The Theory of HPLC. Band Broadening
|
|
- Morris Goodwin
- 7 years ago
- Views:
Transcription
1 The Theory of HPLC Band Broadenng Wherever you see ths symbol, t s mportant to access the on-lne course as there s nteractve materal that cannot be fully shown n ths reference manual.
2 Ams and Objectves Ams and Objectves Ams To llustrate and explan the prncple of Band Broadenng n HPLC To defne the Van Deemter equaton and explan the terms of the equaton To demonstrate the effects of Eddy Dffuson, Longtudnal Dffuson and Mass Transfer on the Effcency of Chromatographc Peaks Objectves At the end of ths Secton you should be able to: To use the Van Deemter coeffcents to llustrate how to optmse the Effcency (N) of chromatographc separatons and to reduce Band Broadenng
3 Content Band Broadenng 3 The Van Deemter Equaton 3 Eddy Dffuson 4 Longtudnal Dffuson 5 Mass Transfer 7 Optmsng Flow Rate 9 Optmsng Partcle Sze 10 Mnmsng System Volumen 11 Glossary 12 Crawford Scentfc 2
4 Band Broadenng The Van Deemter Equaton Band broadenng s a phenomenon that reduces the effcency of the separaton beng carred out leadng to poor resoluton and chromatographc performance. Ths s problematcal n terms of both the qualty of the separaton obtaned and the accuracy wth whch sample components can be quantfed. The degree of band broadenng (loss of effcency) naturally ncreases wth the age of the chromatographc column beng used, but there are measures that can be taken to slow these processes and to optmse column and nstrument condtons to ensure maxmum effcency and mnmum band broadenng. In 1956 J.J. Van Deemter derved an equaton that ncluded the man factors contrbutng to column band broadenng. He descrbed the ndvdual terms (A,B,C & D) and also derved a composte curve whch related plate heght (HETP) to lnear velocty of the moble phase flowng through the column. Whlst t s not mportant to necessarly know and use the equaton on a daly bass t s mportant to understand the terms (or factors) that contrbute to band broadenng, so that we can optmse our separatons. For example, the nteractve dagram opposte shows the reducton n chromatographc performance sustaned when movng from a system extra column volume of 20μL to 80μL. The Van Deemter Equaton and graphcal representaton of the contrbutng terms Comparatve chromatograms from HPLC systems wth 20 and 80μL dead volume showng effects on effcency and resoluton. Crawford Scentfc 3
5 Eddy Dffuson The frst of the factors relatng to band broadenng s that of Eddy Dffuson. Ths s a generc term, often used to descrbe varatons n moble phase flow or analyte flow path wthn the chromatographc column. Eddy dffuson tself relates to the fact that an analyte molecule, wthn a band of analytes, can take one of many paths through the column. These multple paths arse due to nhomogenetes n column packng and small varatons n the partcle sze of the packng materal. Ths multple path effect tends to make the band of analytes broader as t moves through the column. Large Partcles Small Partcles Band broadenng due to Eddy Dffuson (A Term) n columns wth large and small partcles effects on chromatographc peak shape (Effcency (N)). Mnmse Eddy Dffuson by: Selectng well packed columns Usng smaller statonary phase partcles Usng partcles wth a narrow sze dstrbuton Crawford Scentfc 4
6 In fact, the Eddy Dffuson term n the Van Deemter equaton (the A term), s often called the packng term as t reflects the qualty of column packng. Lamnar flow occurs wth standard sze HPLC column packng materals at flow rates up to approxmately 4mL/mn. Non-lamnar flow occurs when usng very large partcle sze packng materal (>40μm) and at hgh flow rates (>5mL/mn.). Ths stuaton s also sometmes referred to as Turbulent Flow and does not occur under normal HPLC condtons customsed HPLC equpment and columns are requred for Turbulent Flow Chromatography. Band broadenng due to Eddy Dffuson (A Term) n columns wth n Lamnar and Non Lamnar moble phase flow profles. One other flow varaton n column chromatography comes from the lamnar flow profle adopted by lquds flowng under pressure through tubes. The flow profle s sad to be lamnar, where lnear velocty near the nner walls of the tubng s lower than n the centre of the column. Ths also tends to produce a broader band of analyte molecules. Longtudnal Dffuson A band of analyte molecules contaned n the njecton solvent wll tend to dsperse n every drecton due to the concentraton gradent at the outer edges of the band. Ths broadenng factor s called Longtudnal dffuson because nsde tubes, the greatest scope for broadenng s along the axs of flow. The band wll broaden n all system tubng, but the worst effects wll be encountered n the column tself. Longtudnal dffuson occurs whenever the HPLC system contans nternal volumes that are larger than necessary and some nstances of ths are: Tubng length too long Tubng that s too wde (nternal dameter) Tubng joned by unons Incorrectly connected Zero Dead Volume fttngs Usng the wrong column nuts and ferrules Usng a detector flow cell that has a large nternal volume Crawford Scentfc 5
7 As can be seen, Longtudnal dffuson has a much larger effect at low moble phase velocty (flow). Therefore, usng hgh lnear velocty (hgh moble phase flow wth narrow columns), wll reduce the effects of ths broadenng factor. Band broadenng due to Longtudnal Dffuson (B Term) n columns wth low and hgh moble phase lnear velocty effects on chromatographc peak shape (Effcency (N)). Mnmse Longtudnal Dffuson by: Usng hgher moble phase flow rates Keep system tubng short and as a narrow as possble (careful wth back-pressure) (<0.12mm.d. s deal) Use correct nuts, ferrules and fttngs wherever possble Crawford Scentfc 6
8 Mass Transfer Ths term n the Van Deemter equaton arses largely due to the fact that the statonary phase materal s porous and the moble phase wthn the pores s stagnant or statonary. The packng materal s porous to allow a very large surface area for separaton to occur. As the analyte molecules move through the stagnant moble phase to reach the surface of the packng materal, they do so by dffuson only. Analyte molecules enterng the pore, those that don t enter the pore and those that penetrate more deeply nto the pore, wll all be held up at that pont to dfferent extents causng a broadenng of the band. Ths s the C term. Mass Transfer (C Term) band broadenng processes n the pore structure of statonary phase partcles Further, the analyte resdence tme n (or on) the statonary phase s also varable agan causng a varaton n eluton tme and band broadenng. These effects may be mnmsed by reducng the sze (dameter) of the packng materal partcle sze to make the pores as shallow as possble. The effects of mass transfer are also lower at lower lnear velocty of the moble phase. Crawford Scentfc 7
9 Large Statonary Phase Partcles Greater possble pore dstance for analyte dffuson Dffuson tme ncreased Dfferences n dffuson tmes out of the pore are amplfed Peak effcency decreases (peak broadens) Small Statonary Phase Partcles Reduced possble pore dstance for analyte dffuson Dffuson tme decreased Dfferences n dffuson tmes out of the pore are reduced Peak effcency ncreases (peak becomes narrower) Mnmse Mass Transfer effects by: Usng smaller (dameter) statonary phase partcles Usng lower moble phase flow rates Heatng the column (at hgher temperatures the dffuson processes are speeded up and the dfferences n eluton tme from the partcle pore are reduced) Effect of moble phase lnear velocty (top) and statonary phase partcle sze (bottom) on Mass Transfer effects and peak shape (Effcency (N)) Crawford Scentfc 8
10 Optmsng Flow Rate Let s look at the composte Van Deemter curve and equaton once agan ths tme usng real world examples - to nvestgate optons for mnmsng band broadenng and optmsng peak effcency. Durng the prevous pages you have seen that the moble phase velocty and the partcle sze of packng materal used, have a fundamental effect on effcency (and therefore band broadenng). Van Deemter relatonshp between moble phase flow rate and peak effcency n HPLC The On-lne course contans an nteractve experment n whch the eluent flow rate can be changed to alter the HETP parameter Although the change n partcle sze does not appear to have a marked effect on the effcency and resoluton of ths separaton, you should study the results carefully Reducng partcle sze (even when usng tradtonal column nternal dameters), has a marked effect on plate heght, whch can be usefully used to mproved the resoluton of separatons, especally where selectvty optons have faled to produce baselne separated peaks The plate heghts obtaned wth very small partcles are extremely low. By combnng short columns wth tradtonal nternal dameter (0.46cm), and small dameter slca packng materal (1.8μm) very short analyss tmes may be acheved. When usng smaller dameter column packng materals, system backpressure should be carefully observed as ncreased backpressure results from the use of small slca partcles Startng wth an nvestgaton of moble phase flow (lnear velocty) you should see that the moble phase flow rate can have an effect on band broadenng, plate heght and hence resoluton. It s mportant to note that there s an optmum flow rate for each separaton (the mnmum pont on the curve correspondng to the lowest plate heght). Whlst ths effect s notceable, t s mnor n comparson wth other varables affectng resoluton and therefore flow rate would be used to fne tune a separaton only. Of course, f you have enough effcency (and resoluton) to run at hgher flow rates then ths wll make the analyss tme shorter however, care should be taken not to exceed the pressure lmt of your HPLC pump! Crawford Scentfc 9
11 Optmsng Partcle Sze Another mportant factor to consder regardng band broadenng s the partcle sze of the statonary phase used. We have seen several nstances where the use of smaller dameter partcles s advantageous to both effcency and resoluton. Van Deemter relatonshp between statonary phase partcle sze and peak effcency n HPLC The On-lne course contans an nteractve experment n whch the effects of changng partcle dameter (d p ) on effcency (band broadenng) and resoluton are presented Although the change n partcle sze does not appear to have a marked effect on the effcency and resoluton of ths separaton, you should study the results carefully Reducng partcle sze (even when usng tradtonal column nternal dameters), has a marked effect on plate heght, whch can be usefully used to mproved the resoluton of separatons, especally where selectvty optons have faled to produce baselne separated peaks The plate heghts obtaned wth very small partcles are extremely low. By combnng short columns wth tradtonal nternal dameter (0.46cm), and small dameter slca packng materal (1.8μm) very short analyss tmes may be acheved. When usng smaller dameter column packng materals, system backpressure should be carefully observed as ncreased backpressure results from the use of small slca partcles It should be noted that whlst smaller dameter partcles are favourable there s a trade wth system backpressure. Small partcles may be used n conjuncton wth hgher moble phase flow rates to produce very fast analyses, but system backpressure needs to be carefully montored. The use of smaller dameter slca partcles (<2μm), wth tradtonal column nternal dameters (.e. 4.6mm), means extra-column dead volume s less mportant than when usng narrow bore columns. Ths can be an advantage when fast HPLC analyss s requred, wthout havng to change the analytcal system hardware to very low dead volume, or very hgh pressure versons. Crawford Scentfc 10
12 Mnmsng System Volumen As prevously dscussed, systems contanng large extra-column volume (tubng, unons, flow cell etc.), show low effcency and hence broadened chromatographc peaks and loss of resoluton. You can use the slder bar to nvestgate the effects of extra column volume. You may want to consder how you could reduce these volumes on your system. Typcal ways mght nclude: reduce tubng length and nternal dameter / reduce the number of unons between tubng / ft column end fttngs approprate to the column type beng used / reduce the njecton loop volume / reduce the detector flow cell volume. Van Deemter relatonshp between extra column dead volume and peak effcency n HPLC Important: The system extra column volume can have a crtcal effect on effcency and therefore resoluton of a separaton You need to also consder the column dead volume, and f n any doubt about the qualty of the column packng, use a new column. Column vods from wthn columns over tme addng very large dead volumes to the system Extra column dead volumes below 20μL should be easly achevable on modern HPLC systems You should consder the volume of the detector flow cell as beng a major contrbutor to extra column volume, along wth any hgh pressure mxng chambers on the HPLC pump System dead volume becomes more crtcal as the nternal dameter, (and to a lesser extent partcle sze), of the column used are reduced It s straghtforward to measure the extra column volume of a system: Remove the column and jon the tubng wth a Zero Dead Volume unon Inject 10μL of 100% strong solvent (acetontrle works wth UV at 200nm) or a soluton of 1% acetone (montor at 265nm) The apex retenton tme (t R ) of the baselne perturbaton due to the passage of the solvent gves the extra column hold up tme of the system (expressed n mnutes) Multply ths tme by the flow rate (n mllltres per mnute) to obtan the extra column volume (n mllltres) Crawford Scentfc 11
13 Apex solvent retenton tme used to determne extra column volume of an HPLC system. Glossary Lnear Velocty The lnear velocty of the moble phase across the average crosssecton of the chromatographc bed or column. It can be calculated from the column flowrate at column temperature (Fc ), the cross-sectonal area of the column (Ac ) and the nterpartcle porosty ( ε): υ = Fc /(εac) In practce the moble phase velocty s usually calculated by dvdng the column length (L) by the retenton tme of an unretaned compound (tm) υ = L/tM System Extra Column Volume the volume of the HPLC system from the pont of njecton to the pont at whch the sample passes out of the detector, MINUS the column dead volume. Ths typcally ncludes the njecton loop, any tubng and unons as well as the detector flow cell where approprate. Tubng Unons Fttngs whch allow the couplng of two peces of tubng n HPLC. May be made from Stanless Steel or and nert polymerc materal such as PEEK (polyether ether ketone). Zero Dead Volume refers to a fttng n whch the nut, ferrule and tubng exactly match the nternal volume of the fttng, leavng no dead space. Ths dead volume tends to cause band broadenng n HPLC by artfcally holdng up analyte molecules n the stagnant (not movng) phase that resdes n the dead volume wthn the fttng. Crawford Scentfc 12
14 Dead Volume Wrong column nuts and ferrules - each column manufacturer uses partcular end fttng types. Specally desgn stanless nuts and ferrules must be used n order to obtan a satsfactory zero dead volume unon wth the column. Some workers use PEEK fttngs that deform to ft the nternal geometry columns from any manufacturer. However, these fttngs do loose ther plastcty and should be regularly replaced to avod band broadenng. Incorrect ferrule and tubng fttng Crawford Scentfc 13
15
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationTopical Workshop for PhD students Adsorption and Diffusion in MOFs Institut für Nichtklassische Chemie, Germany, www.uni-leipzig.
Gas Separaton and Purfcaton Measurement of Breakthrough Curves Topcal Workshop for PhD students Adsorpton and Dffuson n MOFs Adsorpton on Surfaces / Separaton effects Useful features Thermodynamc effect
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationPublished: 2003-01-01. Link to publication
A Thermodesorber for Onlne studes of Combuston Aerosols - Influence of partcle dameter, resdence tme and mass concentraton Dahl, Andreas; Pagels, Joakm Publshed: 2003-01-01 Lnk to publcaton Ctaton for
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationThe Development of Web Log Mining Based on Improve-K-Means Clustering Analysis
The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationTHE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES
The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationViscosity of Solutions of Macromolecules
Vscosty of Solutons of Macromolecules When a lqud flows, whether through a tube or as the result of pourng from a vessel, layers of lqud slde over each other. The force f requred s drectly proportonal
More informationRisk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008
Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationEFFECT OF PARTICLE-SIZE DISTRIBUTION AND PARTICLE POROSITY CHANGES ON MASS-TRANSFER KINETICS
ACTA CHROMATOGRAPHICA, NO. 13, 2003 EFFECT OF PARTICLE-SIZE DISTRIBUTION AND PARTICLE POROSITY CHANGES ON MASS-TRANSFER KINETICS K. Kaczmarsk 1,* and J. Ch. Bellot 2 1 Faculty of Chemstry, Rzeszów Unversty
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,
More information+ + + - - This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationFREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES
FREQUENCY OF OCCURRENCE OF CERTAIN CHEMICAL CLASSES OF GSR FROM VARIOUS AMMUNITION TYPES Zuzanna BRO EK-MUCHA, Grzegorz ZADORA, 2 Insttute of Forensc Research, Cracow, Poland 2 Faculty of Chemstry, Jagellonan
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationMean Molecular Weight
Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of
More informationStudy on Model of Risks Assessment of Standard Operation in Rural Power Network
Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,
More information- 573 A Possible Detector for the Study of Weak Interactions at Fermi Clash R. Singer Argonne National Laboratory
- 573 A Possble Detector for the Study of Weak nteractons at Ferm Clash R. Snger Argonne Natonal Laboratory The purpose of ths paper s to pont out what weak nteracton phenomena may exst for center-of-mass
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationEfficient Striping Techniques for Variable Bit Rate Continuous Media File Servers æ
Effcent Strpng Technques for Varable Bt Rate Contnuous Meda Fle Servers æ Prashant J. Shenoy Harrck M. Vn Department of Computer Scence, Department of Computer Scences, Unversty of Massachusetts at Amherst
More informationComparison of Control Strategies for Shunt Active Power Filter under Different Load Conditions
Comparson of Control Strateges for Shunt Actve Power Flter under Dfferent Load Condtons Sanjay C. Patel 1, Tushar A. Patel 2 Lecturer, Electrcal Department, Government Polytechnc, alsad, Gujarat, Inda
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationOn the Optimal Control of a Cascade of Hydro-Electric Power Stations
On the Optmal Control of a Cascade of Hydro-Electrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationInterlude: Interphase Mass Transfer
Interlude: Interphase Mass Transfer The transport of mass wthn a sngle phase depends drectly on the concentraton gradent of the transportng speces n that phase. Mass may also transport from one phase to
More information1.1 The University may award Higher Doctorate degrees as specified from time-to-time in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
More informationShielding Equations and Buildup Factors Explained
Sheldng Equatons and uldup Factors Explaned Gamma Exposure Fluence Rate Equatons For an explanaton of the fluence rate equatons used n the unshelded and shelded calculatons, vst ths US Health Physcs Socety
More informationActivity Scheduling for Cost-Time Investment Optimization in Project Management
PROJECT MANAGEMENT 4 th Internatonal Conference on Industral Engneerng and Industral Management XIV Congreso de Ingenería de Organzacón Donosta- San Sebastán, September 8 th -10 th 010 Actvty Schedulng
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationTECHNICAL NOTES 3. Hydraulic Classifiers
TECHNICAL NOTES 3 Hydraulc Classfers 3.1 Classfcaton Based on Dfferental Settlng - The Hydrocyclone 3.1.1 General prncples of the operaton of the hydrocyclone The prncple of operaton of the hydrocyclone
More informationHÜCKEL MOLECULAR ORBITAL THEORY
1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ
More informationCompaction of the diamond Ti 3 SiC 2 graded material by the high speed centrifugal compaction process
Archves of Materals Scence and Engneerng Volume 8 Issue November 7 Pages 677-68 Internatonal Scentfc Journal publshed monthly as the organ of the Commttee of Materals Scence of the Polsh Academy of Scences
More informationHollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )
February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976-76-10-00
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationwhere the coordinates are related to those in the old frame as follows.
Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationExhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More information14.74 Lecture 5: Health (2)
14.74 Lecture 5: Health (2) Esther Duflo February 17, 2004 1 Possble Interventons Last tme we dscussed possble nterventons. Let s take one: provdng ron supplements to people, for example. From the data,
More informationTECHNICAL NOTES 4 VIBRATING SCREENS
TECHNICAL NOTES 4 VIBRATING SCREENS Copyrght R P Kng 2000 SIZE CLASSIFICATION It s always necessary to control the sze characterstcs of partculate materal that s fed to process equpment that separates
More informationCalibration and Linear Regression Analysis: A Self-Guided Tutorial
Calbraton and Lnear Regresson Analyss: A Self-Guded Tutoral Part The Calbraton Curve, Correlaton Coeffcent and Confdence Lmts CHM314 Instrumental Analyss Department of Chemstry, Unversty of Toronto Dr.
More informationFace Verification Problem. Face Recognition Problem. Application: Access Control. Biometric Authentication. Face Verification (1:1 matching)
Face Recognton Problem Face Verfcaton Problem Face Verfcaton (1:1 matchng) Querymage face query Face Recognton (1:N matchng) database Applcaton: Access Control www.vsage.com www.vsoncs.com Bometrc Authentcaton
More informationEuropean Collaboration on Lead Cooled Nuclear Reactor Development
European Collaboraton on Lead Cooled Nuclear Reactor Development Jerzy Cetnar Akadema Górnczo-Hutncza w Krakowe 7. Program Ramowy, Dzeń nformacyny Euratom Fsson 2010; Warszawa 8 XII 2009 1 Lead-cooled
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationBERNSTEIN POLYNOMIALS
On-Lne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationCharacterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University
Characterzaton of Assembly Varaton Analyss Methods A Thess Presented to the Department of Mechancal Engneerng Brgham Young Unversty In Partal Fulfllment of the Requrements for the Degree Master of Scence
More informationMONITORING METHODOLOGY TO ASSESS THE PERFORMANCE OF GSM NETWORKS
Electronc Communcatons Commttee (ECC) wthn the European Conference of Postal and Telecommuncatons Admnstratons (CEPT) MONITORING METHODOLOGY TO ASSESS THE PERFORMANCE OF GSM NETWORKS Athens, February 2008
More informationHow To Calculate The Accountng Perod Of Nequalty
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationSTANDING WAVE TUBE TECHNIQUES FOR MEASURING THE NORMAL INCIDENCE ABSORPTION COEFFICIENT: COMPARISON OF DIFFERENT EXPERIMENTAL SETUPS.
STADIG WAVE TUBE TECHIQUES FOR MEASURIG THE ORMAL ICIDECE ABSORPTIO COEFFICIET: COMPARISO OF DIFFERET EXPERIMETAL SETUPS. Angelo Farna (*), Patrzo Faust (**) (*) Dpart. d Ing. Industrale, Unverstà d Parma,
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationTECHNICAL NOTES 8 GRINDING. R. P. King
TECHNICAL NOTES 8 GRINDING R. P. Kng Copyrght R P kng 000 8. Grndng 8.. Grndng acton Industral grndng machnes used n the mneral processng ndustres are mostly of the tumblng mll type. These mlls exst n
More informationTo manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.
Corporate Polces & Procedures Human Resources - Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:
More informationHALL EFFECT SENSORS AND COMMUTATION
OEM770 5 Hall Effect ensors H P T E R 5 Hall Effect ensors The OEM770 works wth three-phase brushless motors equpped wth Hall effect sensors or equvalent feedback sgnals. In ths chapter we wll explan how
More informationEffects of Extreme-Low Frequency Electromagnetic Fields on the Weight of the Hg at the Superconducting State.
Effects of Etreme-Low Frequency Electromagnetc Felds on the Weght of the at the Superconductng State. Fran De Aquno Maranhao State Unversty, Physcs Department, S.Lus/MA, Brazl. Copyrght 200 by Fran De
More informationDamage detection in composite laminates using coin-tap method
Damage detecton n composte lamnates usng con-tap method S.J. Km Korea Aerospace Research Insttute, 45 Eoeun-Dong, Youseong-Gu, 35-333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The con-tap test has the
More informationSimulating injection moulding of microfeatured components
Smulatng njecton mouldng of mcrofeatured components T. Tofteberg 1 * and E. Andreassen 1 1 SINTEF Materals and Chemstry, Oslo, Norway terje.tofteberg@sntef.no; erk.andreassen@sntef.no Numercal smulaton
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems
More informationPolitecnico di Torino. Porto Institutional Repository
Poltecnco d Torno Porto Insttutonal Repostory [Artcle] A cost-effectve cloud computng framework for acceleratng multmeda communcaton smulatons Orgnal Ctaton: D. Angel, E. Masala (2012). A cost-effectve
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationLoop Parallelization
- - Loop Parallelzaton C-52 Complaton steps: nested loops operatng on arrays, sequentell executon of teraton space DECLARE B[..,..+] FOR I :=.. FOR J :=.. I B[I,J] := B[I-,J]+B[I-,J-] ED FOR ED FOR analyze
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More information1 Example 1: Axis-aligned rectangles
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationOutsourcing inventory management decisions in healthcare: Models and application
European Journal of Operatonal Research 154 (24) 271 29 O.R. Applcatons Outsourcng nventory management decsons n healthcare: Models and applcaton www.elsever.com/locate/dsw Lawrence Ncholson a, Asoo J.
More informationRESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL. Yaoqi FENG 1, Hanping QIU 1. China Academy of Space Technology (CAST) yaoqi.feng@yahoo.
ICSV4 Carns Australa 9- July, 007 RESEARCH ON DUAL-SHAKER SINE VIBRATION CONTROL Yaoq FENG, Hanpng QIU Dynamc Test Laboratory, BISEE Chna Academy of Space Technology (CAST) yaoq.feng@yahoo.com Abstract
More informationHelp is a tou ch of a button away. Telecare - keeping you safe and independent in your own home. i Personal emergency equipment
Help s a tou ch of a button away Telecare - keepng you safe and ndependent n your own home Personal emergency equpment 24/7 moble response - ncludng a dgnty savng lftng servce Professonal support Welcome
More informationThe Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1
EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 9-2, 24, pp. 546-555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons
More informationHosted Voice Self Service Installation Guide
Hosted Voce Self Servce Installaton Gude Contact us at 1-877-355-1501 learnmore@elnk.com www.earthlnk.com 2015 EarthLnk. Trademarks are property of ther respectve owners. All rghts reserved. 1071-07629
More informationTraffic-light a stress test for life insurance provisions
MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationTraffic State Estimation in the Traffic Management Center of Berlin
Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D-763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,
More informationRisk Model of Long-Term Production Scheduling in Open Pit Gold Mining
Rsk Model of Long-Term Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationSprayExpo 2.0. Program description. SprayExpo has been developed by
SpraExpo.0 Program descrpton SpraExpo has been developed b Fraunhofer Insttut für Toxkologe und Expermentelle Medzn Nkola-Fuchs-Straße 1 D-3065 Hannover on behalf of the Bundesanstalt für Arbetsschutz
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):1884-1889 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationAnalysis of Reactivity Induced Accident for Control Rods Ejection with Loss of Cooling
Analyss of Reactvty Induced Accdent for Control Rods Ejecton wth Loss of Coolng Hend Mohammed El Sayed Saad 1, Hesham Mohammed Mohammed Mansour 2 Wahab 1 1. Nuclear and Radologcal Regulatory Authorty,
More informationSection C2: BJT Structure and Operational Modes
Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationTypes of Injuries. (20 minutes) LEARNING OBJECTIVES MATERIALS NEEDED
U N I T 3 Types of Injures (20 mnutes) PURPOSE: To help coaches learn how to recognze the man types of acute and chronc njures. LEARNING OBJECTIVES In ths unt, coaches wll learn how most njures occur,
More informationChapter 9 PLUME-IN-GRID TREATMENT OF MAJOR POINT SOURCE EMISSIONS
Chapter 9 PLUME-IN-GRID TREATMENT OF MAJOR POINT SOURCE EMISSIONS N. V. Gllan Earth System Scence Laboratory Unversty of Alabama n Huntsvlle Huntsvlle, Alabama 35899 James M. Godowtch * Atmospherc Modelng
More informationAdaptive Fractal Image Coding in the Frequency Domain
PROCEEDINGS OF INTERNATIONAL WORKSHOP ON IMAGE PROCESSING: THEORY, METHODOLOGY, SYSTEMS AND APPLICATIONS 2-22 JUNE,1994 BUDAPEST,HUNGARY Adaptve Fractal Image Codng n the Frequency Doman K AI UWE BARTHEL
More informationL10: Linear discriminants analysis
L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss
More informationIT09 - Identity Management Policy
IT09 - Identty Management Polcy Introducton 1 The Unersty needs to manage dentty accounts for all users of the Unersty s electronc systems and ensure that users hae an approprate leel of access to these
More informationSIMULATION OF THERMAL AND CHEMICAL RELAXATION IN A POST-DISCHARGE AIR CORONA REACTOR
XVIII Internatonal Conference on Gas Dscharges and Ther Applcatons (GD 2010) Grefswald - Germany SIMULATION OF THERMAL AND CHEMICAL RELAXATION IN A POST-DISCHARGE AIR CORONA REACTOR M. Mezane, J.P. Sarrette,
More information