DISTRIBUTION A: Distribution approved for public release.
|
|
- Rebecca Sutton
- 6 years ago
- Views:
Transcription
1 AFRL-AFOSR-UK-TR Optial otrol of graphee plasmo usig liquid rystal layer 9K New Oe Viktor Yuriyovyh Reshetyak SCIENCE AND TECHNOLOGY CENTER IN UKRAINE 03/0/07 Fial Report DISTRIBUTION A: Distributio approved for publi release. Air Fore Researh Laboratory AF Offie Of Sietifi Researh (AFOSR)/ IOE Arligto, Virgiia 03 Air Fore Materiel Commad
2 FORM SF 98 Page of 3//07 REPORT DOCUMENTATION PAGE Form Approved OMB No The publi reportig burde for this olletio of iformatio is estimated to average hour per respose, iludig the time for reviewig istrutios, searhig existig data soures, gatherig ad maitaiig the data eeded, ad ompletig ad reviewig the olletio of iformatio. Sed ommets regardig this burde estimate or ay other aspet of this olletio of iformatio, iludig suggestios for reduig the burde, to Departmet of Defese, Exeutive Servies, Diretorate ( ). Respodets should be aware that otwithstadig ay other provisio of law, o perso shall be subjet to ay pealty for failig to omply with a olletio of iformatio if it does ot display a urretly valid OMB otrol umber. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.. REPORT DATE (DD-MM-YYYY). REPORT TYPE 3. DATES COVERED (From - To) Fial 0 Jul 05 to 30 Ju TITLE AND SUBTITLE 5a. CONTRACT NUMBER Optial otrol of graphee plasmo usig liquid rystal layer 9K New Oe 5b. GRANT NUMBER STCU-P65 5. PROGRAM ELEMENT NUMBER 60F 6. AUTHOR(S) Viktor Yuriyovyh Reshetyak 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) SCIENCE AND TECHNOLOGY CENTER IN UKRAINE METALISTIV 7A KYIV, UA 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) EOARD Uit 455 APO AE DISTRIBUTION/AVAILABILITY STATEMENT A DISTRIBUTION UNLIMITED: PB Publi Release 8. PERFORMING ORGANIZATION REPORT NUMBER 0. SPONSOR/MONITOR'S ACRONYM(S) AFRL/AFOSR IOE. SPONSOR/MONITOR'S REPORT NUMBER(S) AFRL-AFOSR-UK-TR SUPPLEMENTARY NOTES 4. ABSTRACT The projet is devoted to the basi researh ad establishes possible optial ways to otrol the surfae plasmo polarito i graphee layer. A system omprises the graphee ribbos gratig plaed betwee a emati liquid rystal (LC) ad a isotropi dieletri. Iidet light wave exites a plasmo i the graphee ribbos, whih ifluees the light propagatio i the system. The gratig struture of the graphee moolayer is eessary to provide the plasmo exitatio beause there is a huge wave vetor mismath betwee the graphee plasmoi wave ad the iidet eletromageti wave. I graphee strutures the resoat plasmo frequey depeds o the dieletri properties of layers plaed above ad below the graphee sheet or ribbo. I our ase, it meas that plasmo frequey must deped o the LC dieletri permittivity. The LC dieletri permittivity depeds o the LC diretor orietatioal state, whih a be otrolled by exteral field. Therefore, a propagatio of the surfae plasmo polarito i graphee layer a be tued by reorietig the LC diretor usig exteral eletri or mageti fields. 5. SUBJECT TERMS ovel orgai-iorgai strutures, graphee ad liquid rystal layers,, plasmoi waves i graphee, EOARD, STCU 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF a. REPORT Ulassified b. ABSTRACT Ulassified. THIS PAGE Ulassified ABSTRACT SAR 8. NUMBER OF PAGES 3 9a. NAME OF RESPONSIBLE PERSON CUMMINGS, RUSSELL 9b. TELEPHONE NUMBER (Ilude area ode) Stadard Form 98 (Rev. 8/98) Presribed by ANSI Std. Z39.8
3 STCU PROJECT P65 - FINAL REPORT FF PAGE Short form File/page Exeutive summary SF.do PAGE Cooperatio with foreig ollaborators SF.do PAGE Publiatios SF.do PAGE Prospets of future developmet (for fial report oly) SF.do PAGE Full form Projet mai idea FF.do PAGE Tehial approah FF.do PAGE Tehial progress overview FF.do PAGE 7 Curret status of the projet FF.do PAGE 0 Summary of persoel ommitmet FF.do PAGE 0 Desriptio of travels FF.do PAGE 0 Iformatio about major equipmet ad materials aquired, other diret osts, related to the projet FF.do PAGE 0. Expressio for plasmo frequey i the hybrid system with the LC layer. 4. Results ad Disussio T..do PAGE 3. Plasmo frequey depedee o the orietatioal state of the LC layer. 4. Results ad Disussio T..do PAGE 3 3. Expressios for oeffiiets of light refletio ad trasmissio i the hybrid system. 4. Results ad Disussio T..do PAGE 4 4. Optimal parameters for ative otrol of light propagatio ad refletio. 4. Results ad Disussio T..do PAGE 3 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
4 STCU PROJECT P65 - FINAL REPORT FF PAGE Projet mai idea The projet is devoted to the basi researh ad establishes possible optial ways to otrol the surfae plasmo polarito i graphee layer. A system omprises the graphee ribbos gratig plaed betwee a emati liquid rystal (LC) ad a isotropi dieletri. Iidet light wave exites a plasmo i the graphee ribbos, whih ifluees the light propagatio i the system. The gratig struture of the graphee moolayer is eessary to provide the plasmo exitatio beause there is a huge wave vetor mismath betwee the graphee plasmoi wave ad the iidet eletromageti wave. I graphee strutures the resoat plasmo frequey depeds o the dieletri properties of layers plaed above ad below the graphee sheet or ribbo. I our ase, it meas that plasmo frequey must deped o the LC dieletri permittivity. The LC dieletri permittivity depeds o the LC diretor orietatioal state, whih a be otrolled by exteral field. Therefore, a propagatio of the surfae plasmo polarito i graphee layer a be tued by reorietig the LC diretor usig exteral eletri or mageti fields. After establishig the plasmo freguey depedee o the LC diretor orietatioal state we shall study a light wave propagatio aross the system uder osideratio. We shall alulate the absorptio, refletio, ad trasmissio oeffiiets ad show that otrol of the orietatioal state of the LC layer eables us to maipulate by magitude of the absorptio/refletio maxima. These results will allow suggestig a ew type of the graphee miro-ribbo gratig strutures to otrol light beams propagatio. Tehial approah Depedee of plasmo frequey o the LC diretor orietatioal state. Shemati of the hybrid system, LC graphee moolayer isotropi dieletri, is preseted i Fig.. z d, diretor y ˆ graphee LC σ 3 ε x Fig.. Shemati of the hybrid system: LC graphee moolayer isotropi dieletri. We use the followig desigatios: ˆ is the LC dieletri tesor, graphee surfae odutivity,, is the isotropi dieletri permittivity, is the are the LC diretor agles. We write the Maxwell equatios for system show i Fig. ad seek their solutio i the followig form: ) for the wave i the LC ( z 0) ( ) E E e x x z z iqx t Qz E e e, H e H e, () ) for the wave i the isotropi dieletri ( z 0 ) ( ) E E e x x z z iqx t Qz y y iqx ( Qz E e e, H e H e. () y y iqx ( Q z 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
5 STCU PROJECT P65 - FINAL REPORT FF PAGE 3 Substitutig (), (3) ito Maxwell's equatios we take ito aout that the LC dieletri tesor has a geeral form where o optial frequeies xx xy xz ˆ xy yy yz xz yz zz, (3) ij o ij e o dd i j. (4) Here d is the diretor Cartesia ompoet,, are the refrative idies for ordiary ad extraordiary waves i o e i the LC, respetively. To the expressios obtaied after substitutio (), () ito Maxwell's equatios we must add the boudary oditios, x z0 x z0 y y x z0 z0 E E, H H E (5) Demadig the boudary oditios (5) to be satisfied we obtai after some algebrai trasformatios a dispersio equatio for plasmo wave propagatig i the graphee xxzz xz i, (6) zz 0 q q were xx os si, zz xz o e o o e o os, e o os si os (7) ad the LC diretor agles are show i Fig.. The graphee surfae odutivity i (6), i geeral ase, a be expressed as a sum of two terms, it ra it er, where the first term orrespods to the itrabad eletro trasitios ad the seod term gives otributio from the iterbad trasitios. For kt B ad for the Fermi eergy EF kbt it a be approximately writte as [], ie EF ie EF i / it ra, it er l (8) i/ 4 EF i/ I the oretarded limit q / the dispersio equatio (6) simplifies ad we arrive at expressio q i 0 xxzz xz, (9) It is see that ifluee of the LC orietatioal state o the dispersio equatio is desribed by term 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
6 STCU PROJECT P65 - FINAL REPORT FF PAGE 4, si os os / si si (0) xx zz xz e o o e Refletio ad trasmissio oeffiiets. Cosider a graphee miro-ribbo gratig i the xy-plae plaed betwee a emati LC layer (aisotropi top substrate) ad a isotropi dieletri substrate. Eah miro-ribbo i the gratig is a sigle layer graphee with the ribbo alog the y-axis, where d is the miro-ribbo width ad is the gratig spaig (Fig. ). A plae moohromati wave propagates alog the z-axis from the side of the LC ad exites the plasmos i the graphee miro-ribbos. We assume semi-ifiite substrates that allows us to eglet the effets of multiple refletios; i the y - diretio the system is ifiite. To simplify alulatios we suppose the LC diretor to be oly reorieted i the xz-plae, where the agle desribes the diretor deviatio from the z-axis. We also set the mageti vetor of the iidet wave to be perpediular to the xz-plae (TM-wave). z k i ћω LC y ˆ d e Graphe x Fig.. Shemati of the graphee miro-ribbo gratig struture. d is the ribbo width, is the gratig spaig, is the diretor agle with the z-axis, ˆ is the LC dieletri tesor, is the isotropi substrate dieletri permittivity, is the graphee odutivity, e is a ormal to the graphee plae, ad ki is the wave vetor of a iidet plae moohromati wave. Beause of the strog ofiemet of the surfae plasmo-polaritos (SPPs) i the ribbos, oly the thi layer of the LC substrate ear the graphee ifluees the SPPs. Therefore, we a set the LC diretor orietatio i the whole substrate to be homogeeous ad equal to the diretor orietatio of this layer ear the graphee. The LC optial dieletri tesor a be writte i the form ij oij ( e o ) i j, i x, y, z, where i deotes the ompoets of the diretor =(si,0,os ); o ad e are the refrative idies of the ordiary ad extraordiary waves, respetively []. We suppose that the TM-wave is ormally iidet i the LC o the graphee gratig. As it follows from the Maxwell equatios, eletri ad mageti vetors of this wave i the LC take the form: k E E e E e e, H E e e, E ( / ) E, () i( ki z i i ( ki z i ix x iz z i ix y iz xz zz ix 0 with the dispersio equatio k i. () xz xx zz 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
7 STCU PROJECT P65 - FINAL REPORT FF PAGE 5 For refleted ad trasmitted waves, we use the Fourier-Floquet expasio with respet to the oordiate x. Satisfyig the Maxwell equatios, the eletri ad mageti vetors of these waves a be writte as follows: i) for the refleted wave / E k k e k k e a e H zz r zz r xz x xz r xx z / xx xz zz i ( kxkrz r 0 xx xz / zz a e ey, i ( kxkrz, (3) with the dispersio equatio k k xz xz r xx k zz zz zz ; (4) ii) for the trasmitted wave E e e H i ( k xkt z k k b e t t x z i ( k xkt z t 0 b e ey,, (5) with the dispersio equatio k t k. (6) Here k /, is the umber of a Floquet spatial harmoi. We defie the urret desity i the plae of the graphee gratig as j s ( x) Etx (z = 0) ex, where ( x) withi eah miro-ribbo ad ( x) 0 i the gaps betwee miro-ribbos. Substitutig Etx (z = 0) from eq. (5), we obtai i ( k x j s ( x) ktb e ex. (7) To obtai equatios for oeffiiets a, b of the Fourier-Floquet expasios (3), (5) we use the boudary oditios: e Hi Hr Ht js z0 ex 0, e Ei Er Et z0 ey 0. Now we substitute eqs. (), (3), (5) for eletri ad mageti vetors ad eq.(7) for the urret desity j s ito eqs. (8). The, usig the dispersio equatios (), (4), (6) we arrive at (8) 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
8 STCU PROJECT P65 - FINAL REPORT FF PAGE 6 i x xz 4 ( x) xz xx a b e xx Eix 0 zz 0 zz, (9) a b e Eix 0. (0) i x 4 4 zz Multiplyig eqs. (9), (0) by e i m x the rage [0, ] we obtai the set of equatios for oeffiiets a, b :, where m is a iteger ad itegratig these equatios over x i 4 b E a ix 0 4 zz, () 4 d xz xx zz 0 zz i e mm ( ) m i ( m) d zz ( m) d xx / xz zz 0 4 a m Eix a i e i d E ( ). 0 ix 0 0 I the ifrared ad terahertz spetral regios the itrabad otributio to the graphee odutivity domiates. The, i the radom phase approximatio the D odutivity of graphee a be writte as [3] where ee F () i, (3) i EF is the Fermi eergy of graphee, is the eletro relaxatio time, e is the eletro harge. The refletio ad trasmissio oeffiiets are defied as R E H E H, * * Re( r r) / Re( i i) T E H E H. (4) * * Re( t / Re( i i) 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
9 STCU PROJECT P65 - FINAL REPORT FF PAGE 7 The graphee absorptio oeffiiet is A ( R T). Numerially solvig equatios ()-(3) the oeffiiets a, b are obtaied. Usig formulas (3), (5) to fid the eletri ad mageti vetors of the refleted ad trasmitted waves ad after their substitutio ito formula (4), we alulate the refletio, trasmissio, ad absorptio oeffiiets. Tehial progress overview I Fig. 3 we show depedee of quatity, o the LC diretor agles, for two pairs of the refrative idies of the ordiary ad extraordiary waves i the LC, o, e. Fig. 3., (a) versus, (b) : (a) o.53, e.94 ; (b) o.94, e.53. Below i Fig. 4 we also show for illustratio the ross-setios of futio, by vertial plaes. (a) Fig. 4. Cross-setios of futio, (b) by vertial plaes: (a) o.53, e.94 ;(b) o.94, e.53 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
10 STCU PROJECT P65 - FINAL REPORT FF PAGE 8 Aalyzig formula (0) (or Figs. 3, 4) we a olude that ratio max / mi resposible for iterval of tuig the plasmo wave vetor (or frequey) by the LC diretor reorietatio equals e / oif e oor o / eif o e. It is eessary to ote that i the retarded regio ( q zz / ) where istead of formula (9) we have to use formula (6), the small orretio to this estimatio a arise from zz i deomiator of formula (6). As material of the emati layer, we use the high birefrigee ( 0.4 ) LC mixture W79 with 0.53, e.94 at.064 μm [4]. The birefrigee of W79, whih is kow i visible ad ear-ir regios of spetrum, was extrapolated to mid-ir ad THz frequeies usig the exteded Cauhy dispersio formulas obtaied for the LC mixture E7 [5]. I our study, we hose either a low dieletri ostat material (e.g. hexagoal boro itride, h-bn, hbn - 3 ) [6, 7] or a high dieletri ostat material (silio, Si, Si.7 ) [8] as the isotropi substrate material. The physial parameters of the graphee gratig i our simulatios are as follows: the gratig spaig was fixed at μm, the miro-ribbo width was varied as d 0.3, ad 0.. For evaluatio of the 6 eletro relaxatio time we used the formula EF /( evf ), where is the arrier mobility, vf 30 m s - was the Fermi veloity i graphee [0]. Settig EF 0.64 ev [9] ad the arrier mobility 0.5 m /(V s) we get the arrier satterig time 0.3 ps. The simulatios were performed i the wavelegth rage μm ( THz) with a temperature T 300 K. The overgee of the omputatioal proedure used with respet to higher Fouquet harmois is eessary. I order to esure the required auray of alulatios, it was suffiiet to selet the umber of harmois N 400 i eqs. (), (). Results of our umerial alulatios of absorptio, refletio, ad trasmissio spetra of the graphee gratig are show i Figs. 5 ad 6. Fig. 5 illustrates the hage of the absorptio, refletio, ad trasmissio spetra of the graphee gratig for two limitig values of the LC diretor agle 0 ad 90 o, ad a ribbo width to gratig spaig ratio d / 0.5. Curves ad orrespod to the ases of a isotropi substrate with either a low or a high dieletri ostat, respetively. Maxima i the absorptio ad refletio spetra are related to the exitatio of the plasmos i the graphee miro-ribbos. Withi our frequey rage two plasmo peaks i urves are observed. The ratio of the resoat frequeies orrespodig to these peaks is equal to, whih agrees with the results obtaied i paper [9] for the graphee gratig plaed betwee two isotropi dieletri substrates. As we a see from Fig. 5, values of these maxima deped o the LC diretor orietatio. I partiular, the rotatio of the LC diretor by 90 leads to a hage of the absorptio maximum value by approximately 4% whe (h-bn substrate) ad by 6% whe.7 (Si substrate). 3 Absorptio (a) Wavelegth (m) Refletio, Trasmissio (b) T R Wavelegth (m) (a) (b) Fig. 5. Absorptio (a), refletio ad trasmissio (b) spetra of the graphee miro-ribbo gratig at differet agles of the emati diretor: 0- solid lie, 90 - dash-dot lie. Substrate dieletri ostat: 3 - urves,.7 - urves. Ratio d / 0.5. T R 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
11 STCU PROJECT P65 - FINAL REPORT FF PAGE 9 I Fig. 6, the hage of the absorptio, refletio, ad trasmissio spetra of the graphee gratig at the two limitig values of the LC diretor agle is show for two values of the ribbo width to gratig spaig ratio, d / 0.3 ad d / 0.7. I this ase, the rotatio of the LC diretor by 90 leads to the hage i the absorptio by approximately 4% whe d / 0.3 ad by 8% whe d / 0.7. A ompariso of the results preseted i Figs. 5, 6 shows that the effet of the LC diretor rotatio ireases with a irease of the isotropi substrate dieletri ostat ad the ribbo width to gratig spaig ratio d / Absorptio Wavelegth (m) Refletio, Trasmissio T R Wavelegth (m) a) (b) Fig. 6. Absorptio (a), refletio ad trasmissio (b) spetra of the graphee miro-ribbo gratig at differet agles of the emati diretor: 0 - solid lie, 90 - dash-dot lie. Ratio d / urves, d / urves. Substrate dieletri ostat.7. O sietifi results of the projet oe paper is published, oe paper is prepared for publiatio, ad four reports o iteratioal oferees were delivered. Referees.. H. Lu et al. Si. Rep. 5, 8843; DOI:0.038/srep08443(05).. P. G. de Gees ad J. Prost. The Physis of Liquid Crystals, ser. Iteratioal Series of Moographs o Physis. (Oxford, U. K.: Oxford Uiv. Press, 995). 3. M. Jabla, H. Bulja, ad M. Soljačić, Plasmois i graphee at ifrared frequeies, Phys. Rev. B 80(4), (009). 4. E. Nowiowski-Kruszeliki, J. Kędzierski, Z. Raszewski, L. Jaroszewiz, R. Dąbrowski, M. Kojdeki, W. Pieek, P. Perkowski, K. Garbat, M. Olifierzuk, M. Sutkowski, K. Ogrodik, P. Morawiak, ad E. Miszzyk, High birefrigee liquid rystal mixtures for eletro-optial devies, Optia Appliata 4(), (0). 5. J. Li, S. T. Wu, S. Brugioi, R. Meui, ad S. Faetti, Ifrared refrative idies of liquid rystals, J. Appl. Phys. 97, (005). 6. N. Ohba, K. Miwa, N. Nagasako, ad A. Fukumoto, First-priiples study o strutural, dieletri, ad dyamial properties for three BN polytypes, Phys. Rev. B63(), 507 (00). 7. C. R. Dea, A. F. Youg, I. Meri, C. Lee, L. Wag, S. Sorgefrei, K. Wataabe, T. Taiguhi, P. Kim, K. L. Shepard, ad J. Hoe, Boro itride substrates for high-quality graphee eletrois, Nat. Naotehol. 5(0), 7-76 (00). 8. N. K. Emai, Di Wag, T.-F. Chug, L. J. Prokopeva, A. V. Kildishev, V. M. Shalaev, Y. P. Che, ad A. Boltasseva, Plasmo resoae i multilayer graphee aoribbos, Laser Photois Rev. 9(6), (05). 9. A. Yu. Nikiti, F. Guiea, F. J. Garia-Vidal, ad L. Marti-Moreo, Surfae plasmo ehaed absorptio ad suppressed trasmissio i periodi arrays of graphee ribbos, Phys. Rev. B85(8), (0). R T 3//07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
12 STCU PROJECT P65 - FINAL REPORT FF PAGE 0 0. W. Gao, J. Shu, C. Qiu, ad Q. Xu, Exitatio of plasmoi waves i graphee by guided-mode resoaes, ACS Nao 6(9), (0). Curret status of the projet. Сurret tehial status of the projet: o shedule. Summary of persoel ommitmet. Professors of Taras Shevheko Natioal Uiversity of Kyiv V. Yu. Reshetyak, I. P. Pikevyh ad Dr. V. I. Zadorozhii fulfilled the tasks durig the reported period. Prof. V. Yu. Reshetyak - developed the mathematial model of the hybrid system with the LC layer, - obtaied expressios for plasmo frequey i the hybrid system with the LC layer, - alulated the graphee plasmo frequey i depedee o the orietatioal state of the LC layer, - obtaied equatios desribig light propagatio i the hybrid system with plasmo exitatio i the graphee, - developed umerial methods for alulatio oeffiiets of light refletio ad trasmissio i the hybrid system, - optimized the hybrid system parameters for ative otrol of light propagatio ad refletio. Prof. I.P. Pikevyh - obtaied ad solved equatios for the diretor ad eletri field i the LC ell, - studied the ifluee of ahorig o the LC ell boudaries o the diretor i the ell bulk, - studied the otrol of plasmo frequey by DC field ad iidet light field, - obtaied expressios for oeffiiets of light refletio ad trasmissio i the hybrid system, - studied ifluee of the LC layer orietatioal state o light refletio ad trasmissio i the hybrid system. Dr. V.I. Zadorozhii fulfilled umerial alulatios of light refletio ad trasmissio oeffiiets i depedee o the ahorig oditios o the LC ell boudaries. Variatios i the sheduled amouts of efforts. Prof. V. Yu. Reshetyak ad Prof. I.P. Pikevyh fulfilled the followig tasks plaed iitially for Dr. V.I. Zadorozhii: alulatio of the graphee plasmo frequey i depedee o the orietatioal state of the LC layer (Reshetyak), develop umerial methods for alulatio oeffiiets of light refletio ad trasmissio i the hybrid system (Reshetyak) study the ifluee of ahorig o the LC ell boudaries o the diretor i the ell bulk (Pikevyh). Desriptio of travels. Travel of prof. V. Yu. Reshetyak for partiipatio i Coferee o Photorefrative Materials, Villars, Switzerlad, 6-9 Jue 05. Report was delivered o sietifi results of the projet. Travel of prof. V. Yu. Reshetyak for partiipatio i 9th Iteratioal Cogress o Advaed Eletromageti Materials i Mirowaves ad Optis, Oxford, UK, 7- September 05; Travels of prof. V. Yu. Reshetyak ad prof. I. P. Pikevyh for partiipatio i 6th Topial Meetig o the Optis of Liquid Crystals, Sopot, Polad, 3-8 September, 05. Report was delivered o sietifi results of the projet. Travels of prof. V. Yu. Reshetyak ad prof. I. P. Pikevyh for partiipatio i Iteratioal oferee "Flowig Matter 06", Porto, Portugal, -5 Jauary 06. Report was delivered o sietifi results of the projet. Iformatio about major equipmet ad materials aquired, other diret osts, related to the projet. There was ot purhase of equipmet or materials, ad other diret osts have ot bee spet. Table Rediretio Referee doumets &date () L New requested ategory, or old ategory with ew ost () Grat - FWS Requested ost (ew) (3) Quarter 4 Origial (old) ategory (4) Estimated ost (old) (5) Redireted ost (6) old ew Grats-NFWS, Equipmet, Materials, //07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
13 STCU PROJECT P65 - FINAL REPORT FF PAGE Other diret osts Total //07 DISTRIBUTION A. Approved for publi release: distributio ulimited.
Basic Waves and Optics
Lasers ad appliatios APPENDIX Basi Waves ad Optis. Eletromageti Waves The eletromageti wave osists of osillatig eletri ( E ) ad mageti ( B ) fields. The eletromageti spetrum is formed by the various possible
More information4. Optical Resonators
S. Blair September 3, 2003 47 4. Optial Resoators Optial resoators are used to build up large itesities with moderate iput. Iput Iteral Resoators are typially haraterized by their quality fator: Q w stored
More informationFluids Lecture 2 Notes
Fluids Leture Notes. Airfoil orte Sheet Models. Thi-Airfoil Aalysis Problem Readig: Aderso.,.7 Airfoil orte Sheet Models Surfae orte Sheet Model A aurate meas of represetig the flow about a airfoil i a
More informationTHE MEASUREMENT OF THE SPEED OF THE LIGHT
THE MEASUREMENT OF THE SPEED OF THE LIGHT Nyamjav, Dorjderem Abstrat The oe of the physis fudametal issues is a ature of the light. I this experimet we measured the speed of the light usig MihelsoÕs lassial
More informationQuasi Normal Modes description of transmission properties for Photonic Band Gap structures.
Quasi ormal Modes desriptio of trasmissio properties for Photoi Bad Gap strutures. A. Settimi (1-), S. Severii (3), B. J. Hoeders (4) (1) FILAS (Fiaziaria Laziale di Sviluppo) via A. Farese 3, 19 Roma,
More informationQuasi Normal Modes description. of transmission properties. for Photonic Band Gap structures.
Quasi Normal Modes desriptio of trasmissio properties for Photoi Bad Gap strutures. A. Settimi (1), S. Severii (), B. J. Hoeders (3) (1) INGV (Istituto Nazioale di Geofisia e Vulaologia) via di Viga Murata
More informationI. Existence of photon
I. Existee of photo MUX DEMUX 1 ight is a eletromageti wave of a high frequey. Maxwell s equatio H t E 0 E H 0 t E 0 H 0 1 E E E Aos( kzt ) t propagatig eletrial field while osillatig light frequey (Hz)
More informationAfter the completion of this section the student. V.4.2. Power Series Solution. V.4.3. The Method of Frobenius. V.4.4. Taylor Series Solution
Chapter V ODE V.4 Power Series Solutio Otober, 8 385 V.4 Power Series Solutio Objetives: After the ompletio of this setio the studet - should reall the power series solutio of a liear ODE with variable
More informationME260W Mid-Term Exam Instructor: Xinyu Huang Date: Mar
ME60W Mid-Term Exam Istrutor: Xiyu Huag Date: Mar-03-005 Name: Grade: /00 Problem. A atilever beam is to be used as a sale. The bedig momet M at the gage loatio is P*L ad the strais o the top ad the bottom
More information= 47.5 ;! R. = 34.0 ; n air =
Setio 9: Refratio ad Total Iteral Refletio Tutorial Pratie, page 449 The agle of iidee is 65 The fat that the experimet takes plae i water does ot hage the agle of iidee Give:! i = 475 ;! R = 340 ; air
More informationλ = 0.4 c 2nf max = n = 3orɛ R = 9
CHAPTER 14 14.1. A parallel-plate waveguide is kow to have a utoff wavelegth for the m 1 TE ad TM modes of λ 1 0.4 m. The guide is operated at wavelegth λ 1 mm. How may modes propagate? The utoff wavelegth
More informationPhysics 3 (PHYF144) Chap 8: The Nature of Light and the Laws of Geometric Optics - 1
Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 8. The ature of light Before 0 th etury, there were two theories light was osidered to be a stream of partiles emitted by a
More informationLecture 1: Semiconductor Physics I. Fermi surface of a cubic semiconductor
Leture 1: Semiodutor Physis I Fermi surfae of a ubi semiodutor 1 Leture 1: Semiodutor Physis I Cotet: Eergy bads, Fermi-Dira distributio, Desity of States, Dopig Readig guide: 1.1 1.5 Ludstrom 3D Eergy
More informationME203 Section 4.1 Forced Vibration Response of Linear System Nov 4, 2002 (1) kx c x& m mg
ME3 Setio 4.1 Fored Vibratio Respose of Liear Syste Nov 4, Whe a liear ehaial syste is exited by a exteral fore, its respose will deped o the for of the exitatio fore F(t) ad the aout of dapig whih is
More informationObserver Design with Reduced Measurement Information
Observer Desig with Redued Measuremet Iformatio I pratie all the states aot be measured so that SVF aot be used Istead oly a redued set of measuremets give by y = x + Du p is available where y( R We assume
More informationEffects of Air Humidity on the Performance of a Polymer Insulator under Lightning Induced Voltage Conditions
Effets of Air Humidity o the Performae of a Polymer Isulator uder Lightig Idued Voltage Coditios Mahdi Izadi *, Mohd Zaial Abidi Ab Kadir 2, Chadima Gomes 3, Mohd Syahmi 4, Maryam Hajihai 5,2,3,4,5 Cetre
More informationConstruction of Control Chart for Random Queue Length for (M / M / c): ( / FCFS) Queueing Model Using Skewness
Iteratioal Joural of Sietifi ad Researh Publiatios, Volume, Issue, Deember ISSN 5-5 Costrutio of Cotrol Chart for Radom Queue Legth for (M / M / ): ( / FCFS) Queueig Model Usig Skewess Dr.(Mrs.) A.R. Sudamai
More informationEffect of Magnetic Field on Marangoni Convection in Relatively Hotter or Cooler Liquid Layer
Iteratioal Joural of Advaed Researh i Physial Siee (IJARPS) Volume, Issue, Jauary 05, PP 7-3 ISSN 349-7874 (Prit) & ISSN 349-788 (Olie) www.arjourals.org ffet of Mageti Field o Maragoi Covetio i Relatively
More informationClass #25 Wednesday, April 19, 2018
Cla # Wedesday, April 9, 8 PDE: More Heat Equatio with Derivative Boudary Coditios Let s do aother heat equatio problem similar to the previous oe. For this oe, I ll use a square plate (N = ), but I m
More informationBasic Probability/Statistical Theory I
Basi Probability/Statistial Theory I Epetatio The epetatio or epeted values of a disrete radom variable X is the arithmeti mea of the radom variable s distributio. E[ X ] p( X ) all Epetatio by oditioig
More informationNonparametric Goodness-of-Fit Tests for Discrete, Grouped or Censored Data 1
Noparametri Goodess-of-Fit Tests for Disrete, Grouped or Cesored Data Boris Yu. Lemeshko, Ekateria V. Chimitova ad Stepa S. Kolesikov Novosibirsk State Tehial Uiversity Departmet of Applied Mathematis
More informationDigital Signal Processing. Homework 2 Solution. Due Monday 4 October Following the method on page 38, the difference equation
Digital Sigal Proessig Homework Solutio Due Moda 4 Otober 00. Problem.4 Followig the method o page, the differee equatio [] (/4[-] + (/[-] x[-] has oeffiiets a0, a -/4, a /, ad b. For these oeffiiets A(z
More informationLesson 8 Refraction of Light
Physis 30 Lesso 8 Refratio of Light Refer to Pearso pages 666 to 674. I. Refletio ad Refratio of Light At ay iterfae betwee two differet mediums, some light will be refleted ad some will be refrated, exept
More informationPhysics 30 Lesson 8 Refraction of Light
Physis 30 Lesso 8 Refratio of Light Refer to Pearso pages 666 to 674. I. Refletio ad refratio of light At ay iterfae betwee two differet mediums, some light will be refleted ad some will be refrated, exept
More informationBernoulli Numbers. n(n+1) = n(n+1)(2n+1) = n(n 1) 2
Beroulli Numbers Beroulli umbers are amed after the great Swiss mathematiia Jaob Beroulli5-705 who used these umbers i the power-sum problem. The power-sum problem is to fid a formula for the sum of the
More informationChapter MOSFET
Chapter 17-1. MOFET MOFET-based ICs have beome domiat teholog i the semiodutor idustr. We will stud the followig i this hapter: - Qualitative theor of operatio - Quatitative I D -versus-v D harateristis
More informationANOTHER PROOF FOR FERMAT S LAST THEOREM 1. INTRODUCTION
ANOTHER PROOF FOR FERMAT S LAST THEOREM Mugur B. RĂUŢ Correspodig author: Mugur B. RĂUŢ, E-mail: m_b_raut@yahoo.om Abstrat I this paper we propose aother proof for Fermat s Last Theorem (FLT). We foud
More informationChap.4 Ray Theory. The Ray theory equations. Plane wave of homogeneous medium
The Ra theor equatio Plae wave of homogeeou medium Chap.4 Ra Theor A plae wave ha the dititive propert that it tregth ad diretio of propagatio do ot var a it propagate through a homogeeou medium p vae
More information(Dependent or paired samples) Step (1): State the null and alternate hypotheses: Case1: One-tailed test (Right)
(epedet or paired samples) Step (1): State the ull ad alterate hypotheses: Case1: Oe-tailed test (Right) Upper tail ritial (where u1> u or u1 -u> 0) H0: 0 H1: > 0 Case: Oe-tailed test (Left) Lower tail
More informationNonstandard Lorentz-Einstein transformations
Nostadard Loretz-istei trasformatios Berhard Rothestei 1 ad Stefa Popesu 1) Politehia Uiversity of Timisoara, Physis Departmet, Timisoara, Romaia brothestei@gmail.om ) Siemes AG, rlage, Germay stefa.popesu@siemes.om
More informationESTIMATION OF MACHINING ERRORS ON GLEASON BEVEL
5 th INTERNATIONAL MEETING OF THE CARPATHIAN REGION SPECIALISTS IN THE FIELD OF GEARS ESTIMATION OF MACHINING ERRORS ON GLEASON BEVEL GEAR CUTTING BOB, Daila UNIO SA Satu Mare - 35, Luia Blaga Blvd, 39
More informationElectromagnetic scattering from large aspect ratio lossy dielectric solids in a conducting medium
Eletroageti satterig fro large aspet ratio lossy dieletri solids i a odutig ediu Gary teve aela, Coastal ystes tatio Code R 6703 West Highway 98 Paaa City, Florida 3407-700 Abstrat The spheroidal T-atrix
More informationHomework 6: Forced Vibrations Due Friday April 6, 2018
EN40: Dyais ad Vibratios Hoework 6: Fored Vibratios Due Friday April 6, 018 Shool of Egieerig Brow Uiversity 1. The vibratio isolatio syste show i the figure has 0kg, k 19.8 kn / 1.59 kns / If the base
More informationOptimal Management of the Spare Parts Stock at Their Regular Distribution
Joural of Evirometal Siee ad Egieerig 7 (018) 55-60 doi:10.1765/16-598/018.06.005 D DVID PUBLISHING Optimal Maagemet of the Spare Parts Stok at Their Regular Distributio Svetozar Madzhov Forest Researh
More informationSolutions 3.2-Page 215
Solutios.-Page Problem Fid the geeral solutios i powers of of the differetial equatios. State the reurree relatios ad the guarateed radius of overgee i eah ase. ) Substitutig,, ad ito the differetial equatio
More informationAbsorption and Emission of Radiation: Time Dependent Perturbation Theory Treatment
Absorptio ad Eissio of Radiatio: Tie Depedet Perturbatio Theory Treatet Wat Hailtoia for Charged Partile i E & M Field Need the potetial U. Fore o Charged Partile: 1 F e E V B Fore (geeralized for i Lagragia
More informationSx [ ] = x must yield a
Math -b Leture #5 Notes This wee we start with a remider about oordiates of a vetor relative to a basis for a subspae ad the importat speial ase where the subspae is all of R. This freedom to desribe vetors
More informationRay Optics Theory and Mode Theory. Dr. Mohammad Faisal Dept. of EEE, BUET
Ray Optics Theory ad Mode Theory Dr. Mohammad Faisal Dept. of, BUT Optical Fiber WG For light to be trasmitted through fiber core, i.e., for total iteral reflectio i medium, > Ray Theory Trasmissio Ray
More informationHigh-Frequency Fluctuations of a Modulated, Helical Electron Beam
Publiatios 1996 High-Frequey Flutuatios of a Modulated, Helial Eletro Beam Mark Athoy Reyolds Embry-Riddle Aeroautial Uiversity, reyoldb@erau.edu Follow this ad additioal works at: https://ommos.erau.edu/publiatio
More informationSYNTHESIS OF SIGNAL USING THE EXPONENTIAL FOURIER SERIES
SYNTHESIS OF SIGNAL USING THE EXPONENTIAL FOURIER SERIES Sadro Adriao Fasolo ad Luiao Leoel Medes Abstrat I 748, i Itrodutio i Aalysi Ifiitorum, Leohard Euler (707-783) stated the formula exp( jω = os(
More information1. (a) From Fig we find the smaller wavelength in question to be about 515 nm.
Chapter (a) From Fig - we fid the smaller wavelegth i questio to be about 55 m (b) Similarly, the larger wavelegth is approximately 6 m () From Fig - the wavelegth at whih the eye is most sesitive is about
More informationSummation Method for Some Special Series Exactly
The Iteratioal Joural of Mathematis, Siee, Tehology ad Maagemet (ISSN : 39-85) Vol. Issue Summatio Method for Some Speial Series Eatly D.A.Gismalla Deptt. Of Mathematis & omputer Studies Faulty of Siee
More informationChapter 1. Complex Numbers. Dr. Pulak Sahoo
Chapter 1 Complex Numbers BY Dr. Pulak Sahoo Assistat Professor Departmet of Mathematics Uiversity Of Kalyai West Begal, Idia E-mail : sahoopulak1@gmail.com 1 Module-2: Stereographic Projectio 1 Euler
More information16th International Symposium on Ballistics San Francisco, CA, September 1996
16th Iteratioal Symposium o Ballistis Sa Fraiso, CA, 3-8 September 1996 GURNEY FORULAS FOR EXPLOSIVE CHARGES SURROUNDING RIGID CORES William J. Flis, Dya East Corporatio, 36 Horizo Drive, Kig of Prussia,
More informationOne way Analysis of Variance (ANOVA)
Oe way Aalysis of Variae (ANOVA) ANOVA Geeral ANOVA Settig"Slide 43-45) Ivestigator otrols oe or more fators of iterest Eah fator otais two or more levels Levels a be umerial or ategorial ifferet levels
More informationQuestion 1: The magnetic case
September 6, 018 Corell Uiversity, Departmet of Physics PHYS 337, Advace E&M, HW # 4, due: 9/19/018, 11:15 AM Questio 1: The magetic case I class, we skipped over some details, so here you are asked to
More informationPOWER SERIES METHODS CHAPTER 8 SECTION 8.1 INTRODUCTION AND REVIEW OF POWER SERIES
CHAPTER 8 POWER SERIES METHODS SECTION 8. INTRODUCTION AND REVIEW OF POWER SERIES The power series method osists of substitutig a series y = ito a give differetial equatio i order to determie what the
More informationMeasurement uncertainty of the sound absorption
Measuremet ucertaity of the soud absorptio coefficiet Aa Izewska Buildig Research Istitute, Filtrowa Str., 00-6 Warsaw, Polad a.izewska@itb.pl 6887 The stadard ISO/IEC 705:005 o the competece of testig
More informationAbstract. Fermat's Last Theorem Proved on a Single Page. "The simplest solution is usually the best solution"---albert Einstein
Copyright A. A. Frempog Fermat's Last Theorem Proved o a Sigle Page "5% of the people thik; 0% of the people thik that they thik; ad the other 85% would rather die tha thik."----thomas Ediso "The simplest
More informationLINEAR STABILITY ANALYSIS OF A PLANE-POISEUILLE HYDROMAGNETIC FLOW USING ADOMIAN DECOMPOSITION METHOD
.P.B. Si. Bull., Series A, Vol. 75, Iss., 13 ISSN 13-77 LINEAR STABILITY ANALYSIS OF A PLANE-POISEILLE HYDROMAGNETIC FLOW SING ADOMIAN DECOMPOSITION METHOD Samuel O. ADESANYA 1 I this paper, the small-disturbaes
More informationChapter 4: Angle Modulation
57 Chapter 4: Agle Modulatio 4.1 Itrodutio to Agle Modulatio This hapter desribes frequey odulatio (FM) ad phase odulatio (PM), whih are both fors of agle odulatio. Agle odulatio has several advatages
More informationPHY4905: Nearly-Free Electron Model (NFE)
PHY4905: Nearly-Free Electro Model (NFE) D. L. Maslov Departmet of Physics, Uiversity of Florida (Dated: Jauary 12, 2011) 1 I. REMINDER: QUANTUM MECHANICAL PERTURBATION THEORY A. No-degeerate eigestates
More informationDr R Tiwari, Associate Professor, Dept. of Mechanical Engg., IIT Guwahati,
Dr R Tiwari, Assoiate Professor, Dept. of Mehaial Egg., IIT Guwahati, (rtiwari@iitg.eret.i).3 Measuremet ad Sigal Proessig Whe we ivestigate the auses of vibratio, we first ivestigate the relatioship betwee
More informationOn the description of electromagnetic fields in slow moving media Abstract. Key words 1. Introduction
O the desriptio of eletromageti fields i slow movig media Rozov Adrey Leoidovih St. Petersburg State Polytehi Uiversity Pargolovskaya st., 0-40, St. Petersburg, Russia, 9400 E-mail: rozov20@mail.ru\ Abstrat.
More informationExplicit and closed formed solution of a differential equation. Closed form: since finite algebraic combination of. converges for x x0
Chapter 4 Series Solutios Epliit ad losed formed solutio of a differetial equatio y' y ; y() 3 ( ) ( 5 e ) y Closed form: sie fiite algebrai ombiatio of elemetary futios Series solutio: givig y ( ) as
More information\,. Si2:nal Detection and. Optical AmpUfler or Signal Regenentor ""' Fiber La~er Laser Coupler Driver Diode,-~ [> I I ~ : Modulator. Splice.
Sieal Geeratio!! Ietroi Fiber Laer Laser Coupler Driver Diode, [> I I : Modulator Iterfae I I: t A Trasissio Mediu Splie ptial ApUfler or Sigal Regeetor ""' I N C y Coditioig ' Eletrois I Eletroil Detetor
More informationSTK4011 and STK9011 Autumn 2016
STK4 ad STK9 Autum 6 ypothesis testig Covers (most of) the followig material from hapter 8: Setio 8. Setios 8.. ad 8..3 Setio 8.3. Setio 8.3. (util defiitio 8.3.6) Ørulf Borga Departmet of Mathematis Uiversity
More informationSimilarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall
Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig
More informationPAPER : IIT-JAM 2010
MATHEMATICS-MA (CODE A) Q.-Q.5: Oly oe optio is correct for each questio. Each questio carries (+6) marks for correct aswer ad ( ) marks for icorrect aswer.. Which of the followig coditios does NOT esure
More informationAnalog Filter Synthesis
6 Aalog Filter Sythesis Nam Pham Aubur Uiversity Bogda M. Wilamowsi Aubur Uiversity 6. Itrodutio...6-6. Methods to Sythesize Low-Pass Filter...6- Butterworth Low-Pass Filter Chebyshev Low-Pass Filter Iverse
More informationOrganic Electronic Devices
Orgai letroi Devies Week 3: Charge rasport Leture 3.3: Multiple rap ad Release MR Model Brya W. Boudouris Chemial gieerig Purdue Uiversity Leture Overview ad Learig Objetives Coepts to be Covered i this
More informationLecture 3. Digital Signal Processing. Chapter 3. z-transforms. Mikael Swartling Nedelko Grbic Bengt Mandersson. rev. 2016
Lecture 3 Digital Sigal Processig Chapter 3 z-trasforms Mikael Swartlig Nedelko Grbic Begt Madersso rev. 06 Departmet of Electrical ad Iformatio Techology Lud Uiversity z-trasforms We defie the z-trasform
More informationLesson 4. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)
Lesso 4 Thermomehaial Measuremets for Eergy Systems (MENR) Measuremets for Mehaial Systems ad Produtio (MMER) A.Y. 15-16 Zaaria (Rio ) Del Prete RAPIDITY (Dyami Respose) So far the measurad (the physial
More informationexist for the work of spherical aggregate formation.
ISSN 06-933X Colloid oural 0 Vol 73 No 3 pp 406 47 Pleiades Publishig Ltd 0 Origial Russia Text AK Shhei S Kshevetsiy OS Pelevia 0 published i Kolloidyi Zhural 0 Vol 73 No 3 pp 404 46 iellizatio Kietis
More informationRotational Components of Strong-motion Earthquakes
Rotatioal Compoets of Strog-motio Earthquakes Viet W Lee 1 ad Jiawe Liag 2 1 Professor, Civil & Evirometal Egieerig, Uiv. of Souther Califoria, Los Ageles, CA 90089 USA, vlee@us.edu 2 Professor, Shool
More informationFuzzy Dynamic Characteristic of Concrete. Material under Impact Loads
Proeedigs of the 2d WSEAS It. Coferee o Applied ad Theoretial Mehais, Veie, Italy, November 2-22, 26 222 Fuzzy Dyami Charateristi of Corete Material uder Impat Loa GAO SHIQIAO LIU HAIPENG JIN LEI Shool
More informationCertain inclusion properties of subclass of starlike and convex functions of positive order involving Hohlov operator
Iteratioal Joural of Pure ad Applied Mathematial Siees. ISSN 0972-9828 Volume 0, Number (207), pp. 85-97 Researh Idia Publiatios http://www.ripubliatio.om Certai ilusio properties of sublass of starlike
More informationProbability & Statistics Chapter 8
I. Estimatig with Large Samples Probability & Statistis Poit Estimate of a parameter is a estimate of a populatio parameter give by a sigle umber. Use x (the sample mea) as a poit estimate for (the populatio
More informationLecture III-2: Light propagation in nonmagnetic
A. La Rosa Lecture Notes ALIED OTIC Lecture III2: Light propagatio i omagetic materials 2.1 urface ( ), volume ( ), ad curret ( j ) desities produced by arizatio charges The objective i this sectio is
More informationCONCAVE ELECTRODES II: THEORETICAL FOUNDATIONS
Physis i Mediie ad Biology, vol. 9 a, 1994 CONCAVE ELECTRODES II: THEORETICAL FOUNDATIONS Roberto Suárez-Atola Direió Naioal de Teología Nulear, Miisterio de Idustria, Eergía y Miería, Motevideo, Uruguay
More informationOptimization Methods MIT 2.098/6.255/ Final exam
Optimizatio Methods MIT 2.098/6.255/15.093 Fial exam Date Give: December 19th, 2006 P1. [30 pts] Classify the followig statemets as true or false. All aswers must be well-justified, either through a short
More informationThe axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c.
5.4 Applicatio of Perturbatio Methods to the Dispersio Model for Tubular Reactors The axial dispersio model for tubular reactors at steady state ca be described by the followig equatios: d c Pe dz z =
More informationStatistical Intervals for a Single Sample
3/5/06 Applied Statistics ad Probability for Egieers Sixth Editio Douglas C. Motgomery George C. Ruger Chapter 8 Statistical Itervals for a Sigle Sample 8 CHAPTER OUTLINE 8- Cofidece Iterval o the Mea
More informationProduction Test of Rotary Compressors Using Wavelet Analysis
Purdue Uiversity Purdue e-pubs Iteratioal Compressor Egieerig Coferee Shool of Mehaial Egieerig 2006 Produtio Test of Rotary Compressors Usig Wavelet Aalysis Haishui Ji Shaghai Hitahi Eletrial Appliatio
More informationSession 5. (1) Principal component analysis and Karhunen-Loève transformation
200 Autum semester Patter Iformatio Processig Topic 2 Image compressio by orthogoal trasformatio Sessio 5 () Pricipal compoet aalysis ad Karhue-Loève trasformatio Topic 2 of this course explais the image
More informationTR/46 OCTOBER THE ZEROS OF PARTIAL SUMS OF A MACLAURIN EXPANSION A. TALBOT
TR/46 OCTOBER 974 THE ZEROS OF PARTIAL SUMS OF A MACLAURIN EXPANSION by A. TALBOT .. Itroductio. A problem i approximatio theory o which I have recetly worked [] required for its solutio a proof that the
More informationε > 0 N N n N a n < ε. Now notice that a n = a n.
4 Sequees.5. Null sequees..5.. Defiitio. A ull sequee is a sequee (a ) N that overges to 0. Hee, by defiitio of (a ) N overges to 0, a sequee (a ) N is a ull sequee if ad oly if ( ) ε > 0 N N N a < ε..5..
More informationNUMERICAL METHODS FOR SOLVING EQUATIONS
Mathematics Revisio Guides Numerical Methods for Solvig Equatios Page 1 of 11 M.K. HOME TUITION Mathematics Revisio Guides Level: GCSE Higher Tier NUMERICAL METHODS FOR SOLVING EQUATIONS Versio:. Date:
More informationChapter 8 Hypothesis Testing
Chapter 8 for BST 695: Speial Topis i Statistial Theory Kui Zhag, Chapter 8 Hypothesis Testig Setio 8 Itrodutio Defiitio 8 A hypothesis is a statemet about a populatio parameter Defiitio 8 The two omplemetary
More informationWhat is a Hypothesis? Hypothesis is a statement about a population parameter developed for the purpose of testing.
What is a ypothesis? ypothesis is a statemet about a populatio parameter developed for the purpose of testig. What is ypothesis Testig? ypothesis testig is a proedure, based o sample evidee ad probability
More informationWe are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors
We are ItehOpe the world s leadig publisher of Ope Aess boos Built by sietists for sietists 4 6 M Ope aess boos available Iteratioal authors ad editors Dowloads Our authors are amog the 54 Coutries delivered
More informationSOME NOTES ON INEQUALITIES
SOME NOTES ON INEQUALITIES Rihard Hoshio Here are four theorems that might really be useful whe you re workig o a Olympiad problem that ivolves iequalities There are a buh of obsure oes Chebyheff, Holder,
More informationOptimal design of N-Policy batch arrival queueing system with server's single vacation, setup time, second optional service and break down
Ameria. Jr. of Mathematis ad Siees Vol., o.,(jauary Copyright Mid Reader Publiatios www.jouralshub.om Optimal desig of -Poliy bath arrival queueig system with server's sigle vaatio, setup time, seod optioal
More informationWaves in dielectric media. Waveguiding: χ (r ) Wave equation in linear non-dispersive homogenous and isotropic media
Wves i dieletri medi d wveguides Setio 5. I this leture, we will osider the properties of wves whose propgtio is govered by both the diffrtio d ofiemet proesses. The wveguides re result of the ble betwee
More information10-701/ Machine Learning Mid-term Exam Solution
0-70/5-78 Machie Learig Mid-term Exam Solutio Your Name: Your Adrew ID: True or False (Give oe setece explaatio) (20%). (F) For a cotiuous radom variable x ad its probability distributio fuctio p(x), it
More informationThe Relationship of the Cotangent Function to Special Relativity Theory, Silver Means, p-cycles, and Chaos Theory
Origial Paper Forma, 8, 49 6, 003 The Relatioship of the Cotaget Futio to Speial Relativity Theory, Silver Meas, p-yles, ad Chaos Theory Jay KAPPRAFF * ad Gary W ADAMSON New Jersey Istitute of Tehology,
More informationPrinciples of Communications Lecture 12: Noise in Modulation Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University
Priiples of Commuiatios Leture 1: Noise i Modulatio Systems Chih-Wei Liu 劉志尉 Natioal Chiao ug Uiversity wliu@twis.ee.tu.edu.tw Outlies Sigal-to-Noise Ratio Noise ad Phase Errors i Coheret Systems Noise
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departmet of Electrical Egieerig ad Computer Sciece 6.34 Discrete Time Sigal Processig Fall 24 BACKGROUND EXAM September 3, 24. Full Name: Note: This exam is closed
More informationAn Introduction to Randomized Algorithms
A Itroductio to Radomized Algorithms The focus of this lecture is to study a radomized algorithm for quick sort, aalyze it usig probabilistic recurrece relatios, ad also provide more geeral tools for aalysis
More informationThe beta density, Bayes, Laplace, and Pólya
The beta desity, Bayes, Laplae, ad Pólya Saad Meimeh The beta desity as a ojugate form Suppose that is a biomial radom variable with idex ad parameter p, i.e. ( ) P ( p) p ( p) Applyig Bayes s rule, we
More information(b) What is the probability that a particle reaches the upper boundary n before the lower boundary m?
MATH 529 The Boudary Problem The drukard s walk (or boudary problem) is oe of the most famous problems i the theory of radom walks. Oe versio of the problem is described as follows: Suppose a particle
More informationMichelson's Repetition of the Fizeau Experiment:
Mihelso's Repetitio of the Fizeau Experimet: A Review of the Derivatio ad Cofirmatio of Fresel's Drag Coeffiiet A. A. Faraj a_a_faraj@hotmail.om Abstrat: I this ivestigatio, Mihelso's 1886 repetitio of
More informationLinear Regression Models
Liear Regressio Models Dr. Joh Mellor-Crummey Departmet of Computer Sciece Rice Uiversity johmc@cs.rice.edu COMP 528 Lecture 9 15 February 2005 Goals for Today Uderstad how to Use scatter diagrams to ispect
More informationThe Phi Power Series
The Phi Power Series I did this work i about 0 years while poderig the relatioship betwee the golde mea ad the Madelbrot set. I have fially decided to make it available from my blog at http://semresearch.wordpress.com/.
More informationA proposed discrete distribution for the statistical modeling of
It. Statistical Ist.: Proc. 58th World Statistical Cogress, 0, Dubli (Sessio CPS047) p.5059 A proposed discrete distributio for the statistical modelig of Likert data Kidd, Marti Cetre for Statistical
More informationLinear regression. Daniel Hsu (COMS 4771) (y i x T i β)2 2πσ. 2 2σ 2. 1 n. (x T i β y i ) 2. 1 ˆβ arg min. β R n d
Liear regressio Daiel Hsu (COMS 477) Maximum likelihood estimatio Oe of the simplest liear regressio models is the followig: (X, Y ),..., (X, Y ), (X, Y ) are iid radom pairs takig values i R d R, ad Y
More informationActivity 3: Length Measurements with the Four-Sided Meter Stick
Activity 3: Legth Measuremets with the Four-Sided Meter Stick OBJECTIVE: The purpose of this experimet is to study errors ad the propagatio of errors whe experimetal data derived usig a four-sided meter
More informationLecture 8. Dirac and Weierstrass
Leture 8. Dira ad Weierstrass Audrey Terras May 5, 9 A New Kid of Produt of Futios You are familiar with the poitwise produt of futios de ed by f g(x) f(x) g(x): You just tae the produt of the real umbers
More informationPrinciple Of Superposition
ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give
More informationLecture 7: Properties of Random Samples
Lecture 7: Properties of Radom Samples 1 Cotiued From Last Class Theorem 1.1. Let X 1, X,...X be a radom sample from a populatio with mea µ ad variace σ
More information