Solution chemistry and cytotoxic properties of novel organogold(iii) compounds
|
|
- Amelia Owen
- 6 years ago
- Views:
Transcription
1 Bioorgni & iinl Chemistry 12 (24) Solution hemistry n ytotoxi properties of novel orgnogol(iii) ompouns Luigi ssori,, * Giorn Mron, Mri gostin Cinellu, Mrell Coronnello, Enrio Mini, Chir Gini n Pierluigi Orioli Deprtment of Chemistry, University of Florene, Vi ell Lstrui 3, 519, Sesto Fiorentino, Florene, Itly Deprtment of Chemistry, University of Sssri, Vi Viennz, 71 Sssri, Itly Deprtment of Phrmology, University of Florene, Vile Pierini 6, 5139 Florene, Itly Reeive 13 My 24; epte 1 Septemer 24 ville online 2 Otoer 24 strt The solution ehviour of some novel orgnogol(iii) ompouns ws investigte, n their ytotoxi properties evlute ginst few humn tumour ell lines (278/S, 278/R, MCF7, HT29 n 549). Speifilly, the following ompouns were onsiere: [(ipy m H)(2,6xyliineH)][PF 6 ] (Xyl) n [(ipy m H)(ptoluiineH)][PF 6 ] (Tol) (in whih ipy m = 6(1,1imethylenzyl)2,2 ipyriine), [(py m H)(O) 2 ] (PyO) (in whih py m = 2(1,1imethylenzyl)pyriine) n [(pz Ph H) 3 ]K (Pz) (in whih pz Ph = 1phenylpyrzole). The solution hemistry of these ompouns, uner physiologillike onitions, ws investigte through UV vis sorption n 1 H MR spetrosopies. Signifint ytotoxi effets in vitro were oserve in selete ses. Ó 24 Elsevier Lt. ll rights reserve. 1. Introution Keywors: Orgnogol(III) omplexes; UV vis sorption spetrosopy; 1 H MR spetrosopy; Cytotoxiity; Gol; Cner. * Corresponing uthor. Tel.: ; fx: ; emil: luigi.messori@unifi.it We hve reently shown tht vrious gol(iii) omplexes exhiit promising ytotoxi effets in vitro n re goo nites for further evlution s ntitumour gents. 1 itionl reports on the ntitumour properties of selete gol(iii) omplexes re the result of the reserh tivities of other groups. 2 6 otly, gol(iii) ompouns seem to exert their growth inhiitory effets through mehnisms tht re istint from those of the lssil ntiner pltinum(ii) omplexes. 7 mong the reently teste ompouns, the orgnogol(iii) omplex, [(ipy m H)(OH)][PF 6 ], hrterise y n ppreile stility within physiologil onitions, hs prove to e very tive ginst the 278ell line; 8 t vrine with the pltinum(ii) omplexes, its iologil tivity seems to e unrelte to iret interferene with D funtion n metolism. 8 This prompte us to onsier the solution ehviour n the iologil properties of some itionl gol(iii) ompouns hrterise y the presene of iret ron gol(iii) on; we elieve tht this ltter feture is very importnt for the stilistion of the oxition stte +3 of the gol entre. For this purpose, we took vntge of vrious reent stuies on the synthesis, hrteristion n retivity of gol(iii) ylometllte erivtives In prtiulr, we report here on the solution hemistry n the iologil properties of four orgnogol(iii) ompouns: [(ipy m H)(2,6xyliineH)][PF 6 ] (Xyl) n [(ipy m H)(ptoluiineH)][PF 6 ] (Tol) (in whih ipy m = 6(1,1imethylenzyl) 2,2 ipyriine), 12 [((py m H)(O) 2 ] (PyO) (in whih py m = 2(1,1imethylenzyl)pyriine) 12 n [(pz Ph H) 3 ]K (Pz) (in whih pz Ph =1 phenylpyrzole). 13 The Xyl n Tol ompouns, oth feturing the sme terentte C,, lign, inspire us y the enourging results reently ttine with the prent ompoun [(ipy m H)(OH)][PF 6 ]. Speifilly, we wnte to estlish whether the introution of ulkier lign in the fourth oorintion position might hve effets on the solution ehviour n the phrmologil profile of this orgnogol(iii) ompoun. t vrine, PyO, hving ylometllte C, lign, n Pz, with monoentte C lign, represent exmples of ompouns in whih the gol(iii) entre is less protete thn in the /$ see front mtter Ó 24 Elsevier Lt. ll rights reserve. oi:1.116/j.m
2 64 L. ssori et l. / Bioorg.. Chem. 12 (24) former ses. Remrkly, PyO presents two essile oorintion positions oupie y two ette groups wheres Pz ers three exhngele hlories tht might unergo file hyrolysis within n queous environment. Overll, we hve oserve tht the orgnogol(iii) moieties of ll these ompouns, exept Pz, re generlly stle uner physiologil onitions, n exhiit signifint ytotoxi properties towrs restrite pnel of humn tumour ell lines. Bse on these oservtions, the present ompouns my e of interest for further evlution s ntiner gents Min struturl spets 2. Results The following ompouns hve een onsiere in the present stuy: Xyl, Tol, PyO n Pz (see Sheme 1). The struture in the soli stte hs een etermine only for Xyl; 12 tht of the nlogous ompoun Tol n e eue from spetrosopi t n other physiohemil mesurements. Eqully, the orgnometlli frgments of Pz n PyO re onfiently ssume to mth those of the relte omplexes [(pz Ph H)(3,5 2 py) 2 ] 13 n [ (py m H) 2 ], 14 respetively, whose rystl strutures hve een sertine y Xry iffrtion nlysis. otly, ll these ompouns re hrterise y the presene of iret ron gol on. Xyl n Tol, otine y proton exhnge of [(ipy m H)(OH)][PF 6 ] with 2,6xyliine n ptoluiine, respetively, show signifint enhnement of the hyrophoi properties ompre to the prent omplex. 12 In PyO the ylometllte enzylpyriine provies nitrogen n ron onor to the squre plnr gol(iii) entre; the remining oorintion sites of the squre plne eing oupie y two ette ligns. In Pz the gol(iii) entre is oorinte to ron tom of the 1phenylpyrzole lign n to three hlories. In ll ses, the presene of the ron gol H + PF 6 C(O)O C(O)O [(ipymh)(ptoluiineh)][pf 6 ] [(pymh)(o) 2 ] H [(ipymh)(2,6xyliineh)][pf 6 ] + PF 6 [(pzphh) 3 ]K Sheme 1. Shemti rwing of the four gol(iii) omplexes. K + on is elieve to onfer suffiient reox stility to the gol(iii) entre Solution hemistry The stility in solution of the vrious orgnogol(iii) ompouns ws ssye y simple spetrophotometri mesurements. surements were rrie out within ifferent solvents (DMSO, ihloromethne, wter n the referene physiologil uffer ontining 5mM soium phosphte 1 mm, ph = 7.4). Some signifint spetrophotometri results re shown in Figure 1. Xyl n Tol re stle in orgni solvents suh s ihloromethne or DMSO. Uner these onitions oth ompouns exhiit n intense n in the visile (entre roun 42nm) tht is tenttively ssigne s to gol(iii) hrge trnsfer. The hyrolysis of oth ompouns, either in wter or in physiologillike uffer, is very fst n results into nerly omplete ispperne of the 42nm n; notly, hyrolysis in wter is ompnie y signifint ph erese. However, the UV trnsitions hrteristi of the ipy m sffol (entre t 32nm) 8 re not perture upon hyrolysis. The (ipy m H)(OH)] + speies is most likely forme in oth ses y proton exhnge of the miogol omplexes Xyl n Tol with wter; onomitnt relese of the romti mine tkes ple. Inee, these ompouns n e quntittively otine y the retion of [(ipy m H)(OH)][PF 6 ] with n exess of the orresponing mines, only proviing tht wter, proue y the retion, is remove. 12 Solutions of PyO, either in wter or in orgni solvents, re olourless. When issolve in wter or in the referene uffer, PyO exhiits some hrteristi ns in the ner UV, roun 26nm tht re stle with time. Upon onsiering tht the ette moieties generlly ehve s goo leving groups in queous solutions, we my expet their hyrolysis n replement y hyroxie. pprently, the resulting speies is stle in solution for severl hours. When issolve within orgni solvents, Pz imprts hrteristi yellow olour to the solution. In wter, or in the referene uffer, fst fing of the olour is oserve srie to rpi hyrolysis of gol(iii) oorinte hlories s in the se of the 4 nion. 15 The proess is ompnie y rsti erese in ph. However, this proess my e reverse, lmost ompletely, y ition of exess hlorie, for exmple, Li. otly, the UV spetrum of Pz, issolve in the uffer, shows slow, progressive erese of the min n entre t 25nm (Fig. 1, IV). The proess rehes ompletion within out 12 h t 25 C. We interpret this ehviour in terms of progressive moifition of the hyrolyse speies. Overll, from the ove reporte spetrophotometri experiments, it emerges tht the first three ompouns, following quik hyrolysis of their respetive lile ligns, proue orgnogol(iii)ontining speies tht
3 L. ssori et l. / Bioorg.. Chem. 12 (24) (I) (II) (III) (IV) Figure 1. UV vis spetr of Xyl (I), Tol (II), PyO (III) n Pz (IV). Tres represent the ompouns issolve in DMSO t 5mM onentrtion. Then the DMSO mother solutions of the four ompouns were ilute 1:4 either in pure DMSO (tres ) or in the referene phosphte uffer (tres ) or in wter (tres ). re stle for severl hours uner physiologillike onitions. t vrine, the hyrolysis prout of Pz mnifests lower stility n unergoes further trnsformtions. The ehviour in solution of Xyl n Tol ws further nlyse y 1 H MR spetrosopy. The spetr were reore either in euterte DMSO or in euterte queous solutions. otly, the 1 H MR spetr of Xyl n Tol, in DMSO, exhiit the resonnes hrteristi of the ylometllte ipyriine lign, plus resonnes ssigne to the xyliine or toluiine moieties oorinte to the gol(iii) entre. Upon hyrolysis within the referene euterte uffer, the 1 H MR spetr exhiit some hrteristi moifitions tht re srie to relese of either xyliine or toluiine from gol(iii) oorintion; t the sme time loss of the hrteristi olour is etete. In the finl 1 H MR spetr signls hrteristi of free xyliine or free toluiine re esily reognise (t 6.87, 6.6n 2.6 ppm for xyliine; t 6.97, 6.65 n 2.13ppm for toluiine) in greement with our hypothesis. Thus, the 1 H MR results onfirm the piture oming out from the spetrophotometri mesurements. Xyl n Tol issolve in the uffer rpily hyrolyse their mie ligns. However, the moleulr sffol of these ompouns, hrterise y the presene of iret rontogol on, is pretty stle n oes not show ny sign of reution of the gol(iii) entre Cytotoxi effets Owing to the ppreile stility of the vrious orgnogol(iii)ontining frgments uner physiologillike onitions, ll the ove ompouns oul e evlute in vitro s potentil ytotoxi gents. These orgnogol(iii) ompouns were teste ginst the following humn tumour ell lines: 278/S, 278/R (ovrin ner), MCF7 (rest ner), HT29 (olon ner) n 549 (lung ner). Their growth inhiitory properties were nlyse through the lssil sulforhomineb metho. 12 Results re shown in Tle 1. For omprison purposes, results otine with [(ipy m H)(OH)][PF 6 ] the preursor of Xyl n Tol; oxlipltin n ispltin (oth urrently use s ntiner rugs in the linis) re lso reporte. otly, PyO n Xyl prove to e signifintly tive ginst the two ovrin rinom ell lines, with IC 5 vlues of 2.9±.34 lm n 2.5±.43 lm, respetively, on the 278/S ell line. Crossresistne is reltively moest s it emerges from inspetion of the t otine on the 278/S n 278/R lines. Lower ut still importnt ytotoxi effets were proue y Tol (6.15 ± 1.4 lm) n [(ipy m H)(OH)][PF 6 ] (8.2± 2.lM) on the sme 278/S line. Moest effets were oserve on the MCF7 ell line, exept for Xyl (5.2±.4lM) (5.3±.87 lm); negligile effets were generlly mesure on the HT29 n 549 lines. t vrine with the other orgnogol(iii) ompouns, Pz turne out to e virtully evoi of ytotoxiity towrs ll teste ell lines, proly in reltion to its lower hemil stility profile. It is worthwhile noting tht the three ompouns [ (ipy m H)(OH)][PF 6 ], [(ipy m H)(2,6xyliine H)][PF 6 ] n [(ipy m H)(ptoluiineH)][PF 6 ]
4 642 L. ssori et l. / Bioorg.. Chem. 12 (24) Tle 1. IC 5 (lm) vlues of orgnogol(iii) ompouns in humn tumour ells, sensitive or resistnt to ispltin Compouns IC 5 (lm) 278/S 278/R MCF7 HT Pz 3.2 ± () 33.7 ± 2.15 >5 >5 [(ipy m H)(OH)][PF 6 ] 8.2± ± 1.42 (1.6) 35.3± >5 PyO 2.9 ± ±.1 (2.2) 17.7 ± Xyl 2.5 ± ±.3 (2.3) 5.2 ± Tol 6.15 ± ±.94 (2.3) 18.1 ± Cispltin.33 ± ±.87 (19.3) 5.3 ± ±.23 Oxlipltin.4 ±.12.2 ±.2 (.5).13 ±.1.4 ±.16 Dt were ollete fter 72h exposure to the rugs. IC 5 is efine s the onentrtion of rug require to inhiit ell growth y 5% ompre to ontrol; it is expresse s men ± SE of t lest three etermintions or men of two etermintions; vlues in prentheses ( ) enote the rtios of IC 5 of ispltinresistnt ell line n IC 5 of prentl sensitive ell line. exhiit signifint vritions in their ytotoxi properties ginst the teste ell lines, in spite of the ft tht ll of them most likely trnsform into the sme speies when issolve in the referene uffer. This oservtion implies tht the presene of the 2,6 2 C 6 H 3 H or 4C 6 H 5 H lign ffets somehow the iologil tivities of the ommon orgnogol(iii) entre. 3. Disussion Owing to the enourging in vitro ntitumour properties reently oserve for (ipy m H)(OH)][PF 6 ], new orgnogol(iii) omplexes were prepre, hrterise n teste s potentil ytotoxi gents. The solution ehviour n the stility within physiologillike environment of these novel orgnogol(iii) ompouns ws investigte. In ll ses, the gol(iii) entre oes not unergo reution, eing equtely stilise y the iret rontogol on. However, importnt hyrolysis proesses tke ple. Speifilly, in the se of Xyl n Tol, hyrolysis n relese of either xyliine or toluiine re lerly oserve resulting in the formtion of the prent hyroxoomplex. Both PyO n Pz unergo to some extent hyrolysis of the nioni oligns. fterwrs, further egrtion is oserve in the se of the pyrzolto erivtive, whih ers monoentte C lign. The ytotoxi properties of ll these ompouns were teste ginst the 278/S, 278/R, MCF7, HT29 n 549 humn tumour ell lines. otly, the investigte orgnogol(iii) ompouns, with the exeption of Pz, prove signifintly tive ginst the former tumour ell lines, with ytotoxiity vlues flling in the low miromolr rnge. Some ifferenes were oserve in the tivity ptterns of Xyl n Tol ompre to the referene [(ipy m H)(OH)][PF 6 ] ompoun. 7 Moerte effets were oserve on the MCF7 n HT29 lines, wheres negligile effets were mesure on the 549 line. Overll, similr trens of iologil tivity were ientifie mong the three tive ompouns tht re suggestive of similr mehnism of tion. We elieve tht the speifiity of their iologil effets my e srie to the presene of gol(iii) entre, hrterise y n eptle stility profile uner physiologillike onitions. In the light of these oservtions, the gol(iii) ontining moleulr frgment is very likely to e responsile for the oserve ytotoxi effets, lthough the tul mehnism is not yet unerstoo Chemils 4. Experimentl Common hemil regents were purhse from SIG M Chemil Co. (Milno, Itly) n Phrmi. Fetl lf serum (FCS), ntiiotis, n RPMI164meium were otine from Gio Life Tehnologies Itli (Milno, Itly). Synthesis of [(ipy m H)(2,6xyliineH)][PF 6 ] (Xyl), 12 [(ipy m H)(ptoluiineH)][PF 6 ] ( Tol), 12 [(py m H)(CH 3 COO) 2 ] (PyO) 12 n [(pz Ph H) 3 ]K (Pz). 13 The title ompoun ws prepre oring to Refs. 12 n Eletroni spetr The sorption spetr in the UV vis region were reore on Perkin Elmer Lm 2Bio spetrophotometer operting t room temperture. The eletroni spetr were reore t room temperture, ing smll mounts of freshly prepre, onentrte solutions of the iniviul omplexes in DMSO to, respetively, DMSO, wter or to the referene uffer (5mM phosphte, ph 7.4, 1 mm ); the onentrtions of eh gol(iii) ompoun ws The hyrolysis experiments were rrie out monitoring the eletroni spetr of M gol(iii) omplexes solutions in DMSO over 24 h H MR stuies Solution 1 H MR spetr of the gol(iii) omplexes were reore on Vrin Gemini 2 spetrometer operting t 3MHz. The M solutions were prepre in 6 DMSO n in 5mM PO 3 4, 4mM, ph 7.4 euterte uffer. The spetr were reore immeitely fter issolution.
5 L. ssori et l. / Bioorg.. Chem. 12 (24) Cell ulture n ytotoxiity ssy Cytotoxiity stuies were rrie out on the 278/S, 278/R, MCF7, HT29 n 549 humn tumour ell lines. The ispltinresistnt 278/R ell line ws proue y repete 1h weekly exposure to 5lM of the sensitive prentl ell line. 8 Cell lines were ulture in RPMI164meium (GIBCO Life tehnologies Prout tlog, RPMI 164meium, Ct. no 11817) supplemente with 1% FCS n ntiiotis (streptomyin 1lg/mL n peniillin 1U/mL) t 37 C in5% CO 2 tmosphere n suulture twie weekly. Experiments were onute on exponentilly growing ells. Drugs were issolve in DMSO. Inhiition of ell growth ws etermine fter 72 h rug exposure through the SulforhomineB (SRB) ssy 16 for the ovrin rinom ell lines. Referenes n notes 1. Mron, G.; ssori, L.; Orioli, P. Expert Rev. ntiner Ther. 22, 2, Prish, R. V.; Howe, B. P.; Wright, J. P.; Mk, J.; Prithr, R. G.; Bukley, R. G.; Elsome,. M.; Friker, S. P. Inorg. Chem. 1996, 35, Bukley, R. G.; Elsome,. M.; Friker, S. P.; Henerson, G. R.; Theol, B. R. C.; Prish, R. V.; Howe, B. P.; Kelln, L. R. J.. Chem. 1996, 39, Css, J. S.; Cstño, M. V.; Cifuentes, M. C.; Grí Monteguo, J. C.; Sánhez,.; Soro, J.; rm, U.; J. Inorg. Biohem. 24, 98, Che, C. M.; Sun, R. W.; Yu, W. Y.; Ko, C. B.; Zhu,.; Sun, H. Chem. Commun. (Cm.) 23, 21, Tiekink, E. R. T. Crit. Rev. Onol. Hemtol. 22, 42, ssori, L.; Mron, G. In tl Ions in Biologil Systems; Sigel,., Sigel, H., Es.; Mrel Dekker: etherlns, 24; Vol. 42, pp Mron, G.; Crotti, S.; Colonnello, M.; ssori, L.; Mini, E.; Orioli, P.; Mzzei, T.; Cinellu, M..; Minghetti, G. J.. Chem. 22, 45, Fn, D.; Yng, C.T.; Rnfor, J. D.; Lee, P. F.; Vittl, J. J. J. Chem. So., Dlton Trns. 23, Fn, D.; Yng, C.T.; Rnfor, J. D.; Vittl, J. J.; Lee, P. F. J. Chem. So., Dlton Trns. 23, Goss, C. H..; Henerson, W.; Wilkins,. L.; Evns, C. J. Orgnomet. Chem. 23, 679, Cinellu, M..; Minghetti, G.; Pinn, M. V.; Stooro, S.; Zu,.; Mnssero, M. Eur. J. Inorg. Chem. 23, 12, Minghetti, G.; Cinellu, M..; Pinn, M. V.; Stooro, S.; Zu,.; Mnssero, M. J. Orgnomet. Chem. 1998, 568, Cinellu, M..; Zu,.; Stooro, S.; Minghetti, G.; Mnssero, M.; Snsoni, S. J. Chem. So., Dlton Trns. 1995, Puephtt, R. J. In The Chemistry of Gol; rk, R. J. H., E.; Elsevier: msterm, Shehn, P.; Storeng, R.; Suiero, D.; Monks,.; Mmhon, J.; Visti, D.; Wrren, J. T.; Bokesh, H.; Kenney, S.; Boy, M. R. J. tl. Cner Inst. 199, 82, 117.
6.3.2 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 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 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 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 information22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:
22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)
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 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 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 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 information4-cyanopentanoic acid dithiobenzoate (CPADB) was synthesized as reported by Y.
Eletroni upplementry Mteril (EI) for Journl of Mterils Chemistry B This journl is The Royl oiety of Chemistry 2012 ynthesis of 4-ynopentnoi id dithioenzote (CPADB). 4-ynopentnoi id dithioenzote (CPADB)
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 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 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 informationInteraction of Cu(II) with Cytosine in Britton-Robinson Buffer Solution - A Cyclic Voltammetric Study
Dhk Univ. J. Si. 63(1): 31-36, 215 (Jnury) Intertion of Cu(II) with Cytosine in Britton-Roinson Buffer Solution - A Cyli Voltmmetri Stuy A. A. Shikh *, Jnntul Firws, S. Islm n P. K. Bkshi Deprtment of
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 informationTHE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL
THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny
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 informationF / x everywhere in some domain containing R. Then, + ). (10.4.1)
0.4 Green's theorem in the plne Double integrls over plne region my be trnsforme into line integrls over the bounry of the region n onversely. This is of prtil interest beuse it my simplify the evlution
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 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 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 informationElectronic supporting information
Eletroni supporting informtion Dully Ctioni n Anioni p/temperture-sensitive Injetle yrogels n Potentil Applition s Protein Crrier Cong Tru uynh, Minh Khnh guyen n Doo Sung Lee* 1. Experimentl 1.1. Mterils
More informationCHEM1611 Answers to Problem Sheet 9
CEM1611 Answers to Prolem Sheet 9 1. Tutomers re struturl isomers whih re relte y migrtion of hyrogen tom n the exhnge of single on n jent oule on. Compoun Tutomer 2 2 2 2 2 2 2 2 2 2 2 2. () Whih pir
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 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 informationSolutions to Problem Set #1
CSE 233 Spring, 2016 Solutions to Prolem Set #1 1. The movie tse onsists of the following two reltions movie: title, iretor, tor sheule: theter, title The first reltion provies titles, iretors, n tors
More information1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the
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 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 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 informationDownloaded on T09:14:59Z
Title Investigtion of itive effets in enntioseletive opper-tlyse C- H insertion n romti ition retions of α-izoronyl ompouns Author(s) Slttery, Ctherine.; Clrke, Leslie-Ann; 'eill, Shne T.; Ring, Aoife;
More informationChemistry Practice Exam
Chemistry Prtie Exm 1 2 3 Whih of the following is n element? A rop of merury. A splinter of woo. A rystl of sugr. A rop of wter. Whih of the following nswers ontins only elements? Soium, soium hlorie,
More informationI 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
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 informationLing 3701H / Psych 3371H: Lecture Notes 9 Hierarchic Sequential Prediction
Ling 3701H / Psyh 3371H: Leture Notes 9 Hierrhi Sequentil Predition Contents 9.1 Complex events.................................... 1 9.2 Reognition of omplex events using event frgments................
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 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 informationChem Homework 11 due Monday, Apr. 28, 2014, 2 PM
Chem 44 - Homework due ondy, pr. 8, 4, P.. . Put this in eq 8.4 terms: E m = m h /m e L for L=d The degenery in the ring system nd the inresed sping per level (4x bigger) mkes the sping between the HOO
More informationPOSITIVE IMPLICATIVE AND ASSOCIATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS
Bull. Koren Mth. So. 35 (998), No., pp. 53 6 POSITIVE IMPLICATIVE AND ASSOCIATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS YOUNG BAE JUN*, YANG XU AND KEYUN QIN ABSTRACT. We introue the onepts of positive
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 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 informationCahn-In Gold-Prelog R/S System Revisited: Simplifying Assignment of Configuration in Chiral Compounds
Review Artile imepu Journls http://www.imepu.om Journl of Orgni & Inorgni Chemistry ISSN 7- DOI: 0.767/7-.0000 Chn-In Gol-Prelog R/S System Revisite: Simplifying Assignment of Configurtion in Chirl Compouns
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 informationEXTENSION OF THE GCD STAR OF DAVID THEOREM TO MORE THAN TWO GCDS CALVIN LONG AND EDWARD KORNTVED
EXTENSION OF THE GCD STAR OF DAVID THEOREM TO MORE THAN TWO GCDS CALVIN LONG AND EDWARD KORNTVED Astrt. The GCD Str of Dvi Theorem n the numerous ppers relte to it hve lrgel een evote to shoing the equlit
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 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 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 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 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 informationArrow s Impossibility Theorem
Rep Fun Gme Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Fun Gme Properties Arrow s Theorem Leture Overview 1 Rep 2 Fun Gme 3 Properties
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 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 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 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 information3D modelling of heating of thermionic cathodes by high-pressure arc plasmas
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 39 (2006) 2124 2134 oi:10.1088/0022-3727/39/10/024 3D moelling of heting of thermioni thoes y high-pressure
More informationStereoselective Synthesis
Stereoselective Synthesis Dr Michel Perkins, Fliners University Reference Texts: Stereochemistry of orgnic compouns Ernest L. Eliel New York : Wiley & Sons, c1994. Chpter 12 on stereoselective synthesis
More informationArrow s Impossibility Theorem
Rep Voting Prdoxes Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Voting Prdoxes Properties Arrow s Theorem Leture Overview 1 Rep
More informationarxiv: v2 [math.co] 31 Oct 2016
On exlue minors of onnetivity 2 for the lss of frme mtrois rxiv:1502.06896v2 [mth.co] 31 Ot 2016 Mtt DeVos Dryl Funk Irene Pivotto Astrt We investigte the set of exlue minors of onnetivity 2 for the lss
More informationCS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6
CS311 Computtionl Strutures Regulr Lnguges nd Regulr Grmmrs Leture 6 1 Wht we know so fr: RLs re losed under produt, union nd * Every RL n e written s RE, nd every RE represents RL Every RL n e reognized
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 informationUV-Induced Self-Repairing Polydimethylsiloxane-Polyurethane (PDMS-PUR) Cu- Catalyzed Networks
Eletroni Supplementry Mteril (ESI) for Journl of Mterils Chemistry A. This journl is The Royl Soiety of Chemistry 2014 Supporting Online Mterils UV-Indued Self-Repiring Polydimethylsiloxne-Polyurethne
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 informationAnalytical Techniques Chromatography
Anlytil Tehniques hromtogrphy hromtogrphy is n nlytil tehnique tht seprtes omponents in mixture etween moile phse nd sttionry phse. Types of hromtogrphy inlude: thin-lyer hromtogrphy (TL) plte is oted
More informationdsrna GFP 0 Ca 0 Ca 0 Ca TG Iono Time (s)
Rtio (FL1/FL3) MFI dsrna GFP C dsrna dori C 1 2 1 2 Rtio (FL1/FL3) MFI C 1 2 Rtio (FL1/FL3) MFI C 1 2 C 1 2 C 1 2 Supplementry Figure 1. RNAi-medited depletion of dori hs no effet on the filling stte of
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 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 informationCIT 596 Theory of Computation 1. Graphs and Digraphs
CIT 596 Theory of Computtion 1 A grph G = (V (G), E(G)) onsists of two finite sets: V (G), the vertex set of the grph, often enote y just V, whih is nonempty set of elements lle verties, n E(G), the ege
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 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 informationIntroduction to Olympiad Inequalities
Introdution to Olympid Inequlities Edutionl Studies Progrm HSSP Msshusetts Institute of Tehnology Snj Simonovikj Spring 207 Contents Wrm up nd Am-Gm inequlity 2. Elementry inequlities......................
More informationA Primer on Continuous-time Economic Dynamics
Eonomis 205A Fll 2008 K Kletzer A Primer on Continuous-time Eonomi Dnmis A Liner Differentil Eqution Sstems (i) Simplest se We egin with the simple liner first-orer ifferentil eqution The generl solution
More informationLEARNING OBJECTIVES: BTAT.STAR Discuss the history and harmful health effects of trans fats.
Multiple Choie 1. Hyrogention is.. mnufturing proess tht s hyrogen toms to rbohyrtes b. nturl proess tht tht s hyrogen toms to rbohyrtes. mnufturing proess tht s hyrogen toms to oils. nturl proess tht
More informationZSM-5 zeolite single crystals with b-axis-aligned mesoporous channels as an efficient catalyst for conversion of bulky organic molecules
Supporting informtion ZSM-5 zeolite single rystls with -xis-ligne mesoporous hnnels s n effiient tlyst for onversion of ulky orgni moleules Fujin Liu,,e Tom Willhmmr, Ling Wng, Longfeng Zhu, Qi Sun, Xingju
More informationCompression of Palindromes and Regularity.
Compression of Plinromes n Regulrity. Kyoko Shikishim-Tsuji Center for Lierl Arts Eution n Reserh Tenri University 1 Introution In [1], property of likstrem t t view of tse is isusse n it is shown tht
More informationEffects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue
TITLE: OBJECTIVE: AUTHOR: SPONSORS: Effets of Drought on the Performne of Two Hyrid Bluegrsses, Kentuky Bluegrss nd Tll Fesue Evlute the effets of drought on the visul qulity nd photosynthesis in two hyrid
More informationLaboratory for Foundations of Computer Science. An Unfolding Approach. University of Edinburgh. Model Checking. Javier Esparza
An Unfoling Approh to Moel Cheking Jvier Esprz Lbortory for Fountions of Computer Siene University of Einburgh Conurrent progrms Progrm: tuple P T 1 T n of finite lbelle trnsition systems T i A i S i i
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 informationDorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
orf, R.C., Wn,. T- Equivlent Networks The Eletril Engineering Hndook Ed. Rihrd C. orf Bo Rton: CRC Press LLC, 000 9 T P Equivlent Networks hen Wn University of Cliforni, vis Rihrd C. orf University of
More informationAutomata and Regular Languages
Chpter 9 Automt n Regulr Lnguges 9. Introution This hpter looks t mthemtil moels of omputtion n lnguges tht esrie them. The moel-lnguge reltionship hs multiple levels. We shll explore the simplest level,
More informationOn a Class of Planar Graphs with Straight-Line Grid Drawings on Linear Area
Journl of Grph Algorithms n Applitions http://jg.info/ vol. 13, no. 2, pp. 153 177 (2009) On Clss of Plnr Grphs with Stright-Line Gri Drwings on Liner Are M. Rezul Krim 1,2 M. Siur Rhmn 1 1 Deprtment of
More informationProbability The Language of Chance P(A) Mathletics Instant Workbooks. Copyright
Proility The Lnguge of Chne Stuent Book - Series L-1 P(A) Mthletis Instnt Workooks Copyright Proility The Lnguge of Chne Stuent Book - Series L Contents Topis Topi 1 - Lnguge of proility Topi 2 - Smple
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 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 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 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 information22.Analytical Techniques Chromatography
.Anlytil Tehniques hromtogrphy hromtogrphy is n nlytil tehnique tht seprtes omponents in mixture etween moile phse nd sttionry phse. Types of hromtogrphy inlude: thin-lyer hromtogrphy (TL) plte is oted
More informationAlgorithm Design and Analysis
Algorithm Design nd Anlysis LECTURE 8 Mx. lteness ont d Optiml Ching Adm Smith 9/12/2008 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov, K. Wyne Sheduling to Minimizing Lteness Minimizing
More informationConservation Law. Chapter Goal. 6.2 Theory
Chpter 6 Conservtion Lw 6.1 Gol Our long term gol is to unerstn how mthemticl moels re erive. Here, we will stuy how certin quntity chnges with time in given region (sptil omin). We then first erive the
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 informationLecture 2: Cayley Graphs
Mth 137B Professor: Pri Brtlett Leture 2: Cyley Grphs Week 3 UCSB 2014 (Relevnt soure mteril: Setion VIII.1 of Bollos s Moern Grph Theory; 3.7 of Gosil n Royle s Algeri Grph Theory; vrious ppers I ve re
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 informationElectronic Circuits I Revision after midterm
Eletroni Ciruits I Revision fter miterm Dr. Ahme ElShfee, ACU : Fll 2018, Eletroni Ciruits I -1 / 14 - MCQ1 # Question If the frequeny of the input voltge in Figure 2 36 is inrese, the output voltge will
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 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 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 informationTechnology Mapping Method for Low Power Consumption and High Performance in General-Synchronous Framework
R-17 SASIMI 015 Proeeings Tehnology Mpping Metho for Low Power Consumption n High Performne in Generl-Synhronous Frmework Junki Kwguhi Yukihie Kohir Shool of Computer Siene, the University of Aizu Aizu-Wkmtsu
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 informationMatrix Algebra. Matrix Addition, Scalar Multiplication and Transposition. Linear Algebra I 24
Mtrix lger Mtrix ddition, Sclr Multipliction nd rnsposition Mtrix lger Section.. Mtrix ddition, Sclr Multipliction nd rnsposition rectngulr rry of numers is clled mtrix ( the plurl is mtrices ) nd the
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 informationElectronic Supporting Information for
Eletroni Supplementry Mteril (ESI) for Polymer Chemistry. This journl is The Royl Soiety of Chemistry 2016 Eletroni Supporting Informtion for BODIPY Bse Hyperbrnhe Conjugte Polymers for Deteting Orgni
More information