Tetrahedron: Asymmetry

Size: px
Start display at page:

Download "Tetrahedron: Asymmetry"

Transcription

1 Tetrhedron: Asymmetry 20 (2009) Contents lists ville t Sieneiret Tetrhedron: Asymmetry journl homepge: A onvenient ess to the 1,5-nhydro forms of -tgtose, L-rhmnulose nd -xylulose vi 2-hydroxyglyl esters q Pn Jrglis, Volker Gökel, Frieder W. Lihtenthler * Clemens-Shöpf-Institut für rgnishe Chemie und Biohemie, Tehnishe Universität rmstdt, rmstdt, Germny rtile info strt Artile history: Reeived 26 Ferury 2009 Aepted 18 Mrh 2009 Aville online 22 April 2009 Speil edition of Tetrhedron: Asymmetry in honour of Professor George Fleet s 65th irthdy Zemplén methnolysis or three-step protool omprising hydroxylminolysis, de--etyltion nd deoximintion smoothly nd effiiently onvert the enzoylted 2-hydroxy--glyls of -gltose, L- rhmnose nd -xylose into their onfigurtionlly relted 1,5-nhydro-ketoses, therey providing onvenient ess to the 1,5-nhydro forms of -tgtose, L-rhmnulose nd -xylulose. Invrily otined s morphous solids, they re est hrterized through their highly rystlline oximes. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introdution Potentil pplitions of 1,5-nhydro--frutose 1 s powerful ntioxidnt, 2,3 n ntimiroil gent, 2,3 food dditive 3 or phrmeutil 4 hve generted the elortion of series of hemil nd enzymti syntheses, the most onvenient eing the -1,4- glun lyse-indued degrdtion of strh, 5 nd the Zemplén methnolysis of tetr--etyl-2-hydroxy--glul. 1 f other 1,5- nhydro-ketoses, whih re likely to hve similr pplition profiles, only 1,5-nhydro--tgtose 2 hs eome known, either through lorious seven-step hemil proedure strting from -gltose, 6 or y teril oxidtion of 1,5-nhydro--gltitol, 7 whose quisition from -gltose requires four steps. Relying on the methodology developed for the otention of 1,5- nhydro--frutose, 1 we here desrie onvenient proedures for the onversion of -gltose, L-rhmnose nd -xylose into the 1,5-nhydro derivtives of -tgtose 2, L-rhmnulose 3 nd - xylulose 4, respetively. 2. Results nd disussion ,5-Anhydro--tgtose The methodology reently dvned for the strightforwrd liertion of 1,5-nhydro--frutose from 2-hydroxy--glul esters, 1 (diret Zemplén methnolysis or three-step protool involving enol ester hydroxylminolysis, de--yltion nd deoximtion) ould redily e pplied to the -glto nlogue 5 with only minor experimentl dpttions: Exposure to hydroxylmine hydrohloride in pyridine t mient temperture smoothly onverted q Prt 43 of the series Sugr-erived Building Bloks ; for Prt 42, see Ref. 1. * Corresponding uthor. Tel.: E-mil ddress: lihtenthler@hemie.tu-drmstdt.de (F.W. Lihtenthler). 5 into the E-oxime 6 (82%), redily deprotetle y Zemplén methnolysis to 7 (Sheme 1), oth oximes feture useful properties suh s high rystllinity nd ese of isoltion. Their deoximtion with etldehyde/cl either fforded 1,5-nhydro--tgtose 2 or its triette 8 in exellent yields, yet s reveled y 1 nd 13 C NMR dt, oth umulted s mixtures of the keto nd 2,2-dihydroxy (hydrte) forms in rtios vrying etween 5:2 nd 2:1 in fvour of the monohydrtes. This tendeny towrds elortion of the monohydrte forms in the se of lredy previously oserved y Freimund nd Köpper 7 is in distint ontrst to tht of the 4-epimeri 1,5-nhydro--fruto ompounds: the orresponding ulose triette, nlogously prepred y hydroxylminolysis of the 2-hydroxy--glul ester nd susequent deoximtion, ws otined in rystlline form (89%) s the unhydrted ketose, 1 whilst 1,5-nhydro--frutose 1 fully dopts the 2,2-dihydroxy (hydrte) form in queous solution. 1 2 (-fruto) (-tgto) 3 4 (L-rhmnulo) (-xylulo) In the etylted ulose 8, -elimintion of eti id is filitted y the trns-dixil disposition of -3 nd 4-A; thus onversion to the enolone ester 11 lredy ourred on longer ontt /$ - see front mtter Ó 2009 Elsevier Ltd. All rights reserved. doi: /j.tetsy

2 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) A A A A 5 R R R N 6 R = A 7 R = (6) A A A 8 2 A A A 8 2 d e (7) f EtS g R A R SEt 2 h (10) R SEt A 9 R = A i R = Sheme 1. Retions nd onditions: () N 2 Cl/pyridine, 15 h, rt, 82%; () N/, 20 min, rt, 78%; () etldehyde/cl in CN, 6 h, rt, 95%; (d) N/, 2ht 15 C?rt, 84%; (e) etldehyde/cl in CN, 5 h, rt, 83%; (f) EtS (BF 3, 15 min, rt, 61%; (g) NA/etone, 1 h, rt, 91%; (h) CdC 3 /gcl 2 in wter, 30 min, rt, 69%; (i) N/, 3 h, 0 C, 87%. with sili gel or, for preprtive purposes, y riefly stirring with sodium ette in etone. rptliztion ws redily effeted y exposure to ethnethiol/cl to provide 9, whih ould lso e onverted into 1,5-nhydro--tgtose 2 y Zemplén methnolysis to 10 nd susequent desulfuriztion. By fr the most simple genertion of 1,5-nhydro--tgtose, however, proved to e the diret Zemplén methnolysis of the 2-etoxygltl triette 5 whih, when performed t low temperture, proeeded without -elimintion, oviously due to the formtion of the monomethnolte 8 s the first intermedite rther thn the ketose 8 whih under the slightly si Zemplén onditions would redily undergo -elimintion to enolone ,5-Anhydro-L-rhmnulose Being redily essile in four-step, lrge sle-dptle protool from L-rhmnose, 8 the 2-enzoyloxy-L-rhmnl dienzote 12 ws similrly sujeted to Zemplén methnolysis whih proved to e somewht priious due to its low soluility in methnol nd, hene, omprtively long ontt to the si onditions (N/). owever, when working t low temperture ( 10?0 C) in high dilution nd short-retion times (3 5 min), the prent sugr, 1,5-nhydro--rhmnulose 3 ould e relesed without ppreile formtion (TLC) of side produts; it ws hrterized s n morphous solid, whih in queous solution dopted the 2,2-dihydroxylted (monohydrte) form 3 2. The well-rystllizing dienzote of 1,5-nhydro-L-rhmnulose 15 ould e proured in either one of two wys: through hydroxylminolysis of the L-rhmnl ester 12 nd susequent trnsoximtion of the oxime 14?15, or, lterntively, y triutyltin hydride-promoted deromintion of the rhmnosulosyl romide 13. Not unexpetedly, -elimintion of enzoi id in 15 ws redily indued either y rief heting in pyridine or y stirring with sodium ette in etone to provide the single-stereogeni-entre dihydropyrnone 16, verstile enntiopure six-ron uilding lok (Sheme 2). Exposure of dihydropyrnone 16 to Zemplén methnolysis did not lierte the respetive 2,3-diketone (or enol forms thereof), ut gve the 2-dimethyl etl 17 in uniform retion, oneivly proeeding through ddition of methoxide onto the ronyl group nd susequent 4--?5--enzoyl migrtion (to the methyl yll 18) nd replement of the enzoyloxy group y (18?17). Suh ourse reeives some redene y the detetion of 19 y 1 NMR nd TLC on rief methnolysis, nd y the otention of enzoyl-llomltol 22 on the ttempt to nomerilly refuntionlize dihydropyrnone 16 y photoromintion with NBS (Sheme 3). As oserved for the 6- enzoyloxymethyl nlogue of 16, 9 the romine rdil either enters the nomeri position next to the ronyl group (?20) or the one vinologous thereto (?21), eh eing ple of elorting the -pyrone system vi enzoyl group shifts 10 (rrows in 20 nd 21, respetively). L-Rhmnose 4steps[8] 46% Bz Bz 12 R Br Bz Bz 13 d Bz Bz e X 14 X=N 15 X= f (15) Bz 16 g 17 Sheme 2. Retions nd onditions: () N/, 10?0 C, 84%; () NBS/ in C 2 Cl 2, 30 min, rt, 75%; 8 () N 2 /pyridine in Et, 5 d, rt, 86%; (d) Bu 3 Sn/AIBN in toluene, 5 h, 90 C, 71%; (e) etldehyde/cl in CN, 15 h, rt, 82%; (f) pyridine in CCl 3, 5 min reflux, 87%; (g) N/, 5 min, rt, 68%.

3 954 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) Ph Bz N R R=Bz 17 R= NBS hν Ph Ph Br or Br Bz Sheme ,5-Anhydro--xylulose Applition of the methodology developed for hydroxylminolysis nd Zemplén deyltion to the 2-hydroxy--xyll esters 23 nd 24 proeeded in strightforwrd mnner providing the E-oximes 25 27, the ulose dienzote 28, s well s the respetive diethyldithio etls 29 nd 30, in rystlline form eh nd in stisftory yields. The only peulirity oserved ws tht the form in whih the ulose dienzote 28 umulted on deoximtion of 26 with etldehyde depended on the workup proedure: the ketose s suh or its 2,2-diol (hydrte form), ws seprtely isolle, nd hrterized y their distintly different 1 nd 13 C NMR dt, the former showing its C-2 resonne t 199.4, the hydrte t 91.7 ppm (Sheme 4). Liertion of the unproteted 1,5-nhydro--xylulose 4 ould e effeted from the oxime 27 y trnsoximtion, from the dithioetl 30 y desulfuriztion nd, preprtively most strightforwrd, y Zemplén methnolysis of the 2-etoxy--xyll diette 23. The resulting 1,5-nhydro--pentulose ws hrterized y NMR to e the monohydrte in queous solution, whilst in MS-d 6 or in pyridine-d 5, spetr turned out to e unusully omplex inditing the presene of dimeri forms. R R R 23 R=A 24 R=Bz d (24) 4 e (27) h R R N 25 R=A 26 R=Bz 27 R= R EtS R EtS 29 R=Bz i 30 R= (26) f Bz Bz Bz Sheme 4. Retions nd onditions: () N 2 Cl in TF/ette uffer p 4.5, 20 h, rt or in pyridine 10 d, rt, 79% 25, 75% 26; () etldehyde/2 M Cl in CN, 18 h, rt, 92%; () N/, 1 h, rt, 63%; (d) N/, 2 h, 15 C?rt, then +, 69%; (e) etldehyde/2 M Cl in CN, 5 h, rt, 78%; (f) EtS/BF 3 in CCl 3, 5 min, rt, 88%; (g) pyridine in CCl 3, reflux, 10 min, 82%; (h) CdC 3 /gcl 2 in wter, 30 min, rt, 75%; (i) N/, 3 h, rt, 95%. g With respet to the onformtions dopted y 1,5-nhydro-xylulose 4 nd its derivtives 25 30, 1 NMR dt most notly their J 3,4 nd J 4,5 vlues revel the uloses 4 nd 28, respetively, nd their monohydrtes to e in the 4 C 1 onformtion, whilst the ouplings of the oximes sed on J 3,4 nd J 4,5 vlues of z re est interpreted y their doption of the 0 S 2 ottwist or skew onformtion. 3. Conlusion Bz Bz 4 R R 3 28 N R R 5 2 (R =) 28 2 (R =Bz) 25 R=A 26 R=Bz 27 R= Simple protools sed on diret Zemplén methnolysis or on three-step hydroxylminolysis/deyltion/deoximtion sequene hve een elorted to onvert 2-hydroxyglyl esters of -gltose, L-rhmnose nd -xylose into their onfigurtionlly relted 1,5-nhydro-ketoses. The onvenient ess therey provided to -tgtose, L-rhmnulose nd -xylulose in their 1,5- nhydro forms now renders them ville for evlution of their pplition profiles, most notly of their potentil ntioxidnt properties. Moreover, the methodologies developed for their quisition re pt to e pplile to ny other 2-hydroxyglyl ester, suh s, for exmple, to the perettes of 2-hydroxy- -gull 32, 11 2-hydroxy--lll 33 11,12 nd 2-hydroxy-elloil 34, 13 insmuh s their enol ester hydroxylminolysis smoothly provides the respetive E-oximes in rystlline form eh. Thus, the low temperture Zemplén de--etyltions elorted should similrly proeed in strightforwrd mnner furnishing, for exmple, 1,5-nhydro--sorose from 32 nd its -psio nlogue from 33. In similr fshion, the redily essile dishride-derived 2-hydroxyglyl esters nd their enzoylted mltl, elloil nd ltl nlogues 14 re to generte the underlying 4- -glyosylted 1,5-nhydro--frutoses, should there e need for their vilility.

4 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) A A A A A A (-soro) A N A A A A A A (-psio) A N A A A A A 34 A A A A A N A 37 A A 4. n the E-geometry of 1,5-nhydroketose oximes ximes of pyrnoid 2-ketosugrs, tht is, --glyosiduloses of type I, invrily ssume the Z geometry with the oxime hydroxyl pointing in the diretion of the nomeri entre, proof eing derived from the signifint deshielding of the equtorilly oriented -1 y the oxime hydroxyl whih finds expression in n downfield shift of ppm when going from the prent ketose to its oxime. 15 The Z ssignments were in ft orroorted y severl X-ry strutures. 16 A A I A 1e N X X=Alkyl,A,Cl R R X II 1e N X=,C 3,C 2 R R=,A,Bz Compounds differing from I only y the sene of n nomeri sustituent, tht is, 1,5-nhydroketoximes of type II, would similrly e ntiipted to generlly dopt the E-oxime geometry. This onjeture ould redily e verified y omprison of 1 nd 13 C NMR dt of the oximes nd their prent 2-oxo nlogues. As lerly evident from the juxtposition of the -fruto-onfigured oximes 37 nd to their 2-ulose ounterprts 38 nd 39, the xilly-oriented protons -1 nd -3 show minimlly hnged hemil shifts (f. Tle 1), wheres the equtoril -1 exhiits distint downwrd shift of 0.6 ppm when going from ulose to oxime. This lerly indites tht the oxime hydroxyl group is pointing towrds the nomeri ron rther thn C-3, hene estlishing the E-onfigurtion for oximes R R R' R 3 R 1 1e 1 R = 38 R = A 39 R = Bz 3 R R R A A 1e 42 Bz Bz 37 A βa 4Gl N 43 Bz βbz 4Gl 1 44 Bz αbz 4Gl 45 Bz βbz4gl In the -tgto nd L-rhmnulo ses the respetive downfield shifts for -1e from ketose to oxime re even higher (0.8 ppm), whih n only e rtionlized y the E-geometry of the oximes. In the -xylulo se 28 (Tle 1, X = ) nd 26 (X = N) there is downfield shift of oth, -1e (0.23) nd -1 (0.27 ppm) oviously due dption of the 0 S 2 ot-twist onformtion of the pyrnoid ring, wherein the oxime hydroxyl exerts its deshielding eqully on either of the nomeri hydrogens. The E-geometry of 1,5-nhydroketoximes n similrly e derived from the 13 C hemil shifts of the rons viinl to the ronyl respetively, oximinoronyl group. As doumented y vst literture dt, 17,18 the 13 C resonnes of the ronyl nd oth viinl rons shift upfield on oxime formtion, with the effet for the ron on the sme side s the N group eing greter thn tht for the other. In the se of 3-methyl ylohexnone nd its oxime these upfield shifts re 15.8 ppm for the oxime- deshielded ron, yet still 9.6 ppm for the other (Fig. 1). N Figure C hemil shifts (ppm) of ylohexnone versus those of its oxime. 17 The upfield shift for C-2 from ketone to oxime is signifintly lrger (15.8) thn for C-6 (9.6 ppm). Tle 1 1 NMR dt for -1 nd the nomeri hydrogens of 1,5-nhydroketoses nd ylted derivtives in omprison to those of their E-oximes Configurtion 1,5-Anhydroketoses 1,5-Anhydroketose E-oximes Ref. X = X = N -1e -1-3 Solvent -1e -1-3 Solvent -Fruto CCl MS-d MS-d CCl MS-d CCl CCl CCl Tgto MS-d MS-d MS-d 6 L-Rhmnulo CCl CCl 3 -Xylulo MS-d CCl C-d CCl 3 1,5-Anhydro--frutose 1 nd its -xylulo nlogue 4 dopt in wter ( 2 ) the 2,2-dihydroxy(hydrte) form, nd hene re not suited for omprison. t from this pper. Signl not resolved from glyosyl protons.

5 956 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) Tle 2 13 C NMR dt (ppm) for C-1 through C-3 of 1,5-nhydro-ketoses nd ylted derivtives ompred to those of their E-oximes Configurtion 1,5-Anhydroketoses 1,5-Anhydroketoximes Compd. C-1 C-2 C-3 Solvent Compd. C-1 C-2 C-3 Solvent -Fruto Fruto CCl MS-d 6 -Fruto MS-d CCl 3 -Tgto MS-d 6 -xylulo C-d CCl 3 1,5-Anhydro--frutose 1 forms dimers in the solid stte nd the hydrte in wter, hene is unsuited for omprison. Anlogous shift differenes re oserved for the 13 C resonnes of the four ketose/oxime exmples listed in Tle 2: in the -fruto nd -tgto onfigured ompounds upfield shifts of ppm for the viinl ron deshielded y the oxime hydroxyl, nd 6 7 ppm only for the other, thus eqully proving the E-geometry of the 1,5-nhydroketoximes. In the -xylulose se though this upfield shift differene etween ketose nd ketoxime is nerly equlized understndly, s the 0 S 2 skew-ot onformtion of the pyrnoid ring levels the deshielding effets. 5. Experimentl 5.1. Generl lting points were determined with Bok hot-stge mirosope nd re unorreted. ptil rottions were mesured on Perkin Elmer 241 polrimeter t 20 C using ell of 1 dm pth length; onentrtion () in g/100 ml nd solvent re given in prentheses. 1 nd 13 C NMR spetr were reorded on Bruker ARX-300 spetrometer in CCl 3. Mss spetr were quired on Vrin MAT 311 spetrometer. Mironlyses were determined on Perkin Elmer 240 elementl nlyzer. Anlytil thin lyer hromtogrphy (TLC) ws performed on preoted rk plsti sheets (0.2 mm Sili Gel 60 F 254 ) with detetion y UV light (254 nm) nd either sprying with 2 S 4 (50%) or y dipping into sulphuri id/nisldehyde regent [ontining nisldehyde (1 ml), ond 2 S 4 (9 ml) A (10 ml) nd (85 ml)] followed y heting t 110 C for 10 min. Column nd flsh hromtogrphy ws rried out on Fluk Sili Gel 60 ( mesh) using the speified eluents ,4,6-Tri--etyl-1,5-nhydro--tgtose E-oxime 6 To solution of hydroxylmine hydrohloride (7.4 g) in pyridine (50 ml) ws dded 10.0 g (30.3 mmol) of 2-etoxy--gltl triette 5 19,20 nd the mixture ws stirred t mient temperture for 15 h, followed y pouring into wter (350 ml). Extrtion with CCl 3 (5 100 ml) nd onseutive wshing of the omined extrts with 2 N 2 S 4 (3 100 ml), wter (100 ml), std NC 3 solution (100 ml) nd wter (50 ml), drying (N 2 S 4 ) nd evportion to dryness in vuo left solid residue whih ws rerystllized from Et: 7.51 g (82%) of 6 s well-formed prisms of mp C; ½Š 23 ¼ 44:3 ( 0.5, CCl 3). 1 NMR (300 Mz, MS-d 6 ): d 2.01, 2.03, 2.08 (three 3-s, 3 AC 3 ), 3.94 (1-d, 1-), 3.98 (2-m, 6-2 ), 4.18 (1-dd, 5-), 5.01 (1-d, 1-e), 5.39 (1-d, 4- ), 5.76 (1-d, 3-), (1-s, N), J 1,1 = 14.5, J 3,4 = 3.7, J 4,5 = 0 z. 13 C NMR (75.5 Mz, MS-d 6 ): d 20.2, 20.38, (3 AC 3 ), 60.3 (C-1), 62.1 (C-6), 68.2 nd 68.9 (C-3, C-4), 73.5 (C-5), (C-2), 168.9, 169.9, (3 AC). Anl. Cld for C N 8 (303.26): C, 47.52;, 5.65; N, Found: C, 47.58;, 5.57; N, ,5-Anhydro--tgtose E-oxime 7 Fifty millilitres of 1 M N/ solution were ooled to 0 C with stirring nd oxime 6 (3.03 g, 10 mmol) ws dded, TLC showing omplete onversion within 20 min with the exlusive formtion of 7 (R f = 0.5 in npr/wter 7:3). The solution ws diluted with 200 ml of nd neutrlised y stirring with owex 50 WX8, + form for 10 min. The suspension ws filtered nd the resin ws wshed with methnol. Filtrte nd wshings were evported to volume of out 50 ml whereupon rystlliztion ourred. The preipitte ws redissolved y wrming to llow smooth rystlliztion: 3.05 g (78%) of 7 s fine needles of mp C; ½Š 20 ¼ 12:8 ( 1, ), ½Š22 ¼ 5:0 ( 1, 2); lit. 6 : mp C; ½Š ¼ 9:2 ( 0.5, ). 1 NMR (300 Mz, MS-d 6 ) fter two reevportions from 2 to eliminte, ouplings: d 3.47 (3-m, 5-, 6-2 ), 3.68 (1-d, 1- ), 3.82 (dd, 1, 4-), 4.23 (dd, 1, 3-), 4.85 (1, -1e), (1-s, N), J 1,1 = 13.9, J 3,4 = 3.3, J 4,5 = 0.5 z. 13 C NMR (25.2 Mz, MS-d 6 ): d 59.4 (C-1), 60.4 (C-6), 69.5 nd 69.9 (C-3 nd C-4), 78.3 (C-5), (C-2). MS (F): m/e = 177 (M + ). Anl. Cld for C 6 11 N 5 (177.16): C, 40.68;, 6.26; N, Found: C, 40.43;, 6.19; N, ,4,6-Tri--etyl-1,5-nhydro--tgtose 8 Stirring of 7 in etonitrile solution (4.60 g, 15.2 mmol, in 50 ml) with etldehyde (3.0 ml) nd 1 M Cl (15 ml) for 6 h t mient temperture followed y dilution with wter (250 ml), extrtion with EtA (3 100 ml) nd removl of the solvent from the orgni lyer gve glssy syrup (4.5 g, 95%), whih on the sis of 1 NMR dt in MS-d 6 omprised 2:3 mixture of the keto form 8 nd its monohydrte whih due to its propensity for elimintion of eti id to the enolone 11 in ontt with sili gel ws not ttempted to seprte. 1 NMR (300 Mz, MS-d 6 ), keto form: d 2.03, 2.06 (3 nd 6-s, 3 AC 3 ), 4.05 nd 4.08 (two 1-m, A nd B prt of n ABX system, 6-2 ), 4.09 nd 4.38 (two 1-d, 1-2 ), 4.54 (1-m, X prt of n ABX system, 5-), 5.67 (dd, 1, 4-), 5.88 (1-d, 3-), J 1,1 = 14.5, J 3,4 = 4.0, J 4,5 = 0.9 z; monohydrte: 4.99 (1-d, 3-), 5.23 (dd, 1, 4-), 7.39 nd 7.60 (two 1-s, 2, exhngele with 2, J 3,4 = 5.3, J 4,5 = 5.8 z ,5-Anhydro--tgtose eoximtion of oxime 7 Aetldehyde (1.7 ml, 30 mmol) nd 1 M Cl (15 ml) were dded to suspension of 7 (1.43 g, 8 mmol) in etonitrile (50 ml) nd the mixture ws stirred for 5 h t mient temperture. The resulting ler solution ws diluted with wter (15 ml) nd neutrlised y stirring with n idi resin (Amerlite IR form) nd the filtrte ws evported to dryness in vuo. The syrupy residue ws then eluted from sili gel olumn (3 45 m) with n-propnol/wter (7:3), to give upon evportion of the produt-rrying elutes in vuo, finlly t 0.01 mm, 1.08 g (83%) of 2 s n morphous solid of R f = 0.5 in 7:3 n-pr/wter (extended spot); ½Š 21 ¼ 7:9 ( 0.9, 2); lit. 6 : ½Š ¼ 6:8 ( 1.1, ); MS (F): m/e = 162 [M + ], 163 (M+1), 180 (M+ 2 ). Anl.

6 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) Cld for C (162.14): C, 44.44;, Found: C, 44.29, NMR dt in 2 indite n pproximte 3:2 equilirium etween ketose nd monohydrte form, s previously oserved y Freimund nd Köpper 7 for produt prepred y enzymti oxidtion of 1,5-nhydro--gltitol. 1 NMR (500 Mz, 2 ), keto form: 3.58 (2-m, 6-2 ), 3.92 (2-m, -1, -5), 4.04 (1-d, - 1e) 4.20 (1-dd, -4), 4.45 (1-d, -3); J 1,1 = 14.8; J 3,4 = 3.9, J 4,5 = 0.9 z; hydrte: 3.23 (1-d, -1), 3.43 (1-m, -5), 3.50 nd 3.55 (AB prt of n ABX system, 6-2 ), 3.54 (1-d, -3), 3.59 (1-d, -1e), 3.76 (1-dd, -4); J 1,1 = 12.0, J 3,4 = 3.8; J 4,5 = C NMR (75.2 Mz, 2 ). d (C-2, ketose), 92.5 (C-2, hydrte), 79.9/78.6 (C-5), 76.1/72.1 (C-3), 72.5/72.6 (C-1), 71.7/69.5 (C-4), 61.5/61.3 (C-6) e--etyltion of 2-etoxy--gltl triette 5 A solution of 5 19,20 (2.0 g, 6 mmol) in dry (100 ml) ws ooled to out 15 C (slt ie mixture) followed y the ddition of 5 ml of 1 M N/ solution nd stirring of the mixture for 2 h t 15 C, wherefter the solution ws llowed to wrm to 0 C (1 h). Neutrliztion ws then effeted y stirring with Amerlite IR 120, + form (10 min). Filtrtion nd evportion to dryness in vuo gve slightly yellowish, syrupy residue (910 mg) whih ws eluted from Sephdex L 20 olumn (2 30 m) with wter. Colleting the produt-rrying elutes nd removl of the solvent in vuo, finlly t 0.05 Torr, gve 820 mg (84%) of 2 s n morphous solid, identil with the produt desried under emerptliztion of dithioetl 10 To solution of 1.0 g (2.7 mmol) of 10 in 20 ml of wter were dded CdC 3 (1.8 g, 10 mmol) nd gcl 2 (1.4 g, 5 mmol), nd the mixture ws stirred for 30 min t mient temperture. The insolule mterils re susequently removed y filtrtion through lyer of sili gel. The filtrte ws then sturted with 2 S, nd fter nother filtrtion with sution through sili gel the filtrte ws neutrlised with wekly si ion exhnge resin (Lewtit MP 7080). Removl of the resin nd onentrtion to dryness in vuo left visous syrup whih ws purified y elution from Sephdex L 20 olumn (2 30 m) with wter. Removl of the solvent in vuo from the produt-rrying elutes nd drying of the residue t 0.1 Torr gve 425 mg (69%) of olourless fom, identil (TLC, NMR) with the produt desried under ,4,6-Tri--etyl-1,5-nhydro--tgtose diethyldithioetl 9 Ethnediol (3.7 ml, 50 mmol) nd BF 3 -etherte solution (10 ml) were dded to solution of 1.9 g (10 mmol) of nhydrotgtose triette 8 (mixture of ulose nd hydrte s otined under 5.4) in CCl 3 (30 ml). After 15 min of stirring t mient temperture, the solution ws diluted with 50 ml of CCl 3, neutrlised y wshing with 2 M N nd wter (3 30 ml), dried (N 2 S 4 ) nd evported to dryness in vuo. The resulting syrup, 2.23 g (61%) of 9, ws hromtogrphilly uniform (R f = 0.59 in toluene/etone 2:1) nd ws used for the deetyltion (f. elow). The nlytil smple ws purified y elution from sili gel with 40:1 C 2 Cl 2 /EtA: syrup of ½Š 23 ¼þ15:7 ( 1, CCl 3). 1 NMR (300 Mz, MS-d 6 ): d 1.14 nd 1.16 (two 3-t, 2 EtS- C 3 ), 2.00 nd 2.05 (6- nd 3-s, 3 AC 3 ), 2.65 (4-m, 2 EtSC 2 ), 3.74 nd 3.99 (two 1-d, 1-2 ), 3.99 (1-m, 5-), 4.17 (2-m, 6-2 ), 5.25 (1-dd, 4-), 5.31 (1-d, 3-), J 1,1 = 12.5, J 3,4 = 3.7, J 4,5 = 3.2 z. 13 C NMR (25.2 Mz, CCl 3 ): d 60.3 (C-2), 61.2 (C-6), 66.6 (C-4), 70.3 (C-1), 73.9 nd 74.6 (C-3 nd C-5). Anl. Cld for C S 2 (394.5): C, 48.71;, Found: C, 48.70;, ,5-Anhydro--tgtose diethyldithioetl 10 A solution of 1.54 g (4.1 mmol) of triette 9 in 40 ml of 0.1 M methnoli sodium methoxide ws stirred t 0 C for 3 h nd susequently neutrlised y stirring with owex WXl ( + form). Filtrtion nd evportion of the filtrte in vuo fforded syrup, whih ws hromtogrphed on sili gel (2 30 m olumn) y elution with 2:1 toluene/eta to result in 910 mg (87%) of 10 s olourless syrup of ½Š 20 ¼ 57 ( 1.1, ); R f = 0.43 in n-utnone std with wter. 13 C NMR (25.2 Mz, 2 ): d 61.9 (C-6), 62.4 (C-2), 67.4 (C-4), 72.9 (C-1), 74.6 nd 81.5 (C-3 nd C-5). MS (F): m/e = 268 (M + ), 269 (M + + 1). Anl. Cld for C S 2 (268.4): C, 44.75;, Found: C, 44.70;, (6S)-4-Aetoxy-6-etoxymethyl-2-pyrn-3(6)-one 11 A 1.0 g portion of 8 nd freshly molten NA (2.0 g) were stirred in 50 ml of dry etone for 1 h t room temperture. Filtrtion nd evportion of the filtrte in vuo, nd purifition of the resulting syrup on sili gel olumn (2 30 m) y fst elution with 3:1 n-hexne/eta fforded 1.03 g (91%) of enolone 11 s olourless syrup; ½Š 20 ¼ 42:7 ( 1.2, CCl 3); lit. 7,21 : ¼ 17:7 ( 0.34, C 2Cl 2 ); 1 ½Š ¼ 43:7 ( 1.7, CCl 3 ) nd 13 C NMR dt orresponded with those reported. 7,21 ½Š ,5-Anhydro-L-rhmnulose (1,5-nhydro-6-deoxy-Lfrutose) 3 Five mmol (2.29 g) of 12 8 ws dissolved in 150 ml of nhydrous with slight wrming, then ooled to 5 C with vigorous stirring followed y the ddition of 5 ml of 1 M N/ solution. The mixture ws llowed to wrm to 0?+5 C ny preipitte ourring eing dissolved within 10 min. After out 20 min (TLC monitoring with n-pr/wter 9:1 or 7:3, R f of produt 0.65 nd 0.72, respetively), the retion ws quenhed y stirring with methnol-wshed Amerlite IR 120 ( + form). Filtrtion nd evportion of the filtrte to dryness in vuo left syrup whih ws dissolved in wter nd eluted from Sephdex L 20 olumn (2 30 m) with wter. Evportion of the produt-rrying elutes in vuo, finlly t 0.1 Torr, gve 405 mg (69%) of 3 s n morphous solid. 1 NMR (500 Mz, 2 ): d 1.20 (3-d, C 3 ), 3.16 (1-t, -4), 3.34 (1ddd, -5), 3.37 (1-d, -1), 3.44 (1-d, -3), 3.63 (1-d, - 1e); J 1,1 = 12.3, J 3,4 = J 4,5 = 9.3, J 5,6 = 6.2 z. 13 C NMR (125.7 Mz, 2 ): d 17.4 (C-6), 72.3 (C-1), 74.6 (C-4), 77.0 nd 77.1 (C-3 nd C-5), 93.2 (C-2): Anl. Cld for C (146.14): C, 49.31;, Found: C, 49.24;, ,4-i--enzoyl-1,5-nhydro-L-rhmnulose E-oxime 14 2-Benzoyloxy-L-rhmnl dienzote 12 8 (9.20 g, 20 mmol) ws dded to solution of N 3 Cl (3.5 g, 50 mmol) in 1:1 pyridine/et (100 ml) nd the mixture ws kept t mient temperture for one week nd susequently tken to dryness in vuo. The residue ws dissolved in C 2 Cl 2 (100 ml) nd suessively wshed with 2 M Cl (20 ml) nd std NC 3 solution (2 20 ml), dried (N 2 S 4 ), followed y removl of the solvent in vuo nd rystlliztion of the residue y triturtion with Et: 6.35 g (86%) of 14 s olourless needles; mp C, ½Š 21 ¼þ123 ( 0.5, CCl 3). 1 NMR (300 Mz, CCl 3 ): d 1.35 (3-d, C 3 ), 3.75 (1-m, 5-), 4.00 nd 5.12 (two 1-d, 1-2 ), 5.36 (1-t, 4-), 5.94 (1-d, 3-), (10-m, 2 C 6 5 ), 8.44 (1-s, N); J 1,1 = 16.0, J 3,4 = J 4,5 = 8.0, J 5,6 = 5.9 z. Anl. Cld for C N 6 (369.36): C, 65.03;, 5.19; N, Found: C, 64.91;, 5.10; N, 3.71.

7 958 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) ,4-i--enzoyl-1,5-nhydro-L-rhmnulose eoximtion of oxime 14 Stirring of 14 (3.69 g, 10 mmol) in etonitrile solution (50 ml) with etldehyde (2.3 ml, 40 mmol) nd 2 M Cl (5 ml, 10 mmol) ws done overnight t mient temperture followed y dilution with wter (200 ml) nd extrtion with EtA (3 100 ml). Removl of the solvent from the extrts gve syrup whih rystllized from ether: 2.80 g (79%) of 15 s olourless needles of mp C, ½Š 21 ¼þ109:9 ( 1.1, CCl 3 ). 1 NMR (300 Mz, CCl 3 ): d 1.41 (3-d, C 3 ), 4.11 (1-m, 5-), 4.16 nd 4.33 (two 1-d, 1-2 ), 5.56 (1-t, 4-), 5.86 (1-d, 3-), 7.4 nd 8.0 (two m, 2 C 6 5 ); J 1,1 = 15.8, J 3,4 = J 4,5 = 7.9 z. Anl. Cld for C (354.34): C, 67.79;, Found: C, 67.69;, Redutive deromintion of ulosyl romide 13 To solution of 13 8 (1.1 g, 2 mmol) in toluene (50 ml) were dded zoisoutyronitrile (50 mg, 0.3 mmol) nd triutyltin hydride (880 mg, 3 mmol) nd the mixture ws heted for 5 h t 90 C, followed y ooling nd wshing with 10% queous KF solution (3 20 ml) nd wter. rying (MgS 4 ) nd removl of the solvent in vuo left n oily residue, uniform y TLC, whih ws freed from tin ompounds y rpid hromtogrphy on sili gel olumn (2 20 m) with 2:1 ether/n-pentne pplying pressure to effet this opertion within 10 min. The syrup remining fter evportion of the elute ontining 15 rystllized on triturtion with C 2 Cl 2 /n-hexne to fford 505 mg (71%), identil with the produt desried under Longer ontt of rude 15 with sili gel, for exmple, severl hours on olumn purifition, indued -elimintion of enzoi id to the dihydropyrn one 17; it my e isolted in yields over 80% y slow elution of sili gel olumn (3 30 m) with 2:1 ether/n-pentne (6S)-4-Benzoyloxy-6-methyl-2-pyrn-3(6)-one 16 Pyridine (0.3 ml) ws dded to solution of 15 (1.42 g, 4 mmol) in CCl 3 (10 ml) nd the mixture ws heted for 5 min, followed y evportion to dryness in vuo. Crystlliztion of the residue from fforded 810 g (87%) of 16 s olourless needles; mp 116 C; ½Š 21 ¼ 10:5 ( 1.2, CCl 3). 1 NMR (300 Mz, CCl 3 ): d 1.49 (3-d, C 3 ), 4.26 nd 4.42 (two 1-d, 2-2 ), 4.76 (1-ddt, 6-), 6.72 (1-d, 5-), (5-m, C 6 5 ); J 2,6 = J 5,6 = 1.9, J 6;C3 ¼ 6:9 z. Anl. Cld for C (232.23): C, 67.23;, Found: C, 67.26;, (2S)-5,5-imethoxy-2-methyl-tetrhydropyrn-4-one 17 Two millilitres of 1 M N/ solution were stirred into suspension of enolone 16 (465 mg, 2 mmol) in dry (10 ml) nd the mixture ws neutrlised fter 5 min y ddition of Amerlite IR ( + form). Filtrtion nd evportion of the filtrte to dryness gve olourless oil, whih n e purified y hromtogrphy ( m sili gel olumn, elution with CCl 4 /EtA 2:1) or distilltion t 65 C/0.3 Torr: 235 mg (68%) of 17; ¼ þ154:6 ( 1.3, CCl 3); 1 NMR (300 Mz, CCl 3 ): d 1.33 (3-d, C 3 ), 2.43 nd 2.71 (two 1-d, 3-2 ), 3.29 nd 3.39 (two 3-s, 2 C 3 ), 3.76 (1-ddq, 2-), 3.38 nd 4.24 (two 1-d, 6-2 ); J 2,3 = 2.5 nd 11.0, J 2;C3 ¼ 6:1, J 3,3 = 13.3, J 6,6 = 12.4 z. 13 C NMR (75.5 Mz, CCl 3 ): d 21.5 (C 3 ), 41.4 (C-3), 49.9 (C 3 ), 71.0 (C-6), 75.6 (C-2), 98.3 (C-5), C-4. MS (F, 5 ma): m/ e = 174 (M + ). Anl. Cld for C (174.18): C, 55.17;, Found: C, 54.98;, ½Š Benzoyloxy-2-methyl-4-pyrn-4-one (-enzoylllomltol) 22 N-Bromosuinimide (360 mg, 2.5 mmol) nd BC 3 (0.5 g) were dded to solution of enolone 16 (465 mg, 2 mmol) in Et-free CCl 4 (40 ml), nd the mixture ws irrdited with 450 W IR lmp with vigorous stirring for 20 min, wherefter TLC in 19:1 C 2 Cl 2 /EtA reveled the sene of edut in fvour of severl produts. The mjor one, 22, ws isolted y filtrtion, evportion of the filtrte to dryness nd solution of the residue from sili gel olumn (2 20 m) with 19:1 C 2 Cl 2 /EtA nd rystlliztion from diisopropyl ether: 205 mg (44%) of 22 s needles of mp C. The produt ws identil (mixed mp, 1 NMR) with n uthenti smple ,4-i--etyl-1,5-nhydro--threo-pent-2-ulose E- oxime 25 A mixture of 2,3,4-tri--etyl-1,5-nhydro- -threo-pent-1- enitol (1.03 g, 4 mmol), hydroxylmine hydrohloride (1.0 g), tetrhydrofurn (10 ml) nd ette uffer (p 4.5) ws stirred for 20 h t mient temperture, followed y grdul neutrliztion with std NC 3 solution nd extrtions with CCl 3 (3 20 ml). The CCl 3 extrts were wshed with wter, dried (N 2 S 4 ) nd tken to dryness in vuo. The syrupy residue rystllized on triturtion with Et: 730 mg (79%) of 25 s needles of mp C; ½Š 22 ¼ 58:3(0.3, CCl 3). 1 NMR (300 Mz, CCl 3 ): d 2.06 nd 2.08 (two 3-s, 2 A C 3 ), 3.92 (1-dd, 5-x), 4.28 nd 4.52 (two 14.1 z-d, 1 eh, 1-2 ), 4.66 (1-dd, 5-eq), 4.90 (1-sx, 4-), 5.36 (1-d, 3-), (1-s, N), J 1,1 = 14.1, J 3,4 = 5.0, J 4,5 = 3.1 nd 5.0, J 5,5 = 12.2 z. Anl. Cld for C 9 13 N 6 (231.20): C, 46.75;, 5.67; N, Found: C, 46.70;, 5.59; N, ,4-i--enzoyl-1,5-nhydro--threo-pent-2-ulose E- oxime 26 ydroxylmine hydrohloride (10.0 g, 1.4 mmol) ws dded to solution of 2,3,4-tri--enzoyl-1,5-nhydro--threo-pent-1-enitol (10.0 g, 22.5 mmol) in pyridine (60 ml) nd the mixture ws stirred for 1 h nd then stood for 5 d t mient temperture, followed y stirring into wter (1.5 ml). The preipitte formed ws filtered off, wshed with wter, dried (N 2 S 4 ) nd rerystllized from CCl 3 /Et to give 9.4 g (75%) of olourless needles of mp C, whih onsisted of 10:1 mixture ( 1 NMR) of the E-oxime 26 (R f = 0.56 in 10:1 C 2 Cl 2 /EtA) nd the respetive Z-isomer (R f = 0.49). A 500 mg smple ws sujeted to elution from sili gel olumn (2 20 m) with C 2 Cl 2 /EtA 30:1, the first frtions ontining 220 mg of the pure E-isomer; mp C; ½Š 23 ¼ 111 ( 0.6, CCl 3 ). 1 NMR (500 Mz, CCl 3 ): d 3.89 nd 4.13 (two 1-dd, 5-2 ), 4.48 nd 4.67 (two 1-d, 1-2 ), 5.37 (1-ddd, 4-), 5.86 (1-d, 3-), J 1,1 = 15.1, J 3,4 = 5.6, J 4,5 = 3.4 nd 4.5, J 5,5 = 12.7 z. 13 C NMR (125.7 Mz, CCl 3 ): d 61.7 (C-1), 67.4 (C-5), 69.8 (C-3), 71.0 (C-4), 151,4 ((C-2). Anl. Cld for C N 6 (355.33): C, 64.22;, 4.82; N, Found: C, 64.08;, 4.75; N, The further frtions onsisted of E/Z-mixtures in vrious rtios, whih were not further seprted. 1 NMR (500 Mz, CCl 3 for Z- form): d 4.10 (2-m, 5-2 ), 4.28 nd 4.37 (two 13.0 z-d, 1 eh, 1-2 ), 5.27 (1-ddd, 4-), 6.50 (d, 1, 3-), J 1,1 = 13.0, J 3,4 = J 4,5 = z; most distint differene etween the E/Z-isomers is the hemil shift for -3: 5.86 (E) vs ppm for the Z-form ,5-Anhydro--threo-pent-2-ulose E-oxime 27 xime 26 (3.55 g, 10 mmol, in the form of its 10:1 E/Z-mixture otined ove) ws dissolved in 50 ml ooled (0 C) 1 M N/

8 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) solution nd stirred for 1 h. Susequent neutrliztion with owex 50 WX8 ( + form) filtrtion nd evportion to dryness in vuo left syrup whih ws dissolved in wter (30 ml) nd wshed with ether to remove methyl enzote. The syrup remining fter evportion of the queous phse to dryness in vuo rystllized from wter/i-propnol. Rerystlliztion from the sme solvents fforded 0.93 g (63%) of 27 s fine prisms of mp C; ½Š 20 ¼þ14:8 ( 1, 2). 1 NMR (300 Mz, MSd 6 ): d 3.45 nd 3.76 (two 1-dd, AB prt of ABX system, 5-2 ), 3.54 (1-m, X prt, 4-), 3.90 (1-dd, 3-), 4.04 nd 4.48 (two 1-d, 1-2 ), 5.01 nd 5.32 (two 1-d, 2 ), (1-s, N); J 1,1 = 13.8, J 3,4 = 4.2, J 4,5 = 2.2 nd 3.6, J 5,5 = 11.6 z. 13 C NMR (75.47 Mz, MS-d 6 ): d 58.8 (C-1), 67.3 (C-5), 69.8 (C-3), 70.1 (C-4), (C-2). Anl. Cld for C 5 9 N 4 (147.13): C, 40.81;, 6.17; N, Found: C, 40.72;, 6.12; N, ,4-i--enzoyl-1,5-nhydro--pentulose Monohydrte Pentulose oxime 26 (10.0 g, 30 mmol), in the form of its 10:1 E/Zmixture s otined ove, ws stirred with mixture of etonitrile (250 ml), 2 M Cl (18 ml) nd etldehyde (10 ml) t mient temperture for 18 h nd susequently poured into wter (1 L) with vigorous stirring. The resulting preipitte ws filtered, wshed with wter nd dried (CCl 2 ). issolution in the minimum mount of methnol nd triturtion with 2:1 ylohexne/ether resulted in rystlliztion: 9.3 g (92%) of 28-monohydrte; mp C, ¼ 131 ( 0.6, CCl 3). 1 NMR (300 Mz, MS-d 6 ): d 3.47 nd 3.66 (two 11.5 z-d, 1 eh, 1-2 ), 3.54 nd 4.06 (two 1-ddd, 5-2 ), 5.23 (1-ddd, 4-), 5.38 (d, 1, 3-), 6.20 nd 6.28 (two 1-s, 2, exhngele with 2 ), (10-m, 2 C 6 5 ); J 1,1 = 11.5, ½Š 20 J 3,4 = 9.3, J 4,5 = 5.0 nd 9.7, J 5,5 = 11.0 z. 13 C NMR (75.5 Mz, MS-d 6 ): d 66.7 (C-1), 70.1 (C-4), 78.5 (C-5), 75.9 (C-3), 91.7 (C- 2). Anl. Cld for C (358.33): C, 63.68;, Found: C, 63.54;, Keto-form The retion mixture resulting from deoximtion s desried ove (fter stirring for 18 h), ws sujeted to different workup, y elution with wter (500 ml), extrtion with EtA (3 200 ml), wshing of the omined extrts with wter, drying (N 2 S 4 ) nd removl of the solvent in vuo. The resulting syrup rystllized C 2 Cl 2 /n-hexne or CCl 4 : 8.1 g (75%) of 28 s n morphous produt of mp C nd ½Š 20 ¼ 117 ( 0.6, CCl 3), whih ppered (NMR) to ontin only smll mounts of the monohydrte. 1 NMR (300 Mz, etone- 6 ): d 4.16 (1-dd, 5- ), 4.21 nd 4.44 (two 1-d, 1-2 ), 4.46 (1-ddd, 5-e), 5.73 (1-ddd, 4-), 6.13 (1-d, 3-); J 1,1 = 15.0, J 1,5 = 1.1, J 3,4 = 9.0, J 4,5 = 8.0 nd 5.1, J 5,5 = 12 z. 13 C NMR (75.5 Mz, MS-d 6 ): d 67.5 (C-1), 71.6 (C-4), 73.4 (C-5), 77.3 (C-3), (C-2). Anl. Cld for C (340.32): C, 67.05;, Found: C, 66.85;, ,5-Anhydro--xylulose (1,5-nhydro--threo-pentulose) eoximtion of oxime 27 Aetldehyde (0.56 ml, 10 mmol) nd 1 M Cl (5 ml) were dded to suspension of oxime 27 (440 mg, 3 mmol) in etonitrile (15 ml) nd the mixture ws stirred for 5 h t mient temperture. The resulting ler solution ws diluted with wter (5 ml) nd neutrlised y stirring with n idi resin (Amerlite IR form) nd the filtrte ws evported to dryness in vuo. The syrupy residue ws then eluted from sili gel olumn (2 15 m) with 7:3 n-propnol/wter, to give upon evportion of the produt-rrying elutes in vuo, finlly t 0.01 mm, 265 mg (67%) of 4 s fluffy solid. 1 NMR (300 Mz, 2, 2 h fter solution): d 3.38 nd 3.69 (two 1-d, 1-2 ), 3.40 (1-t, 4-), 3.54 (1-d, 3-), 3.60 nd 3.94 (two 1-dd, 5-2 ), J 1,1 = 12.4, J 3,4 = 8.7, J 4,5 = 7.9 nd 4.7 z. 13 C NMR (75.5 Mz, 2 ): d 66.9 (C-1), 70.2 (C-4), 71.9 (C-3), 78.2 (C-5), 92.5 (C-2). Anl. Cld for C (132.11): C, 45.45;, Found: C, 45.34;, e--etyltion of 2-etoxy--xyll diette 23 A methnoli solution of (1.29 g, 5 mmol, in 80 ml) ws ooled to 15 C (ie slt mixture), nd upon dropwise ddition of 1 M N/ (5 ml) the mixture ws llowed to ome to 0 C within out 1 h (TLC monitoring with n-pr/wter 7:3). Susequent quenhing y stirring methnol-wshed Amerlite IR 120 ( + form) into the still old solution. Filtrtion, evportion of the filtrte in vuo, elution of the residue from n L 20 Sephdex olumn (2 25 m) with wter, evportion of the produt-rrying elutes nd drying, finlly t 0.1 Torr, gve 440 mg (67%) of 4 s fom, identil with respet to 1 nd 13 C NMR dt with the produt desried ove. esulfuriztion of dithioetl y stirring n queous solution with CdC 3 /gcl 2 s desried for 10?2 nd nlogous workup similrly gve 4 in 75% yield ,4-i--enzoyl-1,5-nhydro--threo-pentulose diethyldithioetl 29 Ethnthiol (7.0 ml) nd BF 3 etherte (5 ml) were dded to suspension of ulose monohydrte 28 2 (3.2 g, 8.9 mmol) in CCl 3 (30 ml). The mixture ws stirred for 5 min followed y dilution with CCl 3 (100 ml) nd onseutive wshings with 2 M N nd wter (3 30 ml). rying (N 2 S 4 ) nd evportion in vuo left syrup whih ws purified y elution from sili gel (3 30 m olumn) with 20:1 ylohexne/eta. Removl of the solvents from the produt-rrying frtions (R f = 0.57 in 2:1 ylohexne/eta) fforded 3.5 g (88%) of 29 s olourless syrup; ½Š 20 ¼ 121:4 ( 0.8, CCl 3 ). 1 NMR (300 Mz, MS-d 6 ): d 1.10 nd 1.24 (two 3-t, SEt-C 3 ), 2.70 (4-m, SEt-C 2 ), 3.72 nd 4.21 (two 1-dd, 5-2 ), 3.90 nd 4.07 (two 1-d, 1-2 ), 5.69 (1-ddd, 4-), 5.80 (1-d, 3- ); J 1,1 = 12.6, J 3,4 = 9.5, J 4,5 = 5.5 nd 9.5 z, J 5,5 = 10.5 z. 13 CNMR (75.47 Mz, MS-d 6 ): d 14.1 nd 14.2 (2 SEt-C 3 ), 22.4 nd 22.5 (2 SEt-C 2 ), 62.1 (C-2), 67.2 (C-5), 69.1 (C-4), 72.1 (C-1), 76.0 (C-3). Anl. Cld for C S 2 (446.6): C, 61.86;, Found: C, 61.76;, ,5-Anhydro--threo-pentulose diethyldithioetl 30 To ooled (0 C) 0.1 M N/ solution (100 ml) ws dded 5.5 g (12.3 mmol) of dienzote 29 nd the mixture ws stirred for 3 h t this temperture followed y neutrliztion with n idi resin (owex 50, + form). Filtrtion nd evportion in vuo left syrup whih ws dissolved in wter (50 ml). Wshing with ether (2 5 ml), evportion to dryness nd purifition of the syrupy residue y elution from sili gel ( m) with 20:1 C 2 Cl 2 /EtA gve 2.8 g (95%) of uniform (TLC) morphous produt, whih upon freeze drying of n queous solution rystllized; mp C; ½Š 20 ¼ 79:3 ( 1.1, ). 1 NMR (300 Mz, MS-d 6 ): d 1.13 nd 1.14 (two 3-t, SEt, C 3 ), 2.72 (4-m, SEt- C 2 ), 3.02 (1-m, 4-), 3.41 (1-dd, 3-), 3.46 nd 3.76 (two 1d, 1-2 ), 3.80 (2-m, 4-, 5-), 5.01 nd 5.40 (two 1-d, 2 ); J 1,1 = 12.2, J 3,4 = C NMR (75.47 Mz, MS-d 6 ): d 14.2 nd 14.4 (2 SEt-C 3 ), 21.8 nd 22.6 (2 SEtC 2 ), 64.1 (C-2), 67.7 (C-4), 71.1 (C-5), 73.3 (C-1), 79.8 (C-3). Anl. Cld for C S 2 (238.4): C, 45.35;, Found: 45.18;, Benzoyloxy-2-pyrn-3(6)-one 31 A few drops of pyridine were dded to solution of 680 mg (2 mmol) of ulose dienzote 29 in CCl 3 (10 ml) nd the mixture ws heted t reflux for 10 min. Evportion to dryness nd rerys-

9 960 P. Jrglis et l. / Tetrhedron: Asymmetry 20 (2009) tlliztion of the residue from methnol gve 560 mg (82%) of 31 s olourless needles; mp C. 1 NMR (300 Mz, CCl 3 ): d 4.32 (2-s, 2-2, 4.61 (2-d, 6-2 ), 4.61 (1-t, 5-); J 5,6 = 4.0 z. MS (F): m/e = 218 (M + ). Anl. Cld for C (218.2): C, 66.05;, Found: C, 66.01;, ,4-6-Tri--etyl-1,5-nhydro--sorose E-oxime 35 A solution of hydroxylmine hydrohloride (2.50 g) nd of syrupy 2-etoxy--gull triette (3.90 g, 11.8 mmol) in 30 ml of 1:1 pyridine/et ws mde to stnd for 6 h t mient temperture nd then stirred into wter (300 ml) followed y extrtion with CCl 3 (3 50 ml) nd onseutive wshings of the omined extrts with 2 N Cl (3 50 ml), wter (50 ml) std NCl 3 solution (50 ml) nd wter (50 ml). rying (N 2 S 4 ) nd evportion to dryness in vuo left 3.40 g (95%) of solid residue whih y 1 NMR proved to e 4:1 mixture of E nd Z isomers. Chromtogrphy on sili gel olumn (3 40 m, elution with 10:1 C 2 Cl 2 /EtA) nd proessing of the first produt-rrying frtion gve syrup upon evportion in vuo whih grdully rystllized on drying t 0.01 Torr overnight: 2.85 g (80%) of E- oxime 35; mp C; ½Š 20 ¼ 15:1 ( 0.6, CCl 3). 1 NMR (300 Mz, MS-d 6 ): d 2.03, 2.09 nd 2.10 (three 3-s, 3 A- C 3 ), 3.96 (1-m, 5-), 4.11 (2-m, 6-2 ), 4.01 nd 4.95 (two 13.1 z-d, 1 eh, 1-2 ), 5.00 (1-dd, 4-), 5.23 (1-d, 3-), (1-s, N): J 1,1 = 13.1, J 3,4 = 3.2 z. 13 C NMR (75.47 Mz, MS-d 6 ): d 59.1 (C-1), 62.6 (C-6), 67.9 nd 68.6 (C-3 nd C-4), 71.8 (C-5), (C-2). MS (F): m/e = 304 (M+1), 303 (M + ). Anl. Cld for C N 8 (303.26): C, 47.52;, 5.65; N, Found: C, 47.60;, 5.60; N, The frtions eluted next ontined the E/Z isomers in vrying ompositions s evidened y 1 NMR, the Z-oxime eing lerly differentited y shifts of -3 from 5.23 (E-form) to 6.03 nd one of the -1 protons from 4.95?4.37 ppm ,4-6-Tri--etyl-1,5-nhydro--psiose E-oxime 36 A mixture of hydroxylmine hydrohloride (2.1 g, 20 mmol), pyridine (10 ml), Et (10 ml) nd 3.30 g (10 mmol) of 2-etoxy--lll triette 33 11,12 ws stirred for 6 h t mient temperture nd susequently poured into wter (300 ml). Extrtion with CCl 3 (3 50 ml), nd onseutive wshings of the omined extrts with 2 M Cl, wter, std NC 3 solution nd gin wter, drying (N 2 S4) nd removl of the solvent in vuo left 3.0 g of rystlline produt, whih ws rerystllized from Et: 2.48 g (82%) of 36; mp C; ½Š 20 ¼þ27:2 ( 0.84, CCl 3). 1 NMR (300 Mz, MS-d 6 ): d 1.98, 2.01 nd 2.10 (three -s, 3 A-C 3 ), 4.00 (1-m, -5), 4.02 (1-d, -1), 4.17 (2-m, 6-2 ), 4.84 (1-dd, 4-), 4.91 (1-d, -1e), 5.71 (1-d, -3), (1-s, N); J 1,1 = 14.5, J 3,4 = 3.5, J 4,5 = 8.9 z. 13 C NMR (75.47 Mz, MS-d 6 ): d 20.3, 20.4, 20.5 (3 A-C 3 ), 59.6 (C-1), 62.7 (C-6), 68.1 nd 68.6 (C-3, C-4), 72.7 (C-5), (C-2). MS (F): m/e = 304 (M+1), 303 (M + ). Anl. Cld for C N 8 (303.26): C, 47.52;, 5.65; N, Found: C, 47.30;, 5.55; N, ,6-i--etyl-4--(2,3,4,6-tetr--etyl--gluopyrnosyl)-1,5-nhydro--frutose E-oxime 37 To solution of N 2. Cl (620 mg, 1 mmol) in pyridine (10 ml) ws dded 620 mg (1 mmol) of 2-etoxy-elloil hexette nd the mixture ws stirred t mient temperture for 7 h, susequently diluted with wter (10 ml) nd extrted with CCl 3 (3 10 ml). The omined CCl 3 extrts were wshed with wter, dried (N 2 S 4 ) nd tken to dryness in vuo. The syrupy residue rystllized on triturtion with ethnol: 430 mg (87%) of 37; mp C; ½Š 21 ¼ 22:3 ( 0.3, CCl 3); R f = 0.31 (enzene/eta 10:1). 1 NMR (300 Mz, MS-d 6 ): d = 1.99, 2.01 nd 2.03 (3s, 18, 6 A-C 3 ), 4.03 (15.1 z-d, 1, 1-), (5-m, 5-, 6-2,6 0-2 ), 4.91 (15.1 z-d, 1-e), (5-m, 4-, through 4 0 -), 6.80 (1-d, 3-), 11.4 (14-s, N). Anl. Cld for C N 16 (494.51): C, 58.29;, 6.52; N, Found: C, 58.17;, 6.48; N, Aknowledgements ur thnks re due to Priv.oz. r. Reinhrd usinger for luid disussions on NMR topis nd to the eutshe Forshungsgemeinshft for support of this reserh. Referenes 1. Brehm, M.; Gökel, V..; Jrglis, P.; Lihtenthler, F. W. Tetrhedron: Asymmetry 2008, 19, Ymji, K.; Pd Srker, K.; Mruym, I.; izukuri, S. Plnt d. 2002, 68, See extensive ptent literture ited in: ekny, G.; Lundt, I.; Niedermir, F.; Bihler, S.; Spreitz, J.; Sprenger, F. K.; Stütz, A. E. Crohydr. Res. 2007, 342, Ahrén, B.; olst, J. J.; Yu, S. Eur. J. Phrmol. 2000, 397, () Nkmur, T.; Nto, A.; Tkhshi, Y.; Aknum,. J. Biohem. 1986, 99, 607; () Bute, A.; Bute, R.; effieux, G. Phytohemistry 1988, 27, 3401; () Tguhi, T.; run, M.; kud, J. J. Biotehnol. Appl. Biohem. 1993, 18, 275; (d) Yu, S.; Kenne, M.; Pedersén, M. Biohim. Biophys. At 1995, 1244, 1; (e) Freimund, S.; uwig, A.; Giffhorn, F.; Köpper, S. Chem. Eur. J. 1998, 4, 2442; (f) Fujisue, M.; Yoshing, K.; Muroy, K.; Ae, J.; izukuri, S. J. Appl. Glyosi. 1999, 46, 439;. 6. Brili, P. L.; Berti, G.; Ctlni, G.; Andre, F.; Mirelli, L. Crohydr. Res. 1995, 274, Freimund, S.; Köpper, S. Crohydr. Res. 1998, 308, Lihtenthler, F. W.; tz, T. Eur. J. rg. Chem. 2003, Lihtenthler, F. W.; Jrglis, P.; empe, W. Lieigs Ann. Chem. 1983, For detiled mehnisti disussion of -pyrone formtion from hexoses, see: Lihtenthler, F. W. Pure Appl. Chem. 1978, 50, Shh, R..; Bhl,. P. Crohydr. Res. 1979, 74, g, M.; Tejim, S. Crohydr. Res. 1974, 34, Plötner, A.; Murer, K. Ber. tsh. Chem. Ges. 1931, 64, Lihtenthler, F. W.; Kji, E.; Weprek, S. J. rg. Chem. 1985, 50, () Lemieux, R. U.; Nghushn, T. L.; Gunner, S. W. Cn. J. Chem. 1968, 46, 405; () Lemieux, R. L.; Erl, R. A.; Jmes, K.; Nghushn, T. L. Cn. J. Chem. 1973, 51, () Smitz, Z.; Myszk,.; Ciunik, Z. Crohydr. Res. 1988, 172, 171; () Ciunik, Z.; Pulsen,.; Luger, P.; Smitz, Z.; Myszk,. At Crystllogr., Set. B 1989, 45, 512; () Ciunik, Z.; Szwed, R.; Smitz, Z. Crohydr. Res. 1991, 219, wkes, G. E.; erwig, K.; Roerts, J.. J. rg. Chem. 1974, 39, Kiser, M.; Freierg, W.; Mihlik, M. J. Prkt. Chem. 1996, 338, Murer, K.; Mhn,. Ber. tsh. Chem. Ges. 1927, 60, 1316; Murer, K.; Müller, A. J. rg. Chem. 1930, 63, Ferrier, R. J.; Snkey, G.. J. Chem. So. (C) 1966, Andersen, S. M.; Lundt, I.; Mrussen, J.; Søtofte, L.; Yu, S. Crohydr. Res. 1998, 17, Lihtenthler, F. W.; Li ohe, A.; Cuny, E. Lieigs Ann. Chem. 1983, 1973.

4-cyanopentanoic acid dithiobenzoate (CPADB) was synthesized as reported by Y.

4-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 information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR

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 information

3.15 NMR spectroscopy Different types of NMR There are two main types of NMR 1. C 13 NMR 2. H (proton) NMR

3.15 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 information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR

6.3.2 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 information

Synthesis of chiral 2-methyl-5,6,7,8-tetrahydroquinolines from naturally occurring monoterpenes

Synthesis of chiral 2-methyl-5,6,7,8-tetrahydroquinolines from naturally occurring monoterpenes Generl Ppers ARKIVC 2004 (xiv) 44-50 Synthesis of hirl 2-methyl-5,6,7,8-tetrhydroquinolines from nturlly ourring monoterpenes Giorgio Chelui,* Ginmuro rrù, nd Frno Soolini Diprtimento di Chimi, Università

More information

H 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.

H 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 information

NON-DETERMINISTIC FSA

NON-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 information

Project 6: Minigoals Towards Simplifying and Rewriting Expressions

Project 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 information

Tetrahedron: Asymmetry

Tetrahedron: Asymmetry Tetrhedron: Asymmetry 22 (2011) 740 744 Contents lists vilble t Scienceirect Tetrhedron: Asymmetry journl homepge: www.elsevier.com/locte/tetsy Convenient ccess to 4--glycosylted 1,5-nhydro--fructoses

More information

1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes.

1 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 information

Introduction to Olympiad Inequalities

Introduction 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 information

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and

Lecture 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 information

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.

First 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 information

Intermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths

Intermediate 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 information

Linear Algebra Introduction

Linear Algebra Introduction Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +

More information

Lecture Notes No. 10

Lecture 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 information

The Department of Chemistry, Brown University, Providence, RI The Department of Chemistry, Yale University, New Haven, CT 06520

The Department of Chemistry, Brown University, Providence, RI The Department of Chemistry, Yale University, New Haven, CT 06520 Eletroni Supplementry Mteril (ESI) for Chemil Siene. This journl is The Royl Soiety of Chemistry 2015 Supporting Informtion: Iron Ctlyzed CO 2 Hydrogention to Formte Enhned y Lewis Aid Co-Ctlysts Yunyun

More information

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR 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 information

Generalization of 2-Corner Frequency Source Models Used in SMSIM

Generalization 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 information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

Calix-Tris-Tröger s Bases A New Cavitand Family

Calix-Tris-Tröger s Bases A New Cavitand Family Supplementry Mteril (ESI) for Chemicl Communictions This journl is (c) The Royl Society of Chemistry 200 Clix-Tris-Tröger s Bses A ew Cvitnd Fmily Mrtin Vlík, Jn Čejk, Mrtin vlík, Vldimír Král, Bohumil

More information

1 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. 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 information

CHENG Chun Chor Litwin The Hong Kong Institute of Education

CHENG Chun Chor Litwin The Hong Kong Institute of Education PE-hing Mi terntionl onferene IV: novtion of Mthemtis Tehing nd Lerning through Lesson Study- onnetion etween ssessment nd Sujet Mtter HENG hun hor Litwin The Hong Kong stitute of Edution Report on using

More information

Activities. 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

Activities. 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 information

CHEM1611 Answers to Problem Sheet 9

CHEM1611 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 information

Analytical Techniques Chromatography

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 information

8 THREE PHASE A.C. CIRCUITS

8 THREE PHASE A.C. CIRCUITS 8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),

More information

Chemical Equilibrium

Chemical Equilibrium Chpter 16 Questions 5, 7, 31, 33, 35, 43, 71 Chemil Equilibrium Exmples of Equilibrium Wter n exist simultneously in the gs nd liquid phse. The vpor pressure of H O t given temperture is property ssoited

More information

22.Analytical Techniques Chromatography

22.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 information

A Study on the Properties of Rational Triangles

A 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 information

THE 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 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 information

Matrices SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics (c) 1. Definition of a Matrix

Matrices SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics (c) 1. Definition of a Matrix tries Definition of tri mtri is regulr rry of numers enlosed inside rkets SCHOOL OF ENGINEERING & UIL ENVIRONEN Emple he following re ll mtries: ), ) 9, themtis ), d) tries Definition of tri Size of tri

More information

6.5 Improper integrals

6.5 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 information

TOPIC: LINEAR ALGEBRA MATRICES

TOPIC: LINEAR ALGEBRA MATRICES Interntionl Blurete LECTUE NOTES for FUTHE MATHEMATICS Dr TOPIC: LINEA ALGEBA MATICES. DEFINITION OF A MATIX MATIX OPEATIONS.. THE DETEMINANT deta THE INVESE A -... SYSTEMS OF LINEA EQUATIONS. 8. THE AUGMENTED

More information

CALCULATING REACTING QUANTITIES

CALCULATING 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 information

Exercise 3 Logic Control

Exercise 3 Logic Control Exerise 3 Logi Control OBJECTIVE The ojetive of this exerise is giving n introdution to pplition of Logi Control System (LCS). Tody, LCS is implemented through Progrmmle Logi Controller (PLC) whih is lled

More information

Dorf, R.C., Wan, Z. T- Equivalent Networks The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

Dorf, 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 information

Iowa Training Systems Trial Snus Hill Winery Madrid, IA

Iowa 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 information

Pericyclic Reactions page ELECTROCYCLIC REACTIONS and SIGMATROPIC HYDROGEN SHIFTS

Pericyclic Reactions page ELECTROCYCLIC REACTIONS and SIGMATROPIC HYDROGEN SHIFTS Pericyclic ections pge 3 ELECTCCLIC EACTINS nd SIGMATPIC GEN SIFTS. Selection rules for electrocyclic ring-opening nd ring-closure The Woodwrd-offmnn nlysis (illustrted in section.3) provided the selection

More information

5. Every rational number have either terminating or repeating (recurring) decimal representation.

5. 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 information

anti-addition acidic conditions S N basic conditions CH 18: Ethers and Epoxides

anti-addition acidic conditions S N basic conditions CH 18: Ethers and Epoxides rgnic Chemistry Notes y Jim Mxk C 18: Ethers nd Epoxides jim.mxk@nu.edu Topics: Nming ethers nd understnding ethers inertness Prepring ethers vi Willimson ether synthesis: S N 2 vs E 2 ection of ethers

More information

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.

1 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 information

Chemical Equilibrium. Problem Set: Chapter 16 questions 25, 27, 33, 35, 43, 71

Chemical Equilibrium. Problem Set: Chapter 16 questions 25, 27, 33, 35, 43, 71 Chemil Equilibrium roblem Set: Chpter 16 questions 5, 7, 33, 35, 43, 71 Exmples of Equilibrium Wter n exists simultneously in the gs nd liquid phse. The vpor pressure of H O t given temperture is property

More information

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into

More information

Linear Systems with Constant Coefficients

Linear Systems with Constant Coefficients Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system

More information

Chapter 8 Roots and Radicals

Chapter 8 Roots and Radicals Chpter 8 Roots nd Rdils 7 ROOTS AND RADICALS 8 Figure 8. Grphene is n inredily strong nd flexile mteril mde from ron. It n lso ondut eletriity. Notie the hexgonl grid pttern. (redit: AlexnderAIUS / Wikimedi

More information

Review Topic 14: Relationships between two numerical variables

Review 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 information

Supplementary Information

Supplementary Information Eletroni upplementry Mteril (EI) for Chemil Communitions This journl is The Royl oiety of Chemistry 0 Verstile Grfting Approhes to tr-hped P-Contining Hyrid Polymers using RAFT Polymeriztion nd Clik Chemistry

More information

p-adic Egyptian Fractions

p-adic Egyptian Fractions p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction

More information

CS 573 Automata Theory and Formal Languages

CS 573 Automata Theory and Formal Languages Non-determinism Automt Theory nd Forml Lnguges Professor Leslie Lnder Leture # 3 Septemer 6, 2 To hieve our gol, we need the onept of Non-deterministi Finite Automton with -moves (NFA) An NFA is tuple

More information

SUPPLEMENTAL INFORMATION

SUPPLEMENTAL INFORMATION SUPPLEMENTAL INFORMATION Evlution of Modified Boehm Titrtion Methods for Use with Lignoellulosi Biohrs Rivk B. Fidel, Dvid A. Lird*, Mihel L. Thompson Deprtment of Agronomy, Iow Stte University, Ames,

More information

A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version

A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version A Lower Bound for the Length of Prtil Trnsversl in Ltin Squre, Revised Version Pooy Htmi nd Peter W. Shor Deprtment of Mthemtil Sienes, Shrif University of Tehnology, P.O.Bo 11365-9415, Tehrn, Irn Deprtment

More information

CHAPTER 3. base O N R R = C 5 H 11 OTHP. OBn. OBn. Ti(OiPr) 4, D-( )-DET t-buooh, MS 4Å 20 C, 4 d MOMO. OBn + MOMO OMOM MOMO OH

CHAPTER 3. base O N R R = C 5 H 11 OTHP. OBn. OBn. Ti(OiPr) 4, D-( )-DET t-buooh, MS 4Å 20 C, 4 d MOMO. OBn + MOMO OMOM MOMO OH Chpter 3 1 CPTER 3 1. The produt is the ldehyde, nd the mehnism is nlogous to the DMS-sed oxidtions disussed in Setion 3.2.C. resonle mehnism is shown. Pyridine -oxide ttks the romomethyl moiety vi n S

More information

#A42 INTEGERS 11 (2011) ON THE CONDITIONED BINOMIAL COEFFICIENTS

#A42 INTEGERS 11 (2011) ON THE CONDITIONED BINOMIAL COEFFICIENTS #A42 INTEGERS 11 (2011 ON THE CONDITIONED BINOMIAL COEFFICIENTS Liqun To Shool of Mthemtil Sienes, Luoyng Norml University, Luoyng, Chin lqto@lynuedun Reeived: 12/24/10, Revised: 5/11/11, Aepted: 5/16/11,

More information

Rates of chemical reactions

Rates of chemical reactions Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn

More information

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point

Numbers 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 information

The First Asymmetric Total Syntheses and. Determination of Absolute Configurations of. Xestodecalactones B and C

The First Asymmetric Total Syntheses and. Determination of Absolute Configurations of. Xestodecalactones B and C Supporting Information The First Asymmetric Total Syntheses and Determination of Absolute Configurations of Xestodecalactones B and C Qiren Liang, Jiyong Zhang, Weiguo Quan, Yongquan Sun, Xuegong She*,,

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 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

Comparing the Pre-image and Image of a Dilation

Comparing the Pre-image and Image of a Dilation hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity

More information

A Straightforward Protocol for the Highly Efficient Preparation of. Main-chain Azo Polymers Directly from Bisnitroaromatic Compounds

A 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 information

Test Generation from Timed Input Output Automata

Test Generation from Timed Input Output Automata Chpter 8 Test Genertion from Timed Input Output Automt The purpose of this hpter is to introdue tehniques for the genertion of test dt from models of softwre sed on vrints of timed utomt. The tests generted

More information

Chapter 4rth LIQUIDS AND SOLIDS MCQs

Chapter 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 information

9-1 (a) A weak electrolyte only partially ionizes when dissolved in water. NaHCO 3 is an

9-1 (a) A weak electrolyte only partially ionizes when dissolved in water. NaHCO 3 is an Chpter 9 9- ( A ek electrolyte only prtilly ionizes hen dissolved in ter. NC is n exmple of ek electrolyte. (b A Brønsted-ory cid is cule tht dontes proton hen it encounters bse (proton cceptor. By this

More information

QUADRATIC EQUATION. Contents

QUADRATIC EQUATION. Contents QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,

More information

Learning Partially Observable Markov Models from First Passage Times

Learning Partially Observable Markov Models from First Passage Times Lerning Prtilly Oservle Mrkov s from First Pssge s Jérôme Cllut nd Pierre Dupont Europen Conferene on Mhine Lerning (ECML) 8 Septemer 7 Outline. FPT in models nd sequenes. Prtilly Oservle Mrkov s (POMMs).

More information

1B40 Practical Skills

1B40 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 information

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution

Technische 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 information

Probability. b a b. a b 32.

Probability. b a b. a b 32. Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,

More information

1 From NFA to regular expression

1 From NFA to regular expression Note 1: How to convert DFA/NFA to regulr expression Version: 1.0 S/EE 374, Fll 2017 Septemer 11, 2017 In this note, we show tht ny DFA cn e converted into regulr expression. Our construction would work

More information

a) 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.

a) 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

Chapter 2. Typology of Polymers

Chapter 2. Typology of Polymers Chpter 2. Typology of Polymers 2.1 Types of bonds in Polymers 1. primry ovlent nd metlli bonds 2. hydrogen bonding 3. dipole intertion 2nd fore 4. dispersion fore (vn der Wls fore) 5. ioni bond e.g.) polyproltone,

More information

Maintaining Mathematical Proficiency

Maintaining 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 information

A STUDY OF Q-CONTIGUOUS FUNCTION RELATIONS

A STUDY OF Q-CONTIGUOUS FUNCTION RELATIONS Commun. Koren Mth. So. 31 016, No. 1, pp. 65 94 http://dx.doi.org/10.4134/ckms.016.31.1.065 A STUDY OF Q-CONTIGUOUS FUNCTION RELATIONS Hrsh Vrdhn Hrsh, Yong Sup Kim, Medht Ahmed Rkh, nd Arjun Kumr Rthie

More information

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte

More information

Facile Synthesis of Flavonoid 7-O-Glycosides

Facile Synthesis of Flavonoid 7-O-Glycosides Facile Synthesis of Flavonoid 7-O-Glycosides Ming Li, a Xiuwen Han, a Biao Yu b * a State Key Laboratory of Catalyst, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China

More information

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications

AP 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 information

Spacetime and the Quantum World Questions Fall 2010

Spacetime 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 information

CS241 Week 6 Tutorial Solutions

CS241 Week 6 Tutorial Solutions 241 Week 6 Tutoril olutions Lnguges: nning & ontext-free Grmmrs Winter 2018 1 nning Exerises 1. 0x0x0xd HEXINT 0x0 I x0xd 2. 0xend--- HEXINT 0xe I nd ER -- MINU - 3. 1234-120x INT 1234 INT -120 I x 4.

More information

CS 330 Formal Methods and Models Dana Richards, George Mason University, Spring 2016 Quiz Solutions

CS 330 Formal Methods and Models Dana Richards, George Mason University, Spring 2016 Quiz Solutions CS 330 Forml Methods nd Models Dn Richrds, George Mson University, Spring 2016 Quiz Solutions Quiz 1, Propositionl Logic Dte: Ferury 9 1. (4pts) ((p q) (q r)) (p r), prove tutology using truth tles. p

More information

Supporting Information

Supporting Information Supporting Information Efficient Short Step Synthesis of Corey s Tamiflu Intermediate Nsiama Tienabe Kipassa, Hiroaki kamura, * Kengo Kina, Tetsuo Iwagawa, and Toshiyuki Hamada Department of Chemistry

More information

Trigonometry Revision Sheet Q5 of Paper 2

Trigonometry Revision Sheet Q5 of Paper 2 Trigonometry Revision Sheet Q of Pper The Bsis - The Trigonometry setion is ll out tringles. We will normlly e given some of the sides or ngles of tringle nd we use formule nd rules to find the others.

More information

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R /10/010 Question 1 1 mole of idel gs is rought to finl stte F y one of three proesses tht hve different initil sttes s shown in the figure. Wht is true for the temperture hnge etween initil nd finl sttes?

More information

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE

NEW 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 information

Symmetrical Components 1

Symmetrical Components 1 Symmetril Components. Introdution These notes should e red together with Setion. of your text. When performing stedy-stte nlysis of high voltge trnsmission systems, we mke use of the per-phse equivlent

More information

Physics 1402: Lecture 7 Today s Agenda

Physics 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 information

Supporting Information

Supporting Information Supporting Informtion ICGM, ENSCM, Univ Montpellier, CNRS, 34296 Cedex 5, Montpellier, Frne L-LA monomer ws kindly gifted y Pur nd purified y stirring in dry diethyl ether followed y rerystlliztion in

More information

Arrow s Impossibility Theorem

Arrow 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 information

Matrix Algebra. Matrix Addition, Scalar Multiplication and Transposition. Linear Algebra I 24

Matrix 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 information

Lecture 08: Feb. 08, 2019

Lecture 08: Feb. 08, 2019 4CS4-6:Theory of Computtion(Closure on Reg. Lngs., regex to NDFA, DFA to regex) Prof. K.R. Chowdhry Lecture 08: Fe. 08, 2019 : Professor of CS Disclimer: These notes hve not een sujected to the usul scrutiny

More information

CS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014

CS 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 information

An Efficient Total Synthesis and Absolute Configuration. Determination of Varitriol

An Efficient Total Synthesis and Absolute Configuration. Determination of Varitriol An Efficient Total Synthesis and Absolute Configuration Determination of Varitriol Ryan T. Clemens and Michael P. Jennings * Department of Chemistry, University of Alabama, 500 Campus Dr. Tuscaloosa, AL

More information

Table of Content. c 1 / 5

Table of Content. c 1 / 5 Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................

More information

Parallel sheet structure in cyclopropane γ-peptides stabilized by C-H O hydrogen bonds

Parallel sheet structure in cyclopropane γ-peptides stabilized by C-H O hydrogen bonds Parallel sheet structure in cyclopropane γ-peptides stabilized by C- hydrogen bonds M. Khurram N. Qureshi and Martin D. Smith* Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge

More information

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph?

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph? 95. Which of the following descries the net ionic rection for the hydrolysis of NH4Cl( s)? A. NH4 ( q) Cl & ( q) NH4Cl( s) B. NH Cl & 4 ( s) NH4 ( q) Cl ( q) C. Cl ( q) H O & 2 ( l) HCl( q) OH ( q) D.

More information

ILLUSTRATING 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 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 information

A Photocleavable Linker for the Chemoselective Functionalization of Biomaterials

A Photocleavable Linker for the Chemoselective Functionalization of Biomaterials Electronic Supplementary Information A otocleavable Linker for the Chemoselective Functionalization of Biomaterials Liz Donovan and Paul A. De Bank* Department of armacy and armacology and Centre for Regenerative

More information

MAT 403 NOTES 4. f + f =

MAT 403 NOTES 4. f + f = MAT 403 NOTES 4 1. Fundmentl Theorem o Clulus We will proo more generl version o the FTC thn the textook. But just like the textook, we strt with the ollowing proposition. Let R[, ] e the set o Riemnn

More information

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article Avilble online www.jopr.om Journl of Chemil nd Phrmeutil Reserh, 2013, 5(12):1283-1288 Reserh Artile ISSN : 0975-7384 CODEN(USA) : JCPRC5 Study on osion resistne of zin lloy oting of mehnil plting by eletrohemil

More information

1.3 SCALARS AND VECTORS

1.3 SCALARS AND VECTORS Bridge Course Phy I PUC 24 1.3 SCLRS ND VECTORS Introdution: Physis is the study of nturl phenomen. The study of ny nturl phenomenon involves mesurements. For exmple, the distne etween the plnet erth nd

More information

INTEGRATION. 1 Integrals of Complex Valued functions of a REAL variable

INTEGRATION. 1 Integrals of Complex Valued functions of a REAL variable INTEGRATION NOTE: These notes re supposed to supplement Chpter 4 of the online textbook. 1 Integrls of Complex Vlued funtions of REAL vrible If I is n intervl in R (for exmple I = [, b] or I = (, b)) nd

More information