Parallel Algorithms for Residue Scaling and Error Correction in Residue Arithmetic
|
|
- Polly McDonald
- 6 years ago
- Views:
Transcription
1 Weless Engneeng Technology 8- htt://ddoog/6/wet Publshed Onlne Octobe (htt://wwwscog/ounal/wet) Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc Hao-Yung Lo Tng-We Ln Deatent of Electcal Engneeng Natonal Tsng Hua Unvesty Hsnchu Cty Chnese Tae Eal: hylo@eenthuedutw Receved August d ; evsed Setebe th ; acceted Setebe th Coyght Hao-Yung Lo Tng-We Ln Ths s an oen access atcle dstbuted unde the Ceatve Coons Attbuton Lcense whch ets unestcted use dstbuton eoducton n any edu ovded the ognal wo s oely cted ABSTRACT In ths ae we esent two new algoths n esdue nube systes fo scalng eo coecton The fst algoth s the Cyclc Poety of Resdue-Dgt Dffeence (CPRDD) It s used to seed u the esdue ultle eo coecton due to ts aallel ocesses The second s called the Taget Race Dstance (TRD) It s used to seed u esdue scalng Both of these two algoths ae used wthout the need fo ed Rad Conveson (RC) o Chnese Resdue Theoe (CRT) technques whch ae te consung eque hadwae colety Futheoe the esdue scalng can be efoed n aallel fo any cobnaton of odul set ebes wthout usng loou tables Keywods: Chnese Ree Theoe (CRT); Eo Coecton; Eo Detecton; Paallel Resdue Scalng; Resdue Nube Systes (RNS); Taget Race Dstance (TRD); Taget Resdue-Dgt Dffeence Intoducton Because the esdue nube syste (RNS) oeatons on each esdue dgt ae ndeendent cay fee oety of addton between dgts they can be used n hghseed coutatons such as addton subtacton ultlcaton To ncease the elablty of these oeatons a nube of edundant odul wee added to the ognal RNS odul [RRNS] Ths wll also allow the RNS syste the caablty of eo detecton coecton The ealest wos on eo detecton coecton wee eoted by seveal authos [-] Waston Hastng [] oosed the sngle esdue dgt eo coecton Yau Lu [] suggested a odfcaton wth the table loous usng the ethod above elbau [-6] oosed coecton of the AN code Raachan [] oosed sngle esdue eo coecton Lenns Altan [8-] aled the concet of odulus oecton to desgn an eo chece Etzel Jenns [] used RRNS fo eo detecton coecton n dgtal fltes In [-6] an algoth fo scalng a esdue dgtal eo coecton based on ed ad conveson (RC) was oosed Recently Katt [] has esented a esdue athetc eo coecton schee usng a odul set wth coon factos e the odul n a RNS need not have a awse elatve e In ths study we develoed two new algoths wthout usng RD (ed-ad dgt) o CRT (Chnese eaned Theoe) fo seedng-u the scalng ocesses slfyng the eo detecton coecton n RNS The fst algoth s used fo these uoses though the esdue dgt dffeence cyclc oety (CPRDD) wthn the ange of t whee t n n n wth addtonal odul The odul n ae called the nonedundant odul; n n n ae the edundant odul The nteval s called the legtate n ange whee the nteval t s the llegtate ange whee t n t s the total ange Ths ae s oganzed as follows: Secton II wll descbe the schee the cyclc oety of esdue dgt dffeence (CPRDD) Secton III descbes the Taget Race Dstance (TRD) algoth followed by soe eales Secton IV dscusses esdue scalng eo coecton usng the TRD CPRDD algoths Fnally the concluson s gven n secton V Eo Detecton Coecton Usng Resdue Dgt Dffeence Cyclc Poety Any esdue dgt eesentaton n odul set n has ts cyclc length wth esect to ts odule nube Fo eale f the odul set s ( Coyght ScRes
2 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc ) then the cyclc lengths of any esdue dgts ae esectvely Snce these cyclc lengths ae not equal they ae vey dffcult to use as tools fo eo detecton coecton Actually thee ests the oety of coon (unfo) cyclc length n RNS between esdue dgtal-dffeences (RDD) Consde thee odul set The esdue eesentatons the coesondng dgt-dffeences ae shown n Table defned as the dffeence n value between two dgts d whee d s ae all odulo to ostve values wth esect to f the cycle length of s assgned Note that the esdue dgt-dffeences d n Table ae obtaned fo fo f f Ths dffeence of o n values ay be ostve o negatve deendng uon o o esectvely All negatve values ust be odulo to ostve values Fo eale on staed ow 8 as shown n Table the dgt dffeence n value fo s d It esults n d Fo the cyclc oety of esdue-dgt dffeence (CPRDD) n RNS we now have the followng theoe Theoe Fo a odul set n esdue eesentaton fo n n RNS thee ests a cyclc oety n dffeences between two esdue dgts d o The cyclc length can be assgned ethe to o deendng uon odulo oeaton wth esect to o Poof: Consde the case esectve to the esdue-dgt dffeence (RDD) between two dgts n X n can be n geneal eessed by the equaton d q (-) whee q q ae nteges Fo slcty we only consde the case of assue the case of can be obtaned n a sla way The elated theoe algoth ae descbed as follows ) In cycle (the ntal cycle) we have X wth q d? As Table Cyclc oety of Resdue Dgt Dffeence Decal d d * wth cycle Out of Range we have d wth s s n cycle whee eans the lagest Coyght ScRes
3 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc ntege less than o equal to Thus the RDD has s n the ntal cycle fo each odulus e n cycle d fo all ) Net consde each odulus Snce X X q then d q whee Fo RDD = (fo cycles then ) d wth s s Fo RDD = (not necessay n cycle ) d wth s s Fo RDD = d wth s s cyclc length s Thus the nube of cycles wthn Coollay Fo the above theoe we can ed- ths cyclc length fo N s N fo ately obtan that each cycle n the esdue-dgt dffeence of wll stat at locaton end at locaton N Coollay It s easly shown that thee ests nube of cycles wth esect to the cyclc length of Theoe The algoth of theoe ts coollaes can be etended to two o oe a-wse esdue- Poof Snce the esdue-dgt dffeence of dgt dffeences n eesentaton s a-wse Poof: consde a thee odul set we have two athe legtate ange of ths a-wse RDD s wse odul sets whose RDD (Resdue Dgtal Dffeence) (fo though ) Fo coollay the s d X X q s whee s agan the efeenced odule Assue also a-wse nubes Follow the sae ocedue as ste () as above ) Fo q s d thus d s s Ths shows that d has also s n cycle of The cyclc length s the nube of cycles fo s o ) Fo q s d h (a constant fo any RDD) f s h d h h h h Ths shows that the d h n any locaton has also s h n cycle of The nube of cycles fo Cobnng these thee odul nto one set we have cyclc s stll Coyght ScRes
4 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc length (fo eale ) The nube of cycles fo ae N N N 6 esectvely As shown n Table the RDD as of d d ae All as n each cycle ( ) In geneal n N wth ows n RDD n each ow Ths coletes the oof Eale - Consde a odul set X ts coesondng esdue dgts eesentaton set s The cyclc length s the nube of cycles fo ae N N 8 N esectvely Eo detecton coecton: Befoe the CPRDD algoth used fo eo detecton coecton s descbed soe basc tes n use ust be defned Defnton : Stde dstance S : It s the nceental o deceental dstance between odul n absolute value fo th cycle to th cycle Fo eale: S () Eo detecton Let the odul set be whee ae the nonedundant odul ae the edundant odul Snce the cyclc lengths of CPRDD d s ae constant t s thus easly found that the nube of cycles on tac L fo the statng ont (o othe d ) to ts taget oston In tun the dstance of RDD s can also be found Theoe The nube of cycles on tac L (colun d ) fo any statng ont (say dˆ ) to ts taget oston d can be found usng the equaton below; dˆ S d whee S the stde dstance between odul = the nube of cycles assng though fo statng ont dˆ to the destnaton d on tac L If dˆ then the nube of cycles ae equal to the total cycles fo the statng ont to ts taget oston d Poof: Snce s the nube of cycles fo to d wth esect to odule s the cyclc length thus s the total dstance fo the statng ont ˆd to ts taget oston d The eanng dstance fo on tac L n the th cycle ust d be on the sae ow of on tac L Thus RDD RDD d Once the RDD s of n ae found the eo detecton coecton fo odul can be found ust by coang the calculated cycles o RDD wth the ognal esdue eesentaton a-wse so that the eo odule can be detected The ocedue fo eo detecton by usng CPRDD algoth s suazed as follows ) Choose two ost sgnfcant (lagest) odul as the efeed odul aong the n odul say n n ) Fnd the s dstance of a cycle Sn n n n ) Fnd the dgt dffeence d n n fo X n n n n n ) Ceate the equaton of RDD d o n n n n S d RDD n n n n n n n n n n n ) Solve fo fo Equaton (-) as the n n S d n n n n n n n n (-)? ae nown The value of ust be less than o equal to 6) Fnd the coesondng RDD fo the statng ont to n ) Calculate n n n dstance fo RDD RDD chec the values of n n If these sets nubes ae equal then no eo occus; othewse eo ests We tae the sla nuecal as eale - to vefy ths algoth (CPRDD) Eale - Assue that a odul set nube X whose es- the eo detecton can be descbed as follows Let us begn ou ocedues fo the RDD d Snce S s dstance of a cycle d d due eesentaton s 6 If an eo occus at X 6 d 6 8 Then Nd S 8 Solve fo let wthn legtate ange then Coyght ScRes
5 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc The coesondng RDD fo these two ay dstances ae esectvely RDD 6 RDD 6 Thus the geneated esults of the esdue eesentaton fo RDD ae esectvely RDD 6 X 6 X Snce the calculated esults of X X ae not dentcal thee ust be eos n one of these odul We cannot detene whch one s eoneous To locate the odule whee the eo ests at least one addtonal (edundant) odule ust be used The ocedue fo eo coecton by usng CPRDD algoth s essental the sae as the eo detecton Howeve two addtonal edundant odul ust be added fo one eo coecton Note that only one edundant odulus added fo eo detecton ) Choose o as a efeed odulus ) Fnd as the sae oce- dues of eo detecton stes - ) Eane the values of If coon value ests aong then no eo occus If thee s one only one say that has no coon value wth all othe then an eo ets n odulus Ths coletes the eo coecton ocedues The followng eale s llustated hee to vefy ths algoth Eale - Eo coecton As befoe we can futhe locate coect a sngle eo by addng two edundant odul Let us use the sae eale The odul set whee ae edundant odul the esdue X eesentaton 6 If a sngle eo occus at eg X s assgned as a efeence odule then d 6 d d d Fo CPRDD algoth we can fnd the nube of cycles fo these RDD s S S S S Snce the cycle length s all above be less than 6 Thus we have 6 6 values ust If no eos occu all s ae equal e Coaed to the above esults wth awse odul only eets ths condton Thee ests no such value n Ths shows that the odule s faulty theefoe we can coect t as follows: snce the RDD cycle length Thus 6 Ths coletes the eo coecton Note that the above CPRDD s fo each esdue-dgt dffeence d can be ocessed n aallel In addton f the efeenced odule s assgned to the eoneous odule by chance eg ths algoth wll fal to locate the eo In ths case thee ae no s values that can be found to atch ths condton The way to solve the oble s of couse to assgn any othe odul eg o The hadwae desgn fo the oosed algoth n Eale - s shown n Fgue The Taget Race Dstance (TRD) Schee The conveson o decodng technque fo esdue eesentaton to X n bnay s usually accolshed usng the ed-ad dgt (RD) o Chnese eaned theoe (CRT) An otal atched aallel convete of ths nd can be seen n [] The RD s shown by the followng eesson wth weghted nubes: a a a a n n n wth n whee n s the ed-ad conveson (RC) of Otzaton can be obtaned usng ths ethod as the accessed table loou te s eactly equal to the ght addton te afte edate colun stage fo the tee netwo of the addes Coyght ScRes
6 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc ' ' ' ' ' d d ' d d d s s s ' s sp s s 6 q * 6 * 6 Coae atch ccuts * ultle adde = 6 Fgue The hadwae leentaton fo the oosed eo coecton locaton algoth can be accolshed wthout usng loou tables Howeve te s stll consued eadng a lage nube of loou tables Addtonal hadwae colety s equed by the adde-tee netwos An algoth called the taget ace dstance was wth a sle stuctue was develoed fo hgh-seed conveson TRD algoth Suose each esdue nube n the RNS X has ts own tac L the dstance ove tac L fo (statng ont) to X (end ont) though cycles can be eessed usng D Obvously the ay (no ultles of ) dstance of s D To obtan the X fo ts n esdue eesentaton of we ust fnd a taget such that tavesng the sae dstances ove tacs l l l esectvely e when the TRD dstance of each taget s eached then D D D The TRD dstance of X can be found fo the followng theoe: Theoe Consde the sle case of two odul sets Its esdue eesentaton tagets ae esectvely Let D be the ay dstance of esdue fo to on the tac L D be the ay dstance of fo to on tac L Then the TRD dstance fo these two esdues that have the sae TRD dstances can be obtaned by the followng equaton TRD (-) In addton can be calculated fo the equaton D Coyght ScRes
7 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc whee s the cyclc length of s nube of cycles all of the nteges Poof: It s easy to show that the above TRD s the coon taget dstance of Snce And X thus TRD X s the TRD dstances fo both of Coollay: It s evdent that the above theoe can be etended to n odul set n esdue nube n The coesondng TRD of n ae theefoe TRD n n n n In addton can be solved fo the followng equatons whee Note that n ae the tagets of odul n esectvely the TRD n s the dstance that has equal tac lengths e L L Ln L That s; L L L L n n Eale - Let the odul set be the esdue eesentaton be The ocedues to fnd the TRD dstance can be descbed as follows: ) Fnd the ay dstance D D of esdue snce s equed thus TRD ) Reeat the ocedue to fnd the nube of cycles the last TRD dstances (destnatons) TRD TRD Snce ˆ ˆ thus TRD TRD ˆ 6 6 thus TRD 8 TRD The fnal TRD dstance s the coon dstncton of ths syste fo tagets e TRD X Ths esult can be vefed as follows: Fgue Shows the TRD s on tacs l l l l esectvely Eo detecton coecton by TRD algoth A edundant esdue nube syste wth edundant odul wll allow detecton of any sngle eo [] Consde the odul set the coect esdue e- X 6 Let us esentaton Tac L L L L ( = ) ( = ) ( = ) ( = ) K = K = K = L L = = 6 = TRD( ) TRD( ) 8 = TRD( ) = TRD( ) = TRD( ) 8 = TRD( ) TRD( ) TRD( ) Fgue TRD s on tac L L L L Coyght ScRes
8 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc assue that s the edundant odul wth a sngle eo X F 6 esdue eesentaton The TRD theoe can be used to detect ths eo We fnd that fnal TRD fo does not fall nto the legtate ange as follows e R F TRD TRD TRD TRDTRD ˆ 6 TRD 6 ˆ 6 TRD 6 8 The fnal TRD dstance TRD 8 8 If we need to locate coect ths odule eo anothe edundant odule ust be added Let us assue that fo ths equeent n the above esdue eesentaton The cuent edundant odul set s the coect esdue eesentaton s 6 Let us assue that ae the edundant odul Wth a sngle eo F 6 The TRD theoe can agan be used to locate coect ths eo We fnd that fnal TRD s fo dose not fall n the legtate ange but othe fnal TRD s fo 6 do falls n the legtate ange: ) TRD fo TRD TRD TRD ˆ 8 TRD 6 out of legtate ange ) TRD fo TRD TRD 6 ; ˆ 8 TRD 8 ˆ TRD wthn legtate ange Thus the eo s located at odule ust be coected to Ths algoth can also be used fo ultle eo coectons Howeve at least thee edundant odul ae equed The ocedues ae sla Scalng wth Eo Coecton The above oosed algoth used fo eo detecton coecton has the advantage of not equng loou tables No CRT (Chnese esdue theoe) decodng ocesses ae equed Howeve t s stll te consung eques etensve hadwae colety fo each odule havng ultle-value nuts to the atch unt selectng a coect one as a outut To ove ths dawbac an otal atchng algoth s oosed hee fo the eo coecton The followng two theoes wll be used an eale follows Theoe Let be two elatve e nubes n RNS fo odule odule esectvely Then thee ust est the elaton eesented by the equaton whee so assung The that ae estcted to nteges Poof: As a fst ste let It s easly seen that wll be satsfed Net consde Snce thee ae two dffeent a cobnaton thus the dffeence between of wll always be satsfed fo whee s estcted n nteges Theoe 6 If the values of n the equaton ae nown then can always be detened fo equaton whee o ae wthn the ange: o Poof: Let the dffeence value of be equal to d then d wll be the nteges wthn the ange between e o These two eessons show that we can always select an ntege value wthn the nteval between o to satsfy the Coyght ScRes
9 6 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc condtons d o d Eale - Let Fnd the nu values of esectvely fo the followng equaton : Snce we have d o (-) (-) fo Equaton (-) so fo Equaton (-) so fo Ths esult can be vefed by substtutng nto the above equaton Theoe 6 s vey useful as shown n the followng eale In Theoe of Secton III the nube of cycles on tac L fo the statng ont to ts taget oston d can be eessed by settng dˆ e s d o s d (-) whee s s the odule stde dstance efeng to odule Slaly the nube of cycles on tac l fo the statng ont to ts taget oston can be eessed by settng dˆ e; s d o s d (-) Snce fo theoe the cyclc length of the esdue dgts dffeences efeence to odule s constant (unfo) then thee ust est a condton c s c s Elnatng the above tes fo Equatons (-) (-) c c c d c d D D S o (-6) S o (-) S o (-8) Elnatng fo Equaton s (-) (-6) solve fo fo (-) o 8 Chec fo Equaton (-) 6 Ths shows that the eo occus at odule Fo ths esult we can edately obtan 6 Notng that t ay haen that the assgned efeenced eoy odul falls concdentally wth eo eoy odule In ths occuence we cannot fnd the coect (nteges) values of P P wthn the legtate ange It sees that ths algoth can only detect eo To colete the eo coecton ocedue we can sly change the efeenced odule to any othe follow the sae ocedue as befoe Ths guaantees that the oosed algoth n Theoe wll also wo well n ths case The hadwae stuctue fo llustatng ths algoth s shown n Fgue The oosed TRD (taget Race Dstance) schee used fo eo coecton can be used fo scalng assgnng nubes n a esdue nube syste A edundant esdue nube syste (RRNS) s defned as befoe n an RNS wth addtonal odul The odul ae called the nonedundant odul whle the eta odul ae the edundant odul The nteval s called the legtate ange whee the nteval s the llegtate ange whee whee c c s the total ange In the D c d c d RRNS the negatve nubes wthn the dynac ange Eale - ae eesented as states at the ue etee of the total Let the odul set ange whch s at of the llegtate ange The os 6 the eo the eo occus at tve ebes ae aed to the nteval Follow the sae ocedues of the Eale - to use ths algoth f s odd o f s even The negatve S o (-) nubes ae aed to the nteval Coyght ScRes
10 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc ' ' ' ' ' - d s - d ' 6P P s d d s s' d - s' RO X s s s s *+ X= d d ' d d ' d 6 d ' d d ' Fault syndos Fgue In the bloc daga usng otal atchng between ultles P P the esdue dgts ae coected by - = d f s odd o f s even [] The one-to-one coesondence between the nteges of the dynac ange the states of the legtate ange n the RRNS can be establshed usng a olaty shft [] The olaty shft s defned as below X X fo even X fo odd whee X denotes the value X afte a olaty shft X f s odd so that X a olaty shft needs to be efoed o to coectng o scalng snce X belongs to the legtate ange If a e e s n- sngle esdue dgt eo toduced coesonds to odules then afte a olaty shft X E X we whee X e w s the ultlcatve nvese of e w e w e The odul denotes a sngle esdue dgt eo ust fall wthn the llegtate ange [] Snce can be ee- Coyght ScRes
11 8 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc sented unquely by a a a whee a s ae the coeffcent fo the Chnese Ree Theoe (CRT) e a whee a Note that the edundant dgts a a a ae zeos f no eo s ntoduced whle at least one edundant dgt s not equal to zeo f a sngle eo s nto- duced Theefoe t has the sae eanng that o a a a s used to be the entes of the eo coecton ) s an d ) Although the eos detecton coecton descbed n secton II have been slfed the ocesses due to no need of CRT conveson It s stll hadwae cole te consung fo the esdue scalng oeaton To ove ths dawbac a dect esdue-scalng algoth can be used It s fleble dect to detect event the eos The fleblty eans that the scalng facto can be abtay chosen any sngle odule such as e not necessaly begnnng fo to n ode The dect caablty eans no equeent fo CRT etenson ocesses fo decodng o loou tables The followng theoe (theoe ) eale ae clafed Theoe If the scalng facto K s one of the odule set the esdue dgts ae esectvely then the esdue dgt scaled by a facto y can be obtaned usng the equaton y (-) Poof: It s easy to show that when Equaton (-) s dvded by on both sde we have y y (-) Eale - Fo convenent coason of the oosed TRD algoth to othe schees such as aeaed n [] we tae the sae nuecal eale n [] Let the odul set 6 whee ae egula odul 6 ae edundant odul Then 6 6 X The suffcent cond- tons fo coectng sngle esdue dgts eos ae ) s o s o a The au s 6 ) { } a o The a Thus the odul set satsfes the necessay suffcent condtons fo coectng sngle eos dgt Assue X 8 a sngle dgt eo e s ntoduced then X 8 Afte a olaty shft X X Follow the sae ocedues as shown n Eale - CPRDD s aled fo coecton wthout the need fo usng a table ) Assgn the odul as the efeence odul the followng esdue dgt efeences ts coesondng CPRDD equatons: s d ae obtaned d d d d ; ; ; ; d 6 6 ) Choose two hghest dgt dffeence as one a fo equal taget ace dstance eg 6 Then the tue ay RDD equatons ae (-) And 6 (-) whee ae selected so that the two RDD ae equal dstances ) Elnatng tes n Equaton s (-) (-) by uttng 6 whee then ) Substtutng nto equatons (-) (-) esectvely we have then 6 also 6 Coyght ScRes
12 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc ) Checng othe thee RDD s The only dffeent odule esdue occus on odule nube at e The thee taget dstances can be fo any odule esdue say (ecet ) The esdue eesentaton of X s theefoe X 8 If a sngle dgt eo e s ntoduced then X 8 The coesondng eo s theefoe 6 6 X X e Afte a olaty shft 8 8 the scalng facto K to s 8 6 The fnal ste ust K use a loou table to obtan the esult [] K Fo vefyng ou oosed algoth the table of the coesondng s not equed as n [] The o- K cesses fo fndng coectng a sngle eo based on ou ethod ae descbed below ) Fnd the esdue dgt dffeence to a selected odule say as befoe 8 Fo vefyng that ou oosed algoth detects coects sngle eo wthout usng a table the sae nuecal eale s used to descbe the ocedue as follows: d Then d d d d6 6 ) Choose two hghest dgt dffeences as one a fo equal taget ace dstances eg 6 the followng two equatons can be obtaned: (-a) (-b) 6 ) Elnatng tes n (-a) (-b) by uttng 6 then ) Substtutng nto Equaton s (-a) (-b) esectvely we have then 6 also 6 X X X X 8 Obvously the eo s located at thus e X X Futheoe the CPRDD algoth can be used dectly n aallel fo esdue scalng eo coecton Thus the ocess s geatly seeded u Eale - Fo convenent coason the sae nuec eale as n [] s llustated hee Consde 6 scalng facto K If an nut X a sngle esdue dgt eo e coesondng to Then X 6 Afte a olaty shft ) Dvdng by afte subtactng fo 6 ths leads Coyght ScRes
13 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc ) Dvdng by afte subtactng fo 6 6 ; ; ; 6 6 Snce fo above only does not atch wth all othe s e 6 6 Theefoe thee occus an eo at Once ths eo s detected t s easly found coected fo the above equatons 6 whch n tun 6 X that 6 6 Dvded by ; 6; ; ; 6 ; Dvded by 6 ; ; ; The hadwae stuctue of ths eale fo the esdue scalng s shown n Fgue Actually ths algoth can be dvded by any abtay odul Eale - Dvded by any abtay odul say t ust subtact fo X Then ; ; ; ; 6 6 ; chec 8 8 Ths esults It can be seen fo above that 6 6 whch ae equal each othe as eected Eale -6 Fo ocessng two esdue scalngs eo coectons n aallel we tae Eale - as an llustaton Let scalng facto K e the fst esdue scalng facto s the second one s o vese vesa It s easly shown that the etended CPRDD algoth s used can be coleted n one cycle That s ; 8 ; ; ; The esult s dentcal X e whch ae dentcal esults as shown n Eale - Eale - Fo eo coecton 6 * Coyght ScRes
14 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc RDD d Note:select = as odule efeence RDD d _ s 6 s s RO RO RO RO s 6 select coon value 6 < * ultl e 6 6 _ X= 6 Fgue Hadwae stuctue of the esdue scalng nube fo Eale - Ths shows 6 d Fo above esults ths checs that scalng S 6 6 ; d S 6; whch s wthn the accuacy of d S ; the esdue scalng facto d6 S 8; In a geneal case ths te we ust odfy the subtacton of fo the X befoe the ocess of the scalng If s the the coect RDD 6 scalng facto then the subtacton ust change to Theefoe the e- X X whee so that o coecton s ade by d 6 o Let us cons X d X 6 6 whch coesonds to the va- de the followng eale: lue n Eale - n scalng facto (dvdng Eale -8 by at) X of odul set Coyght ScRes
15 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc The scalng facto K s assued Then esdue can be found fo Thus 8 8 Altenatvely t could be fo othe odule whee whch has the sae nube to be subtacted Fo CPRDD algoth the scalng ocesses ae efoed as befoe we then have the followng esults by scalng facto K ; P P ; P P ; P P 8 ; P P ; P P Thus X whch s eactly the value s the ost closed to Ths esult can be checed usng sequental stes as follows: Fo 6; Dvded by : ; ; ; ; Dvded by : q q ; q q ; q q ; q 8 q ; q q 6 6 Ths esult of q shows that the CPRDD algoth has the caablty of aallel ocessng oeatons n esdue scalng eo coectons e any cobnaton odul scalng factos fo Ks of odul set { } can be efoed sultaneously Conclusons The athetc oeatons n the esdue nube syste fo addton subtacton ultlcaton can be seeded u by usng ts aallel ocessng oetes Howeve soe dffcult oeatons such as eo detecton coecton ust go though conveson o decodng ocesses fo the esdue eesentaton to the egonal bnay nube Ths s because the decodng technque s usually accolshed usng the ed-ad dgt (RD) o Chnese Reaned Theoe (CRT) whch ae te consung ocesses equng hadwae colety We oosed two algoths fo scalng eo coecton wthout the need fo loou tables o nceasng the encodng ocess The Cyclc oety of the Resdue-Dgt Dffeence (CPRDD) algoth can detect coect eos fo the RNS cyclc oety Any esdue odul set has a secfc cycle length whch can be obtaned fo the ndvdual esdue nube dffeence each a to a efeence eoy odule Once the cyclc length s nown then the ognal value s easly found n tun the eos can be detected coected The TRD (Taget Race Dstance) algoth cobned wth CPRDD s used fo scalng fo eo detecton coecton The scalng esults eo coecton can be dectly efoed by these two algoths wthout usng RD o CRT Thus the decodng ocess s sgnfcantly educed the hadwae stuctue s geatly slfed Seveal eales ae llustated vefed fo these two algoths REFERENCES [] R W Watson Eo Detecton Coecton Othe Resdue-Inteactng Oeatons n a Redundant Resdue Nube Syste Unvesty of Calfona Beeley Coyght ScRes
16 Paallel Algoths fo Resdue Scalng Eo Coecton n Resdue Athetc 6 [] R W Watson C W Hastngs Self-Checed Coutaton Usng Resdue Athetc Poceedngs of the IEEE Vol No 66 - htt://ddoog//proc66 [] S S S Yau Y C Lu Eo Coecton n Redundant Resdue Nube Systes IEEE Tansactons on Coutes Vol C- No - htt://ddoog//t-c [] D elbau Eo Coecton n Resdue Athetc IEEE Tansactons on Coutes Vol C- No 6 8- [] F Bas P aestn Eo Coectng Poetes of Redundant Resdue Nube Systes IEEE Tansactons on Coutes Vol No - htt://ddoog//t-c [6] F Bas P aestn Eo Detecton Coecton by Poduct Codes n Resdue Nube Systes IEEE Tansactons on Coutes Vol No - htt://ddoog//t-c [] V Raachan Sngle Resdue Eo Coecton n Resdue Nube Systes IEEE Tansactons on Coutes Vol C- No 8 - htt://ddoog//tc8666 [8] W K Lenns E J Altan Self-Checng Poetes of Resdue Nube Eo Checes Based on ed Rad Conveson IEEE Tansactons on Ccuts Systes Vol No 88-6 htt://ddoog// [] W K Lenns Resdue Nube Syste Eo Checng Usng Eed Poecton Electoncs Lettes Vol 8 No 8-8 htt://ddoog//el:86 [] W K Lenns The Desgn of Eo Checes fo Self- Checng Resdue Nube Athetc IEEE Tansactons on Coutes Vol C- No htt://ddoog//tc866 [] H Etzel W K Jenns Redundant Resdue Nube Systes fo Eo Detecton Coecton n Dgtal Fltes IEEE Tansactons on Acoustcs Seech Sgnal Pocessng Vol 8 No [] C C Su H Y Lo An Algoth fo Scalng Sngle Resdue Eo Coecton n Resdue Nube Systes IEEE Tansactons on Coutes Vol No 8-6 htt://ddoog// [] H Y Lo An Otal atched Paallel ed- Rad Convete Jounal of Infoaton Scence Engneeng Vol - [] A P Shenoy R Kuaesan Fast Base Etenson Usng a Redundant odus n RNS IEEE Tansactons on Coutes Vol 8 No 8-6 htt://ddoog//68 [] E D Dclauds G Ol F Pazza A Systolc Redundant Resdue Athetc Eo Coecton Ccut IEEE Tansactons on Coutes Vol No - htt://ddoog//68 [6] S S Wang Y Shau Sngle Resdue Eo coecton Based on K-Te -Poecton IEEE Tansactons on Coutes Vol No - htt://ddoog//68 [] R S Katt A New Resdue Athetc Eo Coecton Schee IEEE Tansactons on Coutes Vol No 6 - htt://ddoog//88 Coyght ScRes
THE EQUIVALENCE OF GRAM-SCHMIDT AND QR FACTORIZATION (page 227) Gram-Schmidt provides another way to compute a QR decomposition: n
HE EQUIVAENCE OF GRA-SCHID AND QR FACORIZAION (page 7 Ga-Schdt podes anothe way to copute a QR decoposton: n gen ectos,, K, R, Ga-Schdt detenes scalas j such that o + + + [ ] [ ] hs s a QR factozaton of
More informationGENERALIZATION OF AN IDENTITY INVOLVING THE GENERALIZED FIBONACCI NUMBERS AND ITS APPLICATIONS
#A39 INTEGERS 9 (009), 497-513 GENERALIZATION OF AN IDENTITY INVOLVING THE GENERALIZED FIBONACCI NUMBERS AND ITS APPLICATIONS Mohaad Faokh D. G. Depatent of Matheatcs, Fedows Unvesty of Mashhad, Mashhad,
More informationRigid Bodies: Equivalent Systems of Forces
Engneeng Statcs, ENGR 2301 Chapte 3 Rgd Bodes: Equvalent Sstems of oces Intoducton Teatment of a bod as a sngle patcle s not alwas possble. In geneal, the se of the bod and the specfc ponts of applcaton
More informationChapter 8. Linear Momentum, Impulse, and Collisions
Chapte 8 Lnea oentu, Ipulse, and Collsons 8. Lnea oentu and Ipulse The lnea oentu p of a patcle of ass ovng wth velocty v s defned as: p " v ote that p s a vecto that ponts n the sae decton as the velocty
More information2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles
/4/04 Chapte 7 Lnea oentu Lnea oentu of a Sngle Patcle Lnea oentu: p υ It s a easue of the patcle s oton It s a vecto, sla to the veloct p υ p υ p υ z z p It also depends on the ass of the object, sla
More informationEngineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems
Engneeng echancs oce esultants, Toques, Scala oducts, Equvalent oce sstems Tata cgaw-hll Companes, 008 Resultant of Two oces foce: acton of one bod on anothe; chaacteed b ts pont of applcaton, magntude,
More informationDistinct 8-QAM+ Perfect Arrays Fanxin Zeng 1, a, Zhenyu Zhang 2,1, b, Linjie Qian 1, c
nd Intenatonal Confeence on Electcal Compute Engneeng and Electoncs (ICECEE 15) Dstnct 8-QAM+ Pefect Aays Fanxn Zeng 1 a Zhenyu Zhang 1 b Lnje Qan 1 c 1 Chongqng Key Laboatoy of Emegency Communcaton Chongqng
More informationgravity r2,1 r2 r1 by m 2,1
Gavtaton Many of the foundatons of classcal echancs wee fst dscoveed when phlosophes (ealy scentsts and atheatcans) ted to explan the oton of planets and stas. Newton s ost faous fo unfyng the oton of
More informationThermoelastic Problem of a Long Annular Multilayered Cylinder
Wold Jounal of Mechancs, 3, 3, 6- http://dx.do.og/.436/w.3.35a Publshed Onlne August 3 (http://www.scp.og/ounal/w) Theoelastc Poble of a Long Annula Multlayeed Cylnde Y Hsen Wu *, Kuo-Chang Jane Depatent
More informationMultistage Median Ranked Set Sampling for Estimating the Population Median
Jounal of Mathematcs and Statstcs 3 (: 58-64 007 ISSN 549-3644 007 Scence Publcatons Multstage Medan Ranked Set Samplng fo Estmatng the Populaton Medan Abdul Azz Jeman Ame Al-Oma and Kamaulzaman Ibahm
More informationAN ALGORITHM FOR CALCULATING THE CYCLETIME AND GREENTIMES FOR A SIGNALIZED INTERSECTION
AN AGORITHM OR CACUATING THE CYCETIME AND GREENTIMES OR A SIGNAIZED INTERSECTION Henk Taale 1. Intoducton o a snalzed ntesecton wth a fedte contol state the cclete and eentes ae the vaables that nfluence
More informationSet of square-integrable function 2 L : function space F
Set of squae-ntegable functon L : functon space F Motvaton: In ou pevous dscussons we have seen that fo fee patcles wave equatons (Helmholt o Schödnge) can be expessed n tems of egenvalue equatons. H E,
More informationPhysics 1501 Lecture 19
Physcs 1501 ectue 19 Physcs 1501: ectue 19 Today s Agenda Announceents HW#7: due Oct. 1 Mdte 1: aveage 45 % Topcs otatonal Kneatcs otatonal Enegy Moents of Ineta Physcs 1501: ectue 19, Pg 1 Suay (wth copason
More informationiclicker Quiz a) True b) False Theoretical physics: the eternal quest for a missing minus sign and/or a factor of two. Which will be an issue today?
Clce Quz I egsteed my quz tansmtte va the couse webste (not on the clce.com webste. I ealze that untl I do so, my quz scoes wll not be ecoded. a Tue b False Theoetcal hyscs: the etenal quest fo a mssng
More informationIf there are k binding constraints at x then re-label these constraints so that they are the first k constraints.
Mathematcal Foundatons -1- Constaned Optmzaton Constaned Optmzaton Ma{ f ( ) X} whee X {, h ( ), 1,, m} Necessay condtons fo to be a soluton to ths mamzaton poblem Mathematcally, f ag Ma{ f ( ) X}, then
More informationA. Thicknesses and Densities
10 Lab0 The Eath s Shells A. Thcknesses and Denstes Any theoy of the nteo of the Eath must be consstent wth the fact that ts aggegate densty s 5.5 g/cm (ecall we calculated ths densty last tme). In othe
More information(8) Gain Stage and Simple Output Stage
EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton
More informationUNIT10 PLANE OF REGRESSION
UIT0 PLAE OF REGRESSIO Plane of Regesson Stuctue 0. Intoducton Ojectves 0. Yule s otaton 0. Plane of Regesson fo thee Vaales 0.4 Popetes of Resduals 0.5 Vaance of the Resduals 0.6 Summay 0.7 Solutons /
More informationChapter 23: Electric Potential
Chapte 23: Electc Potental Electc Potental Enegy It tuns out (won t show ths) that the tostatc foce, qq 1 2 F ˆ = k, s consevatve. 2 Recall, fo any consevatve foce, t s always possble to wte the wok done
More informationGenerating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences
Geneatng Functons, Weghted and Non-Weghted Sums fo Powes of Second-Ode Recuence Sequences Pantelmon Stăncă Aubun Unvesty Montgomey, Depatment of Mathematcs Montgomey, AL 3614-403, USA e-mal: stanca@studel.aum.edu
More informationPhysics 11b Lecture #2. Electric Field Electric Flux Gauss s Law
Physcs 11b Lectue # Electc Feld Electc Flux Gauss s Law What We Dd Last Tme Electc chage = How object esponds to electc foce Comes n postve and negatve flavos Conseved Electc foce Coulomb s Law F Same
More informationA. Proofs for learning guarantees
Leanng Theoy and Algoths fo Revenue Optzaton n Second-Pce Auctons wth Reseve A. Poofs fo leanng guaantees A.. Revenue foula The sple expesson of the expected evenue (2) can be obtaned as follows: E b Revenue(,
More informationDecoupled Three-Phase Load Flow Method for Unbalanced Distribution Systems
MTSUBSH ELETR RESEARH LABORATORES htt://www.el.co Decouled Thee-Phase Load Flow Method fo Unbalanced Dstbuton Systes Sun, H.; Dubey, A.; Nkovsk, D.; Ohno, T.; Takano, T.; Koja, Y. TR212-86 Octobe 212 Abstact
More information24-2: Electric Potential Energy. 24-1: What is physics
D. Iyad SAADEDDIN Chapte 4: Electc Potental Electc potental Enegy and Electc potental Calculatng the E-potental fom E-feld fo dffeent chage dstbutons Calculatng the E-feld fom E-potental Potental of a
More informationPhysics 207 Lecture 16
Physcs 07 Lectue 6 Goals: Lectue 6 Chapte Extend the patcle odel to gd-bodes Undestand the equlbu of an extended object. Analyze ollng oton Undestand otaton about a fxed axs. Eploy consevaton of angula
More informationWeb Page Ranking based on Fuzzy and Learning Automata
Web Page Ranng based on Fuzzy and Leanng Autoata Zoheh Ana Deatent of Coute ngneeng Shabesta Azad Unvesty Shabesta,Ian +98(47)53 zoheh_ana@aushab.ac. Mohaad Reza Meybod Deatent of Coute ngneeng Aab Unvesty
More information8 Baire Category Theorem and Uniform Boundedness
8 Bae Categoy Theoem and Unfom Boundedness Pncple 8.1 Bae s Categoy Theoem Valdty of many esults n analyss depends on the completeness popety. Ths popety addesses the nadequacy of the system of atonal
More informationINTERVAL ESTIMATION FOR THE QUANTILE OF A TWO-PARAMETER EXPONENTIAL DISTRIBUTION
Intenatonal Jounal of Innovatve Management, Infomaton & Poducton ISME Intenatonalc0 ISSN 85-5439 Volume, Numbe, June 0 PP. 78-8 INTERVAL ESTIMATION FOR THE QUANTILE OF A TWO-PARAMETER EXPONENTIAL DISTRIBUTION
More informationStochastic Orders Comparisons of Negative Binomial Distribution with Negative Binomial Lindley Distribution
Oen Jounal of Statcs 8- htt://dxdoog/46/os5 Publshed Onlne Al (htt://wwwscrpog/ounal/os) Stochac Odes Comasons of Negatve Bnomal Dbuton wth Negatve Bnomal Lndley Dbuton Chooat Pudommaat Wna Bodhsuwan Deatment
More informationScalars and Vectors Scalar
Scalas and ectos Scala A phscal quantt that s completel chaacteed b a eal numbe (o b ts numecal value) s called a scala. In othe wods a scala possesses onl a magntude. Mass denst volume tempeatue tme eneg
More informationare positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures.
Lectue 4 8. MRAC Desg fo Affe--Cotol MIMO Systes I ths secto, we cosde MRAC desg fo a class of ult-ut-ult-outut (MIMO) olea systes, whose lat dyacs ae lealy aaetezed, the ucetates satsfy the so-called
More information10/15/2013. PHY 113 C General Physics I 11 AM-12:15 PM MWF Olin 101
10/15/01 PHY 11 C Geneal Physcs I 11 AM-1:15 PM MWF Oln 101 Plan fo Lectue 14: Chapte 1 Statc equlbu 1. Balancng foces and toques; stablty. Cente of gavty. Wll dscuss elastcty n Lectue 15 (Chapte 15) 10/14/01
More informationAnalysis of the chemical equilibrium of combustion at constant volume
Analyss of the chemcal equlbum of combuston at constant volume Maus BEBENEL* *Coesondng autho LIEHNICA Unvesty of Buchaest Faculty of Aeosace Engneeng h. olzu Steet -5 6 Buchaest omana mausbeb@yahoo.com
More informationA Study about One-Dimensional Steady State. Heat Transfer in Cylindrical and. Spherical Coordinates
Appled Mathematcal Scences, Vol. 7, 03, no. 5, 67-633 HIKARI Ltd, www.m-hka.com http://dx.do.og/0.988/ams.03.38448 A Study about One-Dmensonal Steady State Heat ansfe n ylndcal and Sphecal oodnates Lesson
More information5-99C The Taylor series expansion of the temperature at a specified nodal point m about time t i is
Chapte Nuecal Methods n Heat Conducton Specal opc: Contollng the Nuecal Eo -9C he esults obtaned usng a nuecal ethod dffe fo the eact esults obtaned analytcally because the esults obtaned by a nuecal ethod
More informationSystem in Weibull Distribution
Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co
More informationAnalysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic
In the fixed-oint imlementation of a digital filte only the esult of the multilication oeation is quantied The eesentation of a actical multilie with the quantie at its outut is shown below u v Q ^v The
More informationP 365. r r r )...(1 365
SCIENCE WORLD JOURNAL VOL (NO4) 008 www.scecncewoldounal.og ISSN 597-64 SHORT COMMUNICATION ANALYSING THE APPROXIMATION MODEL TO BIRTHDAY PROBLEM *CHOJI, D.N. & DEME, A.C. Depatment of Mathematcs Unvesty
More informationOptimal Design of Step Stress Partially Accelerated Life Test under Progressive Type-II Censored Data with Random Removal for Gompertz Distribution
Aecan Jounal of Appled Matheatcs and Statstcs, 09, Vol 7, No, 37-4 Avalable onlne at http://pubsscepubco/ajas/7//6 Scence and Educaton Publshng DOI:069/ajas-7--6 Optal Desgn of Step Stess Patally Acceleated
More informationA Micro-Doppler Modulation of Spin Projectile on CW Radar
ITM Web of Confeences 11, 08005 (2017) DOI: 10.1051/ tmconf/20171108005 A Mco-Dopple Modulaton of Spn Pojectle on CW Rada Zh-Xue LIU a Bacheng Odnance Test Cente of Chna, Bacheng 137001, P. R. Chna Abstact.
More informationChapter 3: Theory of Modular Arithmetic 38
Chapte 3: Theoy of Modula Aithmetic 38 Section D Chinese Remainde Theoem By the end of this section you will be able to pove the Chinese Remainde Theoem apply this theoem to solve simultaneous linea conguences
More informationAPPLICATIONS OF SEMIGENERALIZED -CLOSED SETS
Intenatonal Jounal of Mathematcal Engneeng Scence ISSN : 22776982 Volume Issue 4 (Apl 202) http://www.mes.com/ https://stes.google.com/ste/mesounal/ APPLICATIONS OF SEMIGENERALIZED CLOSED SETS G.SHANMUGAM,
More informationPHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle
1 PHYS 705: Classcal Mechancs Devaton of Lagange Equatons fom D Alembet s Pncple 2 D Alembet s Pncple Followng a smla agument fo the vtual dsplacement to be consstent wth constants,.e, (no vtual wok fo
More informationSOME NEW SELF-DUAL [96, 48, 16] CODES WITH AN AUTOMORPHISM OF ORDER 15. KEYWORDS: automorphisms, construction, self-dual codes
Факултет по математика и информатика, том ХVІ С, 014 SOME NEW SELF-DUAL [96, 48, 16] CODES WITH AN AUTOMORPHISM OF ORDER 15 NIKOLAY I. YANKOV ABSTRACT: A new method fo constuctng bnay self-dual codes wth
More informationGeneralized Loss Variance Bounds
Int. J. Contem. ath. Scences Vol. 7 0 no. 3 559-567 Genealzed Loss Vaance Bounds Wene Hülmann FRSGlobal Swtzeland Seefeldstasse 69 CH-8008 Züch Swtzeland wene.huelmann@fsglobal.com whulmann@bluewn.ch Abstact
More informationPHY126 Summer Session I, 2008
PHY6 Summe Sesson I, 8 Most of nfomaton s avalable at: http://nngoup.phscs.sunsb.edu/~chak/phy6-8 ncludng the sllabus and lectue sldes. Read sllabus and watch fo mpotant announcements. Homewok assgnment
More informationPARAMETER ADAPTIVE CONTROL OF SWITCHED RELUCTANCE MOTOR DRIVES
RMETER DTIVE CONTROL OF SWITCHED RELUCTNCE MOTOR DRIVES Electcal Dves and owe Electoncs Intenatonal Confeence Slovaka Setebe 3 László Száel Budaest Unvesty of Technology and Econocs Deatent of Electc owe
More informationChapter Fifiteen. Surfaces Revisited
Chapte Ffteen ufaces Revsted 15.1 Vecto Descpton of ufaces We look now at the vey specal case of functons : D R 3, whee D R s a nce subset of the plane. We suppose s a nce functon. As the pont ( s, t)
More informationPhysics Exam II Chapters 25-29
Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do
More informationEnergy in Closed Systems
Enegy n Closed Systems Anamta Palt palt.anamta@gmal.com Abstact The wtng ndcates a beakdown of the classcal laws. We consde consevaton of enegy wth a many body system n elaton to the nvese squae law and
More informationHuman being is a living random number generator. Abstract: General wisdom is, mathematical operation is needed to generate number by numbers.
Huan beng s a lvng o nube geneato Anda Mta Anushat Abasan, Utta halgun -7, /AF, alt Lae, olata, West Bengal, 764, Inda Abstat: Geneal wsdo s, atheatal oeaton s needed to geneate nube by nubes It s onted
More information3. A Review of Some Existing AW (BT, CT) Algorithms
3. A Revew of Some Exstng AW (BT, CT) Algothms In ths secton, some typcal ant-wndp algothms wll be descbed. As the soltons fo bmpless and condtoned tansfe ae smla to those fo ant-wndp, the pesented algothms
More informationTest 1 phy What mass of a material with density ρ is required to make a hollow spherical shell having inner radius r i and outer radius r o?
Test 1 phy 0 1. a) What s the pupose of measuement? b) Wte all fou condtons, whch must be satsfed by a scala poduct. (Use dffeent symbols to dstngush opeatons on ectos fom opeatons on numbes.) c) What
More informationRanks of quotients, remainders and p-adic digits of matrices
axv:1401.6667v2 [math.nt] 31 Jan 2014 Ranks of quotents, emandes and p-adc dgts of matces Mustafa Elshekh Andy Novocn Mak Gesbecht Abstact Fo a pme p and a matx A Z n n, wte A as A = p(a quo p)+ (A em
More informationATMO 551a Fall 08. Diffusion
Diffusion Diffusion is a net tanspot of olecules o enegy o oentu o fo a egion of highe concentation to one of lowe concentation by ando olecula) otion. We will look at diffusion in gases. Mean fee path
More informationThe Impact of the Earth s Movement through the Space on Measuring the Velocity of Light
Journal of Appled Matheatcs and Physcs, 6, 4, 68-78 Publshed Onlne June 6 n ScRes http://wwwscrporg/journal/jap http://dxdoorg/436/jap646 The Ipact of the Earth s Moeent through the Space on Measurng the
More informationSTRUCTURE IN LEGISLATIVE BARGAINING
NOT FOR PUBICATION ONINE APPENDICES FOR STRUCTURE IN EGISATIVE BARGAINING Adan de Goot Ruz Roald Rame Athu Scham APPENDIX A: PROOF FOR PROPOSITION FOR HIGHY STRUCTURED GAME APPENDIX B: PROOFS FOR PROPOSITIONS
More informationFinding Strong Defining Hyperplanes of Production. Possibility Set with Interval Data
Aled Matheatcal Scence, Vol 6, 22, no 4, 97-27 Fndng Stong Defnng Helane of Poducton Poblt Set wth Inteval Data F Hoenzadeh otf a *, G R Jahanhahloo a, S Mehaban b and P Zaan a a Deatent of Matheatc, Scence
More informationThermodynamics of solids 4. Statistical thermodynamics and the 3 rd law. Kwangheon Park Kyung Hee University Department of Nuclear Engineering
Themodynamcs of solds 4. Statstcal themodynamcs and the 3 d law Kwangheon Pak Kyung Hee Unvesty Depatment of Nuclea Engneeng 4.1. Intoducton to statstcal themodynamcs Classcal themodynamcs Statstcal themodynamcs
More informationCSJM University Class: B.Sc.-II Sub:Physics Paper-II Title: Electromagnetics Unit-1: Electrostatics Lecture: 1 to 4
CSJM Unvesty Class: B.Sc.-II Sub:Physcs Pape-II Ttle: Electomagnetcs Unt-: Electostatcs Lectue: to 4 Electostatcs: It deals the study of behavo of statc o statonay Chages. Electc Chage: It s popety by
More informationON THE FRESNEL SINE INTEGRAL AND THE CONVOLUTION
IJMMS 3:37, 37 333 PII. S16117131151 http://jmms.hndaw.com Hndaw Publshng Cop. ON THE FRESNEL SINE INTEGRAL AND THE CONVOLUTION ADEM KILIÇMAN Receved 19 Novembe and n evsed fom 7 Mach 3 The Fesnel sne
More informationSUBSEQUENCE CHARACTERIZAT ION OF UNIFORM STATISTICAL CONVERGENCE OF DOUBLE SEQUENCE
Reseach ad Coucatos atheatcs ad atheatcal ceces Vol 9 Issue 7 Pages 37-5 IN 39-6939 Publshed Ole o Novebe 9 7 7 Jyot cadec Pess htt//yotacadecessog UBEQUENCE CHRCTERIZT ION OF UNIFOR TTITIC CONVERGENCE
More information30 The Electric Field Due to a Continuous Distribution of Charge on a Line
hapte 0 The Electic Field Due to a ontinuous Distibution of hage on a Line 0 The Electic Field Due to a ontinuous Distibution of hage on a Line Evey integal ust include a diffeential (such as d, dt, dq,
More informationFinite Fields and Their Applications
Fnte Felds and Ther Applcatons 5 009 796 807 Contents lsts avalable at ScenceDrect Fnte Felds and Ther Applcatons www.elsever.co/locate/ffa Typcal prtve polynoals over nteger resdue rngs Tan Tan a, Wen-Feng
More informationarxiv: v2 [cs.it] 11 Jul 2014
A faly of optal locally ecoveable codes Itzhak Tao, Mebe, IEEE, and Alexande Bag, Fellow, IEEE axv:1311.3284v2 [cs.it] 11 Jul 2014 Abstact A code ove a fnte alphabet s called locally ecoveable (LRC) f
More informationGroupoid and Topological Quotient Group
lobal Jounal of Pue and Appled Mathematcs SSN 0973-768 Volume 3 Numbe 7 07 pp 373-39 Reseach nda Publcatons http://wwwpublcatoncom oupod and Topolocal Quotent oup Mohammad Qasm Manna Depatment of Mathematcs
More informationSolutions for Homework #9
Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural
More informationLASER ABLATION ICP-MS: DATA REDUCTION
Lee, C-T A Lase Ablaton Data educton 2006 LASE ABLATON CP-MS: DATA EDUCTON Cn-Ty A. Lee 24 Septembe 2006 Analyss and calculaton of concentatons Lase ablaton analyses ae done n tme-esolved mode. A ~30 s
More informationRemember: When an object falls due to gravity its potential energy decreases.
Chapte 5: lectc Potental As mentoned seveal tmes dung the uate Newton s law o gavty and Coulomb s law ae dentcal n the mathematcal om. So, most thngs that ae tue o gavty ae also tue o electostatcs! Hee
More informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More information19 The Born-Oppenheimer Approximation
9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A
More informationCOMP 465: Data Mining More on PageRank
COMP 465: Dt Mnng Moe on PgeRnk Sldes Adpted Fo: www.ds.og (Mnng Mssve Dtsets) Powe Iteton: Set = 1/ 1: = 2: = Goto 1 Exple: d 1/3 1/3 5/12 9/24 6/15 = 1/3 3/6 1/3 11/24 6/15 1/3 1/6 3/12 1/6 3/15 Iteton
More informationALL QUESTIONS ARE WORTH 20 POINTS. WORK OUT FIVE PROBLEMS.
GNRAL PHYSICS PH -3A (D. S. Mov) Test (/3/) key STUDNT NAM: STUDNT d #: -------------------------------------------------------------------------------------------------------------------------------------------
More informationPHYS Week 5. Reading Journals today from tables. WebAssign due Wed nite
PHYS 015 -- Week 5 Readng Jounals today fom tables WebAssgn due Wed nte Fo exclusve use n PHYS 015. Not fo e-dstbuton. Some mateals Copyght Unvesty of Coloado, Cengage,, Peason J. Maps. Fundamental Tools
More informationStellar Astrophysics. dt dr. GM r. The current model for treating convection in stellar interiors is called mixing length theory:
Stella Astophyscs Ovevew of last lectue: We connected the mean molecula weght to the mass factons X, Y and Z: 1 1 1 = X + Y + μ 1 4 n 1 (1 + 1) = X μ 1 1 A n Z (1 + ) + Y + 4 1+ z A Z We ntoduced the pessue
More informationBALANCING OF ROTATING MASSES
www.getyun.co YIS OF HIES IG OF ROTTIG SSES www.getyun.co Rotatng centelne: The otatng centelne beng defned as the axs about whch the oto would otate f not constaned by ts beangs. (lso called the Pncple
More informationDeparture Process from a M/M/m/ Queue
Dearture rocess fro a M/M// Queue Q - (-) Q Q3 Q4 (-) Knowledge of the nature of the dearture rocess fro a queue would be useful as we can then use t to analyze sle cases of queueng networs as shown. The
More informationOptimization Methods: Linear Programming- Revised Simplex Method. Module 3 Lecture Notes 5. Revised Simplex Method, Duality and Sensitivity analysis
Optmzaton Meods: Lnea Pogammng- Revsed Smple Meod Module Lectue Notes Revsed Smple Meod, Dualty and Senstvty analyss Intoducton In e pevous class, e smple meod was dscussed whee e smple tableau at each
More informationOn Pfaff s solution of the Pfaff problem
Zur Pfaff scen Lösung des Pfaff scen Probles Mat. Ann. 7 (880) 53-530. On Pfaff s soluton of te Pfaff proble By A. MAYER n Lepzg Translated by D. H. Delpenc Te way tat Pfaff adopted for te ntegraton of
More informationOn the Latency Bound of Deficit Round Robin
Poceedngs of the Intenatonal Confeence on Compute Communcatons and Netwoks Mam, Floda, USA, Octobe 4 6, 22 On the Latency Bound of Defct Round Robn Sall S. Kanhee and Hash Sethu Depatment of ECE, Dexel
More informationA GENERALIZATION OF A CONJECTURE OF MELHAM. 1. Introduction The Fibonomial coefficient is, for n m 1, defined by
A GENERALIZATION OF A CONJECTURE OF MELHAM EMRAH KILIC 1, ILKER AKKUS, AND HELMUT PRODINGER 3 Abstact A genealization of one of Melha s conectues is pesented Afte witing it in tes of Gaussian binoial coefficients,
More informationVParC: A Compression Scheme for Numeric Data in Column-Oriented Databases
The Intenatonal Aab Jounal of Infomaton Technology VPaC: A Compesson Scheme fo Numec Data n Column-Oented Databases Ke Yan, Hong Zhu, and Kevn Lü School of Compute Scence and Technology, Huazhong Unvesty
More informationV. Principles of Irreversible Thermodynamics. s = S - S 0 (7.3) s = = - g i, k. "Flux": = da i. "Force": = -Â g a ik k = X i. Â J i X i (7.
Themodynamcs and Knetcs of Solds 71 V. Pncples of Ievesble Themodynamcs 5. Onsage s Teatment s = S - S 0 = s( a 1, a 2,...) a n = A g - A n (7.6) Equlbum themodynamcs detemnes the paametes of an equlbum
More information9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor
Mcoelectoncs Ccut Analyss and Desgn Donald A. Neamen Chapte 5 The pola Juncton Tanssto In ths chapte, we wll: Dscuss the physcal stuctue and opeaton of the bpola juncton tanssto. Undestand the dc analyss
More informationOur focus will be on linear systems. A system is linear if it obeys the principle of superposition and homogenity, i.e.
SSTEM MODELLIN In order to solve a control syste proble, the descrptons of the syste and ts coponents ust be put nto a for sutable for analyss and evaluaton. The followng ethods can be used to odel physcal
More informationOn Maneuvering Target Tracking with Online Observed Colored Glint Noise Parameter Estimation
Wold Academy of Scence, Engneeng and Technology 6 7 On Maneuveng Taget Tacng wth Onlne Obseved Coloed Glnt Nose Paamete Estmaton M. A. Masnad-Sha, and S. A. Banan Abstact In ths pape a compehensve algothm
More informationFoundations of Arithmetic
Foundatons of Arthmetc Notaton We shall denote the sum and product of numbers n the usual notaton as a 2 + a 2 + a 3 + + a = a, a 1 a 2 a 3 a = a The notaton a b means a dvdes b,.e. ac = b where c s an
More informationIntegral Vector Operations and Related Theorems Applications in Mechanics and E&M
Dola Bagayoko (0) Integal Vecto Opeatons and elated Theoems Applcatons n Mechancs and E&M Ι Basc Defnton Please efe to you calculus evewed below. Ι, ΙΙ, andιιι notes and textbooks fo detals on the concepts
More informationChapter 8: Fast Convolution. Keshab K. Parhi
Cater 8: Fat Convoluton Keab K. Par Cater 8 Fat Convoluton Introducton Cook-Too Algort and Modfed Cook-Too Algort Wnograd Algort and Modfed Wnograd Algort Iterated Convoluton Cyclc Convoluton Degn of Fat
More informationOptimal System for Warm Standby Components in the Presence of Standby Switching Failures, Two Types of Failures and General Repair Time
Intenatonal Jounal of ompute Applcatons (5 ) Volume 44 No, Apl Optmal System fo Wam Standby omponents n the esence of Standby Swtchng Falues, Two Types of Falues and Geneal Repa Tme Mohamed Salah EL-Shebeny
More informationCorrespondence Analysis & Related Methods
Coespondence Analyss & Related Methods Ineta contbutons n weghted PCA PCA s a method of data vsualzaton whch epesents the tue postons of ponts n a map whch comes closest to all the ponts, closest n sense
More informationDiscrete Memoryless Channels
Dscrete Meorless Channels Source Channel Snk Aount of Inforaton avalable Source Entro Generall nos, dstorted and a be te varng ow uch nforaton s receved? ow uch s lost? Introduces error and lts the rate
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationTime Warp Edit Distance
Tme Wa Edt Dstance PIERRE-FRNÇOIS MRTEU ee-fancos.mateau@unv-ubs.f VLORI UNIVERSITE EUROPEENNE DE RETGNE CMPUS DE TONNIC T. YVES COPPENS P 573 567 VNNES CEDEX FRNCE FERURY 28 TECNICL REPORT N : VLORI.28.V5
More informationEvent Shape Update. T. Doyle S. Hanlon I. Skillicorn. A. Everett A. Savin. Event Shapes, A. Everett, U. Wisconsin ZEUS Meeting, October 15,
Event Shape Update A. Eveett A. Savn T. Doyle S. Hanlon I. Skllcon Event Shapes, A. Eveett, U. Wsconsn ZEUS Meetng, Octobe 15, 2003-1 Outlne Pogess of Event Shapes n DIS Smla to publshed pape: Powe Coecton
More informationKhintchine-Type Inequalities and Their Applications in Optimization
Khntchne-Type Inequaltes and The Applcatons n Optmzaton Anthony Man-Cho So Depatment of Systems Engneeng & Engneeng Management The Chnese Unvesty of Hong Kong ISDS-Kolloquum Unvestaet Wen 29 June 2009
More informationLINEAR MOMENTUM. product of the mass m and the velocity v r of an object r r
LINEAR MOMENTUM Imagne beng on a skateboad, at est that can move wthout cton on a smooth suace You catch a heavy, slow-movng ball that has been thown to you you begn to move Altenatvely you catch a lght,
More informationCSE-571 Robotics. Ball Tracking in RoboCup. Tracking Techniques. Rao-Blackwelized Particle Filters for State Estimation
CSE-571 Rootcs Rao-Blacwelzed Patcle Fltes fo State Estaton Ball Tacng n RooCup Exteely nosy nonlnea oton of oseve Inaccuate sensng lted pocessng powe Inteactons etween taget and Goal: envonent Unfed faewo
More informationA Branch and Bound Method for Sum of Completion Permutation Flow Shop
UNLV Theses, Dssetatons, Pofessonal Paes, and Castones 5--04 A Banch and Bound ethod fo Sum of Comleton Pemutaton Flow Sho Swana Kodmala Unvesty of Nevada, Las Vegas, swanakodmala@gmal.com Follow ths and
More informationBALANCING OF ROTATING MASSES
VTU EUST PROGRE - 7 YIS OF HIES Subject ode - E 54 IG OF ROTTIG SSES otes opled by: VIJYVITH OGE SSOITE PROFESSOR EPRTET OF EHI EGIEERIG OEGE OF EGIEERIG HSS -57. KRTK oble:94488954 E-al:vvb@cehassan.ac.n
More information