SUPPLEMENTARY INFORMATION

Size: px
Start display at page:

Download "SUPPLEMENTARY INFORMATION"

Transcription

1 doi:1.138/nture1241 Figure S1., TEM imge of gold nnoprtiles.,, Chemil strutures of nioni itrte nd tioni polyurethne opolymer, respetively. Comment: Gold nnoprtiles were synthesized ording to slightly modified literture proedure. 1 The use of itrte for olloidl stiliztion of gold nnoprtiles is expeted to ring out miniml rriers for hrge trnsport etween nnoprtiles, whih is not the se of gold nnoprtiles with stilizers with long liphti hins. As suh, ondutivities of free-stnding LBL films using oleylmines-stilized gold nnoprtiles nd 1,6-hexnedithiol-stilized gold nnoprtiles were 2 x 1-2 S m -1, 2 nd 3.7 x 1-2 S m -1, 3 whih were t lest 1 5 times lower thn tht of 5 x VAF omposite. Tle S1 elow shows more ondutivity dt of LBL films from gold nnoprtiles. Tle S1. Previous ses of LBL films from gold nnoprtiles nd their ondutivity. Dimeter of gold nnoprtiles (nm) Stilizer 5 sodium orohydride Counter polyeletrolyte poly(dillyldimethyl mmonium hloride) 13 itrte poly(dillyldimethyl mmonium hloride) Thikness of film (nm) Condutivity (S m -1 ) (referene) 6 2 x 1 5 (4) x 1 5 (5) 2.5 itrte ethnedithiol x 1 5 (6) 2.5 itrte ethylenedimine 52 2 x 1 5 (7) -2 (2) 9 oleylmine 1,9-nonnedithiol 6 2 x 1-2 (3) 1 1,6-hexnedithiol lknedithiol x 1 1

2 RESEARCH SUPPLEMENTARY INFORMATION Figure S2., Dependene of thikness of the (PU/NP) n film on the numer of the deposition yles. Polyurethne (3P, 4P, 5P ) nd gold nnoprtiles (3A, 4A, 5A ) lyers with the sme numer orrespond to one deposition yle. Thikness hnge ws mesured y ellipsometry s the LBL film ws deposited on silion wfer. Thikness of eh lyer ws verged on the sis of three independent mesurements. Averge thikness inrements for polyurethne nd gold nnoprtiles lyers re 1.89 nm nd 2.4 nm, respetively., UV-Vis sorne spetr mesured every 5 th lyer pirs of LBL ssemlies. The multilyers were formed on oth sides of glss sustrte. The shift of the plsmon pek from 515 nm (free gold nnoprtiles) to nm for LBL films is inditive of strong plsmoni oupling nd nnoprtiles proximity to eh other, whih is enefiil for effiient hrge trnsport etween nnoprtiles. Figure S3. Therml grvimetri nlysis (TGA) of pure gold, pure polyurethne, nd single freestnding, 1x, LBL nd VAF films with different gold ontents. The vol% given in prentheses refers to V f of gold in eh film nd 21.7 vol% is equl to 87.7 wt%. 2

3 RESEARCH Figure S4. Differentil snning lorimetry (DSC) for pure polyurethne, LBL films, VAF films, nd pure gold. Nnoprtile ontents of omposites re given in prentheses nd refer to V f of gold in eh film. 3

4 RESEARCH SUPPLEMENTARY INFORMATION Figure S5. Idelized shemtis of well-dispersed nnoprtiles in LBL nd VAF omposites with distriuted rndom ggregtes (numer of prtiles is sme for oth ses nd spes re filled with polymers in the lttie) in 2D ross-setionl grid rry with peroltion pthwys to nerest neighors of nnoprtiles. Theoretil vlues of V volume frtions, whih refleted site peroltion proility nd filling ftor together, for nnoprtiles omposite ssuming tht () one nnoprtile tkes ple one lttie spot nd () luster is onneted only with nerest neighors, for simple ui lttie, ody-entered ui lttie, nd fe-entered ui lttie re.162,.163, nd.144, respetively 8,9. Figure S6. High-voltge eletron mirosopy (HVEM) imges of 1 x VAF. Imging ws performed on the ruptured point. The speimens were prepred y using FIB. 4

5 RESEARCH. d Figure S7.,, SEM imges of surfes of 5 x LBL nd 5 x VAF in relxed stte fter five onseutive strethes to 11% nd 2%, respetively., d, Stress-strin urves for 5 x LBL nd 5 x VAF fter speifi strething yles with ε=11% nd 2%, respetively. 5

6 RESEARCH SUPPLEMENTARY INFORMATION d I(q) (. u.) 1.E E E E LBL x LBL 1, Cyled 1 LBL x LBL % Pristine Strined 1 VAF AL x VAF 1, 1, Cyled Cyled 1 AL x VAF % Pristine Strined 1.E E q (Å -1 ) Figure S8. Condutivity nd smll-ngle X-ry sttering (SAXS) dt fter reurrent strething yles., Illustrtion of the ondutivity mesurements y two proe method in different diretions fter 1, strething yles with ε=5%. 1: prllel to the tensile diretion efore strin yles, 2: perpendiulr to the tensile diretion efore strin yles, 3: prllel to the tensile diretion fter strin yles, nd 4: perpendiulr to tensile diretion fter strin yles., Resistne dt y two-proe method in the diretions nd reurrent strething yles for 1 x LBL nd 1 x VAF, respetively., SAXS em imges of 1, yled 1 x LBL nd 1xVAF films. Smples were horizntlly pled for mesurements. d, Plots of sttering intensity, I(q), in respet to sttering vetor, q, for 1 x LBL nd 1 x VAF. SAXS mesurements were performed on the enter of the films. 6

7 RESEARCH y = x R² = log σ 2 log σ 2 1 y = 1.173x R² = log (V f V ) log (V f V ) d 1.E+4 1.E+4 σ (S m -1 ) 1.E+2 σ (S m -1 ) 1.E+2 1xLBL x LBL 1xVAF x VAF LBL y Eq. 1 1.E V f (vol%) VAF y Eq. 1 1.E V f (vol%) Figure S9. Experimentl dependene of σ on V f nd its lineriztion ording to the lssil power-lw reltion of 3D peroltion theory.,, Log plots of σ in respet to log(v f V ) with liner fit s desried s Eq. 1 in the min text for 1 x LBL nd 1 x VAF, respetively., d, Comprison of lulted ondutivities nd tul dt of 1 x LBL nd 1 x VAF for unstrined omposites, respetively 1. In order to desrie the ehvior of our nnoprtile omposites in terms of the power-lw of peroltion theory (Eq. 1), the ritil exponents, s, orresponding to oth mterils were determined to e s LBL =1.5 nd s VAF =1.17 from the slopes of dependenies in Fig. S9 nd S9, respetively. The pplition of the lssil peroltion theory to VAF omposite system is impeded y the fundmentl ssumption of individul filler prtiles to e homogeneously dispersed in the mtrix tht Eq.1 is sed on. Despite the suessful lineriztion in the log-log plot in Fig. S9, further pplition of the theory is impeded y signifint gglomertion of gold prtiles lerly visile in Fig. 2k tht result in the distint mismth of experimentl nd predited vlues in Fig. S9d. 7

8 RESEARCH SUPPLEMENTARY INFORMATION Comments to the method of Chun et l. (ondutivity to the unixil strin) The method used y Chun et l., whih desried ondutivity of omposite to the unixil strin y onverting V f to ε nd Poisson s rtio (ν), σ = σ V V (Eq. 1) ( f )s Vgold V f ( ε ) = V ( ε ) 2 V ( ε) = L ( ε) w ( ε) t ( ε) L ( ε) = L ( ε + 1) 2 1 w ( ε) = w (1 ν ε) 2 1 t ( ε) = t (1 ν ε) 2 1 ( ) w1 w2 νw ε = w ε 1 1 t1 t2 νt ( ε) = t ε t w ouldn t perfetly desrie tul deformtion of omposite euse onstnt ν t some point (. ε=4%) ws expeted to mke the volume derese nd negtive, whih is not physil. The ove method nd Eq. 2 in the min text hd sme pplile rnge of strin up to. 11%. 8

9 RESEARCH σ Hopping A = σ exp( ) 1/4 T σ Tunneling B = σ exp( ) 1/2 T d e f Figure S1. Chrge trnsport in polyurethne-nnoprtile nnoomposites.,, Equtions for vrile-rnge hopping nd tunneling mehnisms, respetively 11,12., d, Plots of ln σ vs T -1/4 nd T -1/2 from dt points of 1 x LBL film (Fig. 2F), respetively. e, f, Plots of ln σ vs T -1/4 nd T - 1/2 from dt points of 1 x VAF film (Fig. 2F), respetively. Three different ondution mehnisms re possile etween neighoring gold nnoprtiles: () diret ontt; () vrile-rnge hopping nd () tunneling. The reltive ontriution of hopping nd tunneling mehnisms depends on the shpe of the rrier, the seprtion of the sites nd therml energy 13. Dependene of ondutivity on temperture provides relile riterion y whih ondution mehnism tht domintes the smples n e unveiled. Fitting the equtions for vrile-rnge hopping nd tunneling ondution mehnism demonstrte tht eletron trnsfer mehnism in LBL nd VAF strethle ondutors is governed neither y hopping nor y tunneling: plots of ln σ vs T -1/4 nd T -1/2 drwn from dt points from Fig. 2f with equtions in Fig. S1 nd S1 did not onform to expeted liner dependene. 9

10 RESEARCH SUPPLEMENTARY INFORMATION Figure S11., Eletron moility nd, Crrier onentrtion of 1 x LBL nd 1 x VAF determined y the Hll effet mesurements. 1

11 RESEARCH Figure S12. Photogrphi imges for the set up used in mesuring ondutivity nd lulting ν to tensile strin dependene with four-proe method exemplified for 1 x VAF. Geometril terms re speified. The four proes were pled on the smple s shown in () nd (). Chnge of resistne on the multimeter nd hnge of strin on the disply of tensile mhine (just elow the multimeter) were video reorded together s shown in (). Smple eing strethed ws photogrphed to see hnge of length nd width (one photogrph ws tken every seond) to lulte thikness of smple t eh photogrph under the ssumption of no volume hnge. Video reorded resistne, strin, nd thikness dt were used to lulte dt points for the ondutivity vlues reported in the pper. Clulted Poisson s rtios were s follows: ν LBL, thikness =.26, nd ν LBL, width =.14, ν VAF, thikness =.39, nd ν VAF, width =

12 RESEARCH SUPPLEMENTARY INFORMATION 1 x LBL 1 x LBL tn δ V, 26 C V, 26 C V, 2 C Condition Storge modulus (GP) V, V, R.T. 2 C V, V, 2826 C C.2.2 V, V, 28 C 26 C Condition Frequeny (Hz) Frequeny (Hz) d.5 1 x VAF e x VAF tn δ V, 28 C V, 28 C V, R.T. 2 C Condition Storge modulus (GP) V, 2 C V, 28 C.2 V, 28 C Condition Frequeny (Hz) Frequeny (Hz) Figure S13. Dmping properties of polyurethne-nnoprtile nnoomposites with V t the relevnt tempertures (purple rs) under frequeny rnges from 1-9 Hz with referene onditions with nd.2 V., Experimentl setup for mesuring dmping properties with voltge.,, dmping prmeter tn δ nd storge modulus of 1 x LBL, respetively. d, e, dmping prmeter tn δ nd storge modulus of 1 x VAF, respetively. When.2 V ws pplied, temperture of omposites inresed to 26 C nd 28 C for 1 x LBL nd 1 x VAF, respetively. To show tht hnge of dmping properties t the low frequeny region were minly used y pplied voltge, those with no voltge nd t the temperture of 26 C for 1 x LBL nd 28 C for 1 x VAF were mesured. Dt showed pplied smll voltge signifintly tuned dmping properties espeilly t the low frequeny region while only temperture ouldn t tune the dmping properties t speifi frequeny rnges insted it slightly ffeted over the entire frequeny region. 12

13 RESEARCH REFERENCES 1 Turkevih, J., Stevenson, P. C. & Hillier, J. A Study of the Nuletion nd Growth Proesses in the Synthesis of Colloidl Gold. Disuss Frdy So, (1951). 2 Olihwer, N., Lei, E. W., Hlfr, A. H., Petrov, A. & Vossmeyer, T. Cross-Linked Gold Nnoprtiles on Polyethylene: Resistive Responses to Tensile Strin nd Vpors. ACS Appl Mter Inter 4, (212). 3 Joseph, Y. et l. Self-ssemled gold nnoprtile/lknedithiol films: Preprtion, eletron mirosopy, XPS-nlysis, hrge trnsport, nd vpor-sensing properties. J Phys Chem B 17, (23). 4 Liu, Y. J., Wng, Y. X. & Clus, R. O. Lyer-y-lyer ioni self-ssemly of Au olloids into multilyer thin-films with ulk metl ondutivity. Chem Phys Lett 298, (1998). 5 Kumlngdudsn, P., Tuntrnont, A., Dus, S. T. & Dus, L. Frition of miroeletrodes using flow lyer-y-lyer self ssemly of gold nnoprtiles. Superlttie Mirost 52, (212). 6 Bsrir, F. & Yoon, T. H. Sonition-ssisted lyer-y-lyer deposition of gold nnoprtiles for highly ondutive gold ptterns. Ultrson Sonohem 19, (212). 7 Bsrir, F. & Yoon, T. H. Preprtion of highly ondutive gold ptterns on polyimide vi shking-ssisted lyer-y-lyer deposition of gold nnoprtiles. Colloid Surfe A 393, (212). 8 Stuffer, D. & Ahrony, A. Introdution to peroltion theory. Rev., 2nd edn, (Tylor & Frnis, 1994). 9 Sher, H. & Zllen, R. Critil Density in Peroltion Proesses. J Chem Phys 53, (197). 1 Li, J. & Kim, J.-K. Peroltion threshold of onduting polymer omposites ontining 3D rndomly distriuted grphite nnopltelets. Compos Si Tehnol 67, (27). 11 Mott, N. F. Condution in non-rystlline mterils. Philosophil Mgzine 19, (1969). 12 M, Y. G., Liu, H. J. & Ong, C. K. Eletron trnsport properties in CoAlO omposite ntidot rrys. Europhys Lett 76, (26). 13 Ko, K.-C. & Hwng, W. Eletril trnsport in solids : with prtiulr referene to orgni semiondutors. 1st edn, (Pergmon Press, 1981). 13

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

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

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

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

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

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

SECTION A STUDENT MATERIAL. Part 1. What and Why.?

SECTION A STUDENT MATERIAL. Part 1. What and Why.? SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are

More 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

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

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

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

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

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

polyimide Spray-coated ZrP/epoxy film Spray-coated ZrP/epoxy film glass

polyimide Spray-coated ZrP/epoxy film Spray-coated ZrP/epoxy film glass c d e polyimide Spry-coted ZrP/epoxy film glss Spry-coted ZrP/epoxy film f g Supplementry Figure 1. Opticl microscopy of smectic ( = 0.044) α-zrp/epoxy films., Trnsmission opticl microscopy (TOM) of smectic

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

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

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

Magnetically Coupled Coil

Magnetically Coupled Coil Mgnetilly Coupled Ciruits Overview Mutul Indutne Energy in Coupled Coils Liner Trnsformers Idel Trnsformers Portlnd Stte University ECE 22 Mgnetilly Coupled Ciruits Ver..3 Mgnetilly Coupled Coil i v L

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

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

m A 1 1 A ! and AC 6

m A 1 1 A ! and AC 6 REVIEW SET A Using sle of m represents units, sketh vetor to represent: NON-CALCULATOR n eroplne tking off t n ngle of 8 ± to runw with speed of 6 ms displement of m in north-esterl diretion. Simplif:

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

21.1 Using Formulae Construct and Use Simple Formulae Revision of Negative Numbers Substitution into Formulae

21.1 Using Formulae Construct and Use Simple Formulae Revision of Negative Numbers Substitution into Formulae MEP Jmi: STRAND G UNIT 1 Formule: Student Tet Contents STRAND G: Alger Unit 1 Formule Student Tet Contents Setion 1.1 Using Formule 1. Construt nd Use Simple Formule 1.3 Revision of Negtive Numers 1.4

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

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

Mathematics SKE: STRAND F. F1.1 Using Formulae. F1.2 Construct and Use Simple Formulae. F1.3 Revision of Negative Numbers

Mathematics SKE: STRAND F. F1.1 Using Formulae. F1.2 Construct and Use Simple Formulae. F1.3 Revision of Negative Numbers Mthemtis SKE: STRAND F UNIT F1 Formule: Tet STRAND F: Alger F1 Formule Tet Contents Setion F1.1 Using Formule F1. Construt nd Use Simple Formule F1.3 Revision of Negtive Numers F1.4 Sustitution into Formule

More information

Restraint of purlins for various roof systems

Restraint of purlins for various roof systems NS009 Restrint of purlins for vrious roof systems T. Vrny, M. Brhm & A. Beli ulty of ivil Engineering, zeh Tehnil University, Prh, zehi Astron Buildings S.A., Diekirh, Luxemourg, A memer of the Lind Group

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

for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx

for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion

More 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

(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

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

m m m m m m m m P m P m ( ) m m P( ) ( ). The o-ordinte of the point P( ) dividing the line segment joining the two points ( ) nd ( ) eternll in the r

m m m m m m m m P m P m ( ) m m P( ) ( ). The o-ordinte of the point P( ) dividing the line segment joining the two points ( ) nd ( ) eternll in the r CO-ORDINTE GEOMETR II I Qudrnt Qudrnt (-.+) (++) X X - - - 0 - III IV Qudrnt - Qudrnt (--) - (+-) Region CRTESIN CO-ORDINTE SSTEM : Retngulr Co-ordinte Sstem : Let X' OX nd 'O e two mutull perpendiulr

More information

Polyphase Systems. Objectives 23.1 INTRODUCTION

Polyphase Systems. Objectives 23.1 INTRODUCTION Polyphse Systems 23 Ojetives eome fmilir with the opertion of threephse genertor nd the mgnitude nd phse reltionship etween the three phse voltges. e le to lulte the voltges nd urrents for three-phse Y-onneted

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

Silicon Nanowire Based Single-Molecule SERS Sensor

Silicon Nanowire Based Single-Molecule SERS Sensor Supporting informtion Silicon Nnowire Bsed Single-Molecule SERS Sensor Hui Wng, Xuemei Hn, Xuemei Ou, Chun-Sing Lee, Xiohong Zhng* nd Shuit-Tong Lee S1, A series of Si nnowires coted with compct ggregtes

More information

Reflection Property of a Hyperbola

Reflection Property of a Hyperbola Refletion Propert of Hperol Prefe The purpose of this pper is to prove nltill nd to illustrte geometrill the propert of hperol wherein r whih emntes outside the onvit of the hperol, tht is, etween the

More 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

Supplementary Figure 1 Supplementary Figure 2

Supplementary Figure 1 Supplementary Figure 2 Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully

More information

Linear magnetoresistance due to multipleelectron scattering by low-mobility islands in an inhomogeneous conductor

Linear magnetoresistance due to multipleelectron scattering by low-mobility islands in an inhomogeneous conductor Reeived 2 Jun 212 Aepted 31 Aug 212 Pulished 2 Ot 212 DOI: 1.138/nomms216 Liner mgnetoresistne due to multipleeletron sttering y low-moility islnds in n inhomogeneous ondutor N.V. Kolov 1,2, N. Mori 3,

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 2,2 -dipyridyl on non-formaldehyde electroless copper plating

The influence of 2,2 -dipyridyl on non-formaldehyde electroless copper plating Eletrohimi At 9 () 1789 179 The influene of, -dipyridyl on non-formldehyde eletroless opper plting Jun Li, Hrley Hyden, Pul A. Kohl Shool of Chemil & Biomoleulr Engineering, Georgi Institute of Tehnology,

More 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

Logarithms LOGARITHMS.

Logarithms LOGARITHMS. Logrithms LOGARITHMS www.mthletis.om.u Logrithms LOGARITHMS Logrithms re nother method to lulte nd work with eponents. Answer these questions, efore working through this unit. I used to think: In the

More 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

Electronic Circuits I Revision after midterm

Electronic Circuits I Revision after midterm Eletroni Ciruits I Revision fter miterm Dr. Ahme ElShfee, ACU : Fll 2018, Eletroni Ciruits I -1 / 14 - MCQ1 # Question If the frequeny of the input voltge in Figure 2 36 is inrese, the output voltge will

More information

EE 330/330L Energy Systems (Spring 2012) Laboratory 1 Three-Phase Loads

EE 330/330L Energy Systems (Spring 2012) Laboratory 1 Three-Phase Loads ee330_spring2012_l_01_3phse_lods.do 1/5 EE 330/330L Energy Systems (Spring 2012) Lortory 1 ThreePhse Lods Introdution/Bkground In this lortory, you will mesure nd study the voltges, urrents, impednes,

More information

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

Supporting Information. M13 Virus-Incorporated Biotemplates on Electrode Surfaces to Nucleate Metal Nanostructures by Electrodeposition

Supporting Information. M13 Virus-Incorporated Biotemplates on Electrode Surfaces to Nucleate Metal Nanostructures by Electrodeposition Supporting Informtion M13 Virus-Inorported iotempltes on Eletrode Surfes to Nulete Metl Nnostrutures y Eletrodeposition Shnmugm Mnivnnn [], Inhk Kng [],, Yeji Seo [], Hyo-Eon Jin [,], Seung-Wuk Lee []

More information

Polyphase Systems 22.1 INTRODUCTION

Polyphase Systems 22.1 INTRODUCTION 22 Polyphse Systems 22.1 INTRODUTION n genertor designed to develop single sinusoidl voltge for eh rottion of the shft (rotor) is referred to s single-phse genertor. If the numer of oils on the rotor is

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

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

Solutions to Assignment 1

Solutions to Assignment 1 MTHE 237 Fll 2015 Solutions to Assignment 1 Problem 1 Find the order of the differentil eqution: t d3 y dt 3 +t2 y = os(t. Is the differentil eqution liner? Is the eqution homogeneous? b Repet the bove

More information

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx Clulus Chet Sheet Integrls Definitions Definite Integrl: Suppose f ( ) is ontinuous Anti-Derivtive : An nti-derivtive of f ( ) on [, ]. Divide [, ] into n suintervls of is funtion, F( ), suh tht F = f.

More information

Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag 2 Te thin films

Synergism in binary nanocrystal superlattices leads to enhanced p-type conductivity in self-assembled PbTe/Ag 2 Te thin films Synergism in inry nnorystl superltties leds to enhned p-type ondutivity in self-ssemled PTe/Ag 2 Te thin films JEFFREY J. URBAN 1 *,DMITRIV.TALAPIN 2, ELENA V. SHEVCHENKO 2, CHERIE R. KAGAN 1 AND CHRISTOPHER

More information

Lecture 5: Crystal planes and Miller Indices

Lecture 5: Crystal planes and Miller Indices Leture Notes on Struture of Mtter y Mohmmd Jellur Rhmn, Deprtment of Physis, BUET, Dhk-000 Leture 5: Crystl plnes nd Miller Indies Index system for rystl diretions nd plnes Crystl diretions: Any lttie

More information

Layer-by-layer assembly of two-dimensional materials into wafer-scale heterostructures

Layer-by-layer assembly of two-dimensional materials into wafer-scale heterostructures doi:1.138/nture395 Lyer-y-lyer ssemly of two-dimensionl mterils into wfer-sle heterostrutures Kium Kng 1,,3 *, Kn-Heng Lee 4,5 *, Yimo Hn 4, Hui Go 1,, Sien Xie 4,5, Dvid A. uller 4,6 & Jiwoong Prk 1,,3,5,6

More information

Ab-initio investigation on the stability of H-6 Carbon

Ab-initio investigation on the stability of H-6 Carbon A-initio investigtion on the stility of H-6 Cron Zhris G. Fthenkis A few yers go H-6 Cron hd een proposed s n ll sp 2 three-dimensionl Cron llotrope, with mehnil properties omprle to grphene. However,

More information

THREE DIMENSIONAL GEOMETRY

THREE DIMENSIONAL GEOMETRY MD THREE DIMENSIONAL GEOMETRY CA CB C Coordintes of point in spe There re infinite numer of points in spe We wnt to identif eh nd ever point of spe with the help of three mutull perpendiulr oordintes es

More information

The Stirling Engine: The Heat Engine

The Stirling Engine: The Heat Engine Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines

More information

Preparation of Platinum Nanoparticles in Solution of Polyvinyl Pyrrolydone (PVP) by Laser Ablation Method

Preparation of Platinum Nanoparticles in Solution of Polyvinyl Pyrrolydone (PVP) by Laser Ablation Method VNU Journl of Siene: Mthemtis Physis, Vol. 30, No. 2 (2014) 18-24 Preprtion of Pltinum Nnoprtiles in Solution of Polyvinyl Pyrrolydone (PVP) y Lser Altion Method Nguyen The Binh*, Nguyen Dinh Thnh, Nguyen

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

Novel Fiber-Optical Refractometric Sensor Employing Hemispherically-Shaped Detection Element

Novel Fiber-Optical Refractometric Sensor Employing Hemispherically-Shaped Detection Element Novel Fier-Optil Refrtometri Sensor Employing Hemispherilly-Shped Detetion Element SERGEI KHOTIAINTSEV, VLADIMIR SVIRID Deprtment of Eletril Engineering, Fulty of Engineering Ntionl Autonomous University

More information

are coplanar. ˆ ˆ ˆ and iˆ

are coplanar. ˆ ˆ ˆ and iˆ SML QUSTION Clss XII Mthemtis Time llowed: hrs Mimum Mrks: Generl Instrutions: i ll questions re ompulsor ii The question pper onsists of 6 questions divided into three Setions, B nd C iii Question No

More information

A Matlab/Simulink Model of a Langevin s Ultrasonic Power Transducers

A Matlab/Simulink Model of a Langevin s Ultrasonic Power Transducers Mtl/Simulink Model of Lngevin s Ultrsoni Power Trnsduers Igor Jovnović, Ugleš Jovnović nd Drgn Mnčić strt Ultrsoni sndwih trnsduer, lso known s Lngevin s trnsduer, is hlf-wve resonnt struture tht osilltes

More information

Integration. antidifferentiation

Integration. antidifferentiation 9 Integrtion 9A Antidifferentition 9B Integrtion of e, sin ( ) nd os ( ) 9C Integrtion reognition 9D Approimting res enlosed funtions 9E The fundmentl theorem of integrl lulus 9F Signed res 9G Further

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

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

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

VIBRATION ANALYSIS OF AN ISOLATED MASS WITH SIX DEGREES OF FREEDOM Revision G

VIBRATION ANALYSIS OF AN ISOLATED MASS WITH SIX DEGREES OF FREEDOM Revision G B Tom Irvine Emil: tom@virtiondt.om Jnur 8, 3 VIBRATION ANALYSIS OF AN ISOLATED MASS WITH SIX DEGREES OF FREEDOM Revision G Introdution An vionis omponent m e mounted with isoltor grommets, whih t s soft

More information

Supporting Information Mesoporous graphitic carbon nanodisks fabricated via catalytic carbonization of coordination polymers

Supporting Information Mesoporous graphitic carbon nanodisks fabricated via catalytic carbonization of coordination polymers Supporting Informtion Mesoporous grphiti ron nnodisks frited vi tlyti roniztion of oordintion polymers Pnpn Su, Ling Jing, Jio Zho, Jingwng Yn, Cn Li nd Qihu Yng Stte Key Lortory of Ctlysis, Dlin Institute

More information

SOLUTIONS TO ASSIGNMENT NO The given nonrecursive signal processing structure is shown as

SOLUTIONS TO ASSIGNMENT NO The given nonrecursive signal processing structure is shown as SOLUTIONS TO ASSIGNMENT NO.1 3. The given nonreursive signl proessing struture is shown s X 1 1 2 3 4 5 Y 1 2 3 4 5 X 2 There re two ritil pths, one from X 1 to Y nd the other from X 2 to Y. The itertion

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

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò

Cyclic voltammetry simulation at microelectrode arrays with COMSOL Multiphysics Ò J Appl Eletrohem (009) 39:9 63 DOI 0.007/s0800-009-9797- ORIGINAL PAPER Cyli voltmmetry simultion t miroeletrode rrys with COMSOL Multiphysis Ò Alessndro Lvhi Æ U. Brdi Æ C. Borri Æ S. Cporli Æ A. Fossti

More 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

Polynomials. Polynomials. Curriculum Ready ACMNA:

Polynomials. Polynomials. Curriculum Ready ACMNA: Polynomils Polynomils Curriulum Redy ACMNA: 66 www.mthletis.om Polynomils POLYNOMIALS A polynomil is mthemtil expression with one vrile whose powers re neither negtive nor frtions. The power in eh expression

More information

On the Scale factor of the Universe and Redshift.

On the Scale factor of the Universe and Redshift. On the Sle ftor of the Universe nd Redshift. J. M. unter. john@grvity.uk.om ABSTRACT It is proposed tht there hs been longstnding misunderstnding of the reltionship between sle ftor of the universe nd

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

Probing the strain distribution within a single crystal superalloy during high temperature testing

Probing the strain distribution within a single crystal superalloy during high temperature testing MATEC We of Conferenes 14, 05004 (2014) DOI: 10.1051/mteonf/20141405004 Owned y the uthors, pulished y EDP Sienes, 2014 Proing the strin distriution within single rystl superlloy during high temperture

More information

Instructions. An 8.5 x 11 Cheat Sheet may also be used as an aid for this test. MUST be original handwriting.

Instructions. An 8.5 x 11 Cheat Sheet may also be used as an aid for this test. MUST be original handwriting. ID: B CSE 2021 Computer Orgniztion Midterm Test (Fll 2009) Instrutions This is losed ook, 80 minutes exm. The MIPS referene sheet my e used s n id for this test. An 8.5 x 11 Chet Sheet my lso e used s

More information

Final Exam Review. [Top Bottom]dx =

Final Exam Review. [Top Bottom]dx = Finl Exm Review Are Between Curves See 7.1 exmples 1, 2, 4, 5 nd exerises 1-33 (odd) The re of the region bounded by the urves y = f(x), y = g(x), nd the lines x = nd x = b, where f nd g re ontinuous nd

More information

Figure XX.1.1 Plane truss structure

Figure XX.1.1 Plane truss structure Truss Eements Formution. TRUSS ELEMENT.1 INTRODUTION ne truss struture is ste struture on the sis of tringe, s shown in Fig..1.1. The end of memer is pin juntion whih does not trnsmit moment. As for the

More information

Aluminizing of Nickel-Based Superalloys Grade IN 738 by Powder Liquid Coating

Aluminizing of Nickel-Based Superalloys Grade IN 738 by Powder Liquid Coating Mterils Trnstions, Vol. 51, No. 5 (2010) pp. 982 to 987 #2010 The Jpn Institute of Metls Aluminizing of Nikel-Bse Superlloys Gre IN 738 y Power Liqui Coting Ptm Visuttipitukul 1; *, Nuntiy Limvnutpong

More information

MRS BULLETIN VOLUME 33 OCTOBER

MRS BULLETIN VOLUME 33 OCTOBER Optil Metmgnetism nd Negtive-Index Metmterils Udy K. hettir, Shumin Xio, lexnder V. Kildishev, Wenshn i, sio-kun Yun, Vldimir P. rhev, nd Vldimir M. Shlev strt new lss of rtifiilly strutured mterils lled

More information

Lecture 1 - Introduction and Basic Facts about PDEs

Lecture 1 - Introduction and Basic Facts about PDEs * 18.15 - Introdution to PDEs, Fll 004 Prof. Gigliol Stffilni Leture 1 - Introdution nd Bsi Fts bout PDEs The Content of the Course Definition of Prtil Differentil Eqution (PDE) Liner PDEs VVVVVVVVVVVVVVVVVVVV

More information

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a.

H (2a, a) (u 2a) 2 (E) Show that u v 4a. Explain why this implies that u v 4a, with equality if and only u a if u v 2a. Chpter Review 89 IGURE ol hord GH of the prol 4. G u v H (, ) (A) Use the distne formul to show tht u. (B) Show tht G nd H lie on the line m, where m ( )/( ). (C) Solve m for nd sustitute in 4, otining

More information

UV-Induced Self-Repairing Polydimethylsiloxane-Polyurethane (PDMS-PUR) Cu- Catalyzed Networks

UV-Induced Self-Repairing Polydimethylsiloxane-Polyurethane (PDMS-PUR) Cu- Catalyzed Networks Eletroni Supplementry Mteril (ESI) for Journl of Mterils Chemistry A. This journl is The Royl Soiety of Chemistry 2014 Supporting Online Mterils UV-Indued Self-Repiring Polydimethylsiloxne-Polyurethne

More information

( ) { } [ ] { } [ ) { } ( ] { }

( ) { } [ ] { } [ ) { } ( ] { } Mth 65 Prelulus Review Properties of Inequlities 1. > nd > >. > + > +. > nd > 0 > 4. > nd < 0 < Asolute Vlue, if 0, if < 0 Properties of Asolute Vlue > 0 1. < < > or

More information

Dynamics of grain boundary motion coupled to shear deformation: An analytical model and its verification by molecular dynamics

Dynamics of grain boundary motion coupled to shear deformation: An analytical model and its verification by molecular dynamics PHYSICAL REVIEW B 78, 6416 28 Dynmis of grin boundry motion oupled to sher deformtion: An nlytil model nd its verifition by moleulr dynmis V. A. Ivnov* nd Y. Mishin Deprtment of Physis nd Astronomy, George

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

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB/ Clulus Exm Review Sheet Solutions A Prelulus Type prolems A1 A A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f( x) Set funtion equl to Ftor or use qudrti eqution if qudrti Grph to

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

Non Right Angled Triangles

Non Right Angled Triangles Non Right ngled Tringles Non Right ngled Tringles urriulum Redy www.mthletis.om Non Right ngled Tringles NON RIGHT NGLED TRINGLES sin i, os i nd tn i re lso useful in non-right ngled tringles. This unit

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

Electromagnetism Notes, NYU Spring 2018

Electromagnetism Notes, NYU Spring 2018 Eletromgnetism Notes, NYU Spring 208 April 2, 208 Ation formultion of EM. Free field desription Let us first onsider the free EM field, i.e. in the bsene of ny hrges or urrents. To tret this s mehnil system

More information

Section 1.3 Triangles

Section 1.3 Triangles Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior

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

Supporting Information. Observation of Excitonic Fine Structure in a 2D Transition Metal. Dichalcogenide Semiconductor

Supporting Information. Observation of Excitonic Fine Structure in a 2D Transition Metal. Dichalcogenide Semiconductor FWHM (ev) Normlized Intensity (. u.) Supporting Informtion Oservtion of Exitoni Fine Struture in 2D Trnsition Metl Dihlogenide Semiondutor Jingzhi Shng 1, Xionn Shen 1, Chunxio Cong 1, Nmphung Peimyoo

More information

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities Appendi Prtil dishrges. Reltionship Between Mesured nd Atul Dishrge Quntities A dishrging smple my e simply represented y the euilent iruit in Figure. The pplied lternting oltge V is inresed until the

More information

3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles.

3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles. 3 ngle Geometry MEP Prtie ook S3 3.1 Mesuring ngles 1. Using protrtor, mesure the mrked ngles. () () (d) (e) (f) 2. Drw ngles with the following sizes. () 22 () 75 120 (d) 90 (e) 153 (f) 45 (g) 180 (h)

More information