Interaction of Cu(II) with Cytosine in Britton-Robinson Buffer Solution - A Cyclic Voltammetric Study
|
|
- Fay Lindsey
- 5 years ago
- Views:
Transcription
1 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 Chemistry, Dhk University, Dhk-1, Bnglesh (Reeive : 16 April 214; Aepte : 1 August 214) Astrt Eletrohemil reox ehvior of Cu(II) t ifferent ph in Britton-Roinson (BR) uffer solution hs een investigte using yli voltmmetry t glssy ron eletroe (GCE). Cu(II) shows thoi pek n hump-like pek, n n intense noi pek t ph,.59, 1.59, 3.1 n 4.8. Although t lower ph (.59 n 1.59) thoi pek, hump n n noi pek re oserve, t higher ph (3.1 n 4.8) the hump-like thoi pek isppere. Cyli voltmmetry hs lso een use to oserve the intertion of Cu(II) with ytosine in BR uffer solution t vrious ph. A resonly strong intertion etween Cu(II) n ytosine t ifferent Cu(II)/ytosine molr rtio is oserve t ll the stuie ph. However, mximum intertion ours t 1:4 molr rtio t ph 4.8, this is perhps the most suitle onition for Cu(II)-ytosine intertion. Keywors: Cytosine; Britton-Roinson uffer; Glssy ron eletroe; Pek potentil I. Introution Cytosine is one of the five min nitrogenous ses use in storing n trnsporting geneti informtion within ell 1. It is pyrimiine erivtive, with heteroyli romti ring n two sustituent tthe (n mine group t position 4 n keto group t position 2). The nuleosie of ytosine is ytiine 2. DNA methyltion involves the ition of methyl group to the 5 position of the ytosine pyrimiine ring or the numer 6 nitrogen of the enine purine ring (ytosine n enine re two of the four ses of DNA). DNA methyltion lso plys ruil role in the evelopment of nerly ll types of ner 3. DNA methyltion involves the ition of methyl group to DNA, for exmple, to the numer 5 ron of the ytosine pyrimiine ring, in this se with the speifi effet of reuing gene expression. DNA methyltion t the 5 position of ytosine hs een foun in every verterte exmine. Cytosine plys vitl role in piring, through hyrogen ons with the gunine se of gunosine n eoxygunosine. Cytosine is involve in the geneti oon of 17 mino is n ontrols the essentil fetures of life 4. Although ytosine is se it n t s lign euse of the presene of unpire eletrons on nitrogen n oxygen whih re ville to onte in omplextion retion. Cyli voltmmetri ehviour of ytosinto rige omplexes of ruthenium(ii) n pltinum(ii) with 1-lkyl-2- (rylzo)imizoles were investigte 5. Eletrohemil properties of the omplexes hve een exmine y yli voltmmetry in CH 3 CN in presene of [n-bu 4 N][ClO 4 ] s supporting eletrolyte using Pt-is working eletroe t the sn rte of 5 mv/s. Although severl groups 6-8 hve trie to investigte the eletrohemil intertion of metlytosine with ifferent eletroes, our im is to investigte the intertion of Cu(II) with ytosine in BR uffer meium mintining vrious ph t GCE using yli voltmmetry. II. Experimentl Mterils Anlr gre Cu(NO 3 ) 2.3H 2 O ws purhse from Merk, Germny n use without further purifition. Anlytil gre ytosine (BDH, UK) ws use in this stuy. Aeti i (BDH, UK), phosphori i (Merk, Germny), n ori i (Merk, Germny) were lso use for the preprtion of BR uffer. Soium hyroxie (Merk, Germny) n perhlori i (BDH, UK) were use s it is ville for mintining the ph of the solution. All queous solutions were prepre in ouly istille wter otine from Milli-Q wter purifition system. The experiments were rrie out t room temperture. Equipments Three eletroes system onsisting of GCE s the working eletroe, Ag/AgCl (st. KCl) s the referene eletroe n pltinum wire s the ounter eletroe ws use. Cyli voltmmetri mesurement ws performe using Computerize Eletrohemil System, Moel HQ-24 evelope y Avne Anlytis, USA. Solution ph ws mesure with ph meter (Miroproessor ph meter, moel ph 211, HANNA Instruments). Methos Preprtion of Britton-Roinson uffer solution For the preprtion of BR uffer solution,.4 M H 3 BO 3,.4 M H 3 PO 4 n.4 M CH 3 COOH solutions were prepre seprtely, n the three solutions were then mixe together with sme volume rtio. By ing.2 M NOH or HClO 4 solution the esire ph vlues (ph vlues re.59, 1.59, 3.1 n 4.8) were juste. Preprtion of metl ion n ytosine solution Metl ion solution of.5 mm Cu(II) ws prepre using BR uffer. For the omplextion stuy,.5, 1., 1.5 n 2. mm ytosine solutions were lso prepre using BR uffer solution. *Author for Corresponene. e-mil: ftshikh@univhk.eu
2 32 A. A. Shikh, Jnntul Firws, S. Islm n P. K. Bkshi Preprtion of working eletroe GCE ws polishe with fine lumin power of.3 miron on wet polishing loth. For oing so prt of the loth ws me wet with eionize wter, n lumin power ws sprinkle over it. The GCE ws then polishe on this surfe y pressing softly the eletroe ginst the polishing surfe for out 1 minutes. A shiny lk mirror like eletroe surfe ws then thoroughly wshe with eionize wter. First of ll, the ell ws fille with esire volume of the experimentl solution n the Teflon p ws ple on the ell. The purging glss tue together with referene eletroe ws inserte through the holes. Uner omputer ontrolle stirring, experimentl solution ws eerte y purging for t lest 1 minutes with % pure nitrogen gs. Thus tres of issolve oxygen were remove from the solution. III. Results n Disussion Cyli voltmmetri investigtion of the reox ehvior of Cu(II) in BR uffer solution, n its intertion with ytosine in n ientil voltmmetri onition hs een performe. The effet of ph for this stuy ws lso exmine. The results re presente elow: Voltmmetri response of Cu(II) in BR uffer solution Cyli voltmmetri stuy of.5 mm Cu(II) in BR uffer t ifferent ph vlues (.59 to 4.8) hs een investigte t GCE within the potentil winow of 5 to -5 mv. At more positive or negtive potentil vlues only non-fri urrent is oserve. Figure 1() shows yli voltmmogrm of.5 mm Cu(II) in BR uffer solution with sn rte of 1 mvs -1 t ph In the forwr sn two thoi peks i p1 ( hump like pek) n i p2 t out 9.84 mv n mv respetively, n in the reverse sn n intense noi pek i p2 t out 67.6 mv re oserve. The thoi peks re ue to the reution of Cu(II) to Cu(I) n Cu(I) to Cu(), while the intense noi pek is for the oxition of Cu() to Cu(II). However, yli voltmmogrm of ytosine in n ientil experimentl onition shows no pek (Figure 1()). Pek urrent, i p 9 i p i p2 i p Fig. 1. Cyli voltmmogrms of ().5 mm Cu(II) n ().5 mm ytosine in Britton-Roinson uffer t ph 1.59 with sn rte of 1 mvs -1 t GCE. Pek urrent, i p mv/s 1 mv/s 75 mv/s 5 mv/s 25 mv/s Fig. 2. Cyli voltmmogrms of.5 mm Cu(II) in Britton- Roinson uffer solution with sn rte of 25, 5, 75, 1 n 125 mvs -1 t ph The effet of the sn rte on the eletrohemil response of Cu(II) t ph 1.59 is lso exmine y gining the yli voltmmogrms of Cu(II) with sn rte of 25, 5, 75, 1 n 125 mvs -1 uner ientil onition. The voltmmogrms re shown in Figure 2. Tle 1. Dt otine from the yli voltmmogrms of.5 mm Cu(II) in Britton-Roinson uffer with ifferent sn rte t ph Sn rte, v (mvs -1 ) Cthoi pek urrent, i p i p1 (-) i p2 (-) APC, i p Cthoi pek potentil, E p (mv) i p2 E p1 E p2 (-) APP, E p (mv) E p2 PCR i p2 /i p2 E p =E p2 E p2 (mv) APC= Anoi pek urrent, APP= Anoi pek potentil, PCR= Pek urrent rtio The reore voltmmogrms re nlyze n vrious prmeters suh s noi n thoi pek urrent, pek potentil seprtion n pek urrent rtio re gthere s shown in Tle 1. It is foun tht with the inrese of sn rte, oth the thoi n noi pek urrents re inrese (Figure 2). This oservtion suggests tht the eletroe proess is uner iffusion ontrolle in BR uffer meium. The noi (E p2 ) n thoi (E p2 ) pek potentil seprtion ( mv) n noi (i p2 ) n thoi (i p2 ) pek urrent rtio ( ) revel tht the reox proess of opper system is qusi-reversile, in greement with the oservtions on the shpe of the thoi n noi peks 9.
3 Intertion of Cu(Ii) with Cytosine in Britton-Roinson Buffer Solution - A Cyli Voltmmetri Stuy 33 The thoi pek is slightly shifte towrs negtive potentil while the noi pek is move little towrs positive potentil with the inese of sn rte. The shifting of the pek potentil t vrious sn rtes lso inites tht the reox proess is shifte from qusi-reversile to irreversile iretion. Figure 3 pprently shows tht the pek urrent for the reox ehvior of opper system in BR uffer ers liner reltionship with squre root of sn rte n it psses through the origin. The rtio of the oxition pek urrent to its orresponing reution ounterprt, i p2 /i p2 is out It is foun (Figure 4) tht the pek urrent rtio is erese with the inrese of sn rte. It is gin in fvor of the ft tht the eletroe proess is iffusion-ontrolle. It is lso in goo greement with the previous stuy 1. 1 Effet of ph on the reox ehvior of Cu(II) The effet of ph on reox ehvior of Cu(II) in BR uffer hs lso een investigte t GCE. Voltmmogrms for Cu(II) in BR uffer t ph.59, 1.59, 3.1 n 4.8 re reore. A series of voltmmogrms t ifferent ph of the solution re shown in Figure 6. Pek urrent, i p Pek urrent, i p Squre root of sn rtes 1/2 (mvs -1 ) 1/2 Fig. 3. Vrition of pek urrent with squre root of sn rte for Cu(II) in Britton-Roinson uffer t ph Pek urrent, i p i p2 /i p Sn rte, v (mvs -1 ) Fig. 4. Pek urrent rtio (i p2 /i p2 ) epenene on sn rte of.5 mm Cu(II) in Britton-Roinson uffer meium t ph The pek potentil seprtion, E p is in etween mv n it is inrese with the inrese of sn rte (Figure 5). It is evient tht the reox proess is qusi-reversile rther thn reversile. 15 Pek urrent, i p Pek potentil seprtion, E p (mv) Pek urrent, ip Sn rte, v (mvs -1 ) Fig. 5. Vrition of pek potentil seprtion with sn rte of.5 mm Cu(II) in Britton- Roinson uffer t ph E (mv) Vs. Ag/AgCl (st. KCl) Fig. 6. Cyli voltmmogrms of.5 mm Cu(II) in Britton- Roinson uffer t ifferent ph: ().59, () 1.59, () 3.1 n () 4.8 t GCE.
4 34 A. A. Shikh, Jnntul Firws, S. Islm n P. K. Bkshi At low ph rnging from.59 to 3.8, thoi pek n hump-like pek, n n intense noi pek re ppere. With the inrese of ph, the first thoi pek urrent grully ereses n finlly isppers t ph 4.8. In generl, oth thoi n noi pek urrents re erese with the inrese of ph, s given in Tle 2. However, oth the noi n thoi peks re ientil in shpe n the pek potentil seprtion is omprle. At low ph limit [Cu(H 2 O) 6 ] 2+ n [Cu(H 2 O) 6-x ] + ions n e Tle 2. Dt otine from the voltmmogrm of Cu(II) t ifferent ph. Solution ph ssume to e present in signifint mount while t high ph (~ 4.8), [Cu(OH)(H 2 O) 5 ] + ion is unerstoo to e the only eletrotive speies 11,12. It hs een mentione efore tht Cu(I) s the solvte ion is stle in numer of nonqueous solvents suh s etonitrile 13, nitromethne 12. In suh solvents, the stility of Cu(I) is ue to the ft tht these solvents solvte Cu(II) less strongly thn oes wter n they solvte Cu(I) more strongly thn oes wter. Pek urrent, i p Pek potentil, E p (mv) Pek potentil seprtion, E p i p2 (-) i p2 (+) E p2 (-) E p2 (+) D Grph 1 Voltmmetri response of Cu(II) in presene of ytosine in BR uffer solution The voltmmogrms of Cu(II) in presene of ytosine in BR uffer t vrious Cu(II)/ytosine molr rtio, 1:1, 1:2, 1:3 n 1:4 hve een reore t ph.59, 1.59, 3.1 n 4.8 t GCE within the sme potentil winow. The reore voltmmogrms of Cu(II), n t vrious Cu(II)/ytosine molr rtio, 1:1, 1:2, 1:3 n 1:4 t ph.59 is shown in Figure 7. At this ph the thoi pek is signifintly reue n lrge reution of the noi pek height is oserve in the voltmmogrms n the pek urrents re reltively lower thn tht of Cu(II) lone. Moreover, the heights of the peks re pprently errti with respet to ytosine onentrtion. The lowest pek urrent is foun t 1:4 molr rtio of Cu(II) to ytosine onentrtion suggesting the mximum intertion ours t this molr rtio. It is note tht the voltmmogrm of ytosine in ientil onition exhiits no noi or thoi pek (Figure 1()) within the stuie potentil winow. Pek urrent, i p ( ) Fig. 7. Cyli voltmmogrms of () Cu(II) (soli), n Cu(II) n ytosine with ifferent molr rtio () 1:1 (otte), () 1:2 (short sh), () 1:3 (sh-ot-ot) n (e) 1:4 (long sh) in Britton-Roinson uffer t ph.59. e Pek urrent, i p ( ) Fig. 8. Cyli voltmmogrms of () Cu(II) (soli), n Cu(II) n ytosine with ifferent molr rtio () 1:1 (otte), () 1:2 (short sh), () 1:3 (sh-ot-ot) n (e) 1:4 (long sh) in Britton-Roinson uffer t ph Figure 8 shows the voltmmogrms of Cu(II), n Cu(II) in presene of ytosine with ifferent molr onentrtion t ph A signifint hnge of the shpe of voltmmogrms is oserve. The thoi pek ompletely isppere (t 1:3 n 1:4 molr rtio) while the noi pek urrent onsierly erese ompre to only Cu(II). The noi pek potentils lso shifte towrs negtive iretion. Furthermore, the heights of the peks re pprently inonsistent with respet to ytosine onentrtion. Sine the lowest pek urrent (Tle 3) is foun for 1:4 molr rtio of Cu(II) to ytosine, the mximum intertion, is inee, ourre t this molr rtio t ph In presene of ytosine, Cu(II) isplys lmost ientil eletrohemil ehvior t ph 3.1 n 4.8. In most of the ses the thoi pek isppers ompletely. The ehviors tht re ommon in oth ses, (i) signifint erese of the pek urrents of Cu(II), (ii) slight shifting of pek potentils, (iii) inonsistent respon of pek urrent with respet to Cu(II)/ytosine molr rtios, n (iii) mximum intertion of Cu(II) with ytosine t their 1:4 molr rtio. The voltmmogrms reore t ph 3.1 n t 4.8 re shown in Figures 9 n 1 respetively. e
5 Intertion of Cu(Ii) with Cytosine in Britton-Roinson Buffer Solution - A Cyli Voltmmetri Stuy 35 9 Pek urrent, i p e Pek urrent, i p e Fig. 9. Cyli voltmmogrms of () Cu(II) (soli), n Cu(II) n ytosine with ifferent molr rtio () 1:1 (otte), () 1:2 (short sh), () 1:3 (sh-ot-ot) n (e) 1:4 (long sh) in Britton-Roinson uffer t ph 3.1. Fig. 1. Cyli voltmmogrms of () Cu(II) (soli), n Cu(II) n ytosine with ifferent molr rtio () 1:1 (otte), () 1:2 (short sh), () 1:3 (sh-ot-ot) n (e) 1:4 (long sh) in Britton-Roinson uffer t ph 4.8. From the ove oservtion it n e onlue tht Cu(II) interts strongly with ytosine t molr rtio of 1:4 t ll stuie ph in BR uffer meium. However, the mximum intertion ours t ph 4.8. The t for the ifferent voltmmogrms reore for Cu(II)/ytosine molr rtio of 1:4 t vrious ph is gthere in Tle 3. Tle 3. The t for the voltmmogrms reore for 1:4 molr rtio of Cu(II)/ytosine t ifferent ph t GCE with sn rte of 1 mvs -1. Solution ph Pek urrent, A Pek potentil, mv Pek urrent Pek potentil rtio (i p /i p ) seprtion, E p i p (-) i p (+) E p (-) E p (+) inites no signifint vlue IV. Conlusion Cyli voltmmogrm of Cu(II) in BR uffer exhiits n intense thoi pek n hump-like pek, n strong noi pek t ll stuie ph. However, t high ph, only thoi n n noi pek re foun. In presene of ytosine the thoi pek urrent of Cu(II) isppere signifintly or ompletely while the noi pek height is reue ppreily with the negtive shifting of pek potentil. This oservtion inites tht the intertion etween Cu(II) n ytosine ours in BR uffer meium t ii ph. Among the stuie ph region mximum intertion is foun t ph 4.8 when the molr rtio of Cu(II)/ytosine is 1:4. Aknowlegement Authors re grteful to the Ministry of Siene n Tehnology, Bnglesh for finnil support. Referenes 1. Berg, J., J. Tymozko n L. Stryer, 27. Biohemistry, 6 th e. W.H. Freemn n Compny. 2. Kossel, A. n H. Steuel, 193. Weitere Untersuhungen üer s Cytosin, Z Physiol Chem., 38, Jenish, R. n A. Bir, 23. Epigeneti regultion of gene expression: how the genome integrtes intrinsi n environmentl signls, Nt.Genet., 33, Kwski, T., K. Suzuki, Y. Hko n K. Soi, 28. Ahirl Nuleose Cytosine Ats s n Origin of Homohirlity of Biomoleules in Conjuntion with Asymmetri Autotlysis, Angew. Chem. Int. E., 47, S. Jsimuin, 26. Synthesis, spetrl n eletrohemil ehviour of ytosinto rige omplexes of ruthenium(ii) n pltinum(ii) with 1-lkyl-2-(rylzo)imizoles, Trns. Met. Chem., 31, Roriguez, M. n A. J. Br, 199. Eletrohemil stuies of the intertion of metl heltes with DNA. 4. Voltmmetri n eletrogenerte hemiluminesent stuies of the intertion of tris(2,2'-ipyriine)osmium(ii) with DNA, Anl. Chem., 62, Hu, L. Z. Bin, H. Li, S. Hn, Y. Yun, L. Go n G. Xu, 29. Ru(py) 2 ppz] 2+ Eletrohemiluminesene Swith n Its Applitions for DNA Intertion Stuy n Lel-free ATP Aptsensor, Anl. Chem., 81, Kurit, R., K. Ari, K. Nkmoto, D. Kto, n O. Niw, 212. Determintion of DNA Methyltion Using
6 36 A. A. Shikh, Jnntul Firws, S. Islm n P. K. Bkshi Eletrohemiluminesene with Surfe Aumulle Coretnt, Anl. Chem., 84, Quentel F. n C. Me, 199. Voltmmetri stuy of the opper-1, 1-phennthroline omplex, Anlyt. Chimi At. 83, Akhtr, H.M.N., M. M. Jml, A. A. Shikh n M. Q. Ehsn, 28. Cyli Voltmmetri Stuy of The Intertion of Copper with Glutmi Ai in Solution, J. Sui Chem. So., 12, Polyn, D. S. n I. Shin, Multistep Chrge Trnsfers in Sttionry Eletroe Polrogrphy, Anl. Chem., 38, J. L. Anerson, J. L. n I. Shin, Cyli voltmmetri stuies of the ph epenene of opper(ii) reution in ii queous nitrte n perhlorte solutions, Anl. Chem., 48, Miller, R. W. Ph. D. Thesis, The University of Illinois, Urn III, 1961.
7 Intertion of Cu(Ii) with Cytosine in Britton-Roinson Buffer Solution - A Cyli Voltmmetri Stuy 37
8 38 A. A. Shikh, Jnntul Firws, S. Islm n P. K. Bkshi
9 Intertion of Cu(Ii) with Cytosine in Britton-Roinson Buffer Solution - A Cyli Voltmmetri Stuy 39
A Cyclic Voltammetric Study of the Redox Reaction of Cu(II) in Presence of Ascorbic Acid in Different ph Media
Dhk Univ. J. Si. 61(2): 161-166, 213 (July) A Cyli Voltmmetri Study of the Redox Retion of Cu(II) in Presene of Asori Aid in Different ph Medi Frhn Hque, M. S. Rhmn, Etmin Ahmed, P. K. Bkshi nd A. A. Shikh*
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 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 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 informationSupporting Information
tom-thik Interlyer Mde of VD-Grown Grphene Film on Seprtor for dvned thium-sulfur tteries Zhenzhen Du 1, hengkun Guo 2, njun Wng 3, jun Hu 1, Song Jin 1, Timing Zhng 1, Honghng Jin 1, Zhiki Qi 1, Sen Xin
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 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 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 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 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 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 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 informationPoly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents
SUPPLEMENTARY INFORMATION Poly(vinylmine) Microgels: ph-responsive Prticles with High Primry Amine Contents Sineent Thioonro, Cory Berkln, Amir H. Milni, Rein Ulijn c n Brin R. Suners, * Polymer Science
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 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 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 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 informationCyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò
J Appl Eletrohem (009) 39:9 63 DOI 0.007/s0800-009-9797- ORIGINAL PAPER Cyli voltmmetry simultion t miroeletrode rrys with COMSOL Multiphysis Ò Alessndro Lvhi Æ U. Brdi Æ C. Borri Æ S. Cporli Æ A. Fossti
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 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 informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
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 informationSupporting Information Mesoporous graphitic carbon nanodisks fabricated via catalytic carbonization of coordination polymers
Supporting Informtion Mesoporous grphiti ron nnodisks frited vi tlyti roniztion of oordintion polymers Pnpn Su, Ling Jing, Jio Zho, Jingwng Yn, Cn Li nd Qihu Yng Stte Key Lortory of Ctlysis, Dlin Institute
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 informationElecrochemical Behaviour of Zinc on Copper and on Vitreous. Carbon Electrodes. The Influence of Gluconate
Portuglie Eletrohimi At 21 (2003) 179-189 PORTUGALIAE ELECTROCHIMICA ACTA Elerohemil Behviour of Zin on Copper nd on Vitreous Cron Eletrodes. The Influene of Gluonte J. Torrent-Burgués *, E. Guus Group
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 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 informationCALCULATING REACTING QUANTITIES
MODULE 2 14 WORKSHEET WORKSHEET For multiple-hoie questions 1 5 irle the letter orresponding to the most orret nswer. 1 The lned eqution for the urning of utnol (C 4 H 9 OH) is given elow: C 4 H 9 OH(l)
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 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 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 informationAppendix 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 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 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 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 informationThe influence of 2,2 -dipyridyl on non-formaldehyde electroless copper plating
Eletrohimi At 9 () 1789 179 The influene of, -dipyridyl on non-formldehyde eletroless opper plting Jun Li, Hrley Hyden, Pul A. Kohl Shool of Chemil & Biomoleulr Engineering, Georgi Institute of Tehnology,
More informationLecture 11 Binary Decision Diagrams (BDDs)
C 474A/57A Computer-Aie Logi Design Leture Binry Deision Digrms (BDDs) C 474/575 Susn Lyseky o 3 Boolen Logi untions Representtions untion n e represente in ierent wys ruth tle, eqution, K-mp, iruit, et
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 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 information6. Photoionization of acridine through singlet and triplet channels
Chpter 6: Photoioniztion of cridine through singlet nd triplet chnnels 59 6. Photoioniztion of cridine through singlet nd triplet chnnels Photoioinztion of cridine (Ac) in queous micelles hs not yet een
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 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 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 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 informationSOME COPLANAR POINTS IN TETRAHEDRON
Journl of Pure n Applie Mthemtis: Avnes n Applitions Volume 16, Numer 2, 2016, Pges 109-114 Aville t http://sientifivnes.o.in DOI: http://x.oi.org/10.18642/jpm_7100121752 SOME COPLANAR POINTS IN TETRAHEDRON
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 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 informationPhysics 1402: Lecture 7 Today s Agenda
1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:
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 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 informationLesson 2.1 Inductive Reasoning
Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,
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 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 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 informationMomentum and Energy Review
Momentum n Energy Review Nme: Dte: 1. A 0.0600-kilogrm ll trveling t 60.0 meters per seon hits onrete wll. Wht spee must 0.0100-kilogrm ullet hve in orer to hit the wll with the sme mgnitue of momentum
More informationMid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours
Mi-Term Exmintion - Spring 0 Mthemtil Progrmming with Applitions to Eonomis Totl Sore: 5; Time: hours. Let G = (N, E) e irete grph. Define the inegree of vertex i N s the numer of eges tht re oming into
More informationSupporting Information. Observation of Excitonic Fine Structure in a 2D Transition Metal. Dichalcogenide Semiconductor
FWHM (ev) Normlized Intensity (. u.) Supporting Informtion Oservtion of Exitoni Fine Struture in 2D Trnsition Metl Dihlogenide Semiondutor Jingzhi Shng 1, Xionn Shen 1, Chunxio Cong 1, Nmphung Peimyoo
More informationThis chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2
1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion
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 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 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 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 informationPhysics Lecture 14: MON 29 SEP
Physics 2113 Physics 2113 Lecture 14: MON 29 SEP CH25: Cpcitnce Von Kleist ws le to store electricity in the jr. Unknowingly, he h ctully invente novel evice to store potentil ifference. The wter in the
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 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 informationH SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready.
Alger Bsis H SERIES Alger Bsis Curriulum Rey www.mthletis.om Copyright 009 P Lerning. All rights reserve. First eition printe 009 in Austrli. A tlogue reor for this ook is ville from P Lerning Lt. ISBN
More informationBehavior Composition in the Presence of Failure
Behvior Composition in the Presene of Filure Sestin Srdin RMIT University, Melourne, Austrli Fio Ptrizi & Giuseppe De Giomo Spienz Univ. Rom, Itly KR 08, Sept. 2008, Sydney Austrli Introdution There re
More informationLesson 2.1 Inductive Reasoning
Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,
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 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 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 information332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006
2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,
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 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 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 informationThe development of nanoscale morphology in polymer:fullerene. photovoltaic blends during solvent casting
Supplementry informtion Supplementry Mteril (ES) for Soft Mtter The development of nnoscle morphology in polymer:fullerene photovoltic lends during solvent csting To Wng, * Aln D. F. Dunr, Pul A. Stniec,
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 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 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 informationa) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points.
Prole 3: Crnot Cyle of n Idel Gs In this prole, the strting pressure P nd volue of n idel gs in stte, re given he rtio R = / > of the volues of the sttes nd is given Finlly onstnt γ = 5/3 is given You
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
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 informationAlpha Algorithm: Limitations
Proess Mining: Dt Siene in Ation Alph Algorithm: Limittions prof.dr.ir. Wil vn der Alst www.proessmining.org Let L e n event log over T. α(l) is defined s follows. 1. T L = { t T σ L t σ}, 2. T I = { t
More informationUniversity of Sioux Falls. MAT204/205 Calculus I/II
University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques
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 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 informationHomework Assignment 3 Solution Set
Homework Assignment 3 Solution Set PHYCS 44 6 Ferury, 4 Prolem 1 (Griffiths.5(c The potentil due to ny continuous chrge distriution is the sum of the contriutions from ech infinitesiml chrge in the distriution.
More informationAB Calculus Review Sheet
AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is
More informationReflection Property of a Hyperbola
Refletion Propert of Hperol Prefe The purpose of this pper is to prove nltill nd to illustrte geometrill the propert of hperol wherein r whih emntes outside the onvit of the hperol, tht is, etween the
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 informationSwitching properties of an arbitrarily excited nonlinear electron-wave directional coupler
Proeedings of the 6th WSEAS Interntionl Conferene on Miroeletronis, Nnoeletronis, Optoeletronis, Istnul, Turkey, My 7-9, 7 1 Swithing properties of n ritrrily exited nonliner eletron-wve diretionl oupler
More informationCHAPTER 20: Second Law of Thermodynamics
CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het
More information( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f
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 informationSupporting Information. M13 Virus-Incorporated Biotemplates on Electrode Surfaces to Nucleate Metal Nanostructures by Electrodeposition
Supporting Informtion M13 Virus-Inorported iotempltes on Eletrode Surfes to Nulete Metl Nnostrutures y Eletrodeposition Shnmugm Mnivnnn [], Inhk Kng [],, Yeji Seo [], Hyo-Eon Jin [,], Seung-Wuk Lee []
More information6.5 Improper integrals
Eerpt from "Clulus" 3 AoPS In. www.rtofprolemsolving.om 6.5. IMPROPER INTEGRALS 6.5 Improper integrls As we ve seen, we use the definite integrl R f to ompute the re of the region under the grph of y =
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 informationFarey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
More informationNetwork Analysis and Synthesis. Chapter 5 Two port networks
Network Anlsis nd Snthesis hpter 5 Two port networks . ntroduction A one port network is completel specified when the voltge current reltionship t the terminls of the port is given. A generl two port on
More informationThermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam
April 08 Therml energy Soures of het Trnsport of het How to use het The First Lw of Thermoynmis U W Or, if we wnt to otin externl work: U W 009 vrije Universiteit msterm Close yle stem power plnt The trik
More information