Efficient Interference Mitigation in mmwave Backhaul Network for High Data Rate 5G Wireless Communications
|
|
- Neal Daniels
- 6 years ago
- Views:
Transcription
1 I. J. Couicaios Newok ad Syse Scieces hp:// ISSN Olie: ISSN Pi: Efficie Iefeece Miigaio i Wave Backhaul Newok fo High Daa Rae 5G Wieless Couicaios Jia Shi 1 Qiag Ni 1 Claudio Paoloi 1 Facois Mage 1 Lacase Uivesiy Lacase UK Whe-AB S.A. Pais Face How o cie his pape: Shi J. Ni Q. Paoloi C. ad Mage F. (017) Efficie Iefeece Miigaio i Wave Backhaul Newok fo High Daa Rae 5G Wieless Couicaios. I. J. Couicaios Newok ad Syse Scieces hps://doi.og/10.436/ijcs b017 Received: Apil Acceped: May Published: May Aac This pape ivesigaes he pefoace of he W bad illiee wave (Wave) backhaul ewok poposed by ou EU TWEETHER pojec. We focus o he dowlik asissio of he Wave backhaul ewok i which each of he hu seves a cluse of base saios (BSs). I he cosideed backhaul ewok available fequecy esouces ae fis allocaed o he dowlik liks wih he cosideaio of faiess issue. I ode o iigae iefeece i he Wave backhaul ewok each opeaes he poposed algoih aely coopeaio ad powe adapaio (CPA). Ou siulaio esuls show ha he backhaul ewok wih Wave capabiliies ca achieve a sigifica bee houghpu pefoace ha he sub-6 GHz ula high fequecy (UHF) backhaul ewok. Fuheoe ou siulaios also eveal ha he poposed CPA algoih ca efficiely coba iefeece i he backhaul ewok. Keywods Wave Couicaio Backhaulig Iefeece Miigaio 1. Ioducio Tadiioal icowave based cellula ewoks ae facig oe ad oe challeges due o he expoeial gowh of daa affic. Shifig he couicaio specu fo adiioal icowave o illiee wave (Wave) is widely ecogized as oe of he bes aacive soluios o fuue wieless couicaio ewoks deadig high-volue capaciy. Moeove Wave sall cell ewoks have bee hough of as a poisig appoach o boos he coveage ad ae of fuue cellula ewoks [1]. Howeve i is ipoa ad challeg- DOI: /ijcs B017 May 6 017
2 J. Shi e al. ig o desig a backhaul ewok coecig o a explosive gowig ube of sall BSs. Wieless backhaul ewok wih Wave capabiliies ca be a poisig cadidae fo fuue wieless couicaio syses due o is advaages of high capaciy eegy efficie low asissio delay ad low cos ec. Mos of he wok abou Wave couicaio i he lieaue aily focuses o chael odelig [] [3] ad is applicabiliy fo idoo/oudoo evioe ove adiioal cellula ewoks i es of he coveage ad ae pobabiliies [4]. By coas liied sudies such as [5] [6] [7] [8] have ivesigaed Wave backhaul ewoks. The auhos i [5] [6] have sudied he esouce allocaio i heeogeeous backhaul ewok which cosiss of boh wied fibe ad Wave wieless couicaios. I [6] he auhos have ivesigaed he heeogeeous backhaul ewok s pefoace i es of packe delay ad have also show he ew backhaul echologies ove he adiioal wied oly echologies. Recely he auhos i [5] have sudied joi schedulig of adio access ad Wave ad fibe backhaul i hybid heeogeeous ewok wih he capabiliies of device-o-device asissios. By coas he auhos i [7] [8] have ivesigaed Wave oly backhaul ewoks. I [7] hey have oly addessed eegy cosupio issue fo a eewable eegy poweed Wave backhaul ewok ad a Sackelbeg gae based picig schee is poposed o aage he affic laecy ove he backhaul ewok. Massive MIMO aided Wave backhaul ewok has bee addessed i [8] whee he hybid pecedig ad cobiig schee is poposed. Agais his backgoud i his pape we ivesigae he pefoace of he W bad Wave backhaul ewok poposed by ou EU TWEETHER pojec [9] [10]. We focus o he dowlik asissio of he Wave backhaul ewok i which each of he hu seves a cluse of base saios (BSs). I he cosideed backhaul ewok he available fequecy esouces ae allocaed o he dowlik liks based o he geedy algoih wih he cosideaio of faiess issue. I ode o iigae iefeece i he Wave backhaul ewok each opeaes he poposed algoih aely coopeaio ad powe adapaio (CPA). The poposed CPA algoih ca se up coopeaive asissios fo he poo liks; eawhile i also uilizes he saegy of powe adapaio o educe he sog iefeece geeaed by he liks. A age of siulaio esuls icludig he ouage pobabiliy ad su ae ae povided o evaluae he pefoace of he Wave backhaul ewok. Ou siulaio esuls show ha ou backhaul ewok wih Wave capabiliies ca sigificaly oupefo he sub-6 GHz ula high fequecy (UHF) backhaul ewok i es of he ouage pobabiliy pefoace. Fuheoe ou siulaios also eveal ha he poposed CPA algoih ca efficiely coba iefeece i he backhaul ewok. The es of he pape is ogaized as follows. Secio povides he syse odel ad saes he ai assupios. Secio 3 descibes he subbad allocaio ehod. Secio 4 poposes he iefeece iigaio schees. Secio 5 171
3 J. Shi e al. deosaes he pefoace esuls. Fially Secio 6 suaizes he coclusios.. Syse Models Ou pojec aely EU TWEETHER poposes ovel W bad Wave based heeogeeous wieless ewoks wih high daa ae disibuio specu- ad eegy-efficiecy. The cocepual sucue of he poposed ewok is show i Figue 1. The ewok odel poposed by EU TWEETHER cosiss of hee ies which ae ifasucue ie backhaul ie ad access ie. Moe specifically i ifasucue ie we ca se up seveal eabis daa liks via fibe opics fo he couicaios bewee he daa cees ad he poi of peseces (PoP) odes ove hudeds of kiloees. I backhaul ie he W bad Wave backhaul liks ae esablished fo he couicaio bewee he PoP odes ad uliple BSs i access ie. Fially access ie suppos he couicaio fo BSs o use eials whee we apply sub-6ghz UHF couicaio liks. I his pape we will focus o ivesigaig he achievable ae pefoace of he Wave backhaul ie poposed by ou EU TWEETHER pojec. I his pape we coside he dowlik asissio of he Wave backhaul ewok which cosiss of N hu ad N BSs. I ode o capue he ai chaaceisics of he ewok poposed by ou EU TWEETHER pojec we assue ha ay wo hu ae sepaaed by a disace of d0 3 k ad he N BSs ae uifoly disibued i he ewok. Fuheoe we also assue ha he disace of a backhaul lik is i he age of 1k d1 k ad ay wo BSs ae sepaaed by a disace of d 0.6 k. The Wave backhaul asissios i he ewok expeiece boh he pahloss effecs ad he sall-scale fadig. To odel pahloss effecs icludig shadowig fo a Wave lik we eploy he odel of [11] ρ + 10αLlog( d) + χl if LoS LdB ( d) = (1) ρ + 10αN + χn if NLoS whee 4π ρ = 0log( ). () f c A Wave couicaio lik is assued o be o-lie-of-sigh (NLoS) if he lie sege joiig he Wave BS ad he use is blocked by buildigs. Ohewise he lik is hough of as lie-of-sigh (LoS). I () f c is he ca- Figue 1. Cocepual ewok sucue poposed by EU TWEETHER pojec. 17
4 J. Shi e al. ie fequecy a he Wave fequecy bad ad d epeses he disace of a lik. Fuheoe α L ad α N ae he pahloss expoes fo LoS ad NLoS cases especively. χ L ad χ N ae shadowig effecs which ae assued o follow zeo ea log oal disibuio. We defie he LoS pobabiliy of a Wave lik as PL ( d ) which is a deceasig fucio of he legh of he couicaio lik ad hece he NLoS pobabiliy of a Wave lik is PN( d) = 1 PL( d). Whe a lik becoes loge i has a highe pobabiliy of beig a NLoS lik. Noe ha he pobabiliy PL ( d ) ca be chaaceized by blockage odels accodig o vaious couicaio evioes. Fo he sake of heoeical sudy we deploy he secoed aea odel o chaaceize he pacical aay paes. Le us deoe gm ( θ φ ) ad gm ( θ φ ) as he secoed aea paes fo a ad a BS especively. M M ae he ai lobe dieciviy gais ad ae he back lobe dieciviy gais while θ θ ae he beawidhs of he aeas. Le he boe sigh diecios be φ ad φ which ae assued o be 0. Fo sipliciy we assue he aea gai fo a desied sigal lik is G= MM. Howeve each lik ay also have soe iefeece liks ad he aea gai fo a iefeece lik is deoed as G which ca be give by θθ MM wih pobabiliy p= 4π (1 θ) θ M wih pobabiliy p= 4 G π = (3) θ(1 θ) M wih pobabiliy p= 4π (1 θ)(1 θ) wih pobabiliy p=. 4π I (3) we assue he beawidh of a aea such as θ θ ae idepedely ad uifoly disibued i (0 π ]. I ou Wave backhaul ewok each is able o asi ifoaio o is sevig BSs by usig all specu of B Hz available i W bad. Fuheoe we assue a couicaes wih is sevig BSs based o ohogoal fequecy divisio uliplexig (OFDM) eployig M subbads. Hece i he dowlik asissio of he backhaul ewok he achievable ae of a BS seved by is o a subbad ca be wie as ( γ ) R = b log 1 + j. (4) I (4) b is he badwidh of subbad. We defie = {1 N} ( ) icludes he idexes of hu. j coais he idexes of he BSs seved by j hece we have N j =. icludes he idexes of M subbads available i he ewok. I (4) ( j γ ) is he sigal-o-iefeeceplus-oise ae (SINR) of BS seved by j o subbad ad i is defied by γ P G ( L ) h. 1 = I + bσ (5) 173
5 J. Shi e al. I (5) P is he asissio powe of j o subbad ad he asissio powe fo all subchaels ae assued o be he sae. I addiio o he lage-scale fadig effec each couicaio lik also expeieces he sall-scale fadig such as ( j h ) which is he idepede Rayleigh fadig chael bewee j ad BS o subbad. Fuheoe we assue ha all he couicaio liks have he sae oise powe which is deoed by σ i (5). Noe ha I i (5) is he iefeece powe ha suffeed by he asissio fo j o BS. I he cosideed Wave backhaul ewok each fis eeds o assig he available specu esouce o he is sevig BSs i ohe wod each is equied o allocae he M ube of subbads available o is BSs. Howeve he asissios i he ewok will suffe fo he iefeece geeaed by hei co-subbad liks. Theefoe afe subbad allocaio we opeae he poposed iefeece iigaio algoih fo he liks suffeig sog iefeece i ode o ipove he ewok s houghpu pefoace. Le us ow fis discuss he subbad allocaio. 3. Subbad Allocaio As eioed i Secio a is assued o eploy all he available fequecy bads o couicae wih is sevig BSs based o OFDM schee. Theefoe j eeds o allocae M subbads o is ube of BSs aiig o axiize he su ae of he backhaul liks. I ode o achieve he bes ade-off bewee he pefoace ad ipleeaio coplexiy each eploys he geedy algoih fo subbad allocaio. I his pape fo sipliciy ad wihou loss of geealiy he ube of subbads available is lage ha he ube of BSs seved by each i.e. M j. Based o he geedy algoih each allocaes he M subbads i M ieaios i which duig each a ieaio he bes available subbad is assiged. Meawhile o achieve he bes faiess of allocaio ou allocaio oivaes o allocae each BS he sae ube of subbads. I his case he subbad allocaio duig a ieaio ca be descibed as (6) P G h = ax ˆ ( j ) L bσ ( ) whee j icludes he idexes of he subbads assiged o BS seved by ( ) j. ˆ j coais he idexes of he BSs havig he leas ube of subbads assiged. I his way ou subbad allocaio ca esue he bes faiess i es of allocaio. Afe he subbad allocaio he liks usig he sae subbad will cause iefeece o each ohe. Hece he SINR of a couicaio lik such as he SINR i (5) fo BS of j o subbad becoes γ P G ( L ) h P G ( L ) h 1 1 = = ( u) ( u) ( u) 1 ( u) ( u) P G ( L ) h + bσ I + bσ u u j u u j (7) (8) 174
6 J. Shi e al. ( ) whee G u is give i (3). Kow fo (8) he hough-pu pefoace of he ewok ay be sigificaly degaded by a couicaio lik expeiecig sog iefeece. To ipove he ewok s pefoace we eed o opeae iefeece iigaio o eove sog iefeece. 4. Iefeece Miigaio Fo he sake of ipovig houghpu pefoace of ou Wave backhaul ewok i his secio we popose a ovel iefeece iigaio schee aely coopeaio ad powe adapaio (CPA). Afe he subbad allocaio discussed i Secio 3 a desied couicaio lik ay suffe fo sog iefeece iposed by ohe liks usig he sae subbad. Hece he CPA algoih is opeaed fo he poo liks which eihe expeiece sog iefeece fo hei co-subbad liks o geeaig sog iefeece o hei co-subbad liks. Le us deoe he se of he poo backhaul couicaio liks o subbad as Φ give by Φ =Φˆ Φ (9) Φ ˆ = { η < η j } (10) Φ = { Φ } (11) ˆ j whee η is he sigal-o-iefeece (SIR) heshold. I (9)-(11) η is he SIR of he lik ad i ca be wie as η P ( L ) h 1 = ( u) I u u j (1) ( u) whee I is give i (8). The poposed CPA algoih uilizes BS coopeaio o iigae iefeece i he backhaul ewok i which he space ie block codig (STBC) aided coopeaive asissio ca be esablished fo he poo liks. Whe he coopeaio fo he asissio o BS is se up by j ad q he SINR i (8) fo he lik becoes γ P ( L ) h + I 1 ( q) = ( u) I + bσ q u j q. (13) Kow fo (13) he achievable daa ae of BS ca be sigificaly ipoved whe he iefeece I iposed by q is sog. I addiio o ( q) coopeaio ou CPA algoih also eploys he saegy of powe adapaio. I ha case if a lik suffes fo sog iefeece a ay educe he asi powe fo he liks while guaaeeig he iiu sevice qualiy of he lik ove a age of a leas 1 k. By doig his he liks poweed dow will o cause sog iefeece o ohe liks ad hece he su ae of he backhaul ewok will be ipoved. I his pape ou CPA algoih ais o axiize he su ae of he poo liks which ca be expessed as 175
7 J. Shi e al. whee { } s j = ag ax R (14) j Φ = s j coais he iefeece iigaio saegies. Specifically ( ) = eas j asis ifoaio wih he powe P o BS o subbad. By coas ( j ) s = 0 eas ha j asis ifoaio o BS o subbad wih he educed powe β P whee 0 β 1. Noe ha he value of β is elaed o he iiu daa ae equiee ad he iiu asissio age which ca be se up accodig o ewok equiees. Fuheoe i ode o iiize he sigalig bude he hu ae oly equied o exchage biay iefeece ifoaio. Fo ( q) exaple he biay iefeece ifoaio fo I i (13) ca be defied by: ˆ ( q) I 1 = (sog iefeece) if ( q I ) > I ohewise ˆ ( q I ) = 0 (sall iefeece) whee I is he iefeece heshold. Based o he opiizaio poble i (14) he piciples of ou CPA algoih ca be give as follows. 5. Pefoace Resuls I his secio we povide a age of siulaio esuls fo deosaig he achievable pefoace icludig he ouage pobabiliy ad su ae of ou backhaul ewok wih he aid of W bad Wave couicaio. Specifically we also evaluae he pefoace of he poposed CPA algoih i es of iigaig iefeece i he ewok. Fo he sake of heoeical sudy we assue ha hee ae N = 3 hu i he ewok ad fo all siulaios he ube of subbads is M = N /3. Fuheoe we assue ha he oise powe of each lik is assued o be he sae which is σ. The ohe siulaio paaees ae suaized i Table 1. I Figue we ivesigae he ouage pobabiliy pefoace of he Wave backhaul (BH) ewok which is copaed wih he pefoace of he sub-6 GHz UHF oly backhaul ewok. The ouage pobabiliy is defied as he pobabiliy ha he liks i he ewok achieve he daa aes below he iiu ae equiee R τ. Fo he UHF oly backhaul ewok we assue ha he available badwidh is B = 0 MHz ad he caie fequecy is f c =.4 GHz. Wihou loss of geealiy he ohe assupios ae he sae as hose fo he Wave backhaul ewok. Oeved fo Figue he Table 1. Siulaio paaees fo Wave backhaul ewok. Paaee Value Paaee Value B 1 GHz σ 174 db/hz f c 94 GHz P 46 db ( j ) M 10 db M 10 db 10 db 10 db α L.09 α N 3.34 Sd ( χ L ) 5.0 db Sd ( χ N ) 7.6 db 176
8 J. Shi e al. Wave backhaul ewok ca sigificaly oupefo he UHF ewok i all diffee iiu ae equiee sceaios. As show wih he aid of he poposed CPA algoih he Wave backhaul ewok ca achieve a bee ouage pobabiliy pefoace ad a bigge pefoace gap ca be oeved i he age of 0.1GHz R τ 1GHz. Fuheoe whe he SIR heshold η ges highe he CPA algoih ca assis he ewok o achieve a highe pefoace. This is because he CPA algoih opeaes iefeece iigaio fo a lage ube of couicaio liks i he ewok. I Figue 3 we show he ouage pobabiliy of he Wave backhaul ewok wih ad wihou eployig he poposed CPA algoih whe cosideig he diffee BS desiies. Fis of all we ca see ha whe he ube of BSs ges bigge he ouage pobabiliy of he ewok ges highe. This oevaio iplies ha he backhaul couicaio liks have highe pobabiliies of expeiecig sog iefeece as he desiy of BSs seved by he ewok iceases. Secod ou poposed CPA algoih ca sigificaly faciliae he ewok by efficiely iigaig iefeece. The pefoace gai of eployig he CPA says oughly he sae fo all diffee BS desiy sceaios. A las oce agai we oeve ha he ouage pobabiliy becoes salle as he SIR heshold ges bigge i which oe liks ae beefied fo he CPA algoih. Fially Figue 4 shows he effec of he hesholds η ad I o he pefoace of he CPA algoih. I he figue we oce oe shows he sigifica pefoace ipovee of he Wave backhaul ewok by usig he CPA o coba iefeece. As show he su ae of he poo liks iceases as he SIR heshold η o he iefeece heshold I iceases. This is because he CPA opeaes iefeece iigaio fo oe ube of he poo liks as he ube of he poo liks iceases. Howeve i his case i also Figue. Ouage pobabiliy of he backhaul ewoks whe eployig vaious values of R τ 177
9 J. Shi e al. equies highe ipleeaio coplexiy ad cos. Theefoe i is ipoa o choose pope SIR ad ICI hesholds by joily cosideig he syse equiee ipleeaio coplexiy as well as desiable pefoace. Fo Figue 3 ad Figue 4 we ca coclude ha he poposed CPA algoih ca faciliae ou Wave back-haul ewok o achieve a bee pefoace. Figue 3. Ouage pobabiliy of he W bad Wave backhaul ewoks havig diffee desiies of BSs whe assuig 0.3 R τ = Gbps. Figue 4. Su ae of he poo liks i he W bad Wave backhaul ewok eployig he CPA algoih ude he vaious SIR heshold η ad ICI heshold I. 178
10 J. Shi e al. 6. Coclusio I his pape we have ivesigaed he pefoace of he W bad Wave backhaul ewok poposed by ou EU TWEETHER pojec. I ode o ipove he ewok s houghpu pefoace we have poposed he CPA algoih o iigae iefeece i he Wave backhaul ewok. Whe he CPA algoih is eployed he hu ae allowed o se up coopeaive asissios fo he poo liks aleaively he hu ae equied o educe he asissio powe fo soe liks ha geeae sog iefeece o ohe liks. We have povided a age of siulaio esuls icludig he ouage pobabiliy ad su ae of he backhaul ewok. Ou siulaios have show ha ou Wave backhaul ewok ca sigificaly oupefo he UHF backhaul ewok. Fuheoe ou siulaios have also iplied ha he poposed CPA algoih ca efficiely coba iefeece so ha he backhaul ewok achieves a clea bee pefoace. We coclude ha he poposed CPA algoih ca be hough of as a poisig soluio fo iefeece iigaio i ou Wave backhaul ewok. Ackowledgees This wok is suppoed by EU H00 TWEETHER pojec ude ga ageee ube Refeeces [1] Gillo G. Adews J. Buzzi S. Choi W. Haly S. Lozao A. Soog A. ad Zhag J. (014) Wha Will 5G Be? IEEE J. Sel. Aeas Cou hps://doi.og/ /jsac [] Rappapo T. e al. (013) Milliee Wave Mobile Couicaios fo 5G Cellula: I Will Wok! IEEE Access hps://doi.og/ /access [3] Raga S. Rappapo T.S. ad Ekip E. (014) Miliee-Wave Cellula Wieless Newoks: Poeials ad Challeges. Poceedigs of he IEEE hps://doi.og/ /jproc [4] Bai T. ad Heah R. (015) Coveage ad Rae Aalysis fo Milliee-Wave Cellula Newoks. IEEE Tas. Wieless Cou hps://doi.og/ /twc [5] Niu Y. Gao C. Li Y. Su L. Ji D. ad Vasilakos A.V. (015) Exploiig Device-o-Device Couicaios i Joi Schedulig of Access ad Backhaul fo Wave Sall Cells. IEEE J. Sel. Aeas Cou hps://doi.og/ /twc [6] Zhag G. Quek T.Q.S. Kououis M. Huag A. ad Sha H. (016) Fudaeals of Heeogeeous Backhaul Desig Aalysis ad Opiizaio. IEEE Tas. Cou hps://doi.og/ /tcomm [7] Li D. Saad W. ad Hog C.S. (016) Decealized Reewable Eegy Picig ad Allocaio fo Milliee Wave Cellula Backhaul. IEEE J. Sel. Aeas Cou hps://doi.og/ /jsac [8] Gao Z. Dai L. Mi D. Wag Z. Ia M.A. ad Shaki M.Z. (015) MWave Massive-MIMO-Based Wieless Backhaul fo he 5G Ula-Dese Newok. IEEE 179
11 J. Shi e al. Wieless Couicaios hps://doi.og/ /mwc [9] EU TWEETHER Pojec Weie. hps://weehe.eu/ [10] Paoloi C. Leizia R. Napoli F. Ni Q. Reie A. Ziea R. Ade F. Pha K. Koze V. Mage F. Buciu I. Raiez A. Rocchi M. Mailie M. ad Vila R. (015) Hoizo 00 TWEETHER Pojec fo W-Bad High Daa Rae Wieless Couicaios. IEEE 16h Ieaioal Vacuu Elecoics Cofeece (IVEC 015) Apil 015. hps://doi.og/ /ivec [11] Xu X. Saad W. Zhag X. Xu X. ad Zhou S. (015) Joi Deploye of Sall Cells ad Wieless Backhaul Liks i Nex-Geeaio Newoks. IEEE Couicaios Lees hps://doi.og/ /lcomm Subi o ecoed ex auscip o SCIRP ad we will povide bes sevice fo you: Accepig pe-subissio iquiies hough Eail Facebook LikedI Twie ec. A wide selecio of jouals (iclusive of 9 subjecs oe ha 00 jouals) Povidig 4-hou high-qualiy sevice Use-fiedly olie subissio syse Fai ad swif pee-eview syse Efficie ypeseig ad poofeadig pocedue Display of he esul of dowloads ad visis as well as he ube of cied aicles Maxiu disseiaio of you eseach wok Subi you auscip a: hp://papesubissio.scip.og/ O coac ijcs@scip.og 180
Spectrum of The Direct Sum of Operators. 1. Introduction
Specu of The Diec Su of Opeaos by E.OTKUN ÇEVİK ad Z.I.ISMILOV Kaadeiz Techical Uivesiy, Faculy of Scieces, Depae of Maheaics 6080 Tabzo, TURKEY e-ail adess : zaeddi@yahoo.co bsac: I his wok, a coecio
More informationABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES
Available olie a h://sciog Egieeig Maheaics Lees 2 (23) No 56-66 ISSN 249-9337 ABSLUE INDEED SUMMABILIY FACR F AN INFINIE SERIES USING QUASI-F-WER INCREASING SEQUENCES SKAIKRAY * RKJAI 2 UKMISRA 3 NCSAH
More informationComparing Different Estimators for Parameters of Kumaraswamy Distribution
Compaig Diffee Esimaos fo Paamees of Kumaaswamy Disibuio ا.م.د نذير عباس ابراهيم الشمري جامعة النهرين/بغداد-العراق أ.م.د نشات جاسم محمد الجامعة التقنية الوسطى/بغداد- العراق Absac: This pape deals wih compaig
More informationAvailable online at J. Math. Comput. Sci. 2 (2012), No. 4, ISSN:
Available olie a h://scik.og J. Mah. Comu. Sci. 2 (22), No. 4, 83-835 ISSN: 927-537 UNBIASED ESTIMATION IN BURR DISTRIBUTION YASHBIR SINGH * Deame of Saisics, School of Mahemaics, Saisics ad Comuaioal
More informationParameter Optimization of Multi-element Synthetic Aperture Imaging Systems
Paaee Opiizaio of Muli-elee Syheic Apeue Iagig Syses Vea Beha Isiue fo Paallel Pocessig Bulgaia Acadey of Scieces 5-A Acad. G. Bochev S., Sofia 1113, Bulgaia E-ail: beha@bas.bg Received: Jauay 19, 7 Acceped:
More informationCameras and World Geometry
Caeas ad Wold Geoe How all is his woa? How high is he caea? Wha is he caea oaio w. wold? Which ball is close? Jaes Has Thigs o eebe Has Pihole caea odel ad caea (pojecio) ai Hoogeeous coodiaes allow pojecio
More informationThe Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues
Alied Maheaical Sciece Vol. 8 o. 5 747-75 The No-Tucaed Bul Aival Queue M x /M/ wih Reei Bali Sae-Deede ad a Addiioal Seve fo Loe Queue A. A. EL Shebiy aculy of Sciece Meofia Uiveiy Ey elhebiy@yahoo.co
More informationSupplementary Information
Supplemeay Ifomaio No-ivasive, asie deemiaio of he coe empeaue of a hea-geeaig solid body Dea Ahoy, Daipaya Saka, Aku Jai * Mechaical ad Aeospace Egieeig Depame Uivesiy of Texas a Aligo, Aligo, TX, USA.
More informationINF 5460 Electronic noise Estimates and countermeasures. Lecture 13 (Mot 10) Amplifier Architectures
NF 5460 lecoic oise simaes ad couemeasues Lecue 3 (Mo 0) Amplifie Achiecues Whe a asiso is used i a amplifie, oscillao, file, seso, ec. i will also be a eed fo passive elemes like esisos, capacios ad coils
More informationTransistor configurations: There are three main ways to place a FET/BJT in an architecture:
F3 Mo 0. Amplifie Achiecues Whe a asiso is used i a amplifie, oscillao, file, seso, ec. i will also be a eed fo passive elemes like esisos, capacios ad coils o povide biasig so ha he asiso has he coec
More informationLow-Complexity Turbo Receiver for MIMO SC-FDMA Communication Systems
Poceedigs of he Wold Cogess o Egieeig 5 ol I WCE 5, Jly - 3, 5, Lodo,.K. Low-Coplexiy bo Receive fo IO SC-FDA Coicaio Syses Fag-Bia eg, Y-Ka Chag ad Yig- Yag Absac liple-ip liple-op (IO) echologies ae
More informationStrong Result for Level Crossings of Random Polynomials
IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh
More informationهقارنت طرائق تقذير هعلواث توزيع كاها ري املعلوتني
هقارنت طرائق تقذير هعلواث توزيع كاها ري املعلوتني يف حالت البياناث املفقودة باستخذام احملاكاة د أ. الباحثة ظافر حسين رشيد جامعة بغداد- كمية االدارة واالقتصاد قسم االحصاء آوات سردار وادي املستخلص Maxiu
More informationRelations on the Apostol Type (p, q)-frobenius-euler Polynomials and Generalizations of the Srivastava-Pintér Addition Theorems
Tish Joal of Aalysis ad Nmbe Theoy 27 Vol 5 No 4 26-3 Available olie a hp://pbssciepbcom/ja/5/4/2 Sciece ad Edcaio Pblishig DOI:269/ja-5-4-2 Relaios o he Aposol Type (p -Fobeis-Ele Polyomials ad Geealizaios
More informationON POINTWISE APPROXIMATION OF FUNCTIONS BY SOME MATRIX MEANS OF FOURIER SERIES
M aheaical I equaliies & A pplicaios Volue 19, Nube 1 (216), 287 296 doi:1.7153/ia-19-21 ON POINTWISE APPROXIMATION OF FUNCTIONS BY SOME MATRIX MEANS OF FOURIER SERIES W. ŁENSKI AND B. SZAL (Couicaed by
More informationÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
More informationApplications of force vibration. Rotating unbalance Base excitation Vibration measurement devices
Applicaios of foce viaio Roaig ualace Base exciaio Viaio easuee devices Roaig ualace 1 Roaig ualace: Viaio caused y iegulaiies i he disiuio of he ass i he oaig copoe. Roaig ualace 0 FBD 1 FBD x x 0 e 0
More informationExercise 3 Stochastic Models of Manufacturing Systems 4T400, 6 May
Exercise 3 Sochasic Models of Maufacurig Sysems 4T4, 6 May. Each week a very popular loery i Adorra pris 4 ickes. Each ickes has wo 4-digi umbers o i, oe visible ad he oher covered. The umbers are radomly
More informationRedes de Computadores
Redes de Compuadoes Deay Modes i Compue Newoks Maue P. Ricado Facudade de Egehaia da Uivesidade do Poo » Wha ae he commo muipexig saegies?» Wha is a Poisso pocess?» Wha is he Lie heoem?» Wha is a queue?»
More informationB. Maddah INDE 504 Simulation 09/02/17
B. Maddah INDE 54 Simulaio 9/2/7 Queueig Primer Wha is a queueig sysem? A queueig sysem cosiss of servers (resources) ha provide service o cusomers (eiies). A Cusomer requesig service will sar service
More informationSTUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE WEIBULL DISTRIBUTION
Inenaional Jounal of Science, Technology & Managemen Volume No 04, Special Issue No. 0, Mach 205 ISSN (online): 2394-537 STUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE
More informationCAPACITY ANALYSIS OF ASYMPTOTICALLY LARGE MIMO CHANNELS. Georgy Levin
CAPACITY ANALYSIS OF ASYMPTOTICALLY LAGE MIMO CANNELS by Geogy Levi The hesis submied o he Faculy of Gaduae ad Posdocoal Sudies i paial fulfillme of he equiemes fo he degee of DOCTO OF PILOSOPY i Elecical
More informationEXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D. S. Palimkar
Ieraioal Joural of Scieific ad Research Publicaios, Volue 2, Issue 7, July 22 ISSN 225-353 EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D S Palikar Depare of Maheaics, Vasarao Naik College, Naded
More informationStrong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA
Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics
More informationDegree of Approximation of Fourier Series
Ieaioal Mahemaical Foum Vol. 9 4 o. 9 49-47 HIARI Ld www.m-hiai.com h://d.doi.og/.988/im.4.49 Degee o Aoimaio o Fouie Seies by N E Meas B. P. Padhy U.. Misa Maheda Misa 3 ad Saosh uma Naya 4 Deame o Mahemaics
More informationRelation (12.1) states that if two points belong to the convex subset Ω then all the points on the connecting line also belong to Ω.
Lectue 6. Poectio Opeato Deiitio A.: Subset Ω R is cove i [ y Ω R ] λ + λ [ y = z Ω], λ,. Relatio. states that i two poits belog to the cove subset Ω the all the poits o the coectig lie also belog to Ω.
More informationNumerical Solution of Sine-Gordon Equation by Reduced Differential Transform Method
Poceedigs of he Wold Cogess o Egieeig Vol I WCE, July 6-8,, Lodo, U.K. Nueical Soluio of Sie-Godo Equaio by Reduced Diffeeial Tasfo Mehod Yıldıay Kesi, İbahi Çağla ad Ayşe Beül Koç Absac Reduced diffeeial
More informationMoment Generating Function
1 Mome Geeraig Fucio m h mome m m m E[ ] x f ( x) dx m h ceral mome m m m E[( ) ] ( ) ( x ) f ( x) dx Mome Geeraig Fucio For a real, M () E[ e ] e k x k e p ( x ) discree x k e f ( x) dx coiuous Example
More informationElectromagnetic Wave Absorber with Isotropic and Anisotropic Metamaterials
Ieaioal Joual of Maeials Sciece ad Applicaios 07; 6(6): 30-308 hp://www.sciecepublishiggoup.co/j/ijsa doi: 0.648/j.ijsa.070606.6 ISSN: 37-635 (Pi); ISSN: 37-643 (Olie) Elecoageic Wave Absobe wih Isoopic
More informationThe Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type. S. Khademloo and H. Mohammadnia. afrouzi
Wold Alied cieces Joal (8): 898-95 IN 88-495 IDOI Pblicaios = h x g x x = x N i W whee is a eal aamee is a boded domai wih smooh boday i R N 3 ad< < INTRODUCTION Whee s ha is s = I his ae we ove he exisece
More informationOutline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem
adial diffsio eqaio Febay 4 9 Diffsio Eqaios i ylidical oodiaes ay aeo Mechaical Egieeig 5B Seia i Egieeig Aalysis Febay 4, 9 Olie eview las class Gadie ad covecio boday codiio Diffsio eqaio i adial coodiaes
More informationOne of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of
Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo
More informationODEs II, Supplement to Lectures 6 & 7: The Jordan Normal Form: Solving Autonomous, Homogeneous Linear Systems. April 2, 2003
ODEs II, Suppleme o Lecures 6 & 7: The Jorda Normal Form: Solvig Auoomous, Homogeeous Liear Sysems April 2, 23 I his oe, we describe he Jorda ormal form of a marix ad use i o solve a geeral homogeeous
More informationThe Central Limit Theorems for Sums of Powers of Function of Independent Random Variables
ScieceAsia 8 () : 55-6 The Ceal Limi Theoems fo Sums of Poes of Fucio of Idepede Radom Vaiables K Laipapo a ad K Neammaee b a Depame of Mahemaics Walailak Uivesiy Nakho Si Thammaa 86 Thailad b Depame of
More informationFBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf
.4 Base Exiaio Ipoa lass of vibaio aalysis Peveig exiaios fo passig fo a vibaig base hough is ou io a suue Vibaio isolaio Vibaios i you a Saellie opeaio Dis dives, e. FBD of SDOF Base Exiaio x() y() Syse
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationNeutron Slowing Down Distances and Times in Hydrogenous Materials. Erin Boyd May 10, 2005
Neu Slwig Dw Disaces ad Times i Hydgeus Maeials i Byd May 0 005 Oulie Backgud / Lecue Maeial Neu Slwig Dw quai Flux behavi i hydgeus medium Femi eame f calculaig slwig dw disaces ad imes. Bief deivai f
More informationECSE Partial fraction expansion (m<n) 3 types of poles Simple Real poles Real Equal poles
ECSE- Lecue. Paial facio expasio (m
More information10.3 Autocorrelation Function of Ergodic RP 10.4 Power Spectral Density of Ergodic RP 10.5 Normal RP (Gaussian RP)
ENGG450 Probabiliy ad Saisics for Egieers Iroducio 3 Probabiliy 4 Probabiliy disribuios 5 Probabiliy Desiies Orgaizaio ad descripio of daa 6 Samplig disribuios 7 Ifereces cocerig a mea 8 Comparig wo reames
More informationIn this section we will study periodic signals in terms of their frequency f t is said to be periodic if (4.1)
Fourier Series Iroducio I his secio we will sudy periodic sigals i ers o heir requecy is said o be periodic i coe Reid ha a sigal ( ) ( ) ( ) () or every, where is a uber Fro his deiiio i ollows ha ( )
More information, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t
Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission
More informationGeneralized Fibonacci-Type Sequence and its Properties
Geelized Fibocci-Type Sequece d is Popeies Ompsh Sihwl shw Vys Devshi Tuoil Keshv Kuj Mdsu (MP Idi Resech Schol Fculy of Sciece Pcific Acdemy of Highe Educio d Resech Uivesiy Udipu (Rj Absc: The Fibocci
More informationExtremal graph theory II: K t and K t,t
Exremal graph heory II: K ad K, Lecure Graph Theory 06 EPFL Frak de Zeeuw I his lecure, we geeralize he wo mai heorems from he las lecure, from riagles K 3 o complee graphs K, ad from squares K, o complee
More informationIntroduction to Mobile Robotics Mapping with Known Poses
Iroducio o Mobile Roboics Mappig wih Kow Poses Wolfra Burgard Cyrill Sachiss Mare Beewi Kai Arras Why Mappig? Learig aps is oe of he fudaeal probles i obile roboics Maps allow robos o efficiely carry ou
More informationM-ary Detection Problem. Lecture Notes 2: Detection Theory. Example 1: Additve White Gaussian Noise
Hi ue Hi ue -ay Deecio Pole Coide he ole of decidig which of hyohei i ue aed o oevig a ado vaiale (veco). he efoace cieia we coide i he aveage eo oailiy. ha i he oailiy of decidig ayhig ece hyohei H whe
More informationMath 7409 Homework 2 Fall from which we can calculate the cycle index of the action of S 5 on pairs of vertices as
Math 7409 Hoewok 2 Fall 2010 1. Eueate the equivalece classes of siple gaphs o 5 vetices by usig the patte ivetoy as a guide. The cycle idex of S 5 actig o 5 vetices is 1 x 5 120 1 10 x 3 1 x 2 15 x 1
More informationBig O Notation for Time Complexity of Algorithms
BRONX COMMUNITY COLLEGE of he Ciy Uiversiy of New York DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE CSI 33 Secio E01 Hadou 1 Fall 2014 Sepember 3, 2014 Big O Noaio for Time Complexiy of Algorihms Time
More informationComputer Propagation Analysis Tools
Compue Popagaion Analysis Tools. Compue Popagaion Analysis Tools Inoducion By now you ae pobably geing he idea ha pedicing eceived signal sengh is a eally impoan as in he design of a wieless communicaion
More informationSOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES
#A17 INTEGERS 9 2009), 181-190 SOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES Deick M. Keiste Depatmet of Mathematics, Pe State Uivesity, Uivesity Pak, PA 16802 dmk5075@psu.edu James A. Selles Depatmet
More informationMultilevel-DFT based Low-Complexity Hybrid Precoding for Millimeter Wave MIMO Systems
Muieve-DFT based Low-Copexiy ybid Pecodig fo Miiee Wave MIMO yses Yu-si Liu, Chiag-e Che, Cheg-Rug Tsai, ad -Yeu (dy Wu, Feow, IEEE Gaduae Isiue of Eecoics Egieeig aioa Taiwa Uivesiy Taipei, Taiwa {ike,
More information). So the estimators mainly considered here are linear
6 Ioic Ecooică (4/7 Moe Geel Cedibiliy Models Vigii ATANASIU Dee o Mheics Acdey o Ecooic Sudies e-il: vigii_siu@yhooco This couicio gives soe exesios o he oigil Bühl odel The e is devoed o sei-lie cedibiliy
More informationLIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF MARCINKIEWICZ OPERATOR
Reseh d ouiios i heis d hei Siees Vo. Issue Pges -46 ISSN 9-699 Puished Oie o Deee 7 Joi Adei Pess h://oideiess.e IPSHITZ ESTIATES FOR UTIINEAR OUTATOR OF ARINKIEWIZ OPERATOR DAZHAO HEN Dee o Siee d Ioio
More informationFresnel Dragging Explained
Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field
More informationInstitute of Actuaries of India
Isiue of cuaries of Idia Subjec CT3-robabiliy ad Mahemaical Saisics May 008 Eamiaio INDICTIVE SOLUTION Iroducio The idicaive soluio has bee wrie by he Eamiers wih he aim of helig cadidaes. The soluios
More informationEnergy Density / Energy Flux / Total Energy in 1D. Key Mathematics: density, flux, and the continuity equation.
ecure Phys 375 Eergy Desiy / Eergy Flu / oal Eergy i D Overview ad Moivaio: Fro your sudy of waves i iroducory physics you should be aware ha waves ca raspor eergy fro oe place o aoher cosider he geeraio
More informationLow-complexity Algorithms for MIMO Multiplexing Systems
Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. :
More informationES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017)
Pae1 Nae Soluios ES 330 Elecroics II Hoework 03 (Fall 017 ue Wedesday, Sepeber 0, 017 Proble 1 You are ive a NMOS aplifier wih drai load resisor R = 0 k. The volae (R appeari across resisor R = 1.5 vols
More informationCombinatorial Approach to M/M/1 Queues. Using Hypergeometric Functions
Inenaional Mahemaical Foum, Vol 8, 03, no 0, 463-47 HIKARI Ld, wwwm-hikaicom Combinaoial Appoach o M/M/ Queues Using Hypegeomeic Funcions Jagdish Saan and Kamal Nain Depamen of Saisics, Univesiy of Delhi,
More informationCHARACTERIZATIONS OF THE NON-UNIFORM IN TIME ISS PROPERTY AND APPLICATIONS
CHARACTERIZATIONS OF THE NON-UNIFORM IN TIME ISS PROPERTY AND APPLICATIONS I. Karafyllis ad J. Tsiias Depare of Maheaics, Naioal Techical Uiversiy of Ahes, Zografou Capus 578, Ahes, Greece Eail: jsi@ceral.ua.gr.
More information1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
More informationInternational Journal of Pure and Applied Sciences and Technology
In. J. Pue Appl. Sci. Technol., 4 (211, pp. 23-29 Inenaional Jounal of Pue and Applied Sciences and Technology ISS 2229-617 Available online a www.ijopaasa.in eseach Pape Opizaion of he Uiliy of a Sucual
More informationCh 3.4 Binomial Coefficients. Pascal's Identit y and Triangle. Chapter 3.2 & 3.4. South China University of Technology
Disc ete Mathem atic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Pigeohole Piciple Suppose that a
More informationOptical flow equation
Opical Flow Sall oio: ( ad ae le ha piel) H() I(++) Be foce o poible ppoe we ake he Talo eie epaio of I: (Sei) Opical flow eqaio Cobiig hee wo eqaio I he lii a ad go o eo hi becoe eac (Sei) Opical flow
More informationLESSON 15: COMPOUND INTEREST
High School: Expoeial Fuctios LESSON 15: COMPOUND INTEREST 1. You have see this fomula fo compoud ieest. Paamete P is the picipal amou (the moey you stat with). Paamete is the ieest ate pe yea expessed
More informationResearch Article On Pointwise Approximation of Conjugate Functions by Some Hump Matrix Means of Conjugate Fourier Series
Hidawi Publishig Copoaio Joual of Fucio Spaces Volue 5, Aicle ID 475, 9 pages hp://dx.doi.og/.55/5/475 Reseach Aicle O Poiwise Appoxiaio of Cojugae Fucios by Soe Hup Maix Meas of Cojugae Fouie Seies W.
More informationS, we call the base curve and the director curve. The straight lines
Developable Ruled Sufaces wih Daboux Fame i iowsi -Space Sezai KIZILTUĞ, Ali ÇAKAK ahemaics Depame, Faculy of As ad Sciece, Ezica Uivesiy, Ezica, Tuey ahemaics Depame, Faculy of Sciece, Aau Uivesiy, Ezuum,
More informationNew Results on Oscillation of even Order Neutral Differential Equations with Deviating Arguments
Advace i Pue Maheaic 9-53 doi: 36/ap3 Pubihed Oie May (hp://wwwscirpog/oua/ap) New Reu o Ociaio of eve Ode Neua Diffeeia Equaio wih Deviaig Ague Abac Liahog Li Fawei Meg Schoo of Maheaica Sye Sciece aiha
More informationGeneral Non-Arbitrage Model. I. Partial Differential Equation for Pricing A. Traded Underlying Security
1 Geneal Non-Abiage Model I. Paial Diffeenial Equaion fo Picing A. aded Undelying Secuiy 1. Dynamics of he Asse Given by: a. ds = µ (S, )d + σ (S, )dz b. he asse can be eihe a sock, o a cuency, an index,
More informationA New Result On A,p n,δ k -Summabilty
OSR Joual of Matheatics (OSR-JM) e-ssn: 2278-5728, p-ssn:239-765x. Volue 0, ssue Ve. V. (Feb. 204), PP 56-62 www.iosjouals.og A New Result O A,p,δ -Suabilty Ripeda Kua &Aditya Kua Raghuashi Depatet of
More informationInternational Journal of Mathematics Trends and Technology (IJMTT) Volume 47 Number 1 July 2017
Iteatioal Joual of Matheatics Teds ad Techology (IJMTT) Volue 47 Nube July 07 Coe Metic Saces, Coe Rectagula Metic Saces ad Coo Fixed Poit Theoes M. Sivastava; S.C. Ghosh Deatet of Matheatics, D.A.V. College
More informationBINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =
wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em
More informationOn Energy-Efficient Node Deployment in Wireless Sesnor Networks
I J Communicaions, Newok and Sysem Sciences, 008, 3, 07-83 Published Online Augus 008 in Scies (hp://wwwscipog/jounal/ijcns/) On Enegy-Efficien Node Deploymen in Wieless Sesno Newoks Hui WANG 1, KeZhong
More informationUltrahigh Frequency Generation in GaAs-type. Two-Valley Semiconductors
Adv. Sudies Theo. Phys. Vol. 3 9 o. 8 93-98 lhigh Fequecy Geeio i GAs-ype Two-Vlley Seicoducos.. sov. K. Gsiov A. Z. Phov d A.. eiel Bu Se ivesiy 3 Z. Khlilov s. Az 48 Bu ciy- Physicl siue o he Azebij
More informationCapítulo. of Particles: Energy and Momentum Methods
Capíulo 5 Kieics of Paicles: Eegy ad Momeum Mehods Mecáica II Coes Ioducio Wok of a Foce Piciple of Wok & Eegy pplicaios of he Piciple of Wok & Eegy Powe ad Efficiecy Sample Poblem 3. Sample Poblem 3.
More informationAn interesting result about subset sums. Nitu Kitchloo. Lior Pachter. November 27, Abstract
A ieresig resul abou subse sums Niu Kichloo Lior Pacher November 27, 1993 Absrac We cosider he problem of deermiig he umber of subses B f1; 2; : : :; g such ha P b2b b k mod, where k is a residue class
More informationResearch Article Strategic Conditions for Opening an Internet Store and Pricing Policies in a Retailer-Dominant Supply Chain
aheaical Pobles in Engineeing Volue 2015, Aicle ID 640719, 15 pages hp://dx.doi.og/10.1155/2015/640719 Reseach Aicle Saegic Condiions fo Opening an Inene Soe and Picing Policies in a Reaile-Doinan Supply
More informationth m m m m central moment : E[( X X) ] ( X X) ( x X) f ( x)
1 Trasform Techiques h m m m m mome : E[ ] x f ( x) dx h m m m m ceral mome : E[( ) ] ( ) ( x) f ( x) dx A coveie wa of fidig he momes of a radom variable is he mome geeraig fucio (MGF). Oher rasform echiques
More informationJournal of Xiamen University (Natural Science)
48 4 2009 7 () Joual of Xiame Uivesiy (Naual Sciece) Vol. 48 No. 4 J ul. 2009, 3 (, 36005) :,,.,,,.,.,. : ;;; : TP 393 :A :043820479 (2009) 0420493206,( dyamic age s). ( muliage sysems),, [ ], [2 ], [3
More informationDynamic h-index: the Hirsch index in function of time
Dyamic h-idex: he Hirsch idex i fucio of ime by L. Egghe Uiversiei Hassel (UHassel), Campus Diepebeek, Agoralaa, B-3590 Diepebeek, Belgium ad Uiversiei Awerpe (UA), Campus Drie Eike, Uiversieisplei, B-260
More informationTechnical Report: Bessel Filter Analysis
Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we
More informationThe Pigeonhole Principle 3.4 Binomial Coefficients
Discete M athematic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Ageda Ch 3. The Pigeohole Piciple
More informationOn a Z-Transformation Approach to a Continuous-Time Markov Process with Nonfixed Transition Rates
Ge. Mah. Noes, Vol. 24, No. 2, Ocobe 24, pp. 85-96 ISSN 229-784; Copyigh ICSRS Publicaio, 24 www.i-css.og Available fee olie a hp://www.gema.i O a Z-Tasfomaio Appoach o a Coiuous-Time Maov Pocess wih Nofixed
More informationSome Integral Mean Estimates for Polynomials
Iteatioal Mathematical Foum, Vol. 8, 23, o., 5-5 HIKARI Ltd, www.m-hikai.com Some Itegal Mea Estimates fo Polyomials Abdullah Mi, Bilal Ahmad Da ad Q. M. Dawood Depatmet of Mathematics, Uivesity of Kashmi
More informationEGR 544 Communication Theory
EGR 544 Commuicaio heory 7. Represeaio of Digially Modulaed Sigals II Z. Aliyazicioglu Elecrical ad Compuer Egieerig Deparme Cal Poly Pomoa Represeaio of Digial Modulaio wih Memory Liear Digial Modulaio
More information6.2 Improving Our 3-D Graphics Pipeline
6.2. IMPROVING OUR 3-D GRAPHICS PIPELINE 8 6.2 Impovig Ou 3-D Gaphics Pipelie We iish ou basic 3D gaphics pipelie wih he implemeaio o pespecive. beoe we do his, we eview homogeeous coodiaes. 6.2. Homogeeous
More informationTwo-Pion Exchange Currents in Photodisintegration of the Deuteron
Two-Pion Exchange Cuens in Phoodisinegaion of he Deueon Dagaa Rozędzik and Jacek Goak Jagieonian Univesiy Kaków MENU00 3 May 00 Wiiasbug Conen Chia Effecive Fied Theoy ChEFT Eecoagneic cuen oeaos wihin
More informationSTK4080/9080 Survival and event history analysis
STK48/98 Survival ad eve hisory aalysis Marigales i discree ime Cosider a sochasic process The process M is a marigale if Lecure 3: Marigales ad oher sochasic processes i discree ime (recap) where (formally
More informationAcademic Forum Cauchy Confers with Weierstrass. Lloyd Edgar S. Moyo, Ph.D. Associate Professor of Mathematics
Academic Forum - Cauchy Cofers wih Weiersrass Lloyd Edgar S Moyo PhD Associae Professor of Mahemaics Absrac We poi ou wo limiaios of usig he Cauchy Residue Theorem o evaluae a defiie iegral of a real raioal
More informationGame Study of the Closed-loop Supply Chain with Random Yield and Random Demand
, pp.105-110 http://dx.doi.og/10.14257/astl.2014.53.24 Gae Study of the Closed-loop Supply Chain with ando Yield and ando Deand Xiuping Han, Dongyan Chen, Dehui Chen, Ling Hou School of anageent, Habin
More informationReinforcement learning
Lecue 3 Reinfocemen leaning Milos Hauskech milos@cs.pi.edu 539 Senno Squae Reinfocemen leaning We wan o lean he conol policy: : X A We see examples of x (bu oupus a ae no given) Insead of a we ge a feedback
More informationStructure and Some Geometric Properties of Nakano Difference Sequence Space
Stuctue ad Soe Geoetic Poeties of Naao Diffeece Sequece Sace N Faied ad AA Baey Deatet of Matheatics, Faculty of Sciece, Ai Shas Uivesity, Caio, Egyt awad_baey@yahooco Abstact: I this ae, we exted the
More informationDavid Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
More informationCHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE
Fameal Joal of Mahemaic a Mahemaical Sciece Vol. 7 Ie 07 Page 5- Thi pape i aailable olie a hp://.fi.com/ Pblihe olie Jaa 0 07 CHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE Caolo
More informationF D D D D F. smoothed value of the data including Y t the most recent data.
Module 2 Forecasig 1. Wha is forecasig? Forecasig is defied as esimaig he fuure value ha a parameer will ake. Mos scieific forecasig mehods forecas he fuure value usig pas daa. I Operaios Maageme forecasig
More informationEconomics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017
Deparme of Ecoomics The Ohio Sae Uiversiy Ecoomics 8723 Macroecoomic Theory Problem Se 2 Professor Sajay Chugh Sprig 207 Labor Icome Taxes, Nash-Bargaied Wages, ad Proporioally-Bargaied Wages. I a ecoomy
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationReview Answers for E&CE 700T02
Review Aswers for E&CE 700T0 . Deermie he curre soluio, all possible direcios, ad sepsizes wheher improvig or o for he simple able below: 4 b ma c 0 0 0-4 6 0 - B N B N ^0 0 0 curre sol =, = Ch for - -
More informationEQUATION SHEET Principles of Finance Exam 1
EQUATION SHEET Piciple of iace Exa INANCIAL STATEMENT ANALYSIS Ne cah flow Ne icoe + Depeciaio ad aoizaio DuPo equaio: ROANe pofi agi Toal ae uove Ne icoe Sale Sale Toal ae DuPo equaio: ROE ROA Equiy uliplie
More informationFujii, Takao; Hayashi, Fumiaki; Iri Author(s) Oguro, Kazumasa.
TileDesigig a Opimal Public Pesio Fujii, Takao; Hayashi, Fumiaki; Ii Auho(s) Oguo, Kazumasa Ciaio Issue 3- Dae Type Techical Repo Tex Vesio publishe URL hp://hdl.hadle.e/86/54 Righ Hiosubashi Uivesiy Reposioy
More informationA note on characterization related to distributional properties of random translation, contraction and dilation of generalized order statistics
PobSa Foum, Volume 6, July 213, Pages 35 41 ISSN 974-3235 PobSa Foum is an e-jounal. Fo eails please visi www.pobsa.og.in A noe on chaaceizaion elae o isibuional popeies of anom anslaion, conacion an ilaion
More information