Combinations of analgesics as active principles in commercial
|
|
- Bertina Hutchinson
- 6 years ago
- Views:
Transcription
1 676 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, 2001 DRUGS, COSMETICS, FORENSIC SCIENCES Applition of Liqui Chromtogrphy to the Simultneous Determintion of Aetylsliyli Ai, Cffeine, Coeine, Pretmol, Pyrioxine, n Thimine in Phrmeutil Preprtions NATIVIDAD RAMOS-MARTOS,FRANCISCO AGUIRRE-GÓMEZ, n ANTONIO MOLINA-DÍAZ 1 University of Jén, Fulty of Experimentl Sienes, Deprtment of Physil n Anlytil Chemistry, E Jén, Spin LUIS F. CAPITÁN-VALLVEY University of Grn, Fulty of Sienes, Deprtment of Anlytil Chemistry, E Grn, Spin This pper esries rpi reverse-phse liqui hromtogrphi metho, with UV etetion, for the simultneous etermintion of etylsliyli i, ffeine, oeine, pretmol, pyrioxine, n thimine in phrmeutil preprtions. A reverse-phse C 18 Nuleosil olumn is use. The moile phse onsists of 2 suessive elunts: wter (5 min) n etonitrile wter ( , v/v; 9 min), oth juste to ph 2.1 with phosphori i. Before etermintion etylsliyli i is ompletely onverte to sliyli i y lkline hyrolysis. Sliyli i, ffeine, pretmol, pyrioxine, n thimine re ll etete t 285 nm, wheres oeine is etete t 240 nm. Clirtion urves were liner for sliyli i, ffeine, pretmol, n pyrioxine in the rnge of mg/l, n for oeine n thimine in the rnge of mg/l. The metho ws pplie to the nlysis of 13 fortifie ommeril phrmeutil preprtions. Reoveries rnge from 92.6 to 105.5%, with reltive stnr evitions of %. Comintions of nlgesis s tive priniples in ommeril phrmeutil preprtions usully ontin 2 or more of the most ommon, i.e., etylsliyli i (ASA), sliylmie, pretmol (PCT), n oeine (CO), together with entrl nervous system stimulnts, e.g., ffeine (CF). Gs hromtogrphy (1, 2) n liqui hromtogrphy (LC; 3 5) hve een use for the etermintion of these nlgesis. However, the LC methos evelope for this purpose el usully with only 2 or 3 ompouns (5 7). UV etetion is usully use (8 12), sometimes with preolumn erivtiztion (13). Reeive April 24, Aepte y JM July 20, Author to whom orresponene shoul e resse; e-mil: molin@ujen.es. Some vitmins of the B-group, e.g., thimine (TH) n pyrioxine (PY), re foun long with nlgesis or entrl nervous system stimulnts in phrmeutil preprtions. LC provies numerous methos for the seprtion n etermintion of vitmins of the B-group in ifferent mtrixes: foos (14 16), meil foos (17), infnt formul (18), n phrmeutils (19, 20). Nevertheless, only one metho hs een pulishe for the simultneous etermintion of oth wter-solule vitmins n nlgesis or entrl nervous system stimulnts (9). The metho llows the etermintion of only 2 of the ove mentione nlgesis n 1 vitmin B in phrmeutil preprtion. In this pper, we esrie n LC metho for the simultneous etermintion of 6 tive priniples in phrmeutils. Three of them re nlgesis: ASA, CO, n PCT; 2 re wter-solule vitmins: PY n TH; n one is entrl nervous system stimulnt: CF. The metho esrie is sensitive, rpi, n relile n provies urte results in nlyses of phrmeutil preprtions. Experimentl Regents () Stok solutions. Stok solutions t g/l for sliyli i (SA; Fluk, Mri, Spin), CF (Pnre, Brelon, Spin), PY hyrohlorie (Fluk), n PCT (Fluk), n t g/l for CO (Aelló, Mri, Spin) n TH hyrohlorie (Fluk) were prepre y issolution of the pproprite mounts in wter (LC gre). All hemils were nlytil gre, n ultrpure wter ws use. Stok solutions of vitmins were store t 4 C. Working solutions were prepre ily y suitle ilution. () Moile phses. Methnol (Fluk), etonitrile (Fluk), n ultrpure wter were use. Phosphori i (Pnre, Mri, Spin) ws e to just the ph of the moile phses fter the etonitrile n wter were mixe. Ultrpure wter ws otine from Milli-Q Plus system (Millipore, Mri, Spin; LC gre).
2 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, Tle 1. LC prmeters otine uner the operting onitions of the evelope metho Anlyte Retention time, t R(min) Cpity ftor, k Asymmetry ftor, SF Resolution, R s Thimine Pyrioxine Pretmol Coeine Cffeine Sliyli i Flow rte of moile phse = 1 ml/min; olumn temperture = 35 C. k =(t R t 0 )/t 0, where t R = retention time of eh ompoun, n t 0 = retention time of the elunt (unretine ompoun). SF = rtio of the 2 hlf-withs t 10% pek height. R s =2 Z/(W +W ), where Z = istne etween the mxim of 2 onseutive peks, n W n W = pek withs. Figure 1. Liqui hromtogrm otine y the evelope metho n showing the seprtion of the 6 ompouns. Conitions: etetor 285 nm; onentrtion of eh ompoun 200 mg/l. Peks: 1=TH;2=PY;3=PCT;4=CO;5= CF; n 6 = SA.
3 678 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, 2001 Tle 2. Sttistil prmeters of lirtion urves otine for the evelope metho Anlyte Interept Slope SD SD r F Sliyli i Cffeine Coeine Pretmol Pyrioxine Thimine Stnr evition of the interept. Stnr evition of the slope. Correltion oeffiient. F rtio. Apprtus () Liqui hromtogrph. Moel HP 1050 (Hewlett-Pkr Co., Aronle, PA). () LC olumn. Nuleosil C 18 stinless steel, mm, 5 µm prtile size (No. 2515; Shrlu Siene, Brelon, Spin). () Asorne etetor. Hewlett-Pkr ioe-rry etetor HP 1040 M series II with vrile wvelength rnge of nm. Spetr of the elutes n sorne mesurements t 285 n 240 nm were otine t time intervls of s. Tretment of Smples The ontents of psules re quntittively trnsferre, n tlets re rushe to fine power for issolution in wter y sonition. The solutions re then filtere through 0.45 µm pore size Millipore filter, n the filtrtes re ilute to pproprite volume with LC gre wter. To otin the omplete trnsformtion of ASA to SA, lkline hyrolysis is performe for phrmeutils ontining ASA y treting the smple with 1M NOH solution n heting t 60 C for 30 min. Suitle ilutions re me in ll ses efore the smple solutions re injete. LC Conitions The following proeure is use for ll smples: wter (ph 2.1) s the moile phse for 5 min n then etonitrile wter ( , v/v) for 9 min, t flow rte of 1 ml/min. The etetion wvelength is set t 285 nm for SA, CF, PCT, PY, n TH n t 240 nm for CO. The working olumn temperture is 35 C. The smple volume injete is 10 µl. The hromtogrphi prmeters otine uner these onitions re summrize in Tle 1. Tle 3. Anlytil prmeters lulte for the evelope metho R DL, mg/l Compoun LDR, mg/l Anlyte onentrtion, 100 mg/l Anlyte onentrtion, 400 mg/l Test I Test II e Sliyli i Cffeine Pyrioxine Thimine f Coeine f Pretmol LDR = liner ynmi rnge. RSD = reltive stnr evition. DL = etetion limit. From ref. 21. e From ref. 22: DL = S y/x n 2 n 1 ; = slope; n S y/x = stnr evition of y-resiuls. f Anlyte onentrtion = 800 mg/l.
4 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, Tle 4. Reovery of sliyli i, ffeine, pyrioxine, thimine, oeine, n pretmol from syntheti mixtures Sliyli i Cffeine Pyrioxine Thimine Coeine Pretmol Anlyte foun, mg/l Anlyte foun, mg/l Anlyte foun, mg/l Anlyte foun, mg/l Anlyte foun, mg/l Anlyte foun, mg/l Level of eh nlyte e, mg/l ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.7 Eh vlue is the men of 3 replite etermintions. SD = stnr evition. Anlyte e t 400 mg/l. Anlyte e t 1000 mg/l. LC Proeure A10µL liquot of solution ontining the nlytes in their liner ynmi onentrtion rnges re injete into the liqui hromtogrph: mg/l for SA, CF, PCT, n PY n mg/l for CO n TH. A flow rte of 1 ml/min n working olumn temperture of 35 C re use. The ompouns re seprte on reverse-phse C 18 Nuleosil olumn, with moile phse onsisting of the 2 suessive elunts esrie ove, oth juste to ph 2.1 with phosphori i efore the wter n etonitrile re mixe. After ll the ompouns re seprte, the wter is psse through the olumn for 4 min. Asorne pek res re mesure in ll ses. Results n Disussion Temperture n Flow Rte In the propose LC metho, the temperture vrition n the flow rte for the resolution of the system i not hve ny signifint influene on the nlytil signl. However, temperture of 35 C ws use euse it llowe liqui phse with lower visosity, n flow rte of 1 ml/min, whih ws pproprite for the working pressure of the hromtogrphi equipment, ws use to shorten the time require to perform the nlysis. Orer of Elution Preliminry stuies with severl elunt systems were onute to selet the most effetive elunt for the seprtion of the 6 nlytes of the system. With some elunts, wter t ph 5.0 n etonitrile wter from ( , v/v) to ( , v/v), lso t ph 5, no resolution ws oserve euse of lrge overlp of the signls (for exmple, the CO n PY peks). Moreover, symmetri n very wie peks were otine for wter-solule vitmins. With more ii elunt, etonitrile wter ( , v/v), ph 2.1, thinner peks s well s goo seprtion were hieve for CO with respet to wter-solule vitmins, ut PY n TH were not stisftorily seprte. With only wter t ph 2.1, PY n TH were seprte stisftorily, ut the other 4 ompouns, with lower polrity, were not elute. It oul e expete tht the use of less polr moile phse fter the elution of the wter-solule vitmins woul seprte them. Methnol wter ( , v/v) ws trie, ut it file to proue goo seprtion for CO n PCT. Finlly, etonitrile wter ( , v/v), ph 2.1, gve stisftory resolution of the 4 ompouns. Therefore, the moile phse selete for the most effiient seprtion onsiste of 2 elunts: the first elunt ws wter (LC) juste to ph 2.1 with phosphori i. It llowe the seprtion of the vitmins, whih were retine more wekly in the polr sttionry phse euse of their ioni nture. The seon elunt ws etonitrile wter ( , v/v), lso juste to the sme ph with phosphori i, for the seprtion of the 4 remining omponents of the system. When the elution time for the first elunt ws inrese from 3 to 5 min, the signl from PY ws gretly improve, prouing only 1 pek (elution times of <5 min gve 2 lose peks). This vrile, however, h no in-
5 680 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, 2001 Tle 5. Results for the etermintion of etylsliyli i, ffeine, oeine, n pretmol in ommeril phrmeutil preprtions Aetylsliyli i Cffeine Coeine Pretmol Phrmeutil preprtion Avg. foun ± SD, Avg. foun ± SD, Avg. foun ± SD, Avg. foun ± SD, Anlgils ± ± ± 1 Dolmen ± ± 0.2 Dolvirán ± ± ± 0.2 Fiorinl ± ± ± ± 4 Rinomiine ± ± 1 Eh vlue is the men of 3 replite etermintions. SD = stnr evition. fluene on the resolution of the other ompouns, inluing TH. With the seon elunt, 9 min ws shown to e pproprite to otin stisftory resolution (Tle 1). A typil hromtogrm is shown in Figure 1. Before the next injetion the olumn ws reequilirte y pssing ultrpure wter through the olumn for 4 min. This ws neessry to return the olumn to onitions pproprite for seprtion of the wter-solule vitmins. Only fter this proeure were the peks of the vitmins resolve. Clirtion n Anlytil Prmeters Stnr lirtion grphs for the nlytes were onstrute y plotting pek res proue y injetion of stnr solutions in the following onentrtion rnges: mg/l for SA, CF, PCT, n PY, n mg/l for CO n TH. Clirtion urves were nlyze y regression nlysis, n the orreltion oeffiient (r), slope, n y-interept for eh run were lulte (Tle 2). This proess ws repete 3 times for sttistil nlysis. The etetion limits (DL) for eh ompoun, lulte oring to the riteri of Miller n Miller (21) n Curos et l. (22), s well s the liner ynmi rnges (LDR) n reltive stnr evition (RSD) t 2 nlyte levels re shown in Tle 3. Applitions The propose metho ws use in the simultneous etermintion of the nlytes in oth syntheti mixtures n ommeril phrmeutil formultions. Syntheti mixtures. Solutions ontining the 6 tive priniples t 3 ifferent levels were prepre n nlyze y the propose metho. Three etermintions were performe in ll ses. Results foun were ompletely stisftory (Tle 4). Commeril phrmeutil preprtions. Thirteen ommeril phrmeutils were nlyze y the evelope Tle 6. Results for the etermintion of oeine, pyrioxine, n thimine in ommeril phrmeutil preprtions Coeine Pyrioxine Thimine (NO 3 or HCl) Phrmeutil preprtion Avg. foun ± SD, Avg. foun ± SD, Avg. foun ± SD, Benom ± 3 Coeisán ± 0.5 Conuts ± 0.4 Nervoión ± ± 0.3 Neurovur ± ± 3 Pzronquil ± ± 0.1 Perurets e oeín ± 0.4 Serfoxie ± 3 Eh vlue is the men of 3 replite etermintion. SD = stnr evition. Expresse s pyrioxine α-etoglutrte. Expresse s nhyre pyrioxine phosphoserinte.
6 Tle 7. Reovery of sliyli i, ffeine, pyrioxine, thimine, oeine, n pretmol from fortifie ommeril phrmeutil preprtions Sliyli i Cffeine Pyrioxine Thimine Coeine Pretmol Phrmeutil preprtion Anlgils ± ± ± ± ± ± ± ± ± 1 Dolmen ± ± ± ± ± ± 0.7 Dovirán ± ± ± ± ± ± ± ± ± 1 Fiorinl ± ± ± ± ± ± ± ± ± 2 Nervoión ± ± ± ± ± ± 1 Neurovur ± ± ± ± ± ± 3 Pzronquil ± ± ± ± ± ± 1 Rinomiine ± ± ± ± ± ± 2 Eh vlue is the men of 3 replite etermintions. SD = stnr evition. RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3,
7 682 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, 2001 Conlusions The propose metho llowe suessful seprtion n etermintion of 6 tive priniples: 1 orgni i (SA), 2 lklois (CF n CO), 2 wter-solule vitmins (PY n TH), n phenol erivtive (PCT). The totl time require for the nlysis is reltively shorter thn tht esrie y other reserhers (8, 9, 13) for simpler systems ontining some of these nlytes (ut not ll). Its pplition to phrmeutils fter vlition emonstrte tht the propose metho n e use stisftorily for the etermintion of these nlytes. We ompre the LC proeures propose y the Unite Sttes Phrmopeil Convention (USP; 23) with the evelope metho esrie here. The RSDs of the results otine y the USP methos n this metho re similr; however, the moile phse of this metho is simpler, n lthough the tiling ftors, in generl, re similr, the resolution otine with this metho is etter. In ition, the metho propose in this pper inlues more ompouns; the USP methos for CO usully inlue nother nlgesi (suh s PCT or ASA, ut not oth simultneously), n in no se o they inlue wter-solule vitmins. Aknowlegment We knowlege the finnil support from the Ministerio e Euión y Cultur e Espñ (Direión Generl e Enseñnz Superior e Investigión Científi), projet PB Referenes Figure 2. Typil liqui hromtogrm otine y the evelope metho n showing the seprtion of the 4 ompouns from Fiorinl psules. Conitions: etetor, 285 nm. Peks: 1=PCT;2=CO;3=CF;4= SA; n lost pek = sliylmie. metho fter issolution n suitle ilution s inite in the setion on smple tretment. Results n lel lims y the mnufturer re summrize in Tles 5 n 6. In ition, s hek on the ury of the propose metho, reovery stuy ws performe in whih the respetive tive priniples ontine in severl phrmeutil preprtions were e t 3 levels. Goo reoveries were otine in ll ses (Tle 7). Figure 2 shows the seprtion of the 4 ompouns (PCT, CO, CF, n SA) from Fiorinl psules. (1) Aler, L.L., Overton, M.M., & Smith, D.E. (1971) J. Asso. Off. Anl. Chem. 54, (2) Oesh, M., & Shli, M. (1974) Phrm. At Helv. 49, (3) Auirjeie, A.M., Ael-Hmi, M.E., & Irhim, A. (1989) Anl. Lett. 22, (4) Pirol, R., Breggi, S.R., & De Beneitis, G. (1998) J. Chromtogr. B Appl. 705, (5) El-Shnwny, A., El-Sek, M., Aoul-Khier, A., & Ruker, G. (1991) J. Phrm. Si. 53, (6) Siso, W.R., Rittenhouse, C.T., & Everhrt, L.A. (1985) J. Chromtogr. 348, (7) Siso, W.R., Rittenhouse, C.T., Everhrt, L.A., & MLughin, A.M. (1986) J. Chromtogr. 354, (8) El-Kommos, M.E., & Emr, K.M. (1988) Tlnt 36, (9) Gámiz-Gri, L., & Luque e Cstro, M.D. (1997) J. Liq. Chromtogr. Relt. Tehnol. 20, (10) Ppoynnis, I.N., & Cy, B. (1987) Mirohem. J. 36, (11) Atwell, S.H., Bell, R.G., & Vys, R. (1992) Phrmopeil Forum 18, (12) Sntoni, G., Fi, L., Grtteri, P., Renzi G., & Pinzuti, S. (1992) Int. J. Phrm. 80, (13) Verm, K.K., Snghi, S.K., Jin, A., & Gupt, D. (1987) J. Phrm. Si. 76,
8 RAMOS-MARTOS ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 84, NO. 3, (14) Peter, C.H., Hollmn, J.H., Slngen, P.T., Whstffe, P.J., Southgte, A.T., & Fingls, P.M. (1993) Anlyst 118, (15) Agostini, T.S., & Gooy, H.T. (1997) J. High Resolut. Chromtogr. Chromtogr. Commun. 20, (16) Venem, D.P., Hollmn, C.H., Krin, P.L., Jnssen, T.M., & Mrtinj, B. (1996) J. Agri. Foo Chem. 44, (17) Chse, G.W., Lnen, W.O., Solimn, A.-G.M., & Eitenmiller, R.R., Jr (1993) J. AOAC Int. 76, (18) Chse, G.W., Lnen, W.O., Jr, Eitenmiller, R.R., Jr, & Solimn, A.-G.M. (1992) J. AOAC Int. 75, (19) Amin, M., & Reush, J. (1987) J. Chromtogr. 390, (20) Wng, E., & Hou, W. (1988) J. Chromtogr. 447, (21) Miller, J.C., & Miller, J.N. (1988) Sttistis for Anlytil Chemistry, Ellis Horwoo Lt., Chihester, UK, pp (22) Curos, L., Grí, A., Jiménez, C., & Román, M. (1993) Anl. Lett. 26, (23) The Unite Sttes Phrmopei, The Ntionl Formulry, n 1st 4th Supplements, Offiil Monogrphs (1995) 23r E., Unite Sttes Phrmopeil Convention, In., Rokville, MD
Appendix A: HVAC Equipment Efficiency Tables
Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER
More informationStatistics in medicine
Sttistis in meiine Workshop 1: Sreening n ignosti test evlution Septemer 22, 2016 10:00 AM to 11:50 AM Hope 110 Ftm Shel, MD, MS, MPH, PhD Assistnt Professor Chroni Epiemiology Deprtment Yle Shool of Puli
More informationCounting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs
Isomorphism of Grphs Definition The simple grphs G 1 = (V 1, E 1 ) n G = (V, E ) re isomorphi if there is ijetion (n oneto-one n onto funtion) f from V 1 to V with the property tht n re jent in G 1 if
More informationANALYSIS AND MODELLING OF RAINFALL EVENTS
Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.
More informationfor all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx
Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion
More informationNumbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
More informationLecture 6: Coding theory
Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those
More informationEdexcel Level 3 Advanced GCE in Mathematics (9MA0) Two-year Scheme of Work
Eexel Level 3 Avne GCE in Mthemtis (9MA0) Two-yer Sheme of Work Stuents stuying A Level Mthemtis will tke 3 ppers t the en of Yer 13 s inite elow. All stuents will stuy Pure, Sttistis n Mehnis. A level
More information1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.
1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the
More informationEigenvectors and Eigenvalues
MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.
More informationCS 491G Combinatorial Optimization Lecture Notes
CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,
More informationSurds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233,
Surs n Inies Surs n Inies Curriulum Rey ACMNA:, 6 www.mthletis.om Surs SURDS & & Inies INDICES Inies n surs re very losely relte. A numer uner (squre root sign) is lle sur if the squre root n t e simplifie.
More informationH 4 H 8 N 2. Example 1 A compound is found to have an accurate relative formula mass of It is thought to be either CH 3.
. Spetrosopy Mss spetrosopy igh resolution mss spetrometry n e used to determine the moleulr formul of ompound from the urte mss of the moleulr ion For exmple, the following moleulr formuls ll hve rough
More informationFactorising FACTORISING.
Ftorising FACTORISING www.mthletis.om.u Ftorising FACTORISING Ftorising is the opposite of expning. It is the proess of putting expressions into rkets rther thn expning them out. In this setion you will
More informationLecture Notes No. 10
2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite
More informationCSE 332. Sorting. Data Abstractions. CSE 332: Data Abstractions. QuickSort Cutoff 1. Where We Are 2. Bounding The MAXIMUM Problem 4
Am Blnk Leture 13 Winter 2016 CSE 332 CSE 332: Dt Astrtions Sorting Dt Astrtions QuikSort Cutoff 1 Where We Are 2 For smll n, the reursion is wste. The onstnts on quik/merge sort re higher thn the ones
More information10.7 Assessment criteria for the individual investigation
Unit 6 Prtil Biology n Investigtive Skills 10.7 for the iniviul investigtion Reserh n rtionle There is some ttempt to provie rtionle for the hoie of investigtion in terms of its sope n its reltion to iologil
More informationSection 2.1 Special Right Triangles
Se..1 Speil Rigt Tringles 49 Te --90 Tringle Setion.1 Speil Rigt Tringles Te --90 tringle (or just 0-60-90) is so nme euse of its ngle mesures. Te lengts of te sies, toug, ve very speifi pttern to tem
More informationINVESTIGATION OF THE OSL SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ
Meiterrnen Arheology n Arheometry, Vol. 010, No., pp. 9 98 Copyright 010 MAA Printe in Greee. All rights reserve. INVESTIGATION OF THE SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ G. Kitis 1, N.G. Kiyk,
More informationNecessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 )
Neessry n suient onitions for some two vrile orthogonl esigns in orer 44 C. Koukouvinos, M. Mitrouli y, n Jennifer Seerry z Deite to Professor Anne Penfol Street Astrt We give new lgorithm whih llows us
More informationNow we must transform the original model so we can use the new parameters. = S max. Recruits
MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with
More information8 THREE PHASE A.C. CIRCUITS
8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),
More information3.15 NMR spectroscopy Different types of NMR There are two main types of NMR 1. C 13 NMR 2. H (proton) NMR
.5 NMR spetrosopy Different types of NMR There re two min types of NMR. NMR. (proton) NMR There is only round % in orgni moleules ut modern NMR mhines re sensitive enough to give full spetr for The spetr
More informationTutorial Worksheet. 1. Find all solutions to the linear system by following the given steps. x + 2y + 3z = 2 2x + 3y + z = 4.
Mth 5 Tutoril Week 1 - Jnury 1 1 Nme Setion Tutoril Worksheet 1. Find ll solutions to the liner system by following the given steps x + y + z = x + y + z = 4. y + z = Step 1. Write down the rgumented mtrix
More informationCS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014
S 224 DIGITAL LOGI & STATE MAHINE DESIGN SPRING 214 DUE : Mrh 27, 214 HOMEWORK III READ : Relte portions of hpters VII n VIII ASSIGNMENT : There re three questions. Solve ll homework n exm prolems s shown
More informationAluminizing of Nickel-Based Superalloys Grade IN 738 by Powder Liquid Coating
Mterils Trnstions, Vol. 51, No. 5 (2010) pp. 982 to 987 #2010 The Jpn Institute of Metls Aluminizing of Nikel-Bse Superlloys Gre IN 738 y Power Liqui Coting Ptm Visuttipitukul 1; *, Nuntiy Limvnutpong
More informationA Straightforward Protocol for the Highly Efficient Preparation of. Main-chain Azo Polymers Directly from Bisnitroaromatic Compounds
Supporting Informtion A Strightforwr Protool for the Highly Effiient Preprtion of Min-hin Azo Polymers Diretly from Bisnitroromti Compouns y the Phototlyti Proess Liing Wng, Xingqing Pn, Yin Zho, Yng Chen,
More informationThe Stirling Engine: The Heat Engine
Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines
More informationA Study on the Properties of Rational Triangles
Interntionl Journl of Mthemtis Reserh. ISSN 0976-5840 Volume 6, Numer (04), pp. 8-9 Interntionl Reserh Pulition House http://www.irphouse.om Study on the Properties of Rtionl Tringles M. Q. lm, M.R. Hssn
More informationLinear Algebra Introduction
Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +
More informationAppendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities
Appendi Prtil dishrges. Reltionship Between Mesured nd Atul Dishrge Quntities A dishrging smple my e simply represented y the euilent iruit in Figure. The pplied lternting oltge V is inresed until the
More informationA STUDY OF Q-CONTIGUOUS FUNCTION RELATIONS
Commun. Koren Mth. So. 31 016, No. 1, pp. 65 94 http://dx.doi.org/10.4134/ckms.016.31.1.065 A STUDY OF Q-CONTIGUOUS FUNCTION RELATIONS Hrsh Vrdhn Hrsh, Yong Sup Kim, Medht Ahmed Rkh, nd Arjun Kumr Rthie
More informationNEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE
NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE V.S. Gordeev, G.A. Myskov Russin Federl Nuler Center All-Russi Sientifi Reserh Institute of Experimentl Physis (RFNC-VNIIEF)
More informationERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY
ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri
More informationWeed Management in Strawberry
Wee Siene Wee Mngement in Strwerry Prinipl Investigtor Dr. Steven Fennimore Coopertive Extension Wee Speilist Dept. of Plnt Sienes University of Cliforni, Dvis USDA Agriulturl Reserh Sttion 1636 Est Alisl
More information18.06 Problem Set 4 Due Wednesday, Oct. 11, 2006 at 4:00 p.m. in 2-106
8. Problem Set Due Wenesy, Ot., t : p.m. in - Problem Mony / Consier the eight vetors 5, 5, 5,..., () List ll of the one-element, linerly epenent sets forme from these. (b) Wht re the two-element, linerly
More information6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR
6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht
More informationSIMPLE NONLINEAR GRAPHS
S i m p l e N o n l i n e r G r p h s SIMPLE NONLINEAR GRAPHS www.mthletis.om.u Simple SIMPLE Nonliner NONLINEAR Grphs GRAPHS Liner equtions hve the form = m+ where the power of (n ) is lws. The re lle
More informationCS 360 Exam 2 Fall 2014 Name
CS 360 Exm 2 Fll 2014 Nme 1. The lsses shown elow efine singly-linke list n stk. Write three ifferent O(n)-time versions of the reverse_print metho s speifie elow. Eh version of the metho shoul output
More informationIntermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths
Intermedite Mth Cirles Wednesdy 17 Otoer 01 Geometry II: Side Lengths Lst week we disussed vrious ngle properties. As we progressed through the evening, we proved mny results. This week, we will look t
More informationSection 2.3. Matrix Inverses
Mtri lger Mtri nverses Setion.. Mtri nverses hree si opertions on mtries, ition, multiplition, n sutrtion, re nlogues for mtries of the sme opertions for numers. n this setion we introue the mtri nlogue
More informationActivities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions
MEP: Demonstrtion Projet UNIT 4: Trigonometry UNIT 4 Trigonometry tivities tivities 4. Pythgors' Theorem 4.2 Spirls 4.3 linometers 4.4 Rdr 4.5 Posting Prels 4.6 Interloking Pipes 4.7 Sine Rule Notes nd
More informationSUPPLEMENTAL INFORMATION
SUPPLEMENTAL INFORMATION Evlution of Modified Boehm Titrtion Methods for Use with Lignoellulosi Biohrs Rivk B. Fidel, Dvid A. Lird*, Mihel L. Thompson Deprtment of Agronomy, Iow Stte University, Ames,
More informationReview Topic 14: Relationships between two numerical variables
Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph
More informationNON-DETERMINISTIC FSA
Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is
More informationSolutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite!
Solutions for HW9 Exerise 28. () Drw C 6, W 6 K 6, n K 5,3. C 6 : W 6 : K 6 : K 5,3 : () Whih of the following re iprtite? Justify your nswer. Biprtite: put the re verties in V 1 n the lk in V 2. Biprtite:
More informationProject 6: Minigoals Towards Simplifying and Rewriting Expressions
MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy
More informationPAIR OF LINEAR EQUATIONS IN TWO VARIABLES
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. Two liner equtions in the sme two vriles re lled pir of liner equtions in two vriles. The most generl form of pir of liner equtions is x + y + 0 x + y + 0 where,,,,,,
More informationFirst compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.
0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression
More informationChapter 4rth LIQUIDS AND SOLIDS MCQs
Chpter 4rth LIQUIDS AND SOLIDS MCQs Q.1 Ioni solis re hrterize y () low melting points () goo onutivity in soli stte () high vpour pressure () soluility in polr solvents Q.2 Amorphous solis. () hve shrp
More informationAP CALCULUS Test #6: Unit #6 Basic Integration and Applications
AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationSupporting Information
Supporting Informtion Control Synthesis of Tuulr Hyperrosslinke Polymers for Highly Porous Cron Nnotues Xioyn Wng, Pn Mu, Chong Zhng, Yu Chen, Jinghui Zeng, Feng Wng n Ji-Xing Jing *, Shnxi Key Lortory
More informationAP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals
AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into
More information( ) { } [ ] { } [ ) { } ( ] { }
Mth 65 Prelulus Review Properties of Inequlities 1. > nd > >. > + > +. > nd > 0 > 4. > nd < 0 < Asolute Vlue, if 0, if < 0 Properties of Asolute Vlue > 0 1. < < > or
More informationCS 573 Automata Theory and Formal Languages
Non-determinism Automt Theory nd Forml Lnguges Professor Leslie Lnder Leture # 3 Septemer 6, 2 To hieve our gol, we need the onept of Non-deterministi Finite Automton with -moves (NFA) An NFA is tuple
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More information2.4 Theoretical Foundations
2 Progrmming Lnguge Syntx 2.4 Theoretil Fountions As note in the min text, snners n prsers re se on the finite utomt n pushown utomt tht form the ottom two levels of the Chomsky lnguge hierrhy. At eh level
More informationSOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVEX STOCHASTIC PROCESSES ON THE CO-ORDINATES
Avne Mth Moels & Applitions Vol3 No 8 pp63-75 SOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVE STOCHASTIC PROCESSES ON THE CO-ORDINATES Nurgül Okur * Imt Işn Yusuf Ust 3 3 Giresun University Deprtment
More informationMaintaining Mathematical Proficiency
Nme Dte hpter 9 Mintining Mthemtil Profiieny Simplify the epression. 1. 500. 189 3. 5 4. 4 3 5. 11 5 6. 8 Solve the proportion. 9 3 14 7. = 8. = 9. 1 7 5 4 = 4 10. 0 6 = 11. 7 4 10 = 1. 5 9 15 3 = 5 +
More informationMCH T 111 Handout Triangle Review Page 1 of 3
Hnout Tringle Review Pge of 3 In the stuy of sttis, it is importnt tht you e le to solve lgeri equtions n tringle prolems using trigonometry. The following is review of trigonometry sis. Right Tringle:
More informationSpacetime and the Quantum World Questions Fall 2010
Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1
More information6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR
6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht
More informationProbability. b a b. a b 32.
Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,
More informationILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS
ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS Dvid Miller West Virgini University P.O. BOX 6310 30 Armstrong Hll Morgntown, WV 6506 millerd@mth.wvu.edu
More informationy = c 2 MULTIPLE CHOICE QUESTIONS (MCQ's) (Each question carries one mark) is...
. Liner Equtions in Two Vriles C h p t e r t G l n e. Generl form of liner eqution in two vriles is x + y + 0, where 0. When we onsier system of two liner equtions in two vriles, then suh equtions re lle
More informationSECTION A STUDENT MATERIAL. Part 1. What and Why.?
SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are
More informationAPPROXIMATION AND ESTIMATION MATHEMATICAL LANGUAGE THE FUNDAMENTAL THEOREM OF ARITHMETIC LAWS OF ALGEBRA ORDER OF OPERATIONS
TOPIC 2: MATHEMATICAL LANGUAGE NUMBER AND ALGEBRA You shoul unerstn these mthemtil terms, n e le to use them ppropritely: ² ition, sutrtion, multiplition, ivision ² sum, ifferene, prout, quotient ² inex
More informationIowa Training Systems Trial Snus Hill Winery Madrid, IA
Iow Trining Systems Tril Snus Hill Winery Mdrid, IA Din R. Cohrn nd Gil R. Nonneke Deprtment of Hortiulture, Iow Stte University Bkground nd Rtionle: Over the lst severl yers, five sttes hve een evluting
More informationJ. Environ. Sci. & Natural Resources, 4(2): 83-87, 2011 ISSN
J. Environ. Si. & Nturl Resoures, 4(2): 83-87, 2011 ISSN 1999-7361 Totl Nutrient Uptke y Grin plus Strw n Eonomi of Fertilizer Use of Rie Muttion STL-655 Grown uner Boro Seson in Sline Are M. H. Kir, N.
More informationQUADRATIC EQUATION. Contents
QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,
More informationEstimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models
Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte
More informationSymmetrical Components 1
Symmetril Components. Introdution These notes should e red together with Setion. of your text. When performing stedy-stte nlysis of high voltge trnsmission systems, we mke use of the per-phse equivlent
More informationAPPENDIX. Precalculus Review D.1. Real Numbers and the Real Number Line
APPENDIX D Preclculus Review APPENDIX D.1 Rel Numers n the Rel Numer Line Rel Numers n the Rel Numer Line Orer n Inequlities Asolute Vlue n Distnce Rel Numers n the Rel Numer Line Rel numers cn e represente
More informationParticle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/)
Sutomic Physics: Prticle Physics Lecture 3 Mesuring Decys, Sctterings n Collisions Prticle lifetime n with Prticle ecy moes Prticle ecy kinemtics Scttering cross sections Collision centre of mss energy
More informationTOPIC: LINEAR ALGEBRA MATRICES
Interntionl Blurete LECTUE NOTES for FUTHE MATHEMATICS Dr TOPIC: LINEA ALGEBA MATICES. DEFINITION OF A MATIX MATIX OPEATIONS.. THE DETEMINANT deta THE INVESE A -... SYSTEMS OF LINEA EQUATIONS. 8. THE AUGMENTED
More informationJournal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article
Avilble online www.jopr.om Journl of Chemil nd Phrmeutil Reserh, 2013, 5(12):1283-1288 Reserh Artile ISSN : 0975-7384 CODEN(USA) : JCPRC5 Study on osion resistne of zin lloy oting of mehnil plting by eletrohemil
More informationGeneralization of 2-Corner Frequency Source Models Used in SMSIM
Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville
More informationMonochromatic Plane Matchings in Bicolored Point Set
CCCG 2017, Ottw, Ontrio, July 26 28, 2017 Monohromti Plne Mthings in Biolore Point Set A. Krim Au-Affsh Sujoy Bhore Pz Crmi Astrt Motivte y networks interply, we stuy the prolem of omputing monohromti
More informationLesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.
27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we
More informationSystem Validation (IN4387) November 2, 2012, 14:00-17:00
System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise
More informationsupplementary information
DOI: 1.138/n2131 Protein levels (% of ) e Full-length protein remining (%) 1 5 1 5 1 1 5 5 Hs7 Syt1 Syt2 β-atin CSP +tsyn Hs7 Syt1 Syt2 P4 rin.1.1.1 1 [Trypsin] (g/l) f +tsyn SNARE-omplexes remining (%)
More informationParticle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 3 : Interaction by Particle Exchange and QED. Recap
Prtile Physis Mihelms Term 2011 Prof Mrk Thomson g X g X g g Hnout 3 : Intertion y Prtile Exhnge n QED Prof. M.A. Thomson Mihelms 2011 101 Rep Working towrs proper lultion of ey n sttering proesses lnitilly
More informationMATH 122, Final Exam
MATH, Finl Exm Winter Nme: Setion: You must show ll of your work on the exm pper, legily n in etil, to reeive reit. A formul sheet is tthe.. (7 pts eh) Evlute the following integrls. () 3x + x x Solution.
More informationNote 12. Introduction to Digital Control Systems
Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the
More informationVISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS
AGRICULTURAL ENGINEERING VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS Ltvi University of Agriulture E-mil: ilze.pelee@llu.lv Astrt Use of solr energy inreses every
More informationApplied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005
Applie Gre 9 Assessment of Mthemtis Multiple-Choie Items Winter 2005 Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves remin the sme. . Multiple-Choie
More information1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes.
1 This question is out men ond enthlpies nd their use in the lultion of enthlpy hnges. Define men ond enthlpy s pplied to hlorine. Explin why the enthlpy of tomistion of hlorine is extly hlf the men ond
More informationLecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and
Leture 7: iffusion of Ions: Prt : oupled diffusion of tions nd nions s desried y Nernst-Plnk Eqution Tody s topis Continue to understnd the fundmentl kinetis prmeters of diffusion of ions within n eletrilly
More informationTechnische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution
Tehnishe Universität Münhen Winter term 29/ I7 Prof. J. Esprz / J. Křetínský / M. Luttenerger. Ferur 2 Solution Automt nd Forml Lnguges Homework 2 Due 5..29. Exerise 2. Let A e the following finite utomton:
More informationH (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a.
Chpter Review 89 IGURE ol hord GH of the prol 4. G u v H (, ) (A) Use the distne formul to show tht u. (B) Show tht G nd H lie on the line m, where m ( )/( ). (C) Solve m for nd sustitute in 4, otining
More informationResearch Article. ISSN (Print) *Corresponding author Askari, A
Sholrs Journl of Engineering n Tehnology (SJET) Sh. J. Eng. Teh., 4; (6B):84-846 Sholrs Aemi n Sientifi Pulisher (An Interntionl Pulisher for Aemi n Sientifi Resoures) www.sspulisher.om ISSN 3-435X (Online)
More informationDIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS
Krgujev Journl of Mthemtis Volume 38() (204), Pges 35 49. DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS MOHAMMAD W. ALOMARI Abstrt. In this pper, severl bouns for the ifferene between two Riemn-
More informationLogarithms LOGARITHMS.
Logrithms LOGARITHMS www.mthletis.om.u Logrithms LOGARITHMS Logrithms re nother method to lulte nd work with eponents. Answer these questions, efore working through this unit. I used to think: In the
More information5. Every rational number have either terminating or repeating (recurring) decimal representation.
CHAPTER NUMBER SYSTEMS Points to Rememer :. Numer used for ounting,,,,... re known s Nturl numers.. All nturl numers together with zero i.e. 0,,,,,... re known s whole numers.. All nturl numers, zero nd
More informationImplication Graphs and Logic Testing
Implition Grphs n Logi Testing Vishwni D. Agrwl Jmes J. Dnher Professor Dept. of ECE, Auurn University Auurn, AL 36849 vgrwl@eng.uurn.eu www.eng.uurn.eu/~vgrwl Joint reserh with: K. K. Dve, ATI Reserh,
More informationThe DOACROSS statement
The DOACROSS sttement Is prllel loop similr to DOALL, ut it llows prouer-onsumer type of synhroniztion. Synhroniztion is llowe from lower to higher itertions sine it is ssume tht lower itertions re selete
More informationAlgebra 2 Semester 1 Practice Final
Alger 2 Semester Prtie Finl Multiple Choie Ientify the hoie tht est ompletes the sttement or nswers the question. To whih set of numers oes the numer elong?. 2 5 integers rtionl numers irrtionl numers
More informationFormula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx
Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint
More informationTIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM
Proeeings of ASME VIB 5: th Biennil Conferene on Mehnil Virtion n Noise Septemer 4-8, 5 Long Beh, CA, USA DETC5-84644 TIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM
More information