electrochemstry, Uversty POLITEHNICA of Bucharest, Romaa, e-mal: astefau@gmal.com 3 Assstat, Dept. of Appled Physcal Chemstry ad Electrochemstry, Uversty POLITEHNICA of Bucharest, Romaa, e-mal: cocrla_o@yahoo.com 4 PhD studet, Dept. of Appled Physcal Chemstry ad Electrochemstry, Uversty POLITEHNICA of Bucharest, Romaa

2 38 Olga Iula, Amala Ştefau, Oaa Cocrla, Aca Fedeleş bolg pot wth Messer's [] method or to estmate propertes such as vscosty [3] ad other thermodyamc propertes. Ths work cotue our research o thermodyamc propertes of systems wth glycols [4,5] ad presets expermetal data cocerg refractve dces of the bary ad terary systems cotag water,,4-doxae ad dethylee glycol betwee 93.5 ad 33.5 K. The data for 98.5 K were preseted prevously [6]. The systems wth water ad compouds cotag hydroxyl groups, lke glycols havg both hydrophlc ad hydrophobc groups, are commoly used as chemcal ad bochemcal reacto meda. The most frequetly employed equatos to correlate the refractve dex for lqud mxtures wth specfed composto are those of Loretz-Lorez, Weer, Heller, Gladstoe-Dale, Arago-Bot ad Edwards [7]. Loretz-Lorez equato ca be appled for large composto domas, the others are recommeded for more dluted solutos. Weer ad Heller equatos are vald oly f the volumes are addtve. Arago-Bot equatos have the same advatages ad dsadvatages as Gladstoe-Dale equato: they gve the best results for systems wth ear-deal behavor. By our kowledge, the bary mxtures wth water ad glycols [8,9] are scarcely studed ad the bary ad terary systems wth,4 doxae ad dethylee glycol have ot bee yet studed.. Expermetal Chemcals. The aalytcal-reaget-grade,4-doxae from Merck was dstlled at K to collect the mddle fracto; the water was twce dstlled ad the dethylee glycol (DEG) from Merck was dstlled at K vacuum (aroud 3.87 kpa). The purty of the materals was checked by gas chromatographc aalyss (over 99.5 mass %). The comparso wth lterature of refractve dex values for pure compoets s preseted Table. Apparatus ad procedure. The mxtures wth desred composto were prepared volumetrcally. The accuracy of the mole fracto was estmated at ±0.00. All mxtures were completely mscble over the whole composto rage. Refractve dex of the mxtures at the sodum D-le was measured wth Abbe refractometer, thermostated wth ± 0.05 K accuracy. The precso of the measuremets was ± A average of trplcate measuremets was cosdered.

3 Refractve dex bary ad terary mxtures wth dethylee glycol,,4-doxae ad water 39 Table : Expermetal ad lterature values of refractve dex for pure compouds at 98.5 K Refractve Pure compoud dex, dethylee water,4-doxae D glycol Expermetal Lterature.334 [0].335 [].339 [].400[3].40 [4].440 [5] 3. Results ad dscussos The obtaed expermetal refractve dex values for the bary systems: water + dethylee glycol,,4-doxae + dethylee glycol ad for terary systems: water +,4-doxae +EG, water +,4-doxae + DEG at 93.5 K, K ad 33.5 are preseted K table. For 98.5 K, the varato of the refractve dex wth composto for water +,4-doxae dethylee glycol terary system s showed Fg.. The obtaed data were used to test the Loretz-Lorez, Weer, Heller, Gladstoe-Dale, Arago-Bot ad Edwards mxg rules (Eqs. -6, respectvely) order to predct the refractve dex of bary ad terary mxtures usg refractve dces of pure compoets [6]. = ϕ + ϕ () = ϕ + + () 3 = ϕ m m m = + ( ) + ϕ ( ) = ϕ / (4) = ϕ (5) + ϕ (3) = ϕ + ϕ (6)

4 40 Olga Iula, Amala Ştefau, Oaa Cocrla, Aca Fedeleş I ()-(6), represets the refractve dex of the mxture,, are the refractve dces of pure compoets, φ, φ are the volume fractos of compoets. I order to evaluate the method accuracy, the stadard devato (σ) ad the average percetage devato () were calculated as follows: σ = = ( exp calc ) 0.5 (7) 00 = = exp exp calc (8) where exp, calc are the expermetal ad calculated values ad are the umber of expermetal data. The results of the predctve calculato for the refractve dex, the stadard devato ad average percetage devato are preseted Table 3. For the bary systems the method proposed by Loretz-Lorez, havg a advaced theoretcal support based o the addtve property of the molar refractos of pure compoets, ca be used wth good results for all systems. Good results are obtaed wth Gladstoe Dale, Edwars, Heller ad Weer (very smlar wth Heller) models. Thus, the stadard devato rage betwee 0.04 ad 0., whle the average percetage devato, betwee 0.6 ad 0.8, whe usg Loretz-Lorez equato. For the terary systems the best results are obtaed, as the case of bary systems, wth Loretz-Lorez equato; approprate results are gve by Gladstoe Dale, Heller, Weer ad Edwards equatos, cted order of creasg error of calculato ( %). Geerally, the predcto for bary systems s better tha for the terary oes. From the Table 3 t ca be see that all cases the Loretz-Lorez mxg rule gave the best results. I all cases the Arago-Bot equato gave poor predcto for both bary ad terary systems.

5 Refractve dex bary ad terary mxtures wth dethylee glycol,,4-doxae ad water 4 water ()+ DEG () Refractve dex for bary ad terary mxtures at dfferet temperatures,4-doxae () + DEG () water()+,4-doxae()+deg(3) Table X X X X X X T = 93.5 K T = K

6 4 Olga Iula, Amala Ştefau, Oaa Cocrla, Aca Fedeleş T = 33.5 K DEG (3) water (),4-doxae Fg.. Refractve dex predcto versus composto for the terary system water()+,4- doxae()+deg(3) at 98.5K usg Gladstoe Dale model

7 Refractve dex bary ad terary mxtures wth dethylee glycol,,4-doxae ad water 43 Table 3 Stadard devatos (σ) ad average percetage devato () as results of predctve models at dfferet temperatures System T, K Loretz Lorez σ 0 σ 0 Weer Heller σ 0 Model Gladstoe Dale σ 0 Arago Bot σ 0 Edwards σ 0 water+ DEG,4- doxae+ DEG water+,4- doxae+ DEG Coclusos Two bary ad oe terary systems cotag dethylee glycol were studed order to obta the refractve dex data at dfferet temperatures (93.5 K, 303.5K ad 33.5K). The expermetal data were used to test the capablty predcto of Loretz-Lorez, Weer, Heller, Gladstoe-Dale, Arago- Bot ad Edwards models. All predcto methods represet geerally well the expermetal data. The best results were obtaed wth Loretz-Lorez equato. As expected, the calculated refractve dex wth Arago-Bot equato s usatsfactory. The obtaed data o refractve dex are useful determg the composto of bary ad terary mxtures wth dethylee glycol.

8 44 Olga Iula, Amala Ştefau, Oaa Cocrla, Aca Fedeleş R E F E R E N C E S [] L.B. Ker, L.H. Hall, Molecular Coectvty Chemstry ad Drug Research, Sa Dego, Academc Press, 976 [] C.E. Rechsteer, Bolg Pot, Hadbook of Chemcal Property Estmato, W.J. Lyma, W.F. Reehl ad D. H. Roseblatt, Edtors, Washgto, Amerca Chemcal Socety, 990 [3] R.T. Lagema, J. Am. Chem. Soc., vol. 67, 945, pp [4] O. Iula, I. Nta, O. Cocrla, M. Catrcuc, A. Fedeles, Rev. Chme, Bucurest, vol. 60, o.9, 009, pp [5] A. Fedeles, O. Cocrla, O. Iula,, UPB Sc. Bull., seres B, vol.7, o.4, 009, pp [6] O. Iula, A. Stefau, O. Cocarla, 6th Romaa Iteratoal Coferece o Chemstry ad Chemcal Egeerg, Saa, 9- sept. 009, Romaa, S-3 P-38, pp. S III , ISBN: RICCCE [7] M. Catrcuc, O. Iula, I. Nta, M. Iosf, Aalele Uverstăţ Ovdus Costaţa, Sera: Chme, vol. (XVI), 005, pp [8] J. Alla, A.S. Teja, Ca. J. Chem. Eg., vol. 69, 99, pp [9] R.R. Dresbach, A.K. Doolttle, AIChE J., vol. 6, 960, pp. 50, 53, 57 [0] T.M. Amabhav, B. Gopalakrsha, J. Chem. Eg. Data, vol. 40, 995, pp [] N.G. Tserkezos, I.E. Molou, J. Chem. Eg. Data, vol. 43, 998, pp [] B.S. Hawrylak Adrecyk, C.-E. Gabrel, K. Garce, R. Palepu, J. Soluto Chem., vol. 7, 998, pp [3] A. Peas, E. Calvo, M. Ptos, A. Amgo, R. Bravo, J. Chem. Eg. Data, vol. 45, 005, pp [4] J.N. Nayak, M.I. Aralagupp, T.M. Amabhav, J. Chem. Eg. Data, vol.48, 003, pp.5 56 [5] R. M. Tombaugh, H.S. Chogull, Water Tras. Kasas Acad. Sc., vol. 54, 95, pp [6] A.Z. Tasc, B.D. Djordjevc, D.K. Grozdac, J. Chem. Eg. Data, vol. 37, 99, pp

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities Chemstry 163B Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?

More information

PREDICTION OF VAPOR-LIQUID EQUILIBRIA OF BINARY MIXTURES USING QUANTUM CALCULATIONS AND ACTIVITY COEFFICIENT MODELS

PREDICTION OF VAPOR-LIQUID EQUILIBRIA OF BINARY MIXTURES USING QUANTUM CALCULATIONS AND ACTIVITY COEFFICIENT MODELS Joural of Chemstry, Vol. 47 (5), P. 547-55, 9 PREDICTIO OF VAPOR-LIQUID EQUILIBRIA OF BIARY MIXTURES USIG QUATUM CALCULATIOS AD ACTIVITY COEFFICIET MODELS Receved May 8 PHAM VA TAT Departmet of Chemstry,

More information

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities

Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities Chemstry 163 Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?

More information

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures A Helmholtz eergy equato of state for calculatg the thermodyamc propertes of flud mxtures Erc W. Lemmo, Reer Tller-Roth Abstract New Approach based o hghly accurate EOS for the pure compoets combed at

More information

Estimation of Stress- Strength Reliability model using finite mixture of exponential distributions

Estimation of Stress- Strength Reliability model using finite mixture of exponential distributions Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur

More information

ENGI 4421 Propagation of Error Page 8-01

ENGI 4421 Propagation of Error Page 8-01 ENGI 441 Propagato of Error Page 8-01 Propagato of Error [Navd Chapter 3; ot Devore] Ay realstc measuremet procedure cotas error. Ay calculatos based o that measuremet wll therefore also cota a error.

More information

International Journal of Engineering Science Invention (IJESI) ISSN (Online): , ISSN (Print): PP.

International Journal of Engineering Science Invention (IJESI) ISSN (Online): , ISSN (Print): PP. Iteratoal Joural of geerg Scece Iveto (IJSI) ISSN (Ole): 319 6734, ISSN (Prt): 319 676 www.jes.org PP. 01-06 Partal Molar olumes At Ifte Dluto For The Bary Lqud Mxtures of N-Methyl--Pyrroldoe - A Gree

More information

We have already referred to a certain reaction, which takes place at high temperature after rich combustion.

We have already referred to a certain reaction, which takes place at high temperature after rich combustion. ME 41 Day 13 Topcs Chemcal Equlbrum - Theory Chemcal Equlbrum Example #1 Equlbrum Costats Chemcal Equlbrum Example #2 Chemcal Equlbrum of Hot Bured Gas 1. Chemcal Equlbrum We have already referred to a

More information

Module 1 : The equation of continuity. Lecture 5: Conservation of Mass for each species. & Fick s Law

Module 1 : The equation of continuity. Lecture 5: Conservation of Mass for each species. & Fick s Law Module : The equato of cotuty Lecture 5: Coservato of Mass for each speces & Fck s Law NPTEL, IIT Kharagpur, Prof. Sakat Chakraborty, Departmet of Chemcal Egeerg 2 Basc Deftos I Mass Trasfer, we usually

More information

CHAPTER VI Statistical Analysis of Experimental Data

CHAPTER VI Statistical Analysis of Experimental Data Chapter VI Statstcal Aalyss of Expermetal Data CHAPTER VI Statstcal Aalyss of Expermetal Data Measuremets do ot lead to a uque value. Ths s a result of the multtude of errors (maly radom errors) that ca

More information

Functions of Random Variables

Functions of Random Variables Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,

More information

Lesson 3. Group and individual indexes. Design and Data Analysis in Psychology I English group (A) School of Psychology Dpt. Experimental Psychology

Lesson 3. Group and individual indexes. Design and Data Analysis in Psychology I English group (A) School of Psychology Dpt. Experimental Psychology 17/03/015 School of Psychology Dpt. Expermetal Psychology Desg ad Data Aalyss Psychology I Eglsh group (A) Salvador Chacó Moscoso Susaa Saduvete Chaves Mlagrosa Sáchez Martí Lesso 3 Group ad dvdual dexes

More information

Volumetric and Excess Properties of Binary Liquid Mixtures of Butyl Acetate with Alkoxyethanols At k

Volumetric and Excess Properties of Binary Liquid Mixtures of Butyl Acetate with Alkoxyethanols At k ISS: 3-9653; IC Value: 45.98; SJ Impact Factor:6.887 Volume 5 Issue X, October 07- Avalable at www.jraset.com Volumetrc ad xcess Propertes of Bary Lqud Mxtures of Butyl Acetate wth Alkoxyethaols At 308.5k

More information

Chapter Statistics Background of Regression Analysis

Chapter Statistics Background of Regression Analysis Chapter 06.0 Statstcs Backgroud of Regresso Aalyss After readg ths chapter, you should be able to:. revew the statstcs backgroud eeded for learg regresso, ad. kow a bref hstory of regresso. Revew of Statstcal

More information

Bootstrap Method for Testing of Equality of Several Coefficients of Variation

Bootstrap Method for Testing of Equality of Several Coefficients of Variation Cloud Publcatos Iteratoal Joural of Advaced Mathematcs ad Statstcs Volume, pp. -6, Artcle ID Sc- Research Artcle Ope Access Bootstrap Method for Testg of Equalty of Several Coeffcets of Varato Dr. Navee

More information

Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.?

Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.? Ch 4. Statstcs 4.1 Quattatve aalyss requres : soud kowledge of chemstry : possblty of terfereces WHY do we eed to use STATISTICS Aal. Chem.? ucertaty ests. wll we accept ucertaty always? f ot, from how

More information

Evaluation of uncertainty in measurements

Evaluation of uncertainty in measurements Evaluato of ucertaty measuremets Laboratory of Physcs I Faculty of Physcs Warsaw Uversty of Techology Warszawa, 05 Itroducto The am of the measuremet s to determe the measured value. Thus, the measuremet

More information

General Method for Calculating Chemical Equilibrium Composition

General Method for Calculating Chemical Equilibrium Composition AE 6766/Setzma Sprg 004 Geeral Metod for Calculatg Cemcal Equlbrum Composto For gve tal codtos (e.g., for gve reactats, coose te speces to be cluded te products. As a example, for combusto of ydroge wt

More information

Module 7: Probability and Statistics

Module 7: Probability and Statistics Lecture 4: Goodess of ft tests. Itroducto Module 7: Probablty ad Statstcs I the prevous two lectures, the cocepts, steps ad applcatos of Hypotheses testg were dscussed. Hypotheses testg may be used to

More information

Dynamic Analysis of Axially Beam on Visco - Elastic Foundation with Elastic Supports under Moving Load

Dynamic Analysis of Axially Beam on Visco - Elastic Foundation with Elastic Supports under Moving Load Dyamc Aalyss of Axally Beam o Vsco - Elastc Foudato wth Elastc Supports uder Movg oad Saeed Mohammadzadeh, Seyed Al Mosayeb * Abstract: For dyamc aalyses of ralway track structures, the algorthm of soluto

More information

Cubic Nonpolynomial Spline Approach to the Solution of a Second Order Two-Point Boundary Value Problem

Cubic Nonpolynomial Spline Approach to the Solution of a Second Order Two-Point Boundary Value Problem Joural of Amerca Scece ;6( Cubc Nopolyomal Sple Approach to the Soluto of a Secod Order Two-Pot Boudary Value Problem W.K. Zahra, F.A. Abd El-Salam, A.A. El-Sabbagh ad Z.A. ZAk * Departmet of Egeerg athematcs

More information

Bayes Estimator for Exponential Distribution with Extension of Jeffery Prior Information

Bayes Estimator for Exponential Distribution with Extension of Jeffery Prior Information Malaysa Joural of Mathematcal Sceces (): 97- (9) Bayes Estmator for Expoetal Dstrbuto wth Exteso of Jeffery Pror Iformato Hadeel Salm Al-Kutub ad Noor Akma Ibrahm Isttute for Mathematcal Research, Uverst

More information

Third handout: On the Gini Index

Third handout: On the Gini Index Thrd hadout: O the dex Corrado, a tala statstca, proposed (, 9, 96) to measure absolute equalt va the mea dfferece whch s defed as ( / ) where refers to the total umber of dvduals socet. Assume that. The

More information

ESS Line Fitting

ESS Line Fitting ESS 5 014 17. Le Fttg A very commo problem data aalyss s lookg for relatoshpetwee dfferet parameters ad fttg les or surfaces to data. The smplest example s fttg a straght le ad we wll dscuss that here

More information

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn: Chapter 3 3- Busess Statstcs: A Frst Course Ffth Edto Chapter 2 Correlato ad Smple Lear Regresso Busess Statstcs: A Frst Course, 5e 29 Pretce-Hall, Ic. Chap 2- Learg Objectves I ths chapter, you lear:

More information

Sequential Approach to Covariance Correction for P-Field Simulation

Sequential Approach to Covariance Correction for P-Field Simulation Sequetal Approach to Covarace Correcto for P-Feld Smulato Chad Neufeld ad Clayto V. Deutsch Oe well kow artfact of the probablty feld (p-feld smulato algorthm s a too large covarace ear codtog data. Prevously,

More information

1. The weight of six Golden Retrievers is 66, 61, 70, 67, 92 and 66 pounds. The weight of six Labrador Retrievers is 54, 60, 72, 78, 84 and 67.

1. The weight of six Golden Retrievers is 66, 61, 70, 67, 92 and 66 pounds. The weight of six Labrador Retrievers is 54, 60, 72, 78, 84 and 67. Ecoomcs 3 Itroducto to Ecoometrcs Sprg 004 Professor Dobk Name Studet ID Frst Mdterm Exam You must aswer all the questos. The exam s closed book ad closed otes. You may use your calculators but please

More information

Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model

Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The

More information

A Method for Damping Estimation Based On Least Square Fit

A Method for Damping Estimation Based On Least Square Fit Amerca Joural of Egeerg Research (AJER) 5 Amerca Joural of Egeerg Research (AJER) e-issn: 3-847 p-issn : 3-936 Volume-4, Issue-7, pp-5-9 www.ajer.org Research Paper Ope Access A Method for Dampg Estmato

More information

F A. Review1 7/1/2014. How to prepare for exams. Chapter 10 - GASES PRESSURE IS THE FORCE ACTING ON AN OBJECT PER UNIT AREA MEASUREMENT OF PRESSURE

F A. Review1 7/1/2014. How to prepare for exams. Chapter 10 - GASES PRESSURE IS THE FORCE ACTING ON AN OBJECT PER UNIT AREA MEASUREMENT OF PRESSURE How to prepare for exams 1. Uderstad EXAMLES chapter(s). Work RACICE EXERCISES 3. Work oe problem from each class of problems at ed of chapter 4. Aswer as may questos as tme permts from text web: www.prehall.com/brow

More information

Chapter 13 Student Lecture Notes 13-1

Chapter 13 Student Lecture Notes 13-1 Chapter 3 Studet Lecture Notes 3- Basc Busess Statstcs (9 th Edto) Chapter 3 Smple Lear Regresso 4 Pretce-Hall, Ic. Chap 3- Chapter Topcs Types of Regresso Models Determg the Smple Lear Regresso Equato

More information

EXCESS PROPERTIES IN DIMETHYL SULFOXIDE + 1- BUTANOL AND 1,4-DIOXANE+1-BUTANOL BINARY MIXTURES AT K

EXCESS PROPERTIES IN DIMETHYL SULFOXIDE + 1- BUTANOL AND 1,4-DIOXANE+1-BUTANOL BINARY MIXTURES AT K U.P.B. Sc. Bull., Seres B, Vol. 7, Iss. 4, 009 ISSN 454- ECESS PROPERTIES IN DIMETHYL SULFOIDE + - BUTANOL AND,4-DIOANE+-BUTANOL BINARY MITURES AT 98.5 K Anca FEDELEŞ, Oana CIOCÎRLAN, Olga IULIAN În lucrare

More information

COMPUTERISED ALGEBRA USED TO CALCULATE X n COST AND SOME COSTS FROM CONVERSIONS OF P-BASE SYSTEM WITH REFERENCES OF P-ADIC NUMBERS FROM

COMPUTERISED ALGEBRA USED TO CALCULATE X n COST AND SOME COSTS FROM CONVERSIONS OF P-BASE SYSTEM WITH REFERENCES OF P-ADIC NUMBERS FROM U.P.B. Sc. Bull., Seres A, Vol. 68, No. 3, 6 COMPUTERISED ALGEBRA USED TO CALCULATE X COST AND SOME COSTS FROM CONVERSIONS OF P-BASE SYSTEM WITH REFERENCES OF P-ADIC NUMBERS FROM Z AND Q C.A. MURESAN Autorul

More information

Applying the condition for equilibrium to this equilibrium, we get (1) n i i =, r G and 5 i

Applying the condition for equilibrium to this equilibrium, we get (1) n i i =, r G and 5 i CHEMICAL EQUILIBRIA The Thermodyamc Equlbrum Costat Cosder a reversble reacto of the type 1 A 1 + 2 A 2 + W m A m + m+1 A m+1 + Assgg postve values to the stochometrc coeffcets o the rght had sde ad egatve

More information

Median as a Weighted Arithmetic Mean of All Sample Observations

Median as a Weighted Arithmetic Mean of All Sample Observations Meda as a Weghted Arthmetc Mea of All Sample Observatos SK Mshra Dept. of Ecoomcs NEHU, Shllog (Ida). Itroducto: Iumerably may textbooks Statstcs explctly meto that oe of the weakesses (or propertes) of

More information

Comparison of Parameters of Lognormal Distribution Based On the Classical and Posterior Estimates

Comparison of Parameters of Lognormal Distribution Based On the Classical and Posterior Estimates Joural of Moder Appled Statstcal Methods Volume Issue Artcle 8 --03 Comparso of Parameters of Logormal Dstrbuto Based O the Classcal ad Posteror Estmates Raja Sulta Uversty of Kashmr, Sragar, Ida, hamzasulta8@yahoo.com

More information

Statistics MINITAB - Lab 5

Statistics MINITAB - Lab 5 Statstcs 10010 MINITAB - Lab 5 PART I: The Correlato Coeffcet Qute ofte statstcs we are preseted wth data that suggests that a lear relatoshp exsts betwee two varables. For example the plot below s of

More information

Summary of the lecture in Biostatistics

Summary of the lecture in Biostatistics Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the

More information

MULTIDIMENSIONAL HETEROGENEOUS VARIABLE PREDICTION BASED ON EXPERTS STATEMENTS. Gennadiy Lbov, Maxim Gerasimov

MULTIDIMENSIONAL HETEROGENEOUS VARIABLE PREDICTION BASED ON EXPERTS STATEMENTS. Gennadiy Lbov, Maxim Gerasimov Iteratoal Boo Seres "Iformato Scece ad Computg" 97 MULTIIMNSIONAL HTROGNOUS VARIABL PRICTION BAS ON PRTS STATMNTS Geady Lbov Maxm Gerasmov Abstract: I the wors [ ] we proposed a approach of formg a cosesus

More information

Analyzing Two-Dimensional Data. Analyzing Two-Dimensional Data

Analyzing Two-Dimensional Data. Analyzing Two-Dimensional Data /7/06 Aalzg Two-Dmesoal Data The most commo aaltcal measuremets volve the determato of a ukow cocetrato based o the respose of a aaltcal procedure (usuall strumetal). Such a measuremet requres calbrato,

More information

Research Journal of Chemical Sciences ISSN X Vol. 5(6), 64-72, June (2015)

Research Journal of Chemical Sciences ISSN X Vol. 5(6), 64-72, June (2015) Research Joural of Chemcal Sceces ISSN 3-606X Vol. 5(6), 64-7, Jue (05) Res. J. Chem. Sc. Vapor-Lqud Equlbrum Data Predcto by Advaced Group Cotrbuto Methods for a Bary System of Cyclopetyl methyl ether

More information

Bayes Interval Estimation for binomial proportion and difference of two binomial proportions with Simulation Study

Bayes Interval Estimation for binomial proportion and difference of two binomial proportions with Simulation Study IJIEST Iteratoal Joural of Iovatve Scece, Egeerg & Techology, Vol. Issue 5, July 04. Bayes Iterval Estmato for bomal proporto ad dfferece of two bomal proportos wth Smulato Study Masoud Gaj, Solmaz hlmad

More information

Introduction to local (nonparametric) density estimation. methods

Introduction to local (nonparametric) density estimation. methods Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest

More information

A Robust Total Least Mean Square Algorithm For Nonlinear Adaptive Filter

A Robust Total Least Mean Square Algorithm For Nonlinear Adaptive Filter A Robust otal east Mea Square Algorthm For Nolear Adaptve Flter Ruxua We School of Electroc ad Iformato Egeerg X'a Jaotog Uversty X'a 70049, P.R. Cha rxwe@chare.com Chogzhao Ha, azhe u School of Electroc

More information

A Combination of Adaptive and Line Intercept Sampling Applicable in Agricultural and Environmental Studies

A Combination of Adaptive and Line Intercept Sampling Applicable in Agricultural and Environmental Studies ISSN 1684-8403 Joural of Statstcs Volume 15, 008, pp. 44-53 Abstract A Combato of Adaptve ad Le Itercept Samplg Applcable Agrcultural ad Evrometal Studes Azmer Kha 1 A adaptve procedure s descrbed for

More information

A New Family of Transformations for Lifetime Data

A New Family of Transformations for Lifetime Data Proceedgs of the World Cogress o Egeerg 4 Vol I, WCE 4, July - 4, 4, Lodo, U.K. A New Famly of Trasformatos for Lfetme Data Lakhaa Watthaacheewakul Abstract A famly of trasformatos s the oe of several

More information

= 1. UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Parameters and Statistics. Measures of Centrality

= 1. UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Parameters and Statistics. Measures of Centrality UCLA STAT Itroducto to Statstcal Methods for the Lfe ad Health Sceces Istructor: Ivo Dov, Asst. Prof. of Statstcs ad Neurology Teachg Assstats: Fred Phoa, Krste Johso, Mg Zheg & Matlda Hseh Uversty of

More information

CHEMICAL EQUILIBRIA BETWEEN THE ION EXCHANGER AND GAS PHASE. Vladimir Soldatov and Eugeny Kosandrovich

CHEMICAL EQUILIBRIA BETWEEN THE ION EXCHANGER AND GAS PHASE. Vladimir Soldatov and Eugeny Kosandrovich CHEMICAL EQUILIBRIA BETWEEN THE ION EXCHANGER AND GAS PHASE Vladmr Soldatov ad Eugey Kosadrovch Isttute of Physcal Orgac Chemstry Natoal Academy of Sceces of Belarus, 13, Surgaov St, Msk 2272, Rep. of

More information

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1

STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ  1 STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ

More information

Chapter 8: Statistical Analysis of Simulated Data

Chapter 8: Statistical Analysis of Simulated Data Marquette Uversty MSCS600 Chapter 8: Statstcal Aalyss of Smulated Data Dael B. Rowe, Ph.D. Departmet of Mathematcs, Statstcs, ad Computer Scece Copyrght 08 by Marquette Uversty MSCS600 Ageda 8. The Sample

More information

PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation

PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad

More information

C-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory

C-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory ROAD MAP... AE301 Aerodyamcs I UNIT C: 2-D Arfols C-1: Aerodyamcs of Arfols 1 C-2: Aerodyamcs of Arfols 2 C-3: Pael Methods C-4: Th Arfol Theory AE301 Aerodyamcs I Ut C-3: Lst of Subects Problem Solutos?

More information

Confidence Intervals for Double Exponential Distribution: A Simulation Approach

Confidence Intervals for Double Exponential Distribution: A Simulation Approach World Academy of Scece, Egeerg ad Techology Iteratoal Joural of Physcal ad Mathematcal Sceces Vol:6, No:, 0 Cofdece Itervals for Double Expoetal Dstrbuto: A Smulato Approach M. Alrasheed * Iteratoal Scece

More information

Comparison of Dual to Ratio-Cum-Product Estimators of Population Mean

Comparison of Dual to Ratio-Cum-Product Estimators of Population Mean Research Joural of Mathematcal ad Statstcal Sceces ISS 30 6047 Vol. 1(), 5-1, ovember (013) Res. J. Mathematcal ad Statstcal Sc. Comparso of Dual to Rato-Cum-Product Estmators of Populato Mea Abstract

More information

L5 Polynomial / Spline Curves

L5 Polynomial / Spline Curves L5 Polyomal / Sple Curves Cotets Coc sectos Polyomal Curves Hermte Curves Bezer Curves B-Sples No-Uform Ratoal B-Sples (NURBS) Mapulato ad Represetato of Curves Types of Curve Equatos Implct: Descrbe a

More information

Comparing Different Estimators of three Parameters for Transmuted Weibull Distribution

Comparing Different Estimators of three Parameters for Transmuted Weibull Distribution Global Joural of Pure ad Appled Mathematcs. ISSN 0973-768 Volume 3, Number 9 (207), pp. 55-528 Research Ida Publcatos http://www.rpublcato.com Comparg Dfferet Estmators of three Parameters for Trasmuted

More information

Derivation of 3-Point Block Method Formula for Solving First Order Stiff Ordinary Differential Equations

Derivation of 3-Point Block Method Formula for Solving First Order Stiff Ordinary Differential Equations Dervato of -Pot Block Method Formula for Solvg Frst Order Stff Ordary Dfferetal Equatos Kharul Hamd Kharul Auar, Kharl Iskadar Othma, Zara Bb Ibrahm Abstract Dervato of pot block method formula wth costat

More information

About k-perfect numbers

About k-perfect numbers DOI: 0.47/auom-04-0005 A. Şt. Uv. Ovdus Costaţa Vol.,04, 45 50 About k-perfect umbers Mhály Becze Abstract ABSTRACT. I ths paper we preset some results about k-perfect umbers, ad geeralze two equaltes

More information

Analysis of Lagrange Interpolation Formula

Analysis of Lagrange Interpolation Formula P IJISET - Iteratoal Joural of Iovatve Scece, Egeerg & Techology, Vol. Issue, December 4. www.jset.com ISS 348 7968 Aalyss of Lagrage Iterpolato Formula Vjay Dahya PDepartmet of MathematcsMaharaja Surajmal

More information

Lower Bounds of the Kirchhoff and Degree Kirchhoff Indices

Lower Bounds of the Kirchhoff and Degree Kirchhoff Indices SCIENTIFIC PUBLICATIONS OF THE STATE UNIVERSITY OF NOVI PAZAR SER. A: APPL. MATH. INFORM. AND MECH. vol. 7, (205), 25-3. Lower Bouds of the Krchhoff ad Degree Krchhoff Idces I. Ž. Mlovaovć, E. I. Mlovaovć,

More information

Chapter 8. Inferences about More Than Two Population Central Values

Chapter 8. Inferences about More Than Two Population Central Values Chapter 8. Ifereces about More Tha Two Populato Cetral Values Case tudy: Effect of Tmg of the Treatmet of Port-We tas wth Lasers ) To vestgate whether treatmet at a youg age would yeld better results tha

More information

Chapter 13, Part A Analysis of Variance and Experimental Design. Introduction to Analysis of Variance. Introduction to Analysis of Variance

Chapter 13, Part A Analysis of Variance and Experimental Design. Introduction to Analysis of Variance. Introduction to Analysis of Variance Chapter, Part A Aalyss of Varace ad Epermetal Desg Itroducto to Aalyss of Varace Aalyss of Varace: Testg for the Equalty of Populato Meas Multple Comparso Procedures Itroducto to Aalyss of Varace Aalyss

More information

Lecture 3. Sampling, sampling distributions, and parameter estimation

Lecture 3. Sampling, sampling distributions, and parameter estimation Lecture 3 Samplg, samplg dstrbutos, ad parameter estmato Samplg Defto Populato s defed as the collecto of all the possble observatos of terest. The collecto of observatos we take from the populato s called

More information

STA302/1001-Fall 2008 Midterm Test October 21, 2008

STA302/1001-Fall 2008 Midterm Test October 21, 2008 STA3/-Fall 8 Mdterm Test October, 8 Last Name: Frst Name: Studet Number: Erolled (Crcle oe) STA3 STA INSTRUCTIONS Tme allowed: hour 45 mutes Ads allowed: A o-programmable calculator A table of values from

More information

Convergence of the Desroziers scheme and its relation to the lag innovation diagnostic

Convergence of the Desroziers scheme and its relation to the lag innovation diagnostic Covergece of the Desrozers scheme ad ts relato to the lag ovato dagostc chard Méard Evromet Caada, Ar Qualty esearch Dvso World Weather Ope Scece Coferece Motreal, August 9, 04 o t t O x x x y x y Oservato

More information

Some Applications of the Resampling Methods in Computational Physics

Some Applications of the Resampling Methods in Computational Physics Iteratoal Joural of Mathematcs Treds ad Techoloy Volume 6 February 04 Some Applcatos of the Resampl Methods Computatoal Physcs Sotraq Marko #, Lorec Ekoom * # Physcs Departmet, Uversty of Korca, Albaa,

More information

Study of Correlation using Bayes Approach under bivariate Distributions

Study of Correlation using Bayes Approach under bivariate Distributions Iteratoal Joural of Scece Egeerg ad Techolog Research IJSETR Volume Issue Februar 4 Stud of Correlato usg Baes Approach uder bvarate Dstrbutos N.S.Padharkar* ad. M.N.Deshpade** *Govt.Vdarbha Isttute of

More information

Carbonyl Groups. University of Chemical Technology, Beijing , PR China;

Carbonyl Groups. University of Chemical Technology, Beijing , PR China; Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Supportg Iformato A Theoretcal Study of Structure-Solublty Correlatos of Carbo Doxde Polymers Cotag

More information

ENGI 3423 Simple Linear Regression Page 12-01

ENGI 3423 Simple Linear Regression Page 12-01 ENGI 343 mple Lear Regresso Page - mple Lear Regresso ometmes a expermet s set up where the expermeter has cotrol over the values of oe or more varables X ad measures the resultg values of aother varable

More information

On the Link Between the Concepts of Kurtosis and Bipolarization. Abstract

On the Link Between the Concepts of Kurtosis and Bipolarization. Abstract O the Lk etwee the Cocepts of Kurtoss ad polarzato Jacques SILE ar-ila Uversty Joseph Deutsch ar-ila Uversty Metal Haoka ar-ila Uversty h.d. studet) Abstract I a paper o the measuremet of the flatess of

More information

Midterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes

Midterm Exam 1, section 1 (Solution) Thursday, February hour, 15 minutes coometrcs, CON Sa Fracsco State Uversty Mchael Bar Sprg 5 Mdterm am, secto Soluto Thursday, February 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes eam.. No calculators of ay kd are allowed..

More information

COV. Violation of constant variance of ε i s but they are still independent. The error term (ε) is said to be heteroscedastic.

COV. Violation of constant variance of ε i s but they are still independent. The error term (ε) is said to be heteroscedastic. c Pogsa Porchawseskul, Faculty of Ecoomcs, Chulalogkor Uversty olato of costat varace of s but they are stll depedet. C,, he error term s sad to be heteroscedastc. c Pogsa Porchawseskul, Faculty of Ecoomcs,

More information

Analysis of Variance with Weibull Data

Analysis of Variance with Weibull Data Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad

More information

Statistics Descriptive and Inferential Statistics. Instructor: Daisuke Nagakura

Statistics Descriptive and Inferential Statistics. Instructor: Daisuke Nagakura Statstcs Descrptve ad Iferetal Statstcs Istructor: Dasuke Nagakura (agakura@z7.keo.jp) 1 Today s topc Today, I talk about two categores of statstcal aalyses, descrptve statstcs ad feretal statstcs, ad

More information

STATISTICS 13. Lecture 5 Apr 7, 2010

STATISTICS 13. Lecture 5 Apr 7, 2010 STATISTICS 13 Leture 5 Apr 7, 010 Revew Shape of the data -Bell shaped -Skewed -Bmodal Measures of eter Arthmet Mea Meda Mode Effets of outlers ad skewess Measures of Varablt A quattatve measure that desrbes

More information

Block-Based Compact Thermal Modeling of Semiconductor Integrated Circuits

Block-Based Compact Thermal Modeling of Semiconductor Integrated Circuits Block-Based Compact hermal Modelg of Semcoductor Itegrated Crcuts Master s hess Defese Caddate: Jg Ba Commttee Members: Dr. Mg-Cheg Cheg Dr. Daqg Hou Dr. Robert Schllg July 27, 2009 Outle Itroducto Backgroud

More information

Heat-Integrated Distillation Columns -Analysis and Modellingwith. Advanced Distillation as Supporting Subject

Heat-Integrated Distillation Columns -Analysis and Modellingwith. Advanced Distillation as Supporting Subject Norwega Uversty Of Scece ad Techology Faculty of Egeerg ad Techology Uversty of Belgrade Faculty of Mechacal Egeerg Isttute for Eergy Techology The log-term co-operatve project Master Degree Program: Sustaable

More information

Beam Warming Second-Order Upwind Method

Beam Warming Second-Order Upwind Method Beam Warmg Secod-Order Upwd Method Petr Valeta Jauary 6, 015 Ths documet s a part of the assessmet work for the subject 1DRP Dfferetal Equatos o Computer lectured o FNSPE CTU Prague. Abstract Ths documet

More information

SPECIAL CONSIDERATIONS FOR VOLUMETRIC Z-TEST FOR PROPORTIONS

SPECIAL CONSIDERATIONS FOR VOLUMETRIC Z-TEST FOR PROPORTIONS SPECIAL CONSIDERAIONS FOR VOLUMERIC Z-ES FOR PROPORIONS Oe s stctve reacto to the questo of whether two percetages are sgfcatly dfferet from each other s to treat them as f they were proportos whch the

More information

hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations

hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations HP 30S Statstcs Averages ad Stadard Devatos Average ad Stadard Devato Practce Fdg Averages ad Stadard Devatos HP 30S Statstcs Averages ad Stadard Devatos Average ad stadard devato The HP 30S provdes several

More information

STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1

STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1 STA 08 Appled Lear Models: Regresso Aalyss Sprg 0 Soluto for Homework #. Let Y the dollar cost per year, X the umber of vsts per year. The the mathematcal relato betwee X ad Y s: Y 300 + X. Ths s a fuctoal

More information

Densities and viscosities of aqueous ternary mixtures of 2-amino-2-methyl-1-propanol with ethylenediamine from to K

Densities and viscosities of aqueous ternary mixtures of 2-amino-2-methyl-1-propanol with ethylenediamine from to K Destes ad vscostes of aqueous terary mxtures of 2-amo-2-methyl-1-propaol wth ethyleedame from 303.15 to 343.15 K Rega V. trolzo R&D Ceter for Membrae Techology ad Departmet of Chemcal geerg Chug Yua Chrsta

More information

A tighter lower bound on the circuit size of the hardest Boolean functions

A tighter lower bound on the circuit size of the hardest Boolean functions Electroc Colloquum o Computatoal Complexty, Report No. 86 2011) A tghter lower boud o the crcut sze of the hardest Boolea fuctos Masak Yamamoto Abstract I [IPL2005], Fradse ad Mlterse mproved bouds o the

More information

Bias Correction in Estimation of the Population Correlation Coefficient

Bias Correction in Estimation of the Population Correlation Coefficient Kasetsart J. (Nat. Sc.) 47 : 453-459 (3) Bas Correcto Estmato of the opulato Correlato Coeffcet Juthaphor Ssomboothog ABSTRACT A estmator of the populato correlato coeffcet of two varables for a bvarate

More information

Some Notes on the Probability Space of Statistical Surveys

Some Notes on the Probability Space of Statistical Surveys Metodološk zvezk, Vol. 7, No., 200, 7-2 ome Notes o the Probablty pace of tatstcal urveys George Petrakos Abstract Ths paper troduces a formal presetato of samplg process usg prcples ad cocepts from Probablty

More information

residual. (Note that usually in descriptions of regression analysis, upper-case

residual. (Note that usually in descriptions of regression analysis, upper-case Regresso Aalyss Regresso aalyss fts or derves a model that descres the varato of a respose (or depedet ) varale as a fucto of oe or more predctor (or depedet ) varales. The geeral regresso model s oe of

More information

Fractional Order Finite Difference Scheme For Soil Moisture Diffusion Equation And Its Applications

Fractional Order Finite Difference Scheme For Soil Moisture Diffusion Equation And Its Applications IOS Joural of Mathematcs (IOS-JM e-iss: 78-578. Volume 5, Issue 4 (Ja. - Feb. 3, PP -8 www.osrourals.org Fractoal Order Fte Dfferece Scheme For Sol Mosture Dffuso quato Ad Its Applcatos S.M.Jogdad, K.C.Takale,

More information

Solving Constrained Flow-Shop Scheduling. Problems with Three Machines

Solving Constrained Flow-Shop Scheduling. Problems with Three Machines It J Cotemp Math Sceces, Vol 5, 2010, o 19, 921-929 Solvg Costraed Flow-Shop Schedulg Problems wth Three Maches P Pada ad P Rajedra Departmet of Mathematcs, School of Advaced Sceces, VIT Uversty, Vellore-632

More information

Bounds for the Connective Eccentric Index

Bounds for the Connective Eccentric Index It. J. Cotemp. Math. Sceces, Vol. 7, 0, o. 44, 6-66 Bouds for the Coectve Eccetrc Idex Nlaja De Departmet of Basc Scece, Humates ad Socal Scece (Mathematcs Calcutta Isttute of Egeerg ad Maagemet Kolkata,

More information

THE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE

THE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE THE ROYAL STATISTICAL SOCIETY 00 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER I STATISTICAL THEORY The Socety provdes these solutos to assst caddates preparg for the examatos future years ad for the

More information

2006 Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America

2006 Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America SOLUTION OF SYSTEMS OF SIMULTANEOUS LINEAR EQUATIONS Gauss-Sedel Method 006 Jame Traha, Autar Kaw, Kev Mart Uversty of South Florda Uted States of Amerca kaw@eg.usf.edu Itroducto Ths worksheet demostrates

More information

Topological Indices of Hypercubes

Topological Indices of Hypercubes 202, TextRoad Publcato ISSN 2090-4304 Joural of Basc ad Appled Scetfc Research wwwtextroadcom Topologcal Idces of Hypercubes Sahad Daeshvar, okha Izbrak 2, Mozhga Masour Kalebar 3,2 Departmet of Idustral

More information

Modeling Thermal Conductivity of Concentrated and Mixed-Solvent Electrolyte Systems

Modeling Thermal Conductivity of Concentrated and Mixed-Solvent Electrolyte Systems 5698 Id. Eg. Chem. Res. 28, 47, 5698 579 Modelg Thermal Coductvty of Cocetrated ad Mxed-Solvet Electrolyte Systems Pemg Wag* ad Adrzej Aderko OLI Systems Ic., 18 Amerca Road, Morrs Plas, New Jersey 795

More information

Outline. Point Pattern Analysis Part I. Revisit IRP/CSR

Outline. Point Pattern Analysis Part I. Revisit IRP/CSR Pot Patter Aalyss Part I Outle Revst IRP/CSR, frst- ad secod order effects What s pot patter aalyss (PPA)? Desty-based pot patter measures Dstace-based pot patter measures Revst IRP/CSR Equal probablty:

More information

Liquid-Liquid Equilibria for Ternary Mixtures of (Water + Carboxylic Acid+ MIBK), Experimental, Simulation, and Optimization

Liquid-Liquid Equilibria for Ternary Mixtures of (Water + Carboxylic Acid+ MIBK), Experimental, Simulation, and Optimization World Academy of Scece, Egeerg ad Techology teratoal Joural of Chemcal ad Molecular Egeerg Vol:7, No:6, 03 Lqud-Lqud Equlbra for Terary Mtures of (Water + Carboylc Acd+ MBK, Epermetal, Smulato, ad Optmzato

More information

Chapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements

Chapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements Aoucemets No-Parametrc Desty Estmato Techques HW assged Most of ths lecture was o the blacboard. These sldes cover the same materal as preseted DHS Bometrcs CSE 90-a Lecture 7 CSE90a Fall 06 CSE90a Fall

More information

CHAPTER 3 POSTERIOR DISTRIBUTIONS

CHAPTER 3 POSTERIOR DISTRIBUTIONS CHAPTER 3 POSTERIOR DISTRIBUTIONS If scece caot measure the degree of probablt volved, so much the worse for scece. The practcal ma wll stck to hs apprecatve methods utl t does, or wll accept the results

More information

best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best

best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg

More information

Module 7. Lecture 7: Statistical parameter estimation

Module 7. Lecture 7: Statistical parameter estimation Lecture 7: Statstcal parameter estmato Parameter Estmato Methods of Parameter Estmato 1) Method of Matchg Pots ) Method of Momets 3) Mamum Lkelhood method Populato Parameter Sample Parameter Ubased estmato

More information

02/15/04 INTERESTING FINITE AND INFINITE PRODUCTS FROM SIMPLE ALGEBRAIC IDENTITIES

02/15/04 INTERESTING FINITE AND INFINITE PRODUCTS FROM SIMPLE ALGEBRAIC IDENTITIES 0/5/04 ITERESTIG FIITE AD IFIITE PRODUCTS FROM SIMPLE ALGEBRAIC IDETITIES Thomas J Osler Mathematcs Departmet Rowa Uversty Glassboro J 0808 Osler@rowaedu Itroducto The dfferece of two squares, y = + y

More information