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

Size: px
Start display at page:

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

Transcription

1 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 2 n Pnywt Wngyo 1; * 1 Deprtment of Metllurgil Engineering, Fulty of Engineering, Chullongkorn University, Thiln 2 Grute Shool of Engineering, Fulty of Engineering, Chullongkorn University, Thiln Nikel-se superlloy gre IN738 hs superior reep resistne, however, oxition resistne is the min limittion of this lloy for prtil pplitions t high temperture. Coting of nikel luminie ompouns whih hve high oxition resistne on the IN738 lloys surfe n remrkly inrese the oxition resistne y formtion of Al 2 O 3 film s protetive lyer. Aluminizing y power liqui oting methos is pplie in this reserh. Mixe slurries of Al n Al 2 O 3 powers re pste onto IN 738 smples n hete t 1273 K in rgon tmosphere for 3.6 to 14.4 ks (1 to 4 h). Slurries n e lssifie into four ifferent rtios of Al : Al 2 O 3 : 10 : 0, 7:3, 5:5n 3:7. The mirostruture ws investigte y snning eletron mirosope (SEM) n optil mirosope. Phses in the ote lyer re hrterize y Glning Inient-ngle X-ry Diffrtometer (GIXD) n Eletron Proe Miro Anlysis (EPMA). The results show tht the ote lyer is forme y issolution of nikel into liqui luminum t luminizing temperture resulting in formtion of intermetlli ompoun lyer. The ote lyer onsists of Ni 2 Al 3 s min phse with smll mount of NiAl 3 n AlCr 2. AlCr 2 exists mostly t the lyer jent to the top surfe. For 8.1 n 14.4 ks (2.25 n 4 h) holing time, formtion of AlCr 2 t the interfe of mtrix n ote lyer ours ue to iffusion of luminum from ote lyer into nikel mtrix. The effet of time shows tht longer luminizing time les to formtion of uniform ote lyer. The Al : Al 2 O 3 rtio of either 10 : 0 or 7:3will rete uniform ote lyer with thikness more thn 200 mm. [oi: /mtertrns.m ] (Reeive Novemer 18, 2009; Aepte Ferury 15, 2010; Pulishe April 7, 2010) Keywors: luminizing, nikel luminie, IN738, power liqui oting 1. Introution Tle 1 Chemil omposition of IN738. Nikel-se superlloys gre IN738 is well known s high temperture mteril ue to its superior reep resistne. 1) However, this lloy suffers from low oxition n orrosion resistne. In orer to pply nikel-se superlloys gre IN738 s mhine prts in hot setion uner severe oxitive n orrosive tmosphere, surfe moifition to improve oxition n orrosion resistne is neessry. Mny reserh ttempts relte to protetive film oting hve een one to improve hot orrosion n oxition resistne of IN ) Formtion of intermetlli ompoun, for exmple nikel luminie, overing entire surfe is one wy to inrese oxition resistne of IN738. The nikel luminie lyer ts s n luminum sink, therefore, lumin film n form t high temperture s protetive lyer retring oxygen iffusion s well s oxition. 6) There re severl methos to inrese luminum ontent t the surfe yieling formtion of nikel luminie on the surfe of IN 738. A reently evelope proess is the so-lle power liqui oting proess pplie for luminizing steel. This proess employs psting slurries, whih t s soure for oting mterils, on to the surfe followe y susequent het tretment. The slurry ontins oting metl power, whih is luminum power for luminizing, mixe with other high melting point power, suh s Al 2 O 3. Aition of Al 2 O 3 power helpe retining n ispersing molten luminum to over ll oting res, preventing olesene of molten luminum into seprte pools. Therefore oting lyer ws forme uniformly n evenly on the entire surfe. 7) The purpose of this stuy ws to pply power liqui oting proess to frite nikel luminie lyer whih ws well known s protetive lyer for *Corresponing uthor, E-mil: ptm.v@hul..th, pnywt@ hotmil.om Element Ni Cr Co Ti Al W Mo T C mss% Bl t% Bl oxition in nikel se superlloys. Effet of proessing prmeters whih were slurry omposition n het tretment time on mirostruture n phses of the frite lyer ws investigte. 2. Experimentl Proeure 2.1 Smple preprtion Nikel-se superlloy gre IN738 (hemil omposition shown in Tle 1) ws ut into retngulr shpe with the size of 5 mm 10 mm 5 mm. All smples were polishe y SiC pper to numer 4000 gre. The smples were then rinse in etone y ultrsoni lening mhine for 300 seons. 2.2 Coting Coting slurries were prepre from mixture of Al n Al 2 O 3 powers with vrious Al : Al 2 O 3 rtios: 10 : 0, 7:3, 5:5n 3:7. Alumin power with size of 160 mm ws mixe with 3 mm luminum power. Ethylene glyol ws e into the mixture of Al n Al 2 O 3 powers to liquefy the mixture n this eme the oting slurries. The slurries were pste onto the smples with ensity of 1 kg/m 2 (0.1 g/m 2 ) n were hete uner rgon tmosphere t 473 K, n hel t this temperture for 5.4 ks in orer to remove the ethylene glyol. After tht, the temperture ws inrese to luminizing temperture t 1273 K, n hel for 3.6 ks (1 h), 8.1 ks (2.25 h), n 14.4 ks (4 h). The oting onitions re summrize in Tle 2.

2 Aluminizing of Nikel-Bse Superlloys Gre IN 738 y Power Liqui Coting st su lyer 2 n su-lyer 1 st su-lyer 2 n su-lyer Fig. 1 Cross-setionl mirostruture of IN738 luminize t 1273 K for 3.6 ks with Al : Al 2 O 3 rtio of () 10 : 0, () 7:3, () 5:5n () 3:7. Smple No. Al : Al 2 O 3 power rtio Tle 2 Coting onitions. Time (ks) Temperture (K) Atmosphere 1 10 : Argon 2 7:3 (1 h) 3 5:5 4 3:7 AlCr 2 NiAl 3 Ni 2 Al : :3 (2.25 h) 7 5:5 8 3: : :3 (4 h) 11 5:5 12 3:7 2.3 Chrteriztion Surfe n ross-setionl mirostruture of the ote smples were oserve y n optil mirosope n snning eletron mirosope (SEM). Energy ispersive spetrosopy (EDS) n eletron proe miro nlysis (EPMA) were performe to investigte the istriution of elements in the ote lyer. Phse formtion in the ote lyer ws hrterize y n X-ry iffrtrometer (XRD) n gling inient ngle X-ry iffrtometer (GIXD) t the inient ngle of 5 egree. 3. Results n Disussion 3.1 Phses n mirostruture hrteriztion Figure 1 shows ross-setionl mirostruture of smples whih were luminize y slurries with ifferent Al : Al 2 O 3 rtios for 3.6 ks (smple No. 1 to 4 in Tle 2). It n Fig. 2 GIXD profiles of IN738 luminize t 1273 K for 3.6 ks with ifferent Al : Al 2 O 3 rtios. e seen tht the ifferent Al : Al 2 O 3 rtios ffet uniformity n thikness of the oting lyer. The slurry with higher Al : Al 2 O 3 rtio proues thiker n more uniform ote lyer. In the se of 5:5n 3:7mixing rtios the ote lyer oes not over the entire surfe of IN738 mtrix. This is euse the mount of luminum in the slurries is not suffiient to e uniformly istriute. Moreover, luminum nnot wet nikel surfe euse the formtion of nikel luminie lyer seprtes the liqui luminum n the nikel mtrix elow. Nikel luminie lyer prevents liqui luminum from spreing, therefore nnot over the entire surfe of nikel sustrte. 8) Figure 1() shows the luminize lyer forme on the top surfe of IN738 smple. This mirostruture shows tht nikel n other lloying elements re issolve into liqui luminum t the luminizing temperture resulting in the formtion of luminize lyer on the top surfe. GIXD nlysis t the surfe of Nos. 1 to 4 smples is shown in Fig. 2. At the surfe of smple Nos. 1, 2 n 3, the ote lyer onsists of NiAl 3,Ni 2 Al 3 n AlCr 2, while only

3 984 P. Visuttipitukul, N. Limvnutpong n P. Wngyo AlCr2 NiAl3 Ni2Al3 Fig. 3 GIXD profiles of the smple luminize t 1273 K for 3.6 ks using Al : Al2 O3 rtio of 10 : 0 t the vrious epths from the surfe. Ni2 Al3 peks re etete on the surfe of smple No. 4. It n e seen tht the reltive intensities, whih express volume frtions, of NiAl3 n AlCr2 erese with eresing mount of Al in the slurries ut volume frtion of Ni2 Al3 inreses. The ontrst in ross-setionl mirostruture long the epth from the surfe inites tht severl phses exist in the ote lyer. The ote lyer n e ivie into 2 sulyers: the first su-lyer is the grey olor lyer lote next to the IN738 mtrix, n the seon su-lyer is t the top surfe. It is minly white in olor with some splsh of grey olor phse, s n e seen in Fig. 1(). Investigtion of phses existing t vrious epths from surfe ws one y GIXD s shown in Fig. 3. The GIXD profiles show tht there re NiAl3, Ni2 Al3 n AlCr2 t the surfe. The reltive intensity shows tht the min phses t the top surfe, whih is the seon su-lyer, re NiAl3 n AlCr2. At inresing epth from the surfe, the reltive intensities of NiAl3 n AlCr2 eome lower while the reltive intensity of Ni2 Al3 eomes higher. At epth greter thn 150 mm from the surfe, the first su-lyer, Ni2 Al3 is the min phse. Distriution of luminum, nikel, n hromium elements ws investigte y EDS s shown in Fig. 4. The ote lyer hs higher ontent of luminum thn tht of IN738 mtrix. The first su-lyer hs lower ontent of luminum thn the seon su-lyer, n vie vers for nikel n hromium ontents. The istriution of these elements orrespons well with the result from GIXD, in tht Ni2 Al3 in the first su-lyer hs lower mount of Al thn NiAl3 in the seon su-lyer. EDS line nlysis of the seon sulyer shows lrge mount of luminum t the top surfe, whih eomes less t inresing epth from the surfe. In ontrst, nikel ontent is lowest t the top lyer. Distriution n onentrtion grient of nikel n luminum suggests tht nikel toms iffuse through soli Ni2 Al3 lyer n then issolve into liqui luminum t the luminizing temperture. Effet of luminizing time is shown in Fig. 5. At short luminizing time, there re two istint su-lyers. When the luminizing time is inrese, the thikness of the first sulyer remrkly inreses, where s the thikness of the seon su-lyer ereses. At suffiiently long luminizing time, the seon su-lyer isppers; the mirostruture of ote lyer eomes phsi uniform n ontins only the first su-lyer. Therefore, smple No. 6, whih hs only first su-lyer uniformly ote on the IN 738 is selete for mirostruture n phse nlysis. Smple No. 6 is luminize t 1273 K for 8.1 ks, using slurry of 7 : 3 Al : Al2 O3 rtio. Its EDS nlysis is shown in Fig. 6. The first su-lyer ontins nikel, lrge ontent of luminum n smll ontent of hromium. Figure 7() shows SEM mirogrph of the first su-lyer forme on surfe of smple No. 6. High mgnifition SEM mirogrph of the first su-lyer n the first su-lyer/mtrix interfe re Fig. 4 EDS nlysis of luminize smple t 1273 K for 3.6 ks with Al : Al2 O3 rtio of 7 : 3 () seonry eletron imge () istriution of Ni () istriution of Al n () istriution of Cr.

4 Aluminizing of Nikel-Bse Superlloys Gre IN 738 y Power Liqui Coting 1st su lyer 2n su-lyer 985 1st su lyer e 1st su lyer f Fig. 5 Cross-setionl mirostruture of oting lyer of ifferent oting onitions; () smple No. 1, () smple No. 5, () smple No. 9, () smple No. 2, (e) smple No. 6 n (f) smple No µm Fig. 6 EDS nlysis of luminize smple t 1273 K for 8.1 ks with Al : Al2 O3 rtio of 7 : 3 () seonry eletron imge () istriution of Ni () istriution of Al n () istriution of Cr. shown in Fig. 7() n (), respetively. The ifferent ontrst in Fig. 7() inites three istint phses. EPMA nlysis of re in Fig. 7() is shown in Fig. 8. GIXD nlysis t vrious epth of this smple is shown in Fig. 9. From Fig. 8, it is foun tht the min phse in the first sulyer ontins luminum with high ontent of nikel, the seon phse ontins more luminum n less nikel, n the thir phse ontins high mount of hromium n luminum, with very low mount of nikel. Together with GIXD nlysis whih shows tht there re only Ni2 Al3, NiAl3, n AlCr2 in the first su-lyer, it n e ientifie tht the min phse is Ni2 Al3, the seon phse is NiAl3, n the thir phse is AlCr2. The first su-lyer/mtrix interfe in Fig. 7() ontins preipittes in form of light-olore elongte islns perpeniulr to the interfe in iretion of the first sulyer. EPMA nlysis of the re in Fig. 7() is shown in Fig. 10. It shows tht the preipitte islns re hromium rih phse. At epth etween mm, GIXD revels iffrtion peks t 20.57, n egree orresponing to (002), (110), n (103) rystllogrphi plnes of AlCr2 n iffrtion peks of Ni2 Al3. Therefore, the preipitte islns re ientifie s AlCr Mehnism of ote lyer formtion on IN 738 At luminizing temperture, nikel n lloying elements in IN738 issolve into molten luminum. The onentrtion of nikel in luminum is high t the interfe etween molten luminum n mtrix IN738. As soon s nikel ontent in molten luminum rehes the soluility limit, Ni2 Al3 is forme. Continuous formtion of Ni2 Al3 lyer is y iffusion of nikel toms through the newly forme Ni2 Al3 lyer into liqui luminum. Nikel onentrtion in molten luminum therefore inreses n Ni2 Al3 lyer grows. With inresing luminizing time, the Ni2 Al3 lyer, whih is the first sulyer, grows into liqui luminum.

5 986 P. Visuttipitukul, N. Limvnutpong n P. Wngyo AlCr2 NiAl3 Ni2Al3 Ni3Al mtrix Interfe 100 µm Coting lyer min phse 3r phse 2n phse Fig. 9 GIXD profiles of the smple luminize t 1273 K for 8.1 ks using Al : Al2 O3 rtio of 7 : 3 t the vrious epths from the surfe. 20 µm 5 µm Fig. 7 Cross-setionl mirostruture of () oting lyer () enlrge piture of oting lyer n () enlrge piture t interfe etween mtrix n oting lyer. n 2 phse Fig. 10 EPMA nlysis of interfe of ote lyer n IN738 () k sttering eleltron imge, istriution of Ni, Al n Cr. r 3 phse min phse 20 µm Fig. 8 EPMA nlysis of oting lyer () seonry eletron imge () istriution of Ni () istriution of Al n () istriution of Cr. For short luminizing time of 3.6 ks (1 h), istintion etween the first n the seon su-lyer n e esily me. The thikness of Ni2 Al3 lyer is thin ue to insuffiient time for nikel iffusion through Ni2 Al3 lyer. Therefore, molten luminum remins on the top surfe. During ooling own in the furne, the remining liqui luminum with high nikel ontent trnsforms to Ni2 Al3 n NiAl3 uring soliifition. NiAl3 n only preipitte stle phse t temperture lower thn 1178 K. AlCr2, whih is foun in the seon su-lyer, lso forms uring soliifition. This is ue to the ft tht Ni2 Al3, whih is the first phse forme t the interfe, n issolve Cr out 4 t% t 1273 K, s shown y ternry phse igrm of Ni-Al-Cr in Fig. 11. Dissolve Cr must e ejete from Ni2 Al3 lyer into jent liqui luminum. This results in preipittion of AlCr2 in the lyer jent to the surfe, oexisting with NiAl3 in the seon su-lyer. For long luminizing time, 8.1 n 14.4 ks (2.25 n 4 h), there is suffiient time for nikel iffusion to grow thik Ni2 Al3 lyer; therefore, ll liqui luminum is onsume n trnsforme to Ni2 Al3 s single lyer. This oting lyer n e onsiere s high luminum onentrtion lyer. Aluminum n iffuse into IN738 mtrix t high temperture resulting in growth of Ni2 Al3 into IN738 mtrix. Ejetion of

6 Aluminizing of Nikel-Bse Superlloys Gre IN 738 y Power Liqui Coting 987 Ni 2 Al 3 lyer onsists of Ni 2 Al 3 s min phse oexisting with NiAl 3 n AlCr 2. For short luminizing time, the ote lyer n e ivie into two su-lyers: Ni 2 Al 3 rih lyer esies the IN738 mtrix n NiAl 3 rih lyer t the surfe. For long luminizing time, the ote lyer is uniform onsisting of minly Ni 2 Al 3 with some preipittes of NiAl 3 n AlCr 2. The formtion of the ote lyer is firstly ontrolle y retion of Ni 2 Al 3 formtion etween liqui luminum n nikel. After Ni 2 Al 3 lyer is forme, iffusion of nikel toms through Ni 2 Al 3 lyer ontrols growth of Ni 2 Al 3 lyer into liqui luminum. AlCr 2 islns re lso foun t the interfe etween the ote lyer n the mtrix ue to low soluility of hromium in Ni 2 Al 3. REFERENCES Fig. 11 Ternry phse igrm of Ni-Cr-Al t 1273 K. 9) hromium out of Ni 2 Al 3 ours s isusse ove. The ejete hromium rets with luminum n preipittes s AlCr 2 islns s shown in Fig Conlusions Nikel luminie lyer is suessfully forme y power liqui oting. The pproprite Al : Al 2 O 3 rtios re 7:3or 10 : 0. Thikness of ote lyer rehes to more thn 200 mm fter luminizing for 8.1 ks (2.25 h). This ote 1) R. F. Deker n C. T. Sims: The Superlloys, (John Wieley & Son In., 1972). 2) J. E. Shile: Surf. Cot. Tehnol (2000) 35. 3) G. W. Gowr: Surf. Cot. Tehnol (1998) 73. 4) M. J. Li, X. F. Sun, H. R. Gun, X. X. Jing n Z. Q. Hu: Surf. Cot. Tehnol. 167 (2003) ) R. E. Mlush, P. De n D. H. Boone: Surf. Cot. Tehnol. 36 (1988) ) S. Y. Lee, J. S. Lee, K. B. Kim, G. S. Kim, B. Y. Lee, H. S. Moon, H. B. Eun, J. H. Lee n S. Y. Lee: Intermetllis 11 (2003) ) K. Murkmi, N. Nishi, K. Osmur n Y. Tomot: At Meter. 52 (2004) ) S. W. Ip, R. Srihr, J. M. Toguri, T. F. Stephenson n A. E. M. Wrner: Mter. Si. Eng. A 244 (1998) 31. 9) B. Grushko, W. Kowlski, D. Pvlyuhkov, B. Przepiorzynski n M. Surowie: J. Alloy. Comp. 460 (2008)

Chapter 4rth LIQUIDS AND SOLIDS MCQs

Chapter 4rth LIQUIDS AND SOLIDS MCQs Chpter 4rth LIQUIDS AND SOLIDS MCQs Q.1 Ioni solis re hrterize y () low melting points () goo onutivity in soli stte () high vpour pressure () soluility in polr solvents Q.2 Amorphous solis. () hve shrp

More information

SOME COPLANAR POINTS IN TETRAHEDRON

SOME COPLANAR POINTS IN TETRAHEDRON Journl of Pure n Applie Mthemtis: Avnes n Applitions Volume 16, Numer 2, 2016, Pges 109-114 Aville t http://sientifivnes.o.in DOI: http://x.oi.org/10.18642/jpm_7100121752 SOME COPLANAR POINTS IN TETRAHEDRON

More 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

Supporting Information

Supporting Information Supporting Informtion Control Synthesis of Tuulr Hyperrosslinke Polymers for Highly Porous Cron Nnotues Xioyn Wng, Pn Mu, Chong Zhng, Yu Chen, Jinghui Zeng, Feng Wng n Ji-Xing Jing *, Shnxi Key Lortory

More information

Chemistry Practice Exam

Chemistry Practice Exam Chemistry Prtie Exm 1 2 3 Whih of the following is n element? A rop of merury. A splinter of woo. A rystl of sugr. A rop of wter. Whih of the following nswers ontins only elements? Soium, soium hlorie,

More information

Momentum and Energy Review

Momentum and Energy Review Momentum n Energy Review Nme: Dte: 1. A 0.0600-kilogrm ll trveling t 60.0 meters per seon hits onrete wll. Wht spee must 0.0100-kilogrm ullet hve in orer to hit the wll with the sme mgnitue of momentum

More information

Processing and characterisation of Pr zircon pigment powder

Processing and characterisation of Pr zircon pigment powder Proessing nd hrteristion of Pr ziron pigment powder J. K. Kr* 1, R. Stevens 2 nd C. R. Bowen 2 Prseodymium ziron pigment powders were suessfully prepred t different lintion tempertures with sodium fluoride

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

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

Counting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs

Counting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs Isomorphism of Grphs Definition The simple grphs G 1 = (V 1, E 1 ) n G = (V, E ) re isomorphi if there is ijetion (n oneto-one n onto funtion) f from V 1 to V with the property tht n re jent in G 1 if

More information

Statistics in medicine

Statistics in medicine Sttistis in meiine Workshop 1: Sreening n ignosti test evlution Septemer 22, 2016 10:00 AM to 11:50 AM Hope 110 Ftm Shel, MD, MS, MPH, PhD Assistnt Professor Chroni Epiemiology Deprtment Yle Shool of Puli

More information

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

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply

More information

Solutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite!

Solutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite! Solutions for HW9 Exerise 28. () Drw C 6, W 6 K 6, n K 5,3. C 6 : W 6 : K 6 : K 5,3 : () Whih of the following re iprtite? Justify your nswer. Biprtite: put the re verties in V 1 n the lk in V 2. Biprtite:

More information

I 3 2 = I I 4 = 2A

I 3 2 = I I 4 = 2A ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents

More information

Eigenvectors and Eigenvalues

Eigenvectors and Eigenvalues MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.

More information

Surds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233,

Surds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233, Surs n Inies Surs n Inies Curriulum Rey ACMNA:, 6 www.mthletis.om Surs SURDS & & Inies INDICES Inies n surs re very losely relte. A numer uner (squre root sign) is lle sur if the squre root n t e simplifie.

More information

Appendix A: HVAC Equipment Efficiency Tables

Appendix A: HVAC Equipment Efficiency Tables Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER

More information

Necessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 )

Necessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 ) Neessry n suient onitions for some two vrile orthogonl esigns in orer 44 C. Koukouvinos, M. Mitrouli y, n Jennifer Seerry z Deite to Professor Anne Penfol Street Astrt We give new lgorithm whih llows us

More information

Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 3 : Interaction by Particle Exchange and QED. Recap

Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 3 : Interaction by Particle Exchange and QED. Recap Prtile Physis Mihelms Term 2011 Prof Mrk Thomson g X g X g g Hnout 3 : Intertion y Prtile Exhnge n QED Prof. M.A. Thomson Mihelms 2011 101 Rep Working towrs proper lultion of ey n sttering proesses lnitilly

More 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

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

CS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6

CS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6 CS311 Computtionl Strutures Regulr Lnguges nd Regulr Grmmrs Leture 6 1 Wht we know so fr: RLs re losed under produt, union nd * Every RL n e written s RE, nd every RE represents RL Every RL n e reognized

More information

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS

VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS AGRICULTURAL ENGINEERING VISIBLE AND INFRARED ABSORPTION SPECTRA OF COVERING MATERIALS FOR SOLAR COLLECTORS Ltvi University of Agriulture E-mil: ilze.pelee@llu.lv Astrt Use of solr energy inreses every

More 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

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

A Straightforward Protocol for the Highly Efficient Preparation of. Main-chain Azo Polymers Directly from Bisnitroaromatic Compounds Supporting Informtion A Strightforwr Protool for the Highly Effiient Preprtion of Min-hin Azo Polymers Diretly from Bisnitroromti Compouns y the Phototlyti Proess Liing Wng, Xingqing Pn, Yin Zho, Yng Chen,

More information

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

CS 491G Combinatorial Optimization Lecture Notes

CS 491G Combinatorial Optimization Lecture Notes CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,

More 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

INVESTIGATION OF THE OSL SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ

INVESTIGATION OF THE OSL SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ Meiterrnen Arheology n Arheometry, Vol. 010, No., pp. 9 98 Copyright 010 MAA Printe in Greee. All rights reserve. INVESTIGATION OF THE SIGNAL FROM VERY DEEP TRAPS IN NATURAL QUARTZ G. Kitis 1, N.G. Kiyk,

More 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

CIT 596 Theory of Computation 1. Graphs and Digraphs

CIT 596 Theory of Computation 1. Graphs and Digraphs CIT 596 Theory of Computtion 1 A grph G = (V (G), E(G)) onsists of two finite sets: V (G), the vertex set of the grph, often enote y just V, whih is nonempty set of elements lle verties, n E(G), the ege

More 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

H SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready.

H SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready. Alger Bsis H SERIES Alger Bsis Curriulum Rey www.mthletis.om Copyright 009 P Lerning. All rights reserve. First eition printe 009 in Austrli. A tlogue reor for this ook is ville from P Lerning Lt. ISBN

More 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

Identifying and Classifying 2-D Shapes

Identifying and Classifying 2-D Shapes Ientifying n Clssifying -D Shpes Wht is your sign? The shpe n olour of trffi signs let motorists know importnt informtion suh s: when to stop onstrution res. Some si shpes use in trffi signs re illustrte

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

Factorising FACTORISING.

Factorising FACTORISING. Ftorising FACTORISING www.mthletis.om.u Ftorising FACTORISING Ftorising is the opposite of expning. It is the proess of putting expressions into rkets rther thn expning them out. In this setion you will

More 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

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

Applied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005

Applied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005 Applie Gre 9 Assessment of Mthemtis Multiple-Choie Items Winter 2005 Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves remin the sme. . Multiple-Choie

More information

POSITIVE IMPLICATIVE AND ASSOCIATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS

POSITIVE IMPLICATIVE AND ASSOCIATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS Bull. Koren Mth. So. 35 (998), No., pp. 53 6 POSITIVE IMPLICATIVE AND ASSOCIATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS YOUNG BAE JUN*, YANG XU AND KEYUN QIN ABSTRACT. We introue the onepts of positive

More 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

22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:

22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of: 22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)

More information

Phase Formation through a Stage of Liquid State in Metallic Materials Being Electrodeposited: Recent Experimental Proofs

Phase Formation through a Stage of Liquid State in Metallic Materials Being Electrodeposited: Recent Experimental Proofs Interntionl Journl of Mteril Siene Vol. 2 Iss. 4, Dee me r 2012 Phse Formtion through Stge of Liqui Stte in Metlli Mterils Being Eletroeposite: Reent Experimentl Proofs Oleg B. Girin Deprtment of Mterils

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

ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY

ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri

More information

WORKSHOP 7 PARASOLID SOLID EXAMPLE

WORKSHOP 7 PARASOLID SOLID EXAMPLE WORKSHOP 7 PARASOLID SOLID EXAMPLE WS7-1 WS7-2 Workshop Ojetives Lern some of the steps tht n e use to rete B-rep soli, i.e. extrue surfe, shell, n ege len. Then, rete the finite element moel. Anlyze the

More information

Total score: /100 points

Total score: /100 points Points misse: Stuent's Nme: Totl sore: /100 points Est Tennessee Stte University Deprtment of Computer n Informtion Sienes CSCI 2710 (Trnoff) Disrete Strutures TEST 2 for Fll Semester, 2004 Re this efore

More information

SEMI-EXCIRCLE OF QUADRILATERAL

SEMI-EXCIRCLE OF QUADRILATERAL JP Journl of Mthemtil Sienes Volume 5, Issue &, 05, Pges - 05 Ishn Pulishing House This pper is ville online t http://wwwiphsiom SEMI-EXCIRCLE OF QUADRILATERAL MASHADI, SRI GEMAWATI, HASRIATI AND HESY

More information

CHEM1611 Answers to Problem Sheet 9

CHEM1611 Answers to Problem Sheet 9 CEM1611 Answers to Prolem Sheet 9 1. Tutomers re struturl isomers whih re relte y migrtion of hyrogen tom n the exhnge of single on n jent oule on. Compoun Tutomer 2 2 2 2 2 2 2 2 2 2 2 2. () Whih pir

More information

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

Lecture 8: Abstract Algebra

Lecture 8: Abstract Algebra Mth 94 Professor: Pri Brtlett Leture 8: Astrt Alger Week 8 UCSB 2015 This is the eighth week of the Mthemtis Sujet Test GRE prep ourse; here, we run very rough-n-tumle review of strt lger! As lwys, this

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

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

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

3.15 NMR spectroscopy Different types of NMR There are two main types of NMR 1. C 13 NMR 2. H (proton) NMR .5 NMR spetrosopy Different types of NMR There re two min types of NMR. NMR. (proton) NMR There is only round % in orgni moleules ut modern NMR mhines re sensitive enough to give full spetr for The spetr

More information

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy

More information

Lecture 11 Binary Decision Diagrams (BDDs)

Lecture 11 Binary Decision Diagrams (BDDs) C 474A/57A Computer-Aie Logi Design Leture Binry Deision Digrms (BDDs) C 474/575 Susn Lyseky o 3 Boolen Logi untions Representtions untion n e represente in ierent wys ruth tle, eqution, K-mp, iruit, et

More 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

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

Research Article. ISSN (Print) *Corresponding author Askari, A

Research Article. ISSN (Print) *Corresponding author Askari, A Sholrs Journl of Engineering n Tehnology (SJET) Sh. J. Eng. Teh., 4; (6B):84-846 Sholrs Aemi n Sientifi Pulisher (An Interntionl Pulisher for Aemi n Sientifi Resoures) www.sspulisher.om ISSN 3-435X (Online)

More information

C REVISED PER ECR DEC2015 T.S E.T $ D/C MATING CONNECTOR PART NUMBER WEIGHT. (g)

C REVISED PER ECR DEC2015 T.S E.T $ D/C MATING CONNECTOR PART NUMBER WEIGHT. (g) THIS RWING IS UNPULISHE. OPYRIGHT 00 Y RELESE FOR PULITION LL RIGHTS RESERVE. 00 ISIONS P LTR ESRIPTION TE WN PV 0.7 ISE PER ER0800 E0 T.S E.T 0.7 MTERIL HOUSING:POLYESTER OF GLSS FILLE THERMO PLSTI(UL9V0),

More information

SOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVEX STOCHASTIC PROCESSES ON THE CO-ORDINATES

SOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVEX STOCHASTIC PROCESSES ON THE CO-ORDINATES Avne Mth Moels & Applitions Vol3 No 8 pp63-75 SOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVE STOCHASTIC PROCESSES ON THE CO-ORDINATES Nurgül Okur * Imt Işn Yusuf Ust 3 3 Giresun University Deprtment

More 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

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

A Primer on Continuous-time Economic Dynamics

A Primer on Continuous-time Economic Dynamics Eonomis 205A Fll 2008 K Kletzer A Primer on Continuous-time Eonomi Dnmis A Liner Differentil Eqution Sstems (i) Simplest se We egin with the simple liner first-orer ifferentil eqution The generl solution

More information

Section 2.1 Special Right Triangles

Section 2.1 Special Right Triangles Se..1 Speil Rigt Tringles 49 Te --90 Tringle Setion.1 Speil Rigt Tringles Te --90 tringle (or just 0-60-90) is so nme euse of its ngle mesures. Te lengts of te sies, toug, ve very speifi pttern to tem

More information

Proportions: A ratio is the quotient of two numbers. For example, 2 3

Proportions: A ratio is the quotient of two numbers. For example, 2 3 Proportions: rtio is the quotient of two numers. For exmple, 2 3 is rtio of 2 n 3. n equlity of two rtios is proportion. For exmple, 3 7 = 15 is proportion. 45 If two sets of numers (none of whih is 0)

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

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

Thermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam

Thermal energy 2 U Q W. 23 April The First Law of Thermodynamics. Or, if we want to obtain external work: The trick of using steam April 08 Therml energy Soures of het Trnsport of het How to use het The First Lw of Thermoynmis U W Or, if we wnt to otin externl work: U W 009 vrije Universiteit msterm Close yle stem power plnt The trik

More information

Equivalent fractions have the same value but they have different denominators. This means they have been divided into a different number of parts.

Equivalent fractions have the same value but they have different denominators. This means they have been divided into a different number of parts. Frtions equivlent frtions Equivlent frtions hve the sme vlue ut they hve ifferent enomintors. This mens they hve een ivie into ifferent numer of prts. Use the wll to fin the equivlent frtions: Wht frtions

More information

Angel International School - Manipay

Angel International School - Manipay Gre 6 Angel Interntionl Shool - Mnipy 2 n Term Exmintion Mrh, 2017 Siene Durtion: 02 Hours Inex No:- Prt 1 (1) Unerline the orret nswer. 1) Wht is the isese tht spre y unlen wter? ) Dengue ) Mlri ) Choler

More information

Maximum size of a minimum watching system and the graphs achieving the bound

Maximum size of a minimum watching system and the graphs achieving the bound Mximum size of minimum wthing system n the grphs hieving the oun Tille mximum un système e ontrôle minimum et les grphes tteignnt l orne Dvi Auger Irène Chron Olivier Hury Antoine Lostein 00D0 Mrs 00 Déprtement

More information

Now we must transform the original model so we can use the new parameters. = S max. Recruits

Now we must transform the original model so we can use the new parameters. = S max. Recruits MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with

More 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

Mid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours

Mid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours Mi-Term Exmintion - Spring 0 Mthemtil Progrmming with Applitions to Eonomis Totl Sore: 5; Time: hours. Let G = (N, E) e irete grph. Define the inegree of vertex i N s the numer of eges tht re oming into

More information

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

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and Leture 7: iffusion of Ions: Prt : oupled diffusion of tions nd nions s desried y Nernst-Plnk Eqution Tody s topis Continue to understnd the fundmentl kinetis prmeters of diffusion of ions within n eletrilly

More information

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

Continuous Random Variables

Continuous Random Variables CPSC 53 Systems Modeling nd Simultion Continuous Rndom Vriles Dr. Anirn Mhnti Deprtment of Computer Science University of Clgry mhnti@cpsc.uclgry.c Definitions A rndom vrile is sid to e continuous if there

More information

SIMPLE NONLINEAR GRAPHS

SIMPLE NONLINEAR GRAPHS S i m p l e N o n l i n e r G r p h s SIMPLE NONLINEAR GRAPHS www.mthletis.om.u Simple SIMPLE Nonliner NONLINEAR Grphs GRAPHS Liner equtions hve the form = m+ where the power of (n ) is lws. The re lle

More 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

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

10.7 Assessment criteria for the individual investigation

10.7 Assessment criteria for the individual investigation Unit 6 Prtil Biology n Investigtive Skills 10.7 for the iniviul investigtion Reserh n rtionle There is some ttempt to provie rtionle for the hoie of investigtion in terms of its sope n its reltion to iologil

More 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

Thermal Stability of Ti-C-Ni-Cr and Ti-C-Ni-Cr-Al-Si Nanocomposite Coatings

Thermal Stability of Ti-C-Ni-Cr and Ti-C-Ni-Cr-Al-Si Nanocomposite Coatings Journl of Physics: Conference Series PAPER OPEN ACCESS Therml Stility of Ti-C-Ni-Cr nd Ti-C-Ni-Cr-Al-Si Nnocomposite Cotings To cite this rticle: A V Andreev et l 2015 J. Phys.: Conf. Ser. 652 012057 View

More information

Mathematical Proofs Table of Contents

Mathematical Proofs Table of Contents Mthemtil Proofs Tle of Contents Proof Stnr Pge(s) Are of Trpezoi 7MG. Geometry 8.0 Are of Cirle 6MG., 9 6MG. 7MG. Geometry 8.0 Volume of Right Cirulr Cyliner 6MG. 4 7MG. Geometry 8.0 Volume of Sphere Geometry

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

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

2.4 Theoretical Foundations

2.4 Theoretical Foundations 2 Progrmming Lnguge Syntx 2.4 Theoretil Fountions As note in the min text, snners n prsers re se on the finite utomt n pushown utomt tht form the ottom two levels of the Chomsky lnguge hierrhy. At eh level

More information

Geodesics on Regular Polyhedra with Endpoints at the Vertices

Geodesics on Regular Polyhedra with Endpoints at the Vertices Arnol Mth J (2016) 2:201 211 DOI 101007/s40598-016-0040-z RESEARCH CONTRIBUTION Geoesis on Regulr Polyher with Enpoints t the Verties Dmitry Fuhs 1 To Sergei Thnikov on the osion of his 60th irthy Reeive:

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

Solving the Class Diagram Restructuring Transformation Case with FunnyQT

Solving the Class Diagram Restructuring Transformation Case with FunnyQT olving the lss Digrm Restruturing Trnsformtion se with FunnyQT Tssilo Horn horn@uni-kolenz.e Institute for oftwre Tehnology, University Kolenz-Lnu, Germny FunnyQT is moel querying n moel trnsformtion lirry

More information

On the Spectra of Bipartite Directed Subgraphs of K 4

On the Spectra of Bipartite Directed Subgraphs of K 4 On the Spetr of Biprtite Direte Sugrphs of K 4 R. C. Bunge, 1 S. I. El-Znti, 1, H. J. Fry, 1 K. S. Kruss, 2 D. P. Roerts, 3 C. A. Sullivn, 4 A. A. Unsiker, 5 N. E. Witt 6 1 Illinois Stte University, Norml,

More information

DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS

DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS Krgujev Journl of Mthemtis Volume 38() (204), Pges 35 49. DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS MOHAMMAD W. ALOMARI Abstrt. In this pper, severl bouns for the ifferene between two Riemn-

More information

The DOACROSS statement

The DOACROSS statement The DOACROSS sttement Is prllel loop similr to DOALL, ut it llows prouer-onsumer type of synhroniztion. Synhroniztion is llowe from lower to higher itertions sine it is ssume tht lower itertions re selete

More information

Cahn-In Gold-Prelog R/S System Revisited: Simplifying Assignment of Configuration in Chiral Compounds

Cahn-In Gold-Prelog R/S System Revisited: Simplifying Assignment of Configuration in Chiral Compounds Review Artile imepu Journls http://www.imepu.om Journl of Orgni & Inorgni Chemistry ISSN 7- DOI: 0.767/7-.0000 Chn-In Gol-Prelog R/S System Revisite: Simplifying Assignment of Configurtion in Chirl Compouns

More information

Exam 1 Study Guide. Differentiation and Anti-differentiation Rules from Calculus I

Exam 1 Study Guide. Differentiation and Anti-differentiation Rules from Calculus I Exm Stuy Guie Mth 26 - Clulus II, Fll 205 The following is list of importnt onepts from eh setion tht will be teste on exm. This is not omplete list of the mteril tht you shoul know for the ourse, but

More information

U Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( )

U Q W The First Law of Thermodynamics. Efficiency. Closed cycle steam power plant. First page of S. Carnot s paper. Sadi Carnot ( ) 0-9-0 he First Lw of hermoynmis Effiieny When severl lterntive proesses involving het n work re ville to hnge system from n initil stte hrterize y given vlues of the mrosopi prmeters (pressure p i, temperture

More information

Particle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/)

Particle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/) Sutomic Physics: Prticle Physics Lecture 3 Mesuring Decys, Sctterings n Collisions Prticle lifetime n with Prticle ecy moes Prticle ecy kinemtics Scttering cross sections Collision centre of mss energy

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