Research Article Dual Role of Hydrogen Peroxide in Arabidopsis Guard Cells in Response to Sulfur Dioxide

Size: px
Start display at page:

Download "Research Article Dual Role of Hydrogen Peroxide in Arabidopsis Guard Cells in Response to Sulfur Dioxide"

Transcription

1 Hindwi Pulishing Corportion Advnes in Toxiology, Artile ID 47368, 9 pges Reserh Artile Dul Role of Hydrogen Peroxide in Aridopsis Gurd Cells in Response to Sulfur Dioxide Huiln Yi, 1 Xin Liu, 1,2 Min Yi, 1,3 nd Gng Chen 2 1 Shool of Life Siene, Shnxi University, Tiyun 36, Chin 2 Shnxi Provinil Guoxin Energy Development Group Co., LTD., Tiyun 36, Chin 3 Deprtment of Sttistis, University of Missouri-Columi, Columi, MO 6211, USA Correspondene should e ddressed to Huiln Yi; yihl@sxu.edu.n Reeived 28 April 214; Aepted 8 Septemer 214; Pulished 3 Septemer 214 Ademi Editor: Mugimne Mnjnth Copyright 214 Huiln Yi et l. This is n open ess rtile distriuted under the Cretive Commons Attriution Liense, whih permits unrestrited use, distriution, nd reprodution in ny medium, provided the originl work is properly ited. Sulfur dioxide (SO 2 ) is mjor ir pollutnt nd hs signifint impts on plnt physiology. Plnt n dpt to SO 2 stress y ontrolling stomtl movement, gene expression, nd metoli hnges. Here we show ler evidenes tht SO 2 -triggered hydrogen peroxide (H 2 O 2 ) prodution medited stomtl losure nd ell deth in Aridopsis leves. High levels of SO 2 used irreversile stomtl losure nd deline in gurd ell viility, ut low levels of SO 2 used reversile stomtl losure. Exogenous ntioxidnts sori id (AsA) nd tlse (CAT) or C 2+ ntgonists EGTA nd LCl 3 loked SO 2 -indued stomtl losure nd deline in viility. AsA nd CAT lso loked SO 2 -indued H 2 O 2 nd [C 2+ ] yt elevtion. However, EGTA nd LCl 3 inhiited SO 2 -indued [C 2+ ] yt inrese ut did not suppress SO 2 -indued H 2 O 2 elevtion. These results indite tht H 2 O 2 elevtion triggered stomtl losure nd ell deth vi [C 2+ ] yt signling in SO 2 -stimulted Aridopsis gurd ells. NADPH oxidse inhiitor DPI loked SO 2 -indued ell deth ut not the stomtl losure triggered y low levels of SO 2, inditing tht NADPH oxidsedependent H 2 O 2 prodution plys ritil role in SO 2 toxiity ut is not neessry for SO 2 -indued stomtl losure. Our results suggestthth 2 O 2 prodution nd umultion in SO 2 -stimulted plnts trigger plnt dpttion nd toxiity vi retive oxygen speies mediting C 2+ signling. 1. Introdution Sulfur dioxide (SO 2 ) is hrmful gs tht is emitted lrgely from urning ol, high-sulfur oil, nd fuels. During the pst few dedes, the onentrtion of SO 2 in the tmosphere hs inresed in mny res of the world, espeilly in the developing ountries. High levels of SO 2 n injure mny plnt speies nd vrieties, resulting in photosynthesis deline, growth inhiition, nd even deth [1 4]. Sulfur dioxide enters plnts minly through the open stomt []. One it enters the lef, SO 2 is hydrted to form HSO 3 nd SO 2 3.ThetoxiityofSO 2 is derived from moleulr speies sulfite (SO 2 3 )ndisulfite(hso 3 ) generted fter SO 2 is dissolvedinellulrfluid[6]. Sulfite oxidtion, whih is the detoxifition retion of sulfite to sulfte (SO 2 4 ), leds to the formtion of retive oxygen speies (ROS) in plnt ells [7, 8]. The prodution nd umultion of ROS re one of the key events in plnt response to SO 2 [9 12]. ROS hve een proposed s entrl omponents of plnt response to oth ioti nd ioti stresses. Under suh onditions, ROS my ply two very different roles: exerting dmge or signling the tivtion of defense responses [13, 14]. It hs een reported tht ROS t s signling moleules mediting vriety of physiologil responses, inluding stomtl movement nd gene expression [1 17], lthough they n ttk iomoleules suh s nulei ids, proteins, nd lipids leding to ell dmge nd deth [16, 18, 19]. Results of previous studies hve shown tht plnts n dpt to SO 2 stress y ontrolling stomtl movement nd gene trnsription [11, 12, 2]. Stomtl losure ould protet the leves ginst further entry of the environmentl SO 2, while differentil gene expression ould regulte the metoli routes of plnt ells providing long-term dpttion to environmentl stress. However, up to now, it is not ler if the ROS prodution is losely ssoited with the initil physiologil mehnisms responsile for plnt responses to SO 2 stress.

2 2 Advnes in Toxiology ROS overprodution n trigger plnt dpttion or ell dmge during ioti stress. However, there hs een little overlp etween these two fields of reserh. In the present study, gurd ells of A. thlin leves, whih re welldeveloped model ell system for studying the signl trnsdution in plnt ells [21 23], were employed to investigte theellulrmehnismofplntresponsetoso 2 stress. To the est of our knowledge, this is the first report of H 2 O 2 mediting oth dpttion response (stomtl movement) nd ytotoxiity (ell deth) in plnt response to SO 2 stress. Our results show tht H 2 O 2 elevtion triggered oth stomtl losure nd ell viility loss vi C 2+ signling in SO 2 -treted plnts. 2. Mterils nd Methods 2.1. Plnt Mteril Preprtion. Plnts of Aridopsisthlin (L.) eotype Columi (Col-) were grown in soil (Klsmnn-Deilmnn) in temperture-ontrolled growth rooms t 22 Cwithnvergelightintensityof24μmoL m 1 s 1, 16 h photoperiod per dy, nd 6% reltive humidity. Young fully expnded leves were hrvested from 4- week-old Aridopsis plnts. The xil epidermes were peeled from the underside of eh lef nd ut into smll piees. The isolted epiderml strips were immeditely floted in 1 mm 2-(N-morpholino)ethnesulfoni id (MES; Bio Bsi In.) uffer (1 mm MES-Tris, ph 7., nd mm KCl) Determintion of Stomtl Aperture. The isolted epiderml strips were inuted in 1 mm MES uffer for 2 h, for stomt-opening under ontinuous light of 18 μmol m 2 s 1 t 22 C or for stomt-losuring in the drk, nd then inuted for 2 h in MES uffer ontining ertin mount of SO 2 hydrtes ( mixture of sodium sulfite nd sodium isulfite, 3 : 1 mm/mm, prepred freshly efore use) under ontinuous illumintion of 18 μmol m 2 s 1 t 22 C. Control smples were treted under the sme onditions with 1 mm MES uffer. The isolted epiderml strips were treted with mixture of SO 2 hydrtes nd ertin mount of ntgonists whih inlude NADPH oxidse inhiitor diphenylene iodonium (DPI, Sigm), ntioxidnts tlse (CAT, Sigm), nd sori id (AsA, Sigm) nd C 2+ ntgonists LCl 3 nd ethylene glyol tetreti id (EGTA, Sigm) to exmine the protetive effets. After 2 h of hemil exposure, the epiderml strips were mounted on mirosopy slide, moistened with 1 mm MES uffer, nd overed with slip. Stomtl perture ws mesured y using digitl mirosope mer system (DP72, Olympus) nd n tthed DP2-BSW softwre. At lest three leves nd 3 stomt per lef were mesured in eh tretment nd ll of the experiments were independently repeted t lest three times. Forthereoverygroups,fter2hofhemilexposure,the isolted strips were resuspended in MES uffer for 2 h under ontinuous light followed y stomtl perture mesurement. For time-ourse experiment, the stomtl pertures were exmined every five minutes fter isolted strips were inuted in SO 2 hydrtes Determintion of Cell Viility. Cell viility ws ssessed y using the method of doule stining with fluoresein diette (FDA; Bio Bsi In.) nd propidium iodide (PI; Sigm). After 2 h of hemil exposure, the epiderml strips were simultneously stined with.1 mg L 1 FDA nd 1 μm PI for visulizing ell viility. At lest three leves nd 3 gurd ells per lef were oserved in eh tretment nd ll of the experiments were independently repeted three times Mesurement of Retive Oxygen Speies. Retive oxygen speies in gurd ells of epiderml peels were deteted using 2,7 -dihlorodihydrofluoresein diette (DCFH- DA; Beyotime) ording to the methods desried y Yi et l. [24]. After 2 h of exposure to the hemils, the epiderml strips were inuted in 2 μm DCFH-DA for 3mininthedrk.Themenvlueoffluoreseneintensity, resulting from 6 gurd ells in three independent experiments, represents the intrellulr H 2 O 2 level for eh tretment. 2.. Mesurement of Intrellulr C 2+. The onentrtion of intrellulr C 2+ ([C 2+ ] yt ) ws mesured using fluo-3 etomethoxyester (Fluo-3 AM; Beyotime) s desried in our previous report [24]. The verge fluoresene intensity of Fluo-3 AM otined from three different leves nd 2 gurd ells represents the [C 2+ ] yt level for eh tretment. All experiments were independently repeted three times Sttistil Anlysis. All vlues of men nd stndrd devition (SD) were otined from three independent experiments. Anlysis of vrine (ANOVA) nd Dunnett s t-test were used to determine the signifint differenes mong the ontrol nd series of tretment groups. 3. Results 3.1. SO 2 -Evoked H 2 O 2 Prodution Is Involved in the Regultion of Stomtl Movement. As shown in Figure 1, SO 2 hydrtes promote stomtl losure nd inhiit light-promoted stomtl opening in Aridopsis leves. The width of stomtl perture deresed in onentrtion-dependent mnner ndshowedsignifintdereseftertheisoltedstrips were exposed for 2 h to SO 2 hydrtes t onentrtions of 1 to μm. However, stomtl losure evoked y low SO 2 onentrtions (elow 2 μm)ould e reversed ompletely fter SO 2 removl; otherwise the deline of stomtl perture in high SO 2 onentrtion ( μm) group ould e prtly reversed. Time ourse nlysis of stomtl movement showed tht the dimeter of the stomtl perture deresed mrkedly within the first 3 minutes of exposure to 1 μmso 2 hydrtes nd ontinued to deline t slower rte in the remining 9 minutes of SO 2 exposure (Figure 1()). SO 2 -indued stomtl losure ws ssoited with n elevted H 2 O 2 level in Aridopsis gurd ells. Exposure to SO 2 hydrtes not only used smller stomtl pertures

3 Advnes in Toxiology Stomtl perture (μm) Stomtl perture (μm) Conentrtions of SO 2 hydrtes (μm) Conentrtions of SO 2 hydrtes (μm) Sulfur dioxide tretment Reovery fter sulfur dioxide tretment Pretretment in the drk () () 6 Stomtl perture (μm) Time ourse from 1 μm SO 2 hydrtes (min) () Figure 1: Promotion of stomtl losure y SO 2 nd its reversiility upon SO 2 removl. Stomt of Aridopsis lef epidermis were llowed to open in light [() nd ()] or to lose in the drk () for 2 h nd then were inuted for 2 h in SO 2 hydrtes., A signifint differene t P <. from ontrol., A signifint differene t P <. etween SO 2 tretment nd its reovery group. (Figure 1) ut lso evoked inresed H 2 O 2 level (1.2- to 1.7-fold) in Aridopsis gurd ells (Figure 2). When H 2 O 2 elevtion ws loked y exogenous H 2 O 2 svengers CAT or AsA, SO 2 -indued stomtl losure ws effiiently reversed (Figure 2). These results indite tht H 2 O 2 prodution in SO 2 -stimulted gurd ells medites stomtl movement upon SO 2 stress SO 2 -Evoked H 2 O 2 Elevtion Triggered Cell Deth. To investigte the role of H 2 O 2 in irreversile stomtl losure in response to SO 2, we detet the viility of Aridopsis gurd ells y doule stining with fluoresein diette (FDA) nd propidium iodide (PI). The results showed tht SO 2 indued gurd ell deth in onentrtion-dependent mnner (Figure 3). Cell deth rehed 24% in 6 mm SO 2 hydrtes tretment group, ut no ovious ell deth ould e oserved in 1 to 2 μmso 2 hydrtes tretment groups. The H 2 O 2 level of gurd ells exposed to 2 to 6 mm SO 2 hydrtes showed sttistilly signifint inrese (1.9- to 2.3-fold), whih is higher thn those exposed to 1 to μm SO 2 hydrtes. Moreover, exposure to SO 2 hydrtes simultneously with 2 U ml 1 CAT or.1 mm AsA, SO 2 - indued ell deth ws effiiently loked, ssoited with signifint derese in H 2 O 2 level of gurd ells (Figure 3). These results lerly demonstrte tht n elevted H 2 O 2 level n trigger gurd ell deth leding to stomtl dysfuntion nd irreversile stomtl losure in SO 2 -treted Aridopsis leves. To further onfirm the role of H 2 O 2 in SO 2 toxiity, we investigte the protetive effets of CAT on ell viility

4 4 Advnes in Toxiology A B C D E F Stomtl perture (μm) A B C D E F Reltive intensity of DCFH-DA fluoresene (%) A B C D E F (A) (B) (C) Control 2 μm SO 2 hydrtes 2 μm SO 2 hydrtes +1mM AsA (D) 2 μm SO 2 hydrtes + 2 U ml 1 CAT (E) 2 μm SO 2 hydrtes +.1 mm EGTA (F) 2 μm SO 2 hydrtes +.1 mm LCl 3 Figure 2: Effets of ntioxidnts nd lium ntgonists on SO 2 -indued stomtl losure nd H 2 O 2 elevtion in Aridopsis gurd ells. Different supersript letters indite signifint differenes (P <.1). The sme letters indite no signifint differene. The green fluoresene (DCFH-DA) of gurd ells indites H 2 O 2 ontent. in SO 2 -treted smples. The results showed tht pplition of 1 U ml 1 CAT ould ompletely lok the ell deth evoked y 2 mm nd lower onentrtions of SO 2 hydrtes, ut the ytotoxiity evoked y 6 mm SO 2 hydrtes ws only prtly loked (Figure 4). These results lerly demonstrte tht H 2 O 2 prodution, whih my work together with other moleules, is enough to trigger SO 2 toxiity H 2 O 2 Ation Is Dependent on Its Conentrtions nd Sptil Genertion Ptterns. As shown ove, SO 2 n use stomtl losing nd deline in ell viility, whih is dependent on SO 2 onentrtions nd H 2 O 2 level. However, there ws no ler dividing line etween sfe level nd toxi level. In order to understnd wht onstitutes sfe level, n inhiitor of NADPH oxidse ws used to detet its inhiitory effets. The results show tht pplition of 2 μm NADPH oxidse inhiitor DPI for 2 h mrkedly loked ell dethevokedy2mmso 2 hydrtes. But 2 μm DPIdid not inhiit stomtl losing evoked y 1 μm SO 2 hydrtes (Figure 4). These findings indite tht SO 2 -triggered stomtl losing n e driven y NADPH oxidse-dependent nd -independent H 2 O 2 genertion, ut NADPH oxidsedependent H 2 O 2 genertion is involved in SO 2 -used ytotoxiity H 2 O 2 Ats Upstrem of C 2+ Signling in Response to SO 2 Stress. SO 2 exposure enhned the fluoresene intensity of Fluo-3 AM (C 2+ inditor) in Aridopsis gurd ells. The reltive fluoresene intensity of Fluo-3 AM, resulting from more thn 6 gurd ells per tretment group in three independent experiments, inresed oviously in gurd ells exposed to 1 μmto6mmso 2 hydrtes for 2 h ut deresed mrkedly when isolted strips were treted simultneously with SO 2 hydrtes nd.1 mm lium hnnel loker LCl 3

5 Advnes in Toxiology 3 e 2 Cell deth rtes (%) d Conentrtions of SO 2 hydrtes (mm) Cell deth rtes (%) A B E F G H Reltive intensity of DCFH-DA fluoresene (%) A B H J (A) (B ) (E) (F) Control 6 mm SO 2 hydrtes.1 mm AsA 6 mm SO 2 hydrtes +.1 mm AsA (G) 2 U ml 1 CAT (H) 6 mm SO 2 hydrtes + 2 U ml 1 CAT (J) 6 mm SO 2 hydrtes +.1 mm LCl 3 Figure 3: Sulfur dioxide used viility deline ssoited with H 2 O 2 elevtion in Aridopsis gurd ells. Different supersript letters indite signifint differenes (P <.1). The sme letters indite no signifint differene. (Figure ). These results indite tht SO 2 exposure evokes n elevtion of [C 2+ ] yt level, nd C 2+ influx through C 2+ hnnels in the plsm memrne results in [C 2+ ] yt elevtion. AsshowninFigures2 nd, the ddition of LCl 3 nd lium heltor EGTA to SO 2 hydrtes loked [C 2+ ] yt elevtion, stomtl losure, nd ell deth evoked y SO 2. Stomtl losure nd ell deth ourred with inresed [C 2+ ] yt in SO 2 -treted smples, ut oth of them were signifintly suppressed y.1 mm LCl 3 or EGTA. These results indite tht elevted [C 2+ ] yt level is n importnt stimulus driving stomtl movement nd ytotoxiity. To understnd the pthwys to plnt responses, we study the signling pthwys in Aridopsis gurd ells. As shown in Figures 2, 3, nd, oth ntioxidnts AsA nd CAT nd C 2+ ntgonists LCl 3 nd EGTA n suppress SO 2 -indued stomtl losure nd ell deth, ut pplition of H 2 O 2 svenger CAT (2 U ml 1 ) deresed [C 2+ ] yt elevtion evoked y SO 2, wheres pplition of C 2+ hnnel inhiitor LCl 3 (.1 mm) did not ffet H 2 O 2 elevtion evoked y SO 2. These results onfirm the involvement of C 2+ downstrem of H 2 O 2 prodution, inditing tht H 2 O 2 triggers stomtl movement nd ell deth vi C 2+ signling in plnt response to SO 2 stress. 4. Disussion Plnt ould dpt to environmentl hllenges through vrious mens. Our reent findings showed tht SO 2 fumigtion used n inresed ROS prodution ompnied with differentil gene expression nd stomtl losure in Aridopsis plnts [12, 2]. The results of the present study

6 6 Advnes in Toxiology 3 6 Cell deth rtes (%) d Stomtl perture (μm) A B C B E M A D F (A) (B) (C) (B ) Control 2 mm SO 2 hydrtes 2 mm SO 2 hydrtes + 1 U ml 1 CAT 6 mm SO 2 hydrtes (E) (M) (D) (F) 6 mm SO 2 hydrtes + 1 U ml 1 CAT 6 mm SO 2 hydrtes +2μM DPI 1 μm SO 2 hydrtes 1 μm SO 2 hydrtes +2μM DPI Figure 4: Hydrogen peroxide svenger nd NADPH oxidse inhiitor DPI loked SO 2 -indued ell deth, ut DPI nnot lok SO 2 - indued stomtl losure. Different supersript letters indite signifint differene t P <.1. The sme letters indite no signifint differene. show the evidenes tht H 2 O 2 ts s n importnt signling moleule triggering stomtl movement nd ell deth in plnt response to SO 2. SO 2 -used ell viility deline ould interfere with the norml funtion of stomt to further ffet plnt physiology under environmentl stress. However,theourreneofSO 2 -used gurd ell deth ws ssoited with deresed stomtl perture, suggesting the existene of omplex signling network in plnt responses to environmentl stress. Environmentl hllenges inluding ioti nd ioti stresses ould indue ROS prodution in plnt ells [2]. It hs een doumented tht ROS ply n importnt role in signl trnsdution of stomtl movement regultion nd gene expression tivtion in plnt response to environmentl stresses [26 29]. ROS, whih n e used s rpid long-distne utopropgting signls tht re trnsferred throughout the plnt in response to different environmentl onditions, re widely onsidered to e n importnt plyer in gurd ell signling [26, 3]. The dt presented ove indite requirement for H 2 O 2 prodution in plnt response to SO 2 stress. First, SO 2 indues stomtl losure nd ell dethssoitedwithninresedintrellulrh 2 O 2 level (Figures 2 nd 3). Seond, two types of H 2 O 2 svengers CAT nd AsA ould lok SO 2 -evoked stomtl losure nd ell deth; in prtiulr, the effets of SO 2 t low onentrtions ould e ompletely reversed y CAT (Figures 2 nd 4). Third, H 2 O 2 svenger loks the SO 2 -indued inrese in intrellulr C 2+ required for stomtl losure nd toxiity (Figure ). Our study, vlidting the strong positive orreltion etween intrellulr H 2 O 2 level nd stomtl losure/ell deth, demonstrtes key role of H 2 O 2 s trigger of stomtl losure nd/or gurd ell deth in response to SO 2. Sulfur dioxide inhiited light-promoted stomtl opening nd promoted stomtl losure leding to the smller size of Aridopsis stomt. High onentrtions of SO 2 lso used viility loss of Aridopsis gurd ells. The time ourse experiments show tht H 2 O 2 level of gurd ells inresed grdully during SO 2 exposure (dte not shown); therefore, n inresed H 2 O 2 level in SO 2 -stimulted Aridopsis ells might trigger stomtl losure firstly nd then ell viility loss through ROS-medited ell deth pthwy s shown in V. f ells [24]orthroughthegrdul umultion of free rdil dmge to iomoleules during SO 2 exposure. There re two primry soures of H 2 O 2 in gurd ells: hloroplsts nd plsm memrne-ssoited NADPH oxidse [22, 31, 32]. The results of the time ourse experimentswithsingleellssysusingthefluoresentproe DCFH-DA showed tht H 2 O 2 genertion ws dependent on SO 2 onentrtion nd tht the inrese in fluoresene intensity of hloroplsts ourred signifintly erlier thn within the other regions of gurd ells (dte not shown), demonstrting n enhned H 2 O 2 prodution in hloroplsts of gurd ells. NADPH oxidse in plsm memrne ontriutes to O 2 genertion nd ROS elevtion in plnt responses to ioti stresses [33]. Applition of DPI, whih is widely epted s reltively speifi diret inhiitor of NADPH oxidse, mrkedly loked SO 2 -indued ell deth ut nnot suppress stomtl losure evoked y low onentrtions of SO 2.ThesefindingsinditethtH 2 O 2 - medited stomtl losure in Aridopsis leves exposed to low onentrtions of SO 2 is not dependent on the tivity of plsm memrne NADPH oxidse, ut ell dethevokedyhighonentrtionsofso 2 is NADPH oxidse-dependent.

7 Advnes in Toxiology Cell deth rtes (%) A B I J K N 2 3 Reltive intensity of fluo-3 AM fluoresene (%) Reltive intensity of fluo-3 AM fluoresene (%) A B C D E F A B H J (A) Control (B) 2 μm SO 2 hydrtes (C) 2 μm SO 2 hydrtes +1mM AsA (D) 2 μm SO 2 hydrtes + 2 U ml 1 CAT (E) (F) (B ) (I) 2 μm SO 2 hydrtes +.1 mm EGTA (J) 6 mm SO 2 hydrtes +.1 mm LCl 3 2 μm SO 2 hydrtes +.1 mm LCl 3 6 mm SO 2 hydrtes.1 mm LCl 3 (K) (N) (H).1 mm EGTA 6 mm SO 2 hydrtes +.1 mm EGTA 6 mm SO 2 hydrtes + 2 U ml 1 CAT Figure : Effets of ntioxidnts nd C 2+ ntgonists on SO 2 -indued C 2+ elevtion nd ell deth in Aridopsis gurd ells. Different supersript letters indite signifint differenes (P <.1). The sme letters indite no signifint differene. SO 2 exposureusedstomtllosurendgurdell deth ssoited with [C 2+ ] yt elevtion, wheres pplition of either C 2+ heltor EGTA or C 2+ hnnel inhiitor LCl 3 loking SO 2 -evoked [C 2+ ] yt elevtion, stomtl losure nd ell deth evoked y SO 2 were effetively loked. These results demonstrte tht hnnel-medited C 2+ influx ross the plsm memrne ontriutes to the elevtion of [C 2+ ] yt nd susequent stomtl losure nd ell deth in SO 2 -stimulted gurd ells. However, it is not ler how C 2+ signling reognizes the different situtions of ells to medite pproprite proesses suh s stomtl losure nd ell deth. It hs een found tht H 2 O 2 ould tivte plsm memrne C 2+ hnnels leding to [C 2+ ] yt inrese in plnt ells [34 36]. Therefore, H 2 O 2 tivtion of plsm memrne C 2+ hnnelsmyeentrlstepinso 2 - indued stomtl losure nd/or ell deth. The results of our present study lso showed tht pplition of ntioxidnt CAT nd AsA signifintly deresed SO 2 -evoked [C 2+ ] yt elevtion, ut pplition of C 2+ hnnel loker LCl 3 did not ffet SO 2 -evoked H 2 O 2 inrese, inditing tht H 2 O 2 ts upstrem of C 2+ signling in SO 2 - indued stomtl losure nd/or ell deth. These oservtions were onsistent with other previous reports tht [C 2+ ] yt inrese ws linked to H 2 O 2 prodution nd wsinvolvedinros-meditedstomtllosure/elldeth [37 39]. Therefore, H 2 O 2 elevtion nd susequent tivtion of C 2+ hnnels re events ourring in SO 2 -indued stomtl losure/ell deth. C 2+ influx from extrellulr

8 8 Advnes in Toxiology region results in [C 2+ ] yt inrese, nd then [C 2+ ] yt elevtion medites susequent stomtl losure/ell deth. These results suggested tht H 2 O 2 medites SO 2 -indued stomtl movement/ytotoxiity y trgeting C 2+ hnnels in the plsm memrne. Briefly, environmentl SO 2 hs remrkle effet on the size of the stomtl perture. Exposure to SO 2 indued the overprodution of H 2 O 2 in gurd ells, s shown in other plnt ells exposed to environmentl hllenges [4, 41]. Elevted H 2 O 2 ts in onjuntion with other ftors to tivte stomtl movement nd ell deth under SO 2 stress. Gurd ells re well-developed model system for hrterizing erly signl trnsdution mehnisms in plnts. In this study, the dul role of H 2 O 2 in plnt ells in response to ir pollutnt ws lerly displyed in Aridopsis gurd ells, whih dditionlly roden the role of stomtl gurd ells in ytotoxiity study. Our results suggest tht gurd ells re vlule model system for the study of ytotoxiity in plnt ells.. Conlusion Sulfur dioxide exposure used n elevted H 2 O 2 level in Aridopsis gurd ells. H 2 O 2 elevtion triggered y SO 2 medited oth stomtl losure nd ell deth vi C 2+ signling. Intrellulr C 2+ inrese is neessry for stomtl losure nd ell deth in Aridopsis gurd ells in response to SO 2.H 2 O 2 prodution y NADPH oxidse plys ritil role in SO 2 toxiity; however NADPH oxidse tivtion is suffiient ut not neessry for SO 2 -triggered stomtl losure. Both stomtl losing nd stomtl opening inhiition evoked y SO 2 led to deline in stomtl perture, proteting the lef ginst further entry of the pollutnt ut lso urtiling photosynthesis. Cell deth evoked y high onentrtions of SO 2 indited the ytotoxiity of SO 2, ut might provide pproprite protetion y reduing ROS prodution in Aridopsis plnts. Conflit of Interests The uthors delre tht there is no onflit of interests regrding the pulition of this pper. Aknowledgments This study ws supported y the Ntionl Nturl Siene Foundtion of Chin (Grnt nos , , nd ),ReserhFundfortheDotorlProgrmofHigher Edution of Chin (Grnt no ), nd Shnxi Sholrship Counil of Chin (Grnt no. 2922). Referenes [1] N. M. Drrll, The effet of ir pollutnts on physiologil proesses in plnts, Plnt, Cell & Environment, vol.12,no.1, pp. 1 3, [2] T. Hogetsu nd M. Shishikur, Effets of sulfur dioxide nd ozone on intt leves nd isolted mesophyll ells of groundnut plnts (Arhis hypoge L.), Journl of Plnt Reserh,vol.17, no.3,pp ,1994. [3] M. Noji, M. Sito, M. Nkmur, M. Aono, H. Sji, nd K. Sito, Cysteine synthse overexpression in too onfers tolerne to sulfur-ontining environmentl pollutnts, Plnt Physiology,vol.126,no.3,pp ,21. [4] R. Rkwl, G. K. Agrwl, A. Kuo et l., Defense/stress responses eliited in rie seedlings exposed to the gseous ir pollutnt sulfur dioxide, Environmentl nd Experimentl Botny,vol.49,no.3,pp ,23. [] H. Rennenerg nd C. Hershh, Responses of plnts to tmospheri sulphur, in Plnt Response to Air Pollution, M. Yunus nd M. Il, Eds., pp , John Wiley & Sons, Chihester, UK, [6] H. Pfnz nd U. Heer, Buffer pities of leves, lef ells, nd lef ell orgnelles in reltion to fluxes of potentilly idi gses, Plnt Physiology, vol. 81, pp , [7] K. Asd, Formtion nd svenging of superoxides in hloroplsts, with reltion to injury y sulfur dioxide, Reserh Report of the Ntionl Institute for Environmentl Studies, vol. 11, pp , 198. [8] N. R. Mdmnhi nd R. G. Alsher, Metoli ses for differenes in sensitivity of two pe ultivrs to sulfur dioxide, Plnt Physiology,vol.97,no.1,pp.88 93,1991. [9] K. Tnk, N. Kondo, nd K. Sughr, Aumultion of hydrogen peroxide in hloroplsts of SO 2 -fumigted spinh leves, Plnt nd Cell Physiology, vol. 23, no. 6, pp , [1] R. Hänsh nd R. R. Mendel, Sulfite oxidtion in plnt peroxisomes, Photosynthesis Reserh, vol.86,no.3,pp , 2. [11] E. Girud, A. Ivnov, C. S. Gordon, J. Wheln, nd M. J. Considine, Sulphur dioxide evokes lrge sle reprogrmming of the grpe erry trnsriptome ssoited with oxidtive signlling nd ioti defene responses, Plnt, Cell nd Environment,vol.3,no.2,pp.4 417,212. [12] L. Li nd H. Yi, Differentil expression of Aridopsis defenserelted genes in response to sulfur dioxide, Chemosphere, vol. 87,no.7,pp ,212. [13] J. Dt, S. Vndeneele, E. Vrnová, M. vn Montgu, D. Inzé, nd F. vn Breusegem, Dul tion of the tive oxygen speies during plnt stress responses, Cellulr nd Moleulr Life Sienes,vol.7,no.,pp ,2. [14] P.Shrm,A.B.Jh,R.S.Duey,ndM.Pessrkli, Retive Oxygen speies, oxidtive dmge, nd ntioxidtive defense mehnism in plnts under stressful onditions, Journl of Botny,vol.212,ArtileID21737,26pges,212. [1] S. Neill, R. Desikn, nd J. Hnok, Hydrogen peroxide signlling, Current Opinion in Plnt Biology, vol.,no.,pp , 22. [16] C. Lloi, K. Apel, nd A. Dnon, Retive oxygen signlling: the ltest news, Current Opinion in Plnt Biology, vol.7,no.3, pp , 24. [17]H.B.Sho,L.Y.Chu,Z.H.Lu,ndC.M.Kng, Primry ntioxidnt free rdil svenging nd redox signling pthwys in higher plnt ells, Interntionl Journl of Biologil Sienes,vol.4,no.1,pp.8 14,28. [18] R. Mittler, Oxidtive stress, ntioxidnts nd stress tolerne, Trends in Plnt Siene,vol.7,no.9,pp.4 41,22. [19] S.-H. Hung, C.-W. Yu, nd C. H. Lin, Hydrogen peroxide funtionssstresssignlinplnts, Botnil Bulletin of Ademi Sini,vol.46,no.1,pp.1 1,2.

9 Advnes in Toxiology 9 [2] L. Li, H. Yi, L. Wng, nd X. Li, Effets of sulfur dioxide on the morphologil nd physiologil iohemil prmeters in Aridopsis thlin plnts, Journl of Agro-Environment Siene,vol.27,pp.2 29,28. [21] A. M. Hetherington, Gurd ell signling, Cell,vol.17,no.6, pp , 21. [22] X.Zhng,L.Zhng,F.C.Dong,J.F.Go,D.W.Glrith,nd C.-P. Song, Hydrogen peroxide is involved in sisi idindued stomtl losure in Vii f, Plnt Physiology, vol. 126, no. 4, pp , 21. [23] J. I. Shroeder, G. J. Allen, V. Hugouvieux, J. M. Kwk, nd D. Wner, Gurd ell signl trnsdution, Annul Review of Plnt Biology,vol.2,pp ,21. [24]H.Yi,J.Yin,X.Liu,X.Jing,S.Fn,ndH.Zhng, Sulfur dioxide indued progrmmed ell deth in Vii gurd ells, Eotoxiology nd Environmentl Sfety, vol.78,pp , 212. [2] K. Apel nd H. Hirt, Retive oxygen speies: metolism, oxidtive stress, nd signl trnsdution, Annul Review of Plnt Biology,vol.,pp ,24. [26] R. Desikn, M.-K. Cheung, A. Clrke et l., Hydrogen peroxide is ommon signl for drkness- nd ABA-indued stomtl losure in Pisum stivum, Funtionl Plnt Biology,vol.31,no. 9, pp , 24. [27] N. Suzuki, S. Koussevitzky, R. Mittler, nd G. Miller, ROS nd redox signlling in the response of plnts to ioti stress, Plnt, Cell nd Environment,vol.3,no.2,pp.29 27,212. [28] T. Fuko nd J. Biley-Serres, Plnt responses to hypoxi is survivl lning t? Trends in Plnt Siene, vol.9,no.9, pp ,24. [29] R. Mittler, S. Vnderuwer, M. Gollery, nd F. vn Breusegem, Retiveoxygengenenetworkofplnts, Trends in Plnt Siene, vol. 9, no. 1, pp , 24. [3] Y.Song,Y.Mio,ndC.-P.Song, Behindthesenes:theroles of retive oxygen speies in gurd ells, New Phytologist, vol. 21, no. 4, pp , 214. [31] Z.-M. Pel, Y. Murt, G. Benning et l., Clium hnnels tivted y hydrogen peroxide medite sisi id signlling in gurd ells, Nture, vol. 46, no. 6797, pp , 2. [32] V. D. Petrov nd F. vn Breusegem, Hydrogen peroxide entrl hu for informtion flow in plnt ells, AoB Plnts,vol. 12, no. 1, Artile ID pls14, 212. [33] M. A. Torres nd J. L. Dngl, Funtions of the respirtory urst oxidse in ioti intertions, ioti stress nd development, CurrentOpinioninPlntBiology,vol.8,no.4,pp ,2. [34]R.MhlingmndN.Fedoroff, Stressresponse,elldeth nd signlling: the mny fes of retive oxygen speies, Physiologi Plntrum,vol.119,no.1,pp.6 68,23. [3] I. C. Mori nd J. I. Shroeder, Retive oxygen speies tivtion of plnt C 2+ hnnels. A signling mehnism in polr growth, hormone trnsdution, stress signling, nd hypothetilly mehnotrnsdution, Plnt Physiology, vol. 13, no. 2, pp , 24. [36] D. B. Kiselevsky, Y. E. Kuznetsov, L. A. Vsil ev et l., Effet of C 2+ on progrmmed deth of gurd nd epiderml ells of pe leves, Biohemistry,vol.7,no.,pp ,21. [37] R. Errkhi, A. Duphin, P. Meimoun et l., An erly C 2+ influx is prerequisite to thxtomin A-indued ell deth in Aridopsis thlin ells, Journl of Experimentl Botny, vol. 9, no. 1, pp , 28. [38] S. Orrenius, B. Zhivotovsky, nd P. Nioter, Regultion of ell deth: the lium-poptosis link, Nture Reviews Moleulr Cell Biology,vol.4,no.7,pp.2 6,23. [39] F. Vn Breusegem nd J. F. Dt, Retive oxygen speies in plnt ell deth, Plnt Physiology, vol. 141, no. 2, pp , 26. [4] M. C. de Pinto, V. Loto, nd L. de Gr, Redox regultion in plnt progrmmed ell deth, Plnt, Cell nd Environment,vol. 3,no.2,pp ,212. [41] T. Pfnnshmidt, K. Bräutigm, R. Wgner et l., Potentil regultion of gene expression in photosyntheti ells y redox nd energy stte: pprohes towrds etter understnding, Annls of Botny,vol.13,no.4,pp.99 67,29.

10 Journl of Tropil Mediine Hindwi Pulishing Corportion The Sientifi World Journl Sientifi Hindwi Pulishing Corportion Hindwi Pulishing Corportion Autoimmune Diseses Hindwi Pulishing Corportion Interntionl Journl of Antiiotis Journl of Anesthesiology Reserh nd Prtie Toxins Hindwi Pulishing Corportion Hindwi Pulishing Corportion Hindwi Pulishing Corportion Sumit your mnusripts t Advnes in Phrmologil Sienes Hindwi Pulishing Corportion Journl of Toxiology Hindwi Pulishing Corportion MEDIATORS of INFLAMMATION Emergeny Mediine Interntionl Hindwi Pulishing Corportion Pin Reserh nd Tretment Hindwi Pulishing Corportion Stroke Reserh nd Tretment Journl of Hindwi Pulishing Corportion Addition Hindwi Pulishing Corportion Hindwi Pulishing Corportion Journl of Vines BioMed Reserh Interntionl Hindwi Pulishing Corportion Journl of Hindwi Pulishing Corportion Journl of Interntionl Journl of Phrmeutis Drug Delivery Mediinl Chemistry Hindwi Pulishing Corportion Hindwi Pulishing Corportion Hindwi Pulishing Corportion

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

Effects of Exogenous Melatonin on Photosynthetic Characteristics of. Lettuce Seedlings under NaCl Stress

Effects of Exogenous Melatonin on Photosynthetic Characteristics of. Lettuce Seedlings under NaCl Stress Interntionl Conferene on Energy nd Environmentl Protetion (ICEEP 16) Effets of Exogenous Meltonin on Photosyntheti Chrteristis of Lettue Seedlings under NCl Stress Zesheng Yn1,,Mi Li1, ndyi Tng,* 1 College

More information

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Effets of Applying Aumultor Strw in Soil on Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris under Cdmium Stress Jin Wng1,,

More information

Applying Hyperaccumulator Straw in Cd-Contaminated Soil Enhances Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris

Applying Hyperaccumulator Straw in Cd-Contaminated Soil Enhances Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Applying Hyperumultor Strw in Cd-Contminted Soil Enhnes Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris Jin Wng1,, Keng

More information

dsrna GFP 0 Ca 0 Ca 0 Ca TG Iono Time (s)

dsrna GFP 0 Ca 0 Ca 0 Ca TG Iono Time (s) Rtio (FL1/FL3) MFI dsrna GFP C dsrna dori C 1 2 1 2 Rtio (FL1/FL3) MFI C 1 2 Rtio (FL1/FL3) MFI C 1 2 C 1 2 C 1 2 Supplementry Figure 1. RNAi-medited depletion of dori hs no effet on the filling stte of

More 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

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

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

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

ANALYSIS AND MODELLING OF RAINFALL EVENTS

ANALYSIS 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 information

Effects of Exogenous Nitric Oxide on Photosynthesis, Antioxidant Capacity and Proline Accumulation in Wheat Seedlings Subjected to Osmotic Stress

Effects of Exogenous Nitric Oxide on Photosynthesis, Antioxidant Capacity and Proline Accumulation in Wheat Seedlings Subjected to Osmotic Stress World Journl of Agriulturl Sienes (3): 3733, ISSN 737 IDOSI Pulitions, Effets of Exogenous Nitri Oxide on Photosynthesis, Antioxidnt Cpity nd Proline Aumultion in Whet Seedlings Sujeted to Osmoti Stress,3

More information

supplementary information

supplementary 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 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

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

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

Electronic Supplementary Information (ESI) for:

Electronic Supplementary Information (ESI) for: Eletroni Supplementry Mteril (ESI) for RSC Advnes. This journl is The Royl Soiety of Chemistry 2015 Eletroni Supplementry Informtion (ESI) for: Novel physio-hemil mehnism of the mutgeni tutomeristion of

More information

Multiple stressor effects of ionising (gamma) radiation and non-ionising (UV) radiation in duckweed (Lemna minor)

Multiple stressor effects of ionising (gamma) radiation and non-ionising (UV) radiation in duckweed (Lemna minor) Multiple stressor effets of ionising (gmm) rdition nd non-ionising (UV) rdition in dukweed (Lemn minor) Li Xie 1,2,3, You Song 1,3, Knut Asjørn Solhug 2,3, Ole Christin Lind 2,3, Brit Slu 2,3, Bjørn Johnsen

More information

SUPPLEMENTARY INFORMATION. For

SUPPLEMENTARY INFORMATION. For Eletroni Supplementry Mteril (ESI) for Journl of Mterils Chemistry B. This journl is The Royl Soiety of Chemistry 217 SUPPLEMETARY IFRMATI For Phyoynin-bsed nnorrier s new nnopltform for effiient overoming

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

Identification of an OPR3-independent pathway for jasmonate biosynthesis. Department of Plant Molecular Genetics, National Centre for Biotechnology,

Identification of an OPR3-independent pathway for jasmonate biosynthesis. Department of Plant Molecular Genetics, National Centre for Biotechnology, Supplementry Informtion Identifition of n OPR3-independent pthwy for jsmonte iosynthesis Andre Chini 1, Isel Monte 1, Angel M. Zmrreño 2, Mts Hmerg 3, Steve Lssueur 4, Philippe Reymond 4, Slly Weiss 5,

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

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

Engr354: Digital Logic Circuits

Engr354: Digital Logic Circuits Engr354: Digitl Logi Ciruits Chpter 4: Logi Optimiztion Curtis Nelson Logi Optimiztion In hpter 4 you will lern out: Synthesis of logi funtions; Anlysis of logi iruits; Tehniques for deriving minimum-ost

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

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue TITLE: OBJECTIVE: AUTHOR: SPONSORS: Effets of Drought on the Performne of Two Hyrid Bluegrsses, Kentuky Bluegrss nd Tll Fesue Evlute the effets of drought on the visul qulity nd photosynthesis in two hyrid

More information

Math 32B Discussion Session Week 8 Notes February 28 and March 2, f(b) f(a) = f (t)dt (1)

Math 32B Discussion Session Week 8 Notes February 28 and March 2, f(b) f(a) = f (t)dt (1) Green s Theorem Mth 3B isussion Session Week 8 Notes Februry 8 nd Mrh, 7 Very shortly fter you lerned how to integrte single-vrible funtions, you lerned the Fundmentl Theorem of lulus the wy most integrtion

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

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

TIME AND STATE IN DISTRIBUTED SYSTEMS

TIME AND STATE IN DISTRIBUTED SYSTEMS Distriuted Systems Fö 5-1 Distriuted Systems Fö 5-2 TIME ND STTE IN DISTRIUTED SYSTEMS 1. Time in Distriuted Systems Time in Distriuted Systems euse eh mhine in distriuted system hs its own lok there is

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

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

#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

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

April 8, 2017 Math 9. Geometry. Solving vector problems. Problem. Prove that if vectors and satisfy, then.

April 8, 2017 Math 9. Geometry. Solving vector problems. Problem. Prove that if vectors and satisfy, then. pril 8, 2017 Mth 9 Geometry Solving vetor prolems Prolem Prove tht if vetors nd stisfy, then Solution 1 onsider the vetor ddition prllelogrm shown in the Figure Sine its digonls hve equl length,, the prllelogrm

More information

Hyers-Ulam stability of Pielou logistic difference equation

Hyers-Ulam stability of Pielou logistic difference equation vilble online t wwwisr-publitionsom/jns J Nonliner Si ppl, 0 (207, 35 322 Reserh rtile Journl Homepge: wwwtjnsom - wwwisr-publitionsom/jns Hyers-Ulm stbility of Pielou logisti differene eqution Soon-Mo

More information

THE ANALYSIS AND CALCULATION OF ELECTROMAGNETIC FIELD AROUND OVERHEAD POWER LINE HongWang Yang

THE ANALYSIS AND CALCULATION OF ELECTROMAGNETIC FIELD AROUND OVERHEAD POWER LINE HongWang Yang 5th Interntionl Conferene on Advned Mterils nd Computer Siene (ICAMCS 6) THE ANALYSIS AN CALCULATION OF ELECTROMAGNETIC FIEL AROUN OVERHEA POWER LINE HongWng Yng eprtment of eletril engineering, North

More information

For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then

For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then Slrs-7.2-ADV-.7 Improper Definite Integrls 27.. D.dox Pge of Improper Definite Integrls Before we strt the min topi we present relevnt lger nd it review. See Appendix J for more lger review. Inequlities:

More information

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem. 27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we

More 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

(h+ ) = 0, (3.1) s = s 0, (3.2)

(h+ ) = 0, (3.1) s = s 0, (3.2) Chpter 3 Nozzle Flow Qusistedy idel gs flow in pipes For the lrge vlues of the Reynolds number typilly found in nozzles, the flow is idel. For stedy opertion with negligible body fores the energy nd momentum

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

Finite State Automata and Determinisation

Finite State Automata and Determinisation Finite Stte Automt nd Deterministion Tim Dworn Jnury, 2016 Lnguges fs nf re df Deterministion 2 Outline 1 Lnguges 2 Finite Stte Automt (fs) 3 Non-deterministi Finite Stte Automt (nf) 4 Regulr Expressions

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

GM1 Consolidation Worksheet

GM1 Consolidation Worksheet Cmridge Essentils Mthemtis Core 8 GM1 Consolidtion Worksheet GM1 Consolidtion Worksheet 1 Clulte the size of eh ngle mrked y letter. Give resons for your nswers. or exmple, ngles on stright line dd up

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

University of Sioux Falls. MAT204/205 Calculus I/II

University 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 information

Lecture 6: Coding theory

Lecture 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 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

Effect of resource supply on interactions between foliar endophytic and root mycorrhizal fungi in perennial ryegrass

Effect of resource supply on interactions between foliar endophytic and root mycorrhizal fungi in perennial ryegrass 135 Effet of resoure supply on intertions etween folir endophyti nd root myorrhizl fungi in perennil ryegrss Q. LIU 1,. J. PRSONS 1, H. XUE 1, J.. NEWMN 2 nd S. RSMUSSEN 1 1 greserh, P.B. 118, Plmerston

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

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

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

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

ANALYSIS OF CFD HEAT TRANSFER OF VACUUM FREEZE-DRYING SHELF

ANALYSIS OF CFD HEAT TRANSFER OF VACUUM FREEZE-DRYING SHELF HEFAT202 9 th Interntionl Conferene on Het Trnsfer, Fluid Mehnis nd Thermodynmis 6 8 July 202 Mlt ANALYSIS OF CFD HEAT TRANSFER OF VACUUM FREEZE-DRYING SHELF Hong-Ping Cheng *, Shin-min Tsi 2 * Professor,

More information

Chapter 3. Vector Spaces. 3.1 Images and Image Arithmetic

Chapter 3. Vector Spaces. 3.1 Images and Image Arithmetic Chpter 3 Vetor Spes In Chpter 2, we sw tht the set of imges possessed numer of onvenient properties. It turns out tht ny set tht possesses similr onvenient properties n e nlyzed in similr wy. In liner

More information

3/8" Square (10 mm) Multi-Turn Cermet Trimmer

3/8 Square (10 mm) Multi-Turn Cermet Trimmer 3/8" Squre ( mm) Multi-Turn Cermet FEATURES Industril grde W t 70 C Tests ording to CECC 400 or IEC 60393-1 Contt resistne vrition < 1 % typil Complint to RoHS Diretive 2002/95/EC The Model is smll size

More information

Research Article Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

Research Article Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions Hindwi Pulishing Corportion Journl of Applied Mthemtics Volume 4, Article ID 38686, 6 pges http://dx.doi.org/.55/4/38686 Reserch Article Fejér nd Hermite-Hdmrd Type Inequlities for Hrmoniclly Convex Functions

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

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

Arrow s Impossibility Theorem

Arrow s Impossibility Theorem Rep Voting Prdoxes Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Voting Prdoxes Properties Arrow s Theorem Leture Overview 1 Rep

More information

Petri Nets. Rebecca Albrecht. Seminar: Automata Theory Chair of Software Engeneering

Petri Nets. Rebecca Albrecht. Seminar: Automata Theory Chair of Software Engeneering Petri Nets Ree Alreht Seminr: Automt Theory Chir of Softwre Engeneering Overview 1. Motivtion: Why not just using finite utomt for everything? Wht re Petri Nets nd when do we use them? 2. Introdution:

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

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

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

System Validation (IN4387) November 2, 2012, 14:00-17:00

System Validation (IN4387) November 2, 2012, 14:00-17:00 System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise

More information

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS

SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS SECOND HARMONIC GENERATION OF Bi 4 Ti 3 O 12 FILMS IN-SITU PROBING OF DOMAIN POLING IN Bi 4 Ti 3 O 12 THIN FILMS BY OPTICAL SECOND HARMONIC GENERATION YANIV BARAD, VENKATRAMAN GOPALAN Mterils Reserh Lortory

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

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

AVL Trees. D Oisín Kidney. August 2, 2018

AVL Trees. D Oisín Kidney. August 2, 2018 AVL Trees D Oisín Kidne August 2, 2018 Astrt This is verified implementtion of AVL trees in Agd, tking ides primril from Conor MBride s pper How to Keep Your Neighours in Order [2] nd the Agd stndrd lirr

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

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

Lossless Compression Lossy Compression

Lossless Compression Lossy Compression Administrivi CSE 39 Introdution to Dt Compression Spring 23 Leture : Introdution to Dt Compression Entropy Prefix Codes Instrutor Prof. Alexnder Mohr mohr@s.sunys.edu offie hours: TBA We http://mnl.s.sunys.edu/lss/se39/24-fll/

More information

Part 4. Integration (with Proofs)

Part 4. Integration (with Proofs) Prt 4. Integrtion (with Proofs) 4.1 Definition Definition A prtition P of [, b] is finite set of points {x 0, x 1,..., x n } with = x 0 < x 1

More information

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx

Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint

More 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

Supporting Information. Cytosolic Irradiation of Femtosecond Laser Induces Mitochondria-dependent Apoptosis-like

Supporting Information. Cytosolic Irradiation of Femtosecond Laser Induces Mitochondria-dependent Apoptosis-like Supporting Informtion Cytosolic Irrdition of Femtosecond Lser Induces Mitochondri-dependent Apoptosis-like Cell Deth vi Intrinsic Rective Oxygen Cscdes Jonghee Yoon 1,2, Seung-wook Ryu 1,3, Seunghee Lee

More information

PLANT POPULATION INFLUENCES ON MAIZE PHYSIOLOGICAL RESPONSES TO NITROGEN APPLICATION

PLANT POPULATION INFLUENCES ON MAIZE PHYSIOLOGICAL RESPONSES TO NITROGEN APPLICATION PLANT POPULATION INFLUENCES ON MAIZE PHYSIOLOGICAL RESPONSES TO NITROGEN APPLICATION C.R. Boomsm nd T.J. Vyn Purdue University, West Lfyette, Indin Astrt Pst geneti improvements in mize (Ze mys L.) hve

More information

A Non-parametric Approach in Testing Higher Order Interactions

A Non-parametric Approach in Testing Higher Order Interactions A Non-prmetri Approh in Testing igher Order Intertions G. Bkeerthn Deprtment of Mthemtis, Fulty of Siene Estern University, Chenkldy, Sri Lnk nd S. Smit Deprtment of Crop Siene, Fulty of Agriulture University

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

Algorithm Design and Analysis

Algorithm Design and Analysis Algorithm Design nd Anlysis LECTURE 8 Mx. lteness ont d Optiml Ching Adm Smith 9/12/2008 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov, K. Wyne Sheduling to Minimizing Lteness Minimizing

More information

Vapour compression refrigeration system

Vapour compression refrigeration system www.ookspr.om VTU NEWS VTU NOTES QUESTION PAPERS FORUMS RESULTS Vpour ompression refrigertion system Introdution In vpour ompression system, the refrigernts used re mmoni, ron dioxide, freons et. the refrigernts

More information

Supplementary figure 1

Supplementary figure 1 Supplementry figure 1 Igf 1 mrna 5 15 1 5 Arg1 mrna 16 1 8 Col11 mrna 5 3 1 Mmp 13 mrna 15 1 5 Tslp mrna 3 1 Il5 mrna 3 1-1 Il33 mrna 6 Figure 1s. Kinetis of woun heling ftors n erly Th-type response ytokines

More information

Lecture 18: Species, Hybrids, and QTL. Oct 23, 2006

Lecture 18: Species, Hybrids, and QTL. Oct 23, 2006 Leture 18: Speies, Hyrids, nd QTL Ot 23, 2006 ourse Logistis Reminder: Guest leture Fridy, Novemer 3 Reding posted on wesite 2 nd Reminder: no lss on Wednesdy, Novemer 1 nother 2 nd Reminder: Everyone

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

12.4 Similarity in Right Triangles

12.4 Similarity in Right Triangles Nme lss Dte 12.4 Similrit in Right Tringles Essentil Question: How does the ltitude to the hpotenuse of right tringle help ou use similr right tringles to solve prolems? Eplore Identifing Similrit in Right

More information

Algorithms & Data Structures Homework 8 HS 18 Exercise Class (Room & TA): Submitted by: Peer Feedback by: Points:

Algorithms & Data Structures Homework 8 HS 18 Exercise Class (Room & TA): Submitted by: Peer Feedback by: Points: Eidgenössishe Tehnishe Hohshule Zürih Eole polytehnique fédérle de Zurih Politenio federle di Zurigo Federl Institute of Tehnology t Zurih Deprtement of Computer Siene. Novemer 0 Mrkus Püshel, Dvid Steurer

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

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

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

Supplemental Material

Supplemental Material Supplementl Mteril Sulfmethzine Sorption to Soil: Vegettive Mngement, ph, nd Dissolved Orgni Mtter Effets Bei Chu, Keith W. Goyne *, Stephen H. Anderson, Chung-Ho Lin 2, nd Roert N. Lerh 3 Deprtment of

More information

MATH Final Review

MATH Final Review MATH 1591 - Finl Review November 20, 2005 1 Evlution of Limits 1. the ε δ definition of limit. 2. properties of limits. 3. how to use the diret substitution to find limit. 4. how to use the dividing out

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

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

Ethylene-dependent ethylene-independent ABA regulation of tomato plants colonized by arbuscular mycorrhiza fungi

Ethylene-dependent ethylene-independent ABA regulation of tomato plants colonized by arbuscular mycorrhiza fungi Reserh Ethylene-dependent ethylene-independent ABA regultion of tomto plnts olonized y rusulr myorrhiz fungi José Ángel Mrtín-Rodríguez 1, Rfel León-Morillo 1, Horst Vierheilig 1, Jun Antonio Ompo 1, Jutt

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

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

Supporting Information

Supporting 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 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

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

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