purpose of this paper to show that "retention coefficients" can
|
|
|
- James Griffin
- 10 years ago
- Views:
Transcription
1 Pro. Natl. Aad. Si. USA Vol. 77, No. 3, pp , Marh 1980 Medial Sienes Predition of peptide retention times in high-pressure liquid hromatography on the basis of amino aid omposition (lipophiliity/separation tehniques) JAMES L. MEEK Laboratory of Prelinial Pharmaology, National Institute of Mental Health, Saint Elizabeths Hospital, Washington, D ommuniated by Brue Merrifield, Deember 17,1979 ABSTRAT Analysis of peptides by reverse-phase highpressure liquid hromatography would be simplified if retention times ould be predited by summing the ontribution to retention of eah of the peptide's amino aid side hains. This paper desribes the derivation of values ("retention oeffiients") that represent the ontribution to retention of eah of the ommon amino aids and end groups. Peptide retention times were determined on a Bio-Rad "ODS" olumn at room temperature with a linear gradient from 0.1 M NaIO4, ph 7.4 or 2.1, at 0 min to 60% aetonitrile/0.1 M NaIO4 at 80 min. The NalO4, a haotropi agent, was added to improve peak shape and to minimize onformational effets. Retention oeffiients for the amino aids were omputed by using a Hewlett-Pakard 9815A alulator programmed to hange the retention oeffiients for all amino aids sequentially to obtain a maximum orrelation between atual and predited retention times. orrelations of at ph 7.4 and at ph 2.1 were obtained for 25 peptides inluding gluagon, oxytoin, [Metlenkephalin, neurotensin, and somatostatin. This high degree of orrelation suggests that, for peptides ontaining up to 20 residues, retention is primarily due to partition proesses that involve all the residues. Although steri or onformational fators do have some effet on retention, the data suggest that under the above hromatographi onditions the retention of peptides ontaining up to 20 residues an be predited solely on the basis of their amino aid omposition. This possibility was tested by using data taken from the literature. The possibilities for separating and isolating small peptides have been markedly improved by the introdution of reverse-phase high-pressure liquid hromatography (HPL) (1-5). This tehnique depends upon the hydrophobi interations between a hydroarbonaeous olumn and the peptides to be separated: the more hydrophobi (lipophili) the ompound, the stronger its retention by the olumn. To elute strongly retained ompounds, aqueous solutions (the "mobile phase") ontaining a large amount of organi solvent must be pumped through the olumn. hoie of the optimum mobile phase and hromatographi onditions for given peptides an be found by trial and error after qualitatively examining the balane of hydrophobi and hydrophili amino aids present in the peptide. However, as noted by Molna'r and Horvath (1), it should be possible to obtain quantitative estimates of the hydrophobiity of the amino aids ontained in a peptide, whih will reflet their retention on the reverse-phase olumn. Estimates of hydrophobiity based on otanol/water partition oeffiients exist for many but not all amino aids. By using suh values, O'Hare and Nie (2) noted that the retention order for small peptides was generally orrelated with the sum of the values for the most hydrophobi residues of the peptides. The many deviations they found between the observed order of elution and the lipophiliity estimates presumably derive from the fat that retention The publiation osts of this artile were defrayed in part by page harge payment. This artile must therefore be hereby marked "advertisement" in aordane with 18 U. S solely to indiate this fat. on otadeylsilyl silia gel is a quite different proess from otanol/water partition and from the unavailability of hydrophobiity data for terminal groups of the peptides. It is the purpose of this paper to show that "retention oeffiients" an be derived diretly from HPL data for all amino aids and end groups suh that the retention time of a peptide an be predited from the sum of the retention oeffiients for eah amino aid and end group. MATERIALS AND METHODS Peptides were obtained from Sigma and Peninsula Laboratories (San arlos, A). HPL grade aetonitrile was obtained from Fisher. The HPL system was assembled from modular omponents: a one-hamber glass gradient maker, a pump (Milton Roy, Riviera Beah, FL), and a sample valve (Rheodyne, Berkeley, A). The olumn effluent was passed in series through a variable wavelength photometer (Altex, Berkeley, A) and a filter fluorometer (Farrand, Valhalla, NY). The mobile phase gradient normally used was from 0.1 M NaIO4/0% aetonitrile at 0 min after injetion to 0.1 M Nal04/60% aetonitrile (vol/vol) at 80 min. For separations at ph 7.4, the starting buffer ontained 5 mm phosphate buffer, ph 7.4. For operation at ph 2.1, both starting and final buffers ontained 0.1% phosphori aid (3). Linear gradients from 100% A to 100% B are generated if a solution A is plaed in a mixing hamber and then B is added at 1/2 the rate at whih the mixture is withdrawn (6). The gradient maker onsisted of a 3 X 13 m glass ylinder with two Teflon three-way stopoks and a magneti stirrer. To generate the gradient, the hamber was filled with 40 ml of starting buffer. Final buffer was then added to the hamber at 0.5 ml/min, while the mixture was pumped into the olumn at 1.0 ml/min. Peptides were deteted by absorbane'at 200 or 220 nm or by fluoresene [after the primary amino groups of the peptides had reated with fluoresamine (7)]. With a mobile phase of ph 7.4, the olumn effluent ould reat diretly with fluoresamine, beause the ph optimum for many peptides is near neutral (8). The fluoresamine (10 mg/100 ml of aetonitrile) was added to the effluent at 0.1 ml/min. ontinuous neutralization of the ph 2.1 mobile phase was ahieved by adding the organi base imidazole (1.0 M final onentration) to the fluoresamine/aetonitrile mixture. The retention oeffiients were omputed by repetitive regression analysis: values for eah amino aid were suessively hanged by 0.2 min until maximum orrelation between atual and predited retention times was obtained. Starting values for the retention oeffiients of the neutral and hydrophili amino aids were initially assumed to be zero. Starting values for the lipophili amino aids were obtained by plotting the retention Abbreviation: HPL, high-pressure liquid hromatography. 1632
2 Medial Sienes: Meek times of oligomers (e.g., diphenylalanine, triphenylalanine, tetraphenylalanine, et.) vs. the number of residues; the slope of the plot equals the retention per residue. To ompute the retention oeffiients, a Hewlett-Pakard 9815A alulator was programmed to store these starting retention oeffiients for the 26 amino aids and end groups, to store the atual retention times for the 25 peptides studied, and then to alulate predited retention times for these peptides by summing the retention oeffiients for eah amino aid ontained. After alulating the orrelation oeffiient between predited and atual retention times, 0.2 min was added to the retention oeffiient for an amino aid; the predited retention times and orrelation oeffiient were then again alulated. If the orrelation had been improved by adding 0.2 min to the retention oeffiient, the hange was kept; otherwise the value was returned to that previously used, and 0.2 min was added to the next amino aid and so on. After heking all amino aids to see whether inreasing the retention oeffiient ould inrease the orrelation, 0.2 min was sequentially subtrated from eah amino aid in turn and orrelations were again alulated after eah subtration. At the end of these two yles, the slope of the plot of predited vs. atual retention times was alulated beause the predited and atual times should be equal, not merely be orrelated (proportional). Therefore, if the slope was greater than 1.0, all retention oeffiients were multiplied by 0.99; if the slope was less than 1.0, the values were multiplied by These yles were repeated until a near maximum orrelation had been obtained. RESULTS Table 1 lists the 25 peptides used for alulation of retention oeffiients and their retention times at ph 7.4 and 2.1. As expeted, small neutral peptides (triglyine and pentaalanine) Table 1. Retention times of peptides separated by HPL Retention time, min ompound ph 7.4 ph Triglyine Pentaalanine Divaline Dimethionine TRF Tuftsin Trityrosine [Met]Enkephalin Trileuine [Leu]Enkephalin Ditryptophan Angiotensin II a-endorphin aerulein Oxytoin Gastrin-(12-15) Neurotensin Physalaemin Triphenylalanine LHRF a-melanotropin Bradykinin Eledoisin-related peptide Gluagon Somatostatin Peptides were hromatographed at room temperature on a Bio-Rad ODS olumn with a linear aetonitrile gradient (0.75%0/min). TRF, thyrotropin-releasing fator; LHRF, luteinizing hormone-releasing fator; Eledosin-related peptide, Lys-Phe-Ile-Gly-Leu-Met-NH2. Pro. Natl. Aad. Si. USA 77 ( were only slightly retained. Small peptides with lipophili side hains (e.g., triphenylalanine) and most of the larger biologially ative peptides required muh higher onentration of aetonitrile for elution. Aidifiation of the mobile phase inreased the retention of peptides with free terminal arboxyl groups ([Metlenkephalin and angiotensin II) or with aidi residues [gastrin-(12-15)]. Most peptides with masked arboxyl or arboxyl and amino groups (thyrotropin-releasing fator, oxytoin) had similar retentions at both phs. Peptides ontaining the basi residues lysine or arginine (luteinizing hormone-releasing fator, eledoisin-related peptide) exhibited a dereased retention at lower ph due either to inreased ionization of the amino group or to formation of an ion pair with the perhlorate in the mobile phase. Fig. 1 shows the separation at ph 2.1 of various peptides. The sharpness of the peaks with minimal tailing demonstrates the high resolution possible with HPL. Fig. 1 also demonstrates the differene in detetor seletivity between measurement of absorbane at 220 nm (top trae) and measurement of fluoresamine-indued fluoresene (bottom trae). ompounds suh as thyrotropin-releasing fator (peak 5) without a free amino-terminal group give little or no fluoresene. Fig. 2 shows that there is an approximately linear inrease in retention time for phenylalanine oligomers as phenylalanine residues are added to diphenylalanine. This finding indiates that, with the linear gradient used in these experiments, the addition of eah phenylalanine residue adds approximately the same retention time to the peptide. The slope thus equals the retention added per side hain and peptide bond, but does not inlude the ontribution of the terminal amino or arboxyl groups. Extrapolation of the line to 0 residues gives a positive value, whih represents the ontribution to retention of the end groups. The retention for phenylalanine itself 0.05' D o Q) : IL).1) LL F I1 2 b~~~~. ~~~ _V Retention time, min FIG. 1. Separation of peptides by reverse-phase HPL on a Lihrosorb RP18 olumn. (Upper) Absorbane at 220 nm (0.05 absorbane units full sale). (Lower) Fluoresamine-indued fluoresene. A 40-gl sample ontaining ng of eah peptide was hromatographed at ph 2.1 at room temperature with a flow rate of LO ml/min and an aetonitrile gradient of 0.75%/min. 7 I
3 1634 Medial Sienes: Meek E 0w a) a1) Number of phenylalanine residues FIG. 2. Linearity of retention time with the number of phenylalanine residues. Phenylalanine oligomers were hromatographed by using a linear aetonitrile gradient. The slope of this plot indiates the HPL retention per phenylalanine residue. was not plotted beause the pks for amino aids differ onsiderably from those of peptides and the extent of ionization markedly affets retention. Table 2 lists the retention oeffiients alulated by repeated regression analysis. Amino aids with aromati or aliphati side hains have a marked positive ontribution to retention whih hanges relatively little with ph. Residues with aidi side hains have a marked negative ontribution to retention whih inreases in magnitude as ionization inreases. Basi and neutral residues have little effet on retention. Fig. 3 shows the remarkably high orrelation obtained when plotting the atual retention times from Table 1 vs. the times predited by summing the retention oeffiients listed in Table 2 for eah peptide. It should also be possible to predit retention times when using various other hromatographi onditions. The retention times for several di- and tripeptides (numbers 1, 2, 3, 9, and 19 of Table 1) were determined with several gradient rates and with olumns of several manufaturers. With a gradient rate of 1.5% aetonitrile per min (twie the usual rate), all retention times were 70% of normal. With a gradient rate of 0.5%/min, retention times were inreased to 120% of normal. Retention times for these ompounds obtained with the Bio-Rad olumn were similar to those seen with olumns from Waters Assoiates (10-,m partile size), Lihrosorb (Rheodyne) (5,mn), and Dupont (5,um). That there are minor differenes in retention with different olumns an be noted by omparing Table 1 (Bio-Rad olumn) with Fig. 1 (Lihrosorb olumn). Thyrotropin-releasing fator (peak 5) was shifted about 2 min relative to pentaalanine and divaline; luteinizing hormone-releasing fator was shifted about 2 min relative to [Met]- and [Leu]- enkephalin. TEST OF PREDITIVE ABILITY OF RETENTION OEFFIIENTS To examine how well these retention oeffiients are able to predit times for other peptides and other hromatographi onditions, data were taken from the literature for omparison Pro. Natl. Aad. Si. USA 77 (198 Table 2. Retention oeffiients of amino aid residues Retention oeffiients Amino aid (N) ph7.4 ph 2.1 Tryptophan Phenylalanine Isoleuine *Leuine Tyrosine Methionine Valine Proline Threonine Arginine Alanine Glyine Histidine ystine Lysine Serine Asparagine Glutamine Asparti aid Glutami aid Amino- -OOH -Amide Pyroglutamyl- Aetyl- Tyrosine sulfate (7) (13) (9) (11) (9) (1 (7) (13) (2) (8) (6) (3) (19) (17) (8) (1) (1) L N, number of peptides used for alulation of retention oeffiients that ontained this amino aid. Retention oeffiients (in min) were determined by reverse-phase HPL on a Bio-Rad ODS olumn. The predited retention time for a peptide equals the sum of the retention oeffiients for the amino aids and end groups plus to (the time for elution of unretained ompounds). In these experiments, to = 2.0 min. with predited times. The best available ompilation of retention times for peptides of biologial interest was made by O'Hare and Nie (2). These authors used an aetonitrile gradient at ph 2.1 (as in the present study), although the inorgani ion added (0.1 M phosphate), Hypersil ODS olumn, and triphasi linear gradient differed from the onditions used here. They hose a gradient onsisting of a rapid rate of hange for about the first 6 min, then a 40-min slower rate of hange, and a final 5-min rapid rate. The retention harateristis of ompounds eluting during the seond phase of their hromatographi system should be omparable to those used in the present study, although retention of ompounds eluting between 10 and 15 min might be overestimated due to the influene of the initial rapid gradient. To examine the omparability of the two hromatographi systems, the atual retention times of phenylalanine oligomers was plotted (Fig. 4). Least squares analysis gave a line with a slope of 36 (representing the differene in gradient rates) and a y interept of min [due to the rapid initial gradient used by O'Hare and Nie (2)]. The high orrelation for these three points (0.9983) indiates that, for these ompounds at least, the hromatographi onditions an be ompared. Table 3 lists the atual retention times of ompounds tested by O'Hare and Nie of 31 amino aid residues or less, exluding insulin hains A and B. These latter ompounds ontain ysteine for whih no retention oeffiient had been alulated beause ysteine was not ontained in any of the peptides tested in Table 1. Predited retention times were alulated for the ompounds in Table 3 by summing the retention oeffiients, multiplying
4 Medial Sienes: Meek Pro. Natl. Aad. Si. USA 77 ( E_ w ) " ~~ Atual retention time, min FIG. 3. orrelation of atual retention times vs. times predited by summing retention oeffiients for the amino aids and end groups. Numbers adjaent to the data points indiate the peptides listed in Table 1. (Left) ph 7.4; orrelation = (Right) ph 2.1; orrelation = by the slope from Fig. 4 (36), and adding the y interept (-12.3 min). As seen in Table 3, the predited and atual retention times agree reasonably well, espeially onsidering the differenes in olumns, mobile phases, and gradients. For all peptides up to 20 residues, the average error was 4 min. DISUSSION The basi premise of this study was that it should be possible to derive values that reflet the hydrophobiity (positive or negative) of the amino aids in peptides and that it is the sum of these values that might primarily determine the extent of retention on reverse-phase HPL olumns. Amino aid omposition annot be the only fator determining the extent of retention beause it is possible to separate position isomers with the same omposition (e.g., Gly-Trp and Trp-Gly) (1) and stereoisomers. However, it seemed likely that for small linear peptides, sequene and onformation should have relatively little effet on retention. As shown by these data, this premise appears justified for peptides up to about 20 residues long. There is no evidene that the size of these peptides has any effet on retention. The high exlusion limit of these olumns I E z 0 _. az Phe 2, Retention time in NaIO4, min FIG. 4. omparison of retention times for phenylalanine oligomers in two hromatographi systems. Data of O'Hare and Nie (2) were obtained with a triphasi aetonitrile gradient ontaining NaH2PO4 on a Hypersil ODS olumn. Data in this paper were obtained with a linear aetonitrile gradient ontaining NalO4 on a Bio-Rad ODS olumn. 60 (30,000 for 100-A pore size partiles) makes it unlikely that steri exlusion has a signifiant role in separation of these small peptides. Quite large peptides and even small enzymes an be hromatographed with high resolution by HPL (2), although it is likely that these ompounds are in a partly folded onfiguration. In theory, even higher resolution might be obtained if onditions ould be found in whih all the residues in the moleule were available for interation with the surfae of the stationary phase. Table 3. omparison of data from the literature with predited retention times No. of Retention time, min Error, ompound residues Predited Atual* min [Met]Enkephalin [Leu]Enkephalin ATH-( ATH-(34-39) ATH-( ATH-(4-11) Angiotensin II Substane P-(4-11) Oxytoin [Arg]Vasopressin [Lys]Vasopressin [Arg]Vasotoin Substane P a-msh Neurotensin Somatostatin Bombesin Gastrin ATH-(18-39) ATH-(1-24) Melittin Gluagon ,B-Endorphin * Data were from O'Hare and Nie (2). Preditions of retention times were made by summing retention oeffiients for eah peptide and adding to (2 min). To orret for the different gradient rates used in these studies, the sum of the oeffiients was multiplied by 36 (the slope in Fig. 4). To orret for the biphasi gradient used by O'Hare and Nie, they interept of Fig. 4 (-12 min) was then added. ATH, ortiotropin; MSH, melanoyte-stimulating hormone.
5 1636 Medial Sienes: Meek HOIE OF HROMATOGRAPHI ONDITIONS The ideal mobile phase should allow sharp peaks with minimal tailing, have low absorbane at 200 nm to simplify high-sensitivity detetion, be easy to neutralize to failitate reation with fluoresamine, and have only volatile omponents to allow onentration of the effluent for subsequent analysis. Early reports in whih peptides were hromatographed with methanoli mobile phases ontaining no inorgani salts showed broad peaks of little use onsidering the omplexity of real samples. Molnar and Horvath (1) showed that extremely high resolution ould be obtained with aetonitrile gradients ontaining 0.6 M H104 or 0.1 M phosphate, ph 2.1. However, both these solutions are diffiult to neutralize ontinuously. Use of the strong phosphate buffer at neutral ph also gave exellent results, but the low solubility in aetonitrile of sodium phosphate limits its usefulness. Rubinstein et al. obtained exellent results with an isopropanol gradient and volatile pyridine buffers, but these buffers prelude the use of ultraviolet detetors. The present experiments were performed with NalO4 beause it permitted both reation with fluoresamine and detetion at 220 nm. Unfortunately, NalO4 is not volatile. Preliminary experiments showed that many small peptides gave sharp peaks with only the dilute phosphori aid reommended by Hanok et al. (3) or very dilute sodium phosphate buffer, ph 7.4. However, one ompound (substane P) gave very broad peaks unless Nal04 was added. It may be that the perhlorate bloks adsorption to some exposed sites on the silia beads of the olumn. However, a theoretial reason for using NalO4 is that it is a strong "haotropi" agent-i.e., an inorgani ion that favors the transfer of nonpolar groups to water by altering water struture (9). Suh agents inrease the solubility of lipophili polymers and are likely to break down seondary and tertiary strutures of peptides. It may be that high onentrations of NalO4 will aid in hromatography of very large peptides. The hoie of a linear gradient, started at the time of injetion, was ditated by several onsiderations: (i) it provides optimal peak shape in all regions of the hromatogram, (ii) it is reproduible in all laboratories regardless of the equipment, and (iii) it was hoped that linear gradients would permit estimation of retention times from amino aid omposition. Molbrfr and Horvaith (1) reported that in an isorati (nongradient) Pro. Natl. Aad. Si. USA 77 (198 separation a plot of log k' (the adjusted retention time/to) vs. the number of alanine residues in alanine oligomers yielded a straight line.,snyder and Kirkland (1 reported that with linear gradients on hemially bonded phases log k' was linear with vol% of B over the range 20-90% B. It therefore follows that a linear gradient should give a linear inrease in retention time as residues are added to a homologous series. That this is approximately true is shown in Fig. 3. omplete gradients might not be required for routine separations of a few ompounds; a near optimal gradient program ould be readily designed by prediting the retention times, alulating the aetonitrile onentration at that point (0.75%/min), and hoosing a slightly lower onentration of aetonitrile to bring the retention time into the desired range for k' of 2-10 (1. Although HPL has so far not proven useful in the diret hemial estimation of peptides in rude tissue samples, HPL appears to be the most powerful tool urrently available for the preparative separation and isolation of small peptides and seems to be the ideal method to hek the speifiity of measurements made by site-speifi tests suh as radioimmunoassays or bioassays. Hopefully, the ability to readily predit retention times and to simplify hoie of hromatographi onditions will aid suh studies. 1. Molnar, I. & Horvath,. (1977) J. hromnatogr. 142, O'Hare, M. J. & Nie, E.. (1979) J. hromatogr. 171, Hanok,-W. S., Bishop,. A., Prestidge, R. L., Harding, D. R. K. & Hearn, M. T. W. (1978) Siene 200, Rubinstein, M., Stein, S. & Udenfriend, S. (1977) Pro. Nati. Aad. Si. USA 74, Rivier, J. (1978) J. Liquid hromatogr. 1, Lakshmanan, T. K. & Lieberman, S. (1954) Arh. Biohem Biophys. 53, Udenfriend, S. (1972) Siene 178, Frei, R. W., Mihel, L. & Santi, W. (1976) J. hromatogr. 126, Hatefi, Y. & Hanstein, W. G. (1969) Pro. Nati. Aad. Si. USA 62, Snyder, L. R. & Kirkland, J. J. (1974) in Introdution to Modern Liquid hronatography (Wiley, New York), p. 466.
User s Guide VISFIT: a computer tool for the measurement of intrinsic viscosities
File:UserVisfit_2.do User s Guide VISFIT: a omputer tool for the measurement of intrinsi visosities Version 2.a, September 2003 From: Multiple Linear Least-Squares Fits with a Common Interept: Determination
Chapter 5 Single Phase Systems
Chapter 5 Single Phase Systems Chemial engineering alulations rely heavily on the availability of physial properties of materials. There are three ommon methods used to find these properties. These inlude
Computer Networks Framing
Computer Networks Framing Saad Mneimneh Computer Siene Hunter College of CUNY New York Introdution Who framed Roger rabbit? A detetive, a woman, and a rabbit in a network of trouble We will skip the physial
arxiv:astro-ph/0304006v2 10 Jun 2003 Theory Group, MS 50A-5101 Lawrence Berkeley National Laboratory One Cyclotron Road Berkeley, CA 94720 USA
LBNL-52402 Marh 2003 On the Speed of Gravity and the v/ Corretions to the Shapiro Time Delay Stuart Samuel 1 arxiv:astro-ph/0304006v2 10 Jun 2003 Theory Group, MS 50A-5101 Lawrene Berkeley National Laboratory
THE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES
Proeedings of FEDSM 98 998 ASME Fluids Engineering Division Summer Meeting June 2-25, 998 Washington DC FEDSM98-529 THE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES John D. Wright Proess
A Holistic Method for Selecting Web Services in Design of Composite Applications
A Holisti Method for Seleting Web Servies in Design of Composite Appliations Mārtiņš Bonders, Jānis Grabis Institute of Information Tehnology, Riga Tehnial University, 1 Kalu Street, Riga, LV 1658, Latvia,
Amino Acids, Peptides, Proteins
Amino Acids, Peptides, Proteins Functions of proteins: Enzymes Transport and Storage Motion, muscle contraction Hormones Mechanical support Immune protection (Antibodies) Generate and transmit nerve impulses
Channel Assignment Strategies for Cellular Phone Systems
Channel Assignment Strategies for Cellular Phone Systems Wei Liu Yiping Han Hang Yu Zhejiang University Hangzhou, P. R. China Contat: [email protected] 000 Mathematial Contest in Modeling (MCM) Meritorious
How To Fator
CHAPTER hapter 4 > Make the Connetion 4 INTRODUCTION Developing seret odes is big business beause of the widespread use of omputers and the Internet. Corporations all over the world sell enryption systems
A Three-Hybrid Treatment Method of the Compressor's Characteristic Line in Performance Prediction of Power Systems
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition
INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS
Virginia Department of Taxation INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS www.tax.virginia.gov 2614086 Rev. 01/16 Table of Contents Introdution... 1 Important... 1 Where to Get Assistane... 1 Online File
INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS
Virginia Department of Taxation INCOME TAX WITHHOLDING GUIDE FOR EMPLOYERS www.tax.virginia.gov 2614086 Rev. 07/14 * Table of Contents Introdution... 1 Important... 1 Where to Get Assistane... 1 Online
REDUCTION FACTOR OF FEEDING LINES THAT HAVE A CABLE AND AN OVERHEAD SECTION
C I E 17 th International Conferene on Eletriity istriution Barelona, 1-15 May 003 EUCTION FACTO OF FEEING LINES THAT HAVE A CABLE AN AN OVEHEA SECTION Ljuivoje opovi J.. Elektrodistriuija - Belgrade -
PISTONLESS DUAL CHAMBER ROCKET FUEL PUMP
39 th AIAA/ASE/SAE/ASEE Joint Propulsion Conferene and Exhibit AIAA 2003-4479 20-23 July 2003, Huntsville Alabama PISTONLESS DUAL CHABER ROCKET FUEL PUP Steve Harrington, Ph.D. Flometris, In. Solana Beah,
Classical Electromagnetic Doppler Effect Redefined. Copyright 2014 Joseph A. Rybczyk
Classial Eletromagneti Doppler Effet Redefined Copyright 04 Joseph A. Rybzyk Abstrat The lassial Doppler Effet formula for eletromagneti waves is redefined to agree with the fundamental sientifi priniples
Chapter 1: Introduction
Chapter 1: Introdution 1.1 Pratial olumn base details in steel strutures 1.1.1 Pratial olumn base details Every struture must transfer vertial and lateral loads to the supports. In some ases, beams or
university of illinois library AT URBANA-CHAMPAIGN BOOKSTACKS
university of illinois library AT URBANA-CHAMPAIGN BOOKSTACKS CENTRAL CIRCULATION BOOKSTACKS The person harging this material is responsible for its renewal or its return to the library from whih it was
Pipe Cleaner Proteins. Essential question: How does the structure of proteins relate to their function in the cell?
Pipe Cleaner Proteins GPS: SB1 Students will analyze the nature of the relationships between structures and functions in living cells. Essential question: How does the structure of proteins relate to their
A Comparison of Default and Reduced Bandwidth MR Imaging of the Spine at 1.5 T
9 A Comparison of efault and Redued Bandwidth MR Imaging of the Spine at 1.5 T L. Ketonen 1 S. Totterman 1 J. H. Simon 1 T. H. Foster 2. K. Kido 1 J. Szumowski 1 S. E. Joy1 The value of a redued bandwidth
10.1 The Lorentz force law
Sott Hughes 10 Marh 2005 Massahusetts Institute of Tehnology Department of Physis 8.022 Spring 2004 Leture 10: Magneti fore; Magneti fields; Ampere s law 10.1 The Lorentz fore law Until now, we have been
protection p1ann1ng report
f1re~~ protetion p1ann1ng report BUILDING CONSTRUCTION INFORMATION FROM THE CONCRETE AND MASONRY INDUSTRIES Signifiane of Fire Ratings for Building Constrution NO. 3 OF A SERIES The use of fire-resistive
Measurement of Powder Flow Properties that relate to Gravity Flow Behaviour through Industrial Processing Lines
Measurement of Powder Flow Properties that relate to Gravity Flow ehaviour through Industrial Proessing Lines A typial industrial powder proessing line will inlude several storage vessels (e.g. bins, bunkers,
Chapter 1 Microeconomics of Consumer Theory
Chapter 1 Miroeonomis of Consumer Theory The two broad ategories of deision-makers in an eonomy are onsumers and firms. Eah individual in eah of these groups makes its deisions in order to ahieve some
Granular Problem Solving and Software Engineering
Granular Problem Solving and Software Engineering Haibin Zhu, Senior Member, IEEE Department of Computer Siene and Mathematis, Nipissing University, 100 College Drive, North Bay, Ontario, P1B 8L7, Canada
VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR. A Thesis by. Hong-Tuan Nguyen Vu
VOLTAGE CONTROL WITH SHUNT CAPACITANCE ON RADIAL DISTRIBUTION LINE WITH HIGH R/X FACTOR A Thesis by Hong-Tuan Nguyen Vu Eletrial Engineer, Polytehni University of HCMC, 1993 Submitted to the College of
Chapter 6 A N ovel Solution Of Linear Congruenes Proeedings NCUR IX. (1995), Vol. II, pp. 708{712 Jerey F. Gold Department of Mathematis, Department of Physis University of Utah Salt Lake City, Utah 84112
RATING SCALES FOR NEUROLOGISTS
RATING SCALES FOR NEUROLOGISTS J Hobart iv22 WHY Correspondene to: Dr Jeremy Hobart, Department of Clinial Neurosienes, Peninsula Medial Shool, Derriford Hospital, Plymouth PL6 8DH, UK; Jeremy.Hobart@
4.15 USING METEOSAT SECOND GENERATION HIGH RESOLUTION VISIBLE DATA FOR THE IMPOVEMENT OF THE RAPID DEVELOPPING THUNDERSTORM PRODUCT
4.15 USNG METEOSAT SECOND GENEATON HGH ESOLUTON VSBLE DATA FO THE MPOVEMENT OF THE APD DEVELOPPNG THUNDESTOM PODUCT Oleksiy Kryvobok * Ukrainian HydroMeteorologial nstitute Kyiv, Ukraine Stephane Senesi
Customer Efficiency, Channel Usage and Firm Performance in Retail Banking
Customer Effiieny, Channel Usage and Firm Performane in Retail Banking Mei Xue Operations and Strategi Management Department The Wallae E. Carroll Shool of Management Boston College 350 Fulton Hall, 140
Capacity at Unsignalized Two-Stage Priority Intersections
Capaity at Unsignalized Two-Stage Priority Intersetions by Werner Brilon and Ning Wu Abstrat The subjet of this paper is the apaity of minor-street traffi movements aross major divided four-lane roadways
Another Look at Gaussian CGS Units
Another Look at Gaussian CGS Units or, Why CGS Units Make You Cool Prashanth S. Venkataram February 24, 202 Abstrat In this paper, I ompare the merits of Gaussian CGS and SI units in a variety of different
1.3 Complex Numbers; Quadratic Equations in the Complex Number System*
04 CHAPTER Equations and Inequalities Explaining Conepts: Disussion and Writing 7. Whih of the following pairs of equations are equivalent? Explain. x 2 9; x 3 (b) x 29; x 3 () x - 2x - 22 x - 2 2 ; x
Weighting Methods in Survey Sampling
Setion on Survey Researh Methods JSM 01 Weighting Methods in Survey Sampling Chiao-hih Chang Ferry Butar Butar Abstrat It is said that a well-designed survey an best prevent nonresponse. However, no matter
Findings and Recommendations
Contrating Methods and Administration Findings and Reommendations Finding 9-1 ESD did not utilize a formal written pre-qualifiations proess for seleting experiened design onsultants. ESD hose onsultants
) ( )( ) ( ) ( )( ) ( ) ( ) (1)
OPEN CHANNEL FLOW Open hannel flow is haraterized by a surfae in ontat with a gas phase, allowing the fluid to take on shapes and undergo behavior that is impossible in a pipe or other filled onduit. Examples
VOLUME 13, ARTICLE 5, PAGES 117-142 PUBLISHED 05 OCTOBER 2005 DOI: 10.4054/DemRes.2005.13.
Demographi Researh a free, expedited, online journal of peer-reviewed researh and ommentary in the population sienes published by the Max Plank Institute for Demographi Researh Konrad-Zuse Str. 1, D-157
Electrician'sMathand BasicElectricalFormulas
Eletriian'sMathand BasiEletrialFormulas MikeHoltEnterprises,In. 1.888.NEC.CODE www.mikeholt.om Introdution Introdution This PDF is a free resoure from Mike Holt Enterprises, In. It s Unit 1 from the Eletrial
Neural network-based Load Balancing and Reactive Power Control by Static VAR Compensator
nternational Journal of Computer and Eletrial Engineering, Vol. 1, No. 1, April 2009 Neural network-based Load Balaning and Reative Power Control by Stati VAR Compensator smail K. Said and Marouf Pirouti
Sebastián Bravo López
Transfinite Turing mahines Sebastián Bravo López 1 Introdution With the rise of omputers with high omputational power the idea of developing more powerful models of omputation has appeared. Suppose that
USA Mathematical Talent Search. PROBLEMS / SOLUTIONS / COMMENTS Round 3 - Year 12 - Academic Year 2000-2001
USA Mathematial Talent Searh PROBLEMS / SOLUTIONS / COMMENTS Round 3 - Year - Aademi Year 000-00 Gene A. Berg, Editor /3/. Find the smallest positive integer with the property that it has divisors ending
Context-Sensitive Adjustments of Cognitive Control: Conflict-Adaptation Effects Are Modulated by Processing Demands of the Ongoing Task
Journal of Experimental Psyhology: Learning, Memory, and Cognition 2008, Vol. 34, No. 3, 712 718 Copyright 2008 by the Amerian Psyhologial Assoiation 0278-7393/08/$12.00 DOI: 10.1037/0278-7393.34.3.712
State of Maryland Participation Agreement for Pre-Tax and Roth Retirement Savings Accounts
State of Maryland Partiipation Agreement for Pre-Tax and Roth Retirement Savings Aounts DC-4531 (08/2015) For help, please all 1-800-966-6355 www.marylandd.om 1 Things to Remember Complete all of the setions
Deadline-based Escalation in Process-Aware Information Systems
Deadline-based Esalation in Proess-Aware Information Systems Wil M.P. van der Aalst 1,2, Mihael Rosemann 2, Marlon Dumas 2 1 Department of Tehnology Management Eindhoven University of Tehnology, The Netherlands
Retirement Option Election Form with Partial Lump Sum Payment
Offie of the New York State Comptroller New York State and Loal Retirement System Employees Retirement System Polie and Fire Retirement System 110 State Street, Albany, New York 12244-0001 Retirement Option
H H N - C - C 2 R. Three possible forms (not counting R group) depending on ph
Amino acids - 0 common amino acids there are others found naturally but much less frequently - Common structure for amino acid - C, -N, and functional groups all attached to the alpha carbon N - C - C
RESEARCH SEMINAR IN INTERNATIONAL ECONOMICS. Discussion Paper No. 475. The Evolution and Utilization of the GATT/WTO Dispute Settlement Mechanism
RESEARCH SEMINAR IN INTERNATIONAL ECONOMICS Shool of Publi Poliy The University of Mihigan Ann Arbor, Mihigan 48109-1220 Disussion Paper No. 475 The Evolution and Utilization of the GATT/WTO Dispute Settlement
In order to be able to design beams, we need both moments and shears. 1. Moment a) From direct design method or equivalent frame method
BEAM DESIGN In order to be able to design beams, we need both moments and shears. 1. Moment a) From diret design method or equivalent frame method b) From loads applied diretly to beams inluding beam weight
FOOD FOR THOUGHT Topical Insights from our Subject Matter Experts
FOOD FOR THOUGHT Topial Insights from our Sujet Matter Experts DEGREE OF DIFFERENCE TESTING: AN ALTERNATIVE TO TRADITIONAL APPROACHES The NFL White Paper Series Volume 14, June 2014 Overview Differene
Impedance Method for Leak Detection in Zigzag Pipelines
10.478/v10048-010-0036-0 MEASUREMENT SCIENCE REVIEW, Volume 10, No. 6, 010 Impedane Method for Leak Detetion in igzag Pipelines A. Lay-Ekuakille 1, P. Vergallo 1, A. Trotta 1 Dipartimento d Ingegneria
Effectiveness of a law to reduce alcohol-impaired driving in Japan
Effetiveness of a law to redue alohol-impaired driving in Japan T Nagata, 1,2 S Setoguhi, 3 D Hemenway, 4 M J Perry 5 Original artile 1 Takemi Program, Department of International Health, Harvard Shool
Behavior Analysis-Based Learning Framework for Host Level Intrusion Detection
Behavior Analysis-Based Learning Framework for Host Level Intrusion Detetion Haiyan Qiao, Jianfeng Peng, Chuan Feng, Jerzy W. Rozenblit Eletrial and Computer Engineering Department University of Arizona
Masters Thesis- Criticality Alarm System Design Guide with Accompanying Alarm System Development for the Radioisotope Production L
PNNL-18348 Prepared for the U.S. Department of Energy under Contrat DE-AC05-76RL01830 Masters Thesis- Critiality Alarm System Design Guide with Aompanying Alarm System Development for the Radioisotope
Heat Generation and Removal in Solid State Lasers
Chapter 1 Heat Generation and Removal in Solid State Lasers V. Ashoori, M. Shayganmanesh and S. Radmard Additional information is available at the end of the hapter http://dx.doi.org/10.577/63 1. Introdution
Hierarchical Clustering and Sampling Techniques for Network Monitoring
S. Sindhuja Hierarhial Clustering and Sampling Tehniques for etwork Monitoring S. Sindhuja ME ABSTRACT: etwork monitoring appliations are used to monitor network traffi flows. Clustering tehniques are
Open and Extensible Business Process Simulator
UNIVERSITY OF TARTU FACULTY OF MATHEMATICS AND COMPUTER SCIENCE Institute of Computer Siene Karl Blum Open and Extensible Business Proess Simulator Master Thesis (30 EAP) Supervisors: Luiano Garía-Bañuelos,
Effects of Inter-Coaching Spacing on Aerodynamic Noise Generation Inside High-speed Trains
Effets of Inter-Coahing Spaing on Aerodynami Noise Generation Inside High-speed Trains 1 J. Ryu, 1 J. Park*, 2 C. Choi, 1 S. Song Hanyang University, Seoul, South Korea 1 ; Korea Railroad Researh Institute,
RISK-BASED IN SITU BIOREMEDIATION DESIGN JENNINGS BRYAN SMALLEY. A.B., Washington University, 1992 THESIS. Urbana, Illinois
RISK-BASED IN SITU BIOREMEDIATION DESIGN BY JENNINGS BRYAN SMALLEY A.B., Washington University, 1992 THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Siene in Environmental
THE EFFECT OF WATER VAPOR ON COUNTERFLOW DIFFUSION FLAMES
THE EFFECT OF WATER VAPOR ON COUNTERFLOW DIFFUSION FLAMES by Jaeil Suh and Arvind Atreya Combustion and Heat Tkansfer Laboratory Department of Mehanial Engineering and Applied Mehanis The University of
Price-based versus quantity-based approaches for stimulating the development of renewable electricity: new insights in an old debate
Prie-based versus -based approahes for stimulating the development of renewable eletriity: new insights in an old debate uthors: Dominique FINON, Philippe MENNTEU, Marie-Laure LMY, Institut d Eonomie et
HEAT CONDUCTION. q A q T
HEAT CONDUCTION When a temperature gradient eist in a material, heat flows from the high temperature region to the low temperature region. The heat transfer mehanism is referred to as ondution and the
Recovering Articulated Motion with a Hierarchical Factorization Method
Reovering Artiulated Motion with a Hierarhial Fatorization Method Hanning Zhou and Thomas S Huang University of Illinois at Urbana-Champaign, 405 North Mathews Avenue, Urbana, IL 680, USA {hzhou, huang}@ifpuiuedu
The Organic Chemistry of Amino Acids, Peptides, and Proteins
Essential rganic Chemistry Chapter 16 The rganic Chemistry of Amino Acids, Peptides, and Proteins Amino Acids a-amino carboxylic acids. The building blocks from which proteins are made. H 2 N C 2 H Note:
Previously Published Works UC Berkeley
Previously Published Works UC Berkeley A University of California author or department has made this artile openly available. Thanks to the Aademi Senate s Open Aess Poliy, a great many UC-authored sholarly
A Survey of Usability Evaluation in Virtual Environments: Classi cation and Comparison of Methods
Doug A. Bowman [email protected] Department of Computer Siene Virginia Teh Joseph L. Gabbard Deborah Hix [ jgabbard, hix]@vt.edu Systems Researh Center Virginia Teh A Survey of Usability Evaluation in Virtual
Big Data Analysis and Reporting with Decision Tree Induction
Big Data Analysis and Reporting with Deision Tree Indution PETRA PERNER Institute of Computer Vision and Applied Computer Sienes, IBaI Postbox 30 11 14, 04251 Leipzig GERMANY [email protected],
Amino Acids and Proteins
Amino Acids and Proteins Proteins are composed of amino acids. There are 20 amino acids commonly found in proteins. All have: N2 C α R COO Amino acids at neutral p are dipolar ions (zwitterions) because
Reversed Phase High Presssure Liquid Chromatograhphic Technique for Determination of Sodium Alginate from Oral Suspension
International Journal of PharmTech Research CODEN (USA): IJPRIF ISSN : 0974-4304 Vol.2, No.2, pp 1634-1638, April-June 2010 Reversed Phase High Presssure Liquid Chromatograhphic Technique for Determination
i_~f e 1 then e 2 else e 3
A PROCEDURE MECHANISM FOR BACKTRACK PROGRAMMING* David R. HANSON + Department o Computer Siene, The University of Arizona Tuson, Arizona 85721 One of the diffiulties in using nondeterministi algorithms
IV. -Amino Acids: carboxyl and amino groups bonded to -Carbon. V. Polypeptides and Proteins
IV. -Amino Acids: carboxyl and amino groups bonded to -Carbon A. Acid/Base properties 1. carboxyl group is proton donor! weak acid 2. amino group is proton acceptor! weak base 3. At physiological ph: H
AUDITING COST OVERRUN CLAIMS *
AUDITING COST OVERRUN CLAIMS * David Pérez-Castrillo # University of Copenhagen & Universitat Autònoma de Barelona Niolas Riedinger ENSAE, Paris Abstrat: We onsider a ost-reimbursement or a ost-sharing
A Comparison of Service Quality between Private and Public Hospitals in Thailand
International Journal of Business and Soial Siene Vol. 4 No. 11; September 2013 A Comparison of Servie Quality between Private and Hospitals in Thailand Khanhitpol Yousapronpaiboon, D.B.A. Assistant Professor
Computational Analysis of Two Arrangements of a Central Ground-Source Heat Pump System for Residential Buildings
Computational Analysis of Two Arrangements of a Central Ground-Soure Heat Pump System for Residential Buildings Abstrat Ehab Foda, Ala Hasan, Kai Sirén Helsinki University of Tehnology, HVAC Tehnology,
Conversion of short optical pulses to terahertz radiation in a nonlinear medium: Experiment and theory
PHYSICAL REVIEW B 76, 35114 007 Conversion of short optial pulses to terahertz radiation in a nonlinear medium: Experiment and theory N. N. Zinov ev* Department of Physis, University of Durham, Durham
A Keyword Filters Method for Spam via Maximum Independent Sets
Vol. 7, No. 3, May, 213 A Keyword Filters Method for Spam via Maximum Independent Sets HaiLong Wang 1, FanJun Meng 1, HaiPeng Jia 2, JinHong Cheng 3 and Jiong Xie 3 1 Inner Mongolia Normal University 2
Availability, Reliability, Maintainability, and Capability
Availability, Reliability, Maintainability, and Capability H. Paul Barringer, P.E. Barringer & Assoiates, In. Humble, TX Triplex Chapter Of The Vibrations Institute Hilton Hotel Beaumont, Texas February
An integrated optimization model of a Closed- Loop Supply Chain under uncertainty
ISSN 1816-6075 (Print), 1818-0523 (Online) Journal of System and Management Sienes Vol. 2 (2012) No. 3, pp. 9-17 An integrated optimization model of a Closed- Loop Supply Chain under unertainty Xiaoxia
Journal of Engineering Science and Technology Review 6 (5) (2013) 143-148. Research Article
Jestr Journal o Engineering Siene and Tehnology Review 6 (5) (13) 143-148 Researh Artile JOURNAL OF Engineering Siene and Tehnology Review www.jestr.org Numerial Analyses on Seismi Behaviour o Conrete-illed
Application Note. Determination of Amino acids by UHPLC with automated OPA- Derivatization by the Autosampler. Summary. Fig. 1.
Application Note Determination of Amino acids by UHPLC with automated PA- Derivatization by the Autosampler Category Bio Analysis Matrix - Method UHPLC Keywords Proteinogenic Amino acids, Canonical Amino
An Efficient Network Traffic Classification Based on Unknown and Anomaly Flow Detection Mechanism
An Effiient Network Traffi Classifiation Based on Unknown and Anomaly Flow Detetion Mehanism G.Suganya.M.s.,B.Ed 1 1 Mphil.Sholar, Department of Computer Siene, KG College of Arts and Siene,Coimbatore.
Part A: Amino Acids and Peptides (Is the peptide IAG the same as the peptide GAI?)
ChemActivity 46 Amino Acids, Polypeptides and Proteins 1 ChemActivity 46 Part A: Amino Acids and Peptides (Is the peptide IAG the same as the peptide GAI?) Model 1: The 20 Amino Acids at Biological p See
RADON TOXICITY. Case Studies in Environmental Medicine
Case Studies in Environmental Mediine Course: SS3045 Revision Date: June 2000 Original Date: September 1995 Expiration Date: June 30, 2003 RADON TOXICITY Environmental Alert In the United States, indoor
UNIVERSITY AND WORK-STUDY EMPLOYERS WEB SITE USER S GUIDE
UNIVERSITY AND WORK-STUDY EMPLOYERS WEB SITE USER S GUIDE September 8, 2009 Table of Contents 1 Home 2 University 3 Your 4 Add 5 Managing 6 How 7 Viewing 8 Closing 9 Reposting Page 1 and Work-Study Employers
Using Live Chat in your Call Centre
Using Live Chat in your Call Centre Otober Key Highlights Yesterday's all entres have beome today's ontat entres where agents deal with multiple queries from multiple hannels. Live Chat hat is one now
Lemon Signaling in Cross-Listings Michal Barzuza*
Lemon Signaling in Cross-Listings Mihal Barzuza* This paper analyzes the deision to ross-list by managers and ontrolling shareholders assuming that they have private information with respet to the amount
3 Game Theory: Basic Concepts
3 Game Theory: Basi Conepts Eah disipline of the soial sienes rules omfortably ithin its on hosen domain: : : so long as it stays largely oblivious of the others. Edard O. Wilson (1998):191 3.1 and and
Wireless Networking Guide 2007 www.lexmark.com
Wireless Networking Guide 2007 www.lexmark.om P/N 13L0828 E.C. 3L0101 Contents Installing the printer on a wireless network...4 Wireless network ompatiility...4 Information you will need to set up the
Solving the Game of Awari using Parallel Retrograde Analysis
Solving the Game of Awari using Parallel Retrograde Analysis John W. Romein and Henri E. Bal Vrije Universiteit, Faulty of Sienes, Department of Mathematis and Computer Siene, Amsterdam, The Netherlands
WORKFLOW CONTROL-FLOW PATTERNS A Revised View
WORKFLOW CONTROL-FLOW PATTERNS A Revised View Nik Russell 1, Arthur H.M. ter Hofstede 1, 1 BPM Group, Queensland University of Tehnology GPO Box 2434, Brisbane QLD 4001, Australia {n.russell,a.terhofstede}@qut.edu.au
HEAT EXCHANGERS-2. Associate Professor. IIT Delhi E-mail: [email protected]. P.Talukdar/ Mech-IITD
HEA EXHANGERS-2 Prabal alukdar Assoiate Professor Department of Mehanial Engineering II Delhi E-mail: [email protected] Multipass and rossflow he subsripts 1 and 2 represent the inlet and outlet, respetively..
FIRE DETECTION USING AUTONOMOUS AERIAL VEHICLES WITH INFRARED AND VISUAL CAMERAS. J. Ramiro Martínez-de Dios, Luis Merino and Aníbal Ollero
FE DETECTION USING AUTONOMOUS AERIAL VEHICLES WITH INFRARED AND VISUAL CAMERAS. J. Ramiro Martínez-de Dios, Luis Merino and Aníbal Ollero Robotis, Computer Vision and Intelligent Control Group. University
Henley Business School at Univ of Reading. Pre-Experience Postgraduate Programmes Chartered Institute of Personnel and Development (CIPD)
MS in International Human Resoure Management For students entering in 2012/3 Awarding Institution: Teahing Institution: Relevant QAA subjet Benhmarking group(s): Faulty: Programme length: Date of speifiation:
An Enhanced Critical Path Method for Multiple Resource Constraints
An Enhaned Critial Path Method for Multiple Resoure Constraints Chang-Pin Lin, Hung-Lin Tai, and Shih-Yan Hu Abstrat Traditional Critial Path Method onsiders only logial dependenies between related ativities
Ch18_PT MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch18_PT MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) All of the following can be classified as biomolecules except A) lipids. B) proteins. C)
Pattern Recognition Techniques in Microarray Data Analysis
Pattern Reognition Tehniques in Miroarray Data Analysis Miao Li, Biao Wang, Zohreh Momeni, and Faramarz Valafar Department of Computer Siene San Diego State University San Diego, California, USA [email protected]
Deliverability on the Interstate Natural Gas Pipeline System
DOE/EIA-0618(98) Distribution Category UC-950 Deliverability on the Interstate Natural Gas Pipeline System May 1998 This report was prepared by the, the independent statistial and analytial ageny within
Fixed-income Securities Lecture 2: Basic Terminology and Concepts. Present value (fixed interest rate) Present value (fixed interest rate): the arb
Fixed-inome Seurities Leture 2: Basi Terminology and Conepts Philip H. Dybvig Washington University in Saint Louis Various interest rates Present value (PV) and arbitrage Forward and spot interest rates
Agile ALM White Paper: Redefining ALM with Five Key Practices
Agile ALM White Paper: Redefining ALM with Five Key Praties by Ethan Teng, Cyndi Mithell and Chad Wathington 2011 ThoughtWorks ln. All rights reserved www.studios.thoughtworks.om Introdution The pervasiveness
