Synthesis of Stable Takagi-Sugeno Fuzzy Systems
|
|
|
- Stanley Benson
- 5 years ago
- Views:
Transcription
1 Sytess of Stle Tk-Sueo Fuzzy Systems ENATA PYTELKOVÁ AND PET HUŠEK Deptmet of Cotol Eee Fculty of Electcl Eee, Czec Teccl Uvesty Teccká, 66 7 P 6 CZECH EPUBLIC Astct: - Te ppe dels t te polem of sytess of cotolle to te plt desced y Tk-Sueo fuzzy model t le put-output sumodels te coseuets of ules. A pocedue fo des of te cotolle utee stlty of closed-loop system sed o polyoml ppoc s peseted. Te cotolle sses te sme cctestc polyoml fo ll fesle le susystems. Te peseted metod c e used fo ot cotuous-tme d dscete-tme systems. Key-Wods: - fuzzy system, stlty, polyoml, Dopte euto, put-output model, LTV system Itoducto Tk-Sueo fuzzy systems t le sumodels coseuets of ules offe ood posslty to ppoxmte dymcl evou of ole systems. Oe of te dvtes of suc systems s tt cotolles fo Tk-Sueo fuzzy systems c e desed y ell-ko metods used teoy of le systems. Te polem s stlty lyss of suc closed-loop systems. Te m esults coce stlty lyss of suc systems ee ceved y W, Tk d Gff [8]. Ts ok coces Tk-Sueo fuzzy systems t le stte-spce sumodels. Tey poved tt te polem of stlty lyss of suc systems s euvlet to fd commo postve defte mtx to te udtc Lypuov euto d suested some pocedues o to fd t. Some esults ee pulsed lso [], [4] d [6]. It s so tt te polem of stlty lyss of Tk-Sueo fuzzy systems c e solved y test oust stlty of polyomls t polyomc stuctue of te coeffcets. Some esults coce te sytess of cotolles utee stlty of closed-loop system c e foud fo exmple [] fo Tk- Sueo fuzzy systems t stte-spce sumodels d [3] fo Tk-Sueo fuzzy systems t put-output sumodels. I ot cses te Tk- Sueo fuzzy model of plt d Tk-Sueo fuzzy cotolle e supposed. I ts ppe e metod fo des of le tme-vt cotolle to plt desced y Tk-Sueo fuzzy model t le put-output sumodels te coseuets of ules s peseted. Te metod s sed o polyoml ppoc. Te poposed cotolle sses te sme cctestc polyoml fo ll fesle le susystems d utees stlty of closed-loop system. Te peseted esults e vld ude ssumpto of sloly vy pmetes of te model o ets of ules. Te peseted metod c e used fo ot cotuous-tme d dscete-tme systems. Tk-Sueo fuzzy model of te plt Te Tk-Sueo fuzzy model of te plt s cosdeed, ee te ules e tte te follo fom: THEN y () t s M d d v () t : IF v THEN y ( () ) ( t () ) y t + u () t () t s M d d v () t : IF v s M () t y ( t ) + u ( t ) s M,,,, fo cotuous-tme cse d fo dscete-tme cse espectvely, ee v(t)[v (t),, v (t)] M y u () t () t () () vles of te pemse (some mesule plt vles) fuzzy sets te output of te plt te put to te plt
2 Te follo pocedue ll e deved fo dscete-tme cse, ut t c e folloed fo cotuous-tme system loclly. Te totl output of te fuzzy system s: y () t ee y ( t) y ( t) y( t ) ( ) + u t ( v () M v ( t) ( ) (3) (4) M s te de of memesp of v (t) M. It s ssumed tt v, fo,,, d ( v () > fo ( () ll t. Teefoe ( () v. (5) By pply Z-tsfom to (3) ude te ssumpto of sloly vy ets te follo tsfe fucto of te model of plt s oted: G p Y U G ( z) p ( z) ( z) G ( z) z z p (6) ee G p () z deotes te tsfe fucto of te coseuet of te -t ule. Te m de of ts ppe cossts us polyoml metods fo des of cotolle to te Tk-Sueo fuzzy system desced ove c utees stlty of closed-loop system. I ode to ssue stlty of suc systems, metods dested fo le tme-vt (LTI) systems e ofte used ([3],[6]). Hoeve, ts s ot possle eelly. It s to e empszed tt stlty of le tme-vt (LTV) systems us stlty lyss of coespod foze-tme systems c e uteed oly ude ssumpto of sloly vy pmetes (see [7]) c s ofte omtted. Te uesto o te te of te c s lloed ems useed. Neveteless, te expemets evel tt most cses te desed cotolle stlzes te plt (). Ou m s to fd cotolle tt ould ss te sme cctestc polyoml to ll LTI susystems (fo ll dmssle vtos of ets ). Flev [3] poved tt f (z)(z) fo ll,..., ee (z) s Scu polyoml te stlz cotolle c e lys foud s fuzzy pllel dstuted compesto (PDC). It mes tt te cotolle c e desced y Tk- Sueo fuzzy model t put-output sumodels te coseuets of ules s te sme tecedets t te model of te plt. It c e esly so tt ts s ot possle fo te umetos (z) e mutully dffeet eve y us fuzzy o-pdc. Te follo secto dels t te sytess of LTV cotolle stlz plt () closed loop. Let us oce moe emd tt te esults e vld oly ude ssumpto of sloly vy ets,,...,. 3 Des of te cotolle Te polem of fd stlz cotolle to plt desced y te Tk-Sueo fuzzy model s solved ss te sme cctestc polyoml closed-loop system fo ll fesle LTI susystems. Assume tt te plt s desced y Tk- Sueo fuzzy model () d te ets,,..., e sloly vy. Let te cotolle e LTV system expessed y ts tsfe fucto ee G c (7)
3 de ( z de ( z. (8) Te coeffcets, e some fuctos of te vecto of ets of ules. Ou tsk s to fd tese fuctos so tt te closed-loop system s stle. As t s metoed ove ou ol s to ss te sme cctestc polyoml of te closedloop system fo ll H,.e.: ( z ) + ( z), (9) ee (z) s Scu polyoml of ppopte deee. Te ell-ko codto of solvlty of (9) s tt te etest commo dvso of polyomls (z, d (z, dvdes te polyoml (z) fo ll H,.e. ( z ), ) ( z),. () I ode to ceck ete te codto () s stsfed oe c use te ell-ko lotm fo fd te etest commo dvso of to polyomls [5] t espect to te vecto vle. Hoeve te ette soluto cossts solv te Dopte euto (9). If te soluto does ot exst fo some H t mes tt fo tose H te codto () s volted. Te etest commo dvso c e te esly detemed susttut te vecto (6) d us te stdd lotm metoed ove. If (,) s Scu polyoml te e polyoml (z) s to e cose to e le to solve euto (9) (fo exmple (z) (z)* lys leds to solvle euto (9)). If (,) s ot Scu polyoml te cotolle (7) stlz te plt () y ss te sme cctestc polyoml to ll le susystems c ot e foud. As te closed-loop system t lest oe step dely s to e uteed, de (z,<de (z,. Te deees of polyomls (z,, (z, d (z) c e foud comp deees of polyomls of ot sdes of euto (9): de > de de < de de de de. () Susttut (6) d (8) to (9) te follo euto s oted: de de z z + z z () (). z All solutos of () c e expessed s + f ( z) f ( z) (3) ee (z, d (z, e te ptcul solutos of () d f(z) s ty polyoml. Te detemto of polyomls (z, d (z, s euvlet to solv te system of (de +) le eutos s fom () y comp of ll coeffcets z,,...,de. As te solutos, of ts system e fuctos of te eel soluto s eltvely complcted. To ette udestd te desced pocedue ts pcple ll e so o to llusttve exmples. 3. Exmple Fo ske of smplcty ssume plt desced y te follo to-ule Tk-Sueo fuzzy model: IF y(t-) s M THEN y(t)-.y(t-)+u(t) IF y(t-) s M THEN y(t)-.3y(t-)+u(t)+.4u(t-) M M -c c F. Memesp fuctos Te tsfe fucto of te model s: G p ee () z + () z () z + () z () z + ( ) () z () z + ( ) () z
4 () z z, () z z + () z z +., () z [,]..4 z +.3 Fom () te deees of polyomls (z), (z, d (z, c e detemed s follos: de, de, de. Coose te lol cctestc polyoml (z) s () ( z +.) z. By solv te Dopte euto (9) te fom [ ( z +.) + ( )( z +.3) ][ ( ) z + ( )] + [ z + ( )( z +.4) ] ( ) ( z +.) oe c ot ( ) ( ) ( ). It s ot dffcult to see tt fo.5 tee s o soluto of te Dopte euto. elly, f.5 te te etest commo dvso (.5 ),.5) ) ( z +., z +.) z +. does ot dvde te polyoml (z) d te ecessy codto of solvlty of () s volted. Coose te polyoml (z) s () ( z +.)( z +.) z. Oe ptcul soluto of (9) c e foud s ( ) ( ).4. ( ). +. tt coespods to te LTV cotolle t tsfe fucto + G c ). +. z +.4. o euvletly te tme-dom ( k) (..4 ) u( k ) + (.. ) e( k ) u. I F. d F. 3 te esposes o tl codto of te closed-loop system e so fo c. d c espectvely. It s evdet tt te cotolle stlzes te plt fo ty te of c of..8.6 y(t) c t F. espose of closed-loop system fo c. y(t) c t F. 3 espose of closed-loop system fo c 3. Exmple Assume plt desced y te follo to-ule Tk-Sueo fuzzy model composed fom ustle sumodels:
5 IF y(k-) s THEN y(k)-y(k-)+u(k) IF y(k-) s THEN y(k)-3y(k-)+u(k)+u(k-) F M M \W -c c F. 4 Memesp fuctos Coose te lol cctestc polyoml (z) s () ( z +.5) z. Te Dopte euto (9) tus to [ ( z + ) + ( )( z + 3) ][ ( ) z + ( )] + [ z + ( )( z + ) ] ( ) ( z +.5) fom c oe soluto c e oted s + W F. 5 espose of closed-loop system fo c [ F ( ) ( ) ( ) \W Te tsfe fucto of te cotolle s G c ) z o euvletly te tme-dom u () k (.5.5.5) u( k ) + + ( ) e( k ). I F. 5 d F. 6 te esposes o tl codto of te closed-loop system e so fo c d c espectvely. F. 6 espose of closed-loop system fo c Te fues so tt te cotolle stlzes te closed loop oly fo sloly vy et of ule (c). If te te of vce s e (c) te te poposed metod does ot utee te stlty. 4 Cocluso Te e metod fo fd le tme-vt cotolle to plt desced y Tk-Sueo fuzzy model t le put-output sumodels te coseuets of ules utee stlty of te closed-loop system s toduced. Te metod s sed o ss te sme cctestc polyoml fo ll fesle susystems. Te poposed metod utees te stlty oly fo sloly vy vecto of ets of ules. W 5 Ackoledemet Ts ok s ee suppoted y te Msty of Educto of te Czec epulc ude Poect
6 VS97/34 d y te esec pom No. J4/98:33 Decso Mk d Cotol fo Mufctu of te Czec Teccl Uvesty Pue (sposoed y te Msty of Educto of te Czec epulc). efeeces: [] 'YNY 5 DQG +XãHN 3 6WDELOLW\ I Tk-Sueo Fuzzy Systems t Le Iput-Output Sumodels, Poceeds of IEEE MED,, Pts, Geece [] Fe G., Co S. G., ees N. W. d Ck C. K., Des of Fuzzy Cotol Systems t Guteed Stlty, Fuzzy Sets d Systems, Vol. 85, 997, pp. - [3] Flev D., Polyoml Appoc to te Sytess of Stle Fuzzy Systems, Poceeds of NAFIPS 96, 996, pp. -4. [4] +XãHN 3 DQG 'YNY 5 6WDELOLW\ I Tk-Sueo Fuzzy Systems t Le Iput-Output Sumodels: Polyoml Appoc, Poceeds of IFAC CAO,, St. Petesu, uss [5].XþHUD 9 Alyss d Des of Dscete Le Cotol Systems, Petce Hll, 99 [6] Lo J.-C. d Ce Y.-M., Stlty Issues o Tk-Sueo Fuzzy Model - Pmetc Appoc, IEEE Ts. o Fuzzy Systems, Vol. 7, No. 5, 999, pp [7] Skoo. A. d Lu C. G. Y., Istlty of Sloly Vy Systems, IEEE Ts. o Automtc Cotol, Vol. 7, No., 97, pp [8] W H. O., Tk K., d Gff M. F. A Appoc to Fuzzy Cotol of Nole Systems: Stlty d Des Issues, IEEE Tsctos o Fuzzy Systems, Vol. 4, No., 996, pp. 4-3.
SOLVING SYSTEMS OF EQUATIONS, DIRECT METHODS
ELM Numecl Alyss D Muhem Mecmek SOLVING SYSTEMS OF EQUATIONS DIRECT METHODS ELM Numecl Alyss Some of the cotets e dopted fom Luee V. Fusett Appled Numecl Alyss usg MATLAB. Petce Hll Ic. 999 ELM Numecl
SOME REMARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOMIAL ASYMPTOTE
D I D A C T I C S O F A T H E A T I C S No (4) 3 SOE REARKS ON HORIZONTAL, SLANT, PARABOLIC AND POLYNOIAL ASYPTOTE Tdeusz Jszk Abstct I the techg o clculus, we cosde hozotl d slt symptote I ths ppe the
Minimizing spherical aberrations Exploiting the existence of conjugate points in spherical lenses
Mmzg sphecal abeatos Explotg the exstece of cojugate pots sphecal leses Let s ecall that whe usg asphecal leses, abeato fee magg occus oly fo a couple of, so called, cojugate pots ( ad the fgue below)
Transmuted Generalized Lindley Distribution
Itetol Joul of Memtcs Teds d Techology- olume9 Numbe Juy 06 Tsmuted Geelzed Ldley Dstbuto M. Elghy, M.Rshed d A.W.Shwk 3, Buydh colleges, Deptmet of Memtcl Sttstcs, KSA.,, 3 Isttute of Sttstcl Studes d
are 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
Chapter 17. Least Square Regression
The Islmc Uvest of Gz Fcult of Egeeg Cvl Egeeg Deptmet Numecl Alss ECIV 336 Chpte 7 Lest que Regesso Assocte Pof. Mze Abultef Cvl Egeeg Deptmet, The Islmc Uvest of Gz Pt 5 - CURVE FITTING Descbes techques
( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi
Assgmet /MATH 47/Wte Due: Thusday Jauay The poblems to solve ae umbeed [] to [] below Fst some explaatoy otes Fdg a bass of the colum-space of a max ad povg that the colum ak (dmeso of the colum space)
Discrete Model Parametrization
Poceedings of Intentionl cientific Confeence of FME ession 4: Automtion Contol nd Applied Infomtics Ppe 9 Discete Model Pmetition NOKIEVIČ, Pet Doc,Ing,Cc Deptment of Contol ystems nd Instumenttion, Fculty
10.3 The Quadratic Formula
. Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti
Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates.
CURVE FITTING Descbes techques to ft cuves (cuve fttg) to dscete dt to obt temedte estmtes. Thee e two geel ppoches fo cuve fttg: Regesso: Dt ehbt sgfct degee of sctte. The stteg s to deve sgle cuve tht
The formulae in this booklet have been arranged according to the unit in which they are first
Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge ccog to the ut whch the e fst touce. Thus cte sttg ut m e eque to use the fomule tht wee touce peceg ut e.g. ctes sttg C mght e epecte to use
Chapter Linear Regression
Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use
CS473-Algorithms I. Lecture 3. Solving Recurrences. Cevdet Aykanat - Bilkent University Computer Engineering Department
CS473-Algorthms I Lecture 3 Solvg Recurreces Cevdet Aykt - Blket Uversty Computer Egeerg Deprtmet Solvg Recurreces The lyss of merge sort Lecture requred us to solve recurrece. Recurreces re lke solvg
Difference Sets of Null Density Subsets of
dvces Pue Mthetcs 95-99 http://ddoog/436/p37 Pulshed Ole M (http://wwwscrpog/oul/p) Dffeece Sets of Null Dest Susets of Dwoud hd Dsted M Hosse Deptet of Mthetcs Uvest of Gul Rsht I El: hd@gulc h@googlelco
Parametric Methods. Autoregressive (AR) Moving Average (MA) Autoregressive - Moving Average (ARMA) LO-2.5, P-13.3 to 13.4 (skip
Pmeti Methods Autoegessive AR) Movig Avege MA) Autoegessive - Movig Avege ARMA) LO-.5, P-3.3 to 3.4 si 3.4.3 3.4.5) / Time Seies Modes Time Seies DT Rdom Sig / Motivtio fo Time Seies Modes Re the esut
CBSE , ˆj. cos CBSE_2015_SET-1. SECTION A 1. Given that a 2iˆ ˆj. We need to find. 3. Consider the vector equation of the plane.
CBSE CBSE SET- SECTION. Gv tht d W d to fd 7 7 Hc, 7 7 7. Lt,. W ow tht.. Thus,. Cosd th vcto quto of th pl.. z. - + z = - + z = Thus th Cts quto of th pl s - + z = Lt d th dstc tw th pot,, - to th pl.
Inductance of Cylindrical Coil
SEBIN JOUN OF EETI ENGINEEING Vol. No. Jue 4 4-5 Iductce of ldcl ol G.. vd. Dol N. Păduu stct: Te cldcl coeless d coe cols e used stumet tsfomes d m ote electomgetc devces. I te ppe usg te septo of vles
Fairing of Parametric Quintic Splines
ISSN 46-69 Eglad UK Joual of Ifomato ad omputg Scece Vol No 6 pp -8 Fag of Paametc Qutc Sples Yuau Wag Shagha Isttute of Spots Shagha 48 ha School of Mathematcal Scece Fuda Uvesty Shagha 4 ha { P t )}
The Linear Probability Density Function of Continuous Random Variables in the Real Number Field and Its Existence Proof
MATEC Web of Cofeeces ICIEA 06 600 (06) DOI: 0.05/mateccof/0668600 The ea Pobablty Desty Fucto of Cotuous Radom Vaables the Real Numbe Feld ad Its Estece Poof Yya Che ad Ye Collee of Softwae, Taj Uvesty,
Chapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:
Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,
148 CIVIL ENGINEERING
STRUTUR NYSS fluee es fo Bems d Tusses fluee le sows te vto of effet (eto, se d momet ems, foe tuss) used movg ut lod oss te stutue. fluee le s used to deteme te posto of movele set of lods tt uses te
Chapter Simpson s 1/3 Rule of Integration. ( x)
Cpter 7. Smpso s / Rule o Itegrto Ater redg ts pter, you sould e le to. derve te ormul or Smpso s / rule o tegrto,. use Smpso s / rule t to solve tegrls,. develop te ormul or multple-segmet Smpso s / rule
PROGRESSION AND SERIES
INTRODUCTION PROGRESSION AND SERIES A gemet of umbes {,,,,, } ccodig to some well defied ule o set of ules is clled sequece Moe pecisely, we my defie sequece s fuctio whose domi is some subset of set of
For use in Edexcel Advanced Subsidiary GCE and Advanced GCE examinations
GCE Edecel GCE Mthemtcs Mthemtcl Fomule d Sttstcl Tles Fo use Edecel Advced Susd GCE d Advced GCE emtos Coe Mthemtcs C C4 Futhe Pue Mthemtcs FP FP Mechcs M M5 Sttstcs S S4 Fo use fom Ju 008 UA08598 TABLE
GCE AS/A Level MATHEMATICS GCE AS/A Level FURTHER MATHEMATICS
GCE AS/A Level MATHEMATICS GCE AS/A Level FURTHER MATHEMATICS FORMULA BOOKLET Fom Septembe 07 Issued 07 Mesuto Pue Mthemtcs Sufce e of sphee = 4 Ae of cuved sufce of coe = slt heght Athmetc Sees S l d
Mathematically, integration is just finding the area under a curve from one point to another. It is b
Numerl Metods or Eg [ENGR 9] [Lyes KADEM 7] CHAPTER VI Numerl Itegrto Tops - Rem sums - Trpezodl rule - Smpso s rule - Rrdso s etrpolto - Guss qudrture rule Mtemtlly, tegrto s just dg te re uder urve rom
GCE AS and A Level MATHEMATICS FORMULA BOOKLET. From September Issued WJEC CBAC Ltd.
GCE AS d A Level MATHEMATICS FORMULA BOOKLET Fom Septeme 07 Issued 07 Pue Mthemtcs Mesuto Suce e o sphee = 4 Ae o cuved suce o coe = heght slt Athmetc Sees S = + l = [ + d] Geometc Sees S = S = o < Summtos
VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.
Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Fedad P. ee E. Russell Johsto, J. Systems of Patcles Lectue Notes: J. Walt Ole Texas Tech Uesty 003 The Mcaw-Hll Compaes, Ic. ll ghts eseed. Seeth
= y and Normed Linear Spaces
304-50 LINER SYSTEMS Lectue 8: Solutos to = ad Nomed Lea Spaces 73 Fdg N To fd N, we eed to chaacteze all solutos to = 0 Recall that ow opeatos peseve N, so that = 0 = 0 We ca solve = 0 ecusvel backwads
THIS PAGE DECLASSIFIED IAW E
THS PAGE DECLASSFED AW E0 2958 BL K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW E0 2958 B L K THS PAGE DECLASSFED AW E0 2958 THS PAGE DECLASSFED AW EO 2958 THS PAGE DECLASSFED AW EO 2958 THS
MTH 146 Class 7 Notes
7.7- Approxmte Itegrto Motvto: MTH 46 Clss 7 Notes I secto 7.5 we lered tht some defte tegrls, lke x e dx, cot e wrtte terms of elemetry fuctos. So, good questo to sk would e: How c oe clculte somethg
Professor Wei Zhu. 1. Sampling from the Normal Population
AMS570 Pofesso We Zhu. Samplg fom the Nomal Populato *Example: We wsh to estmate the dstbuto of heghts of adult US male. It s beleved that the heght of adult US male follows a omal dstbuto N(, ) Def. Smple
SEPTIC B-SPLINE COLLOCATION METHOD FOR SIXTH ORDER BOUNDARY VALUE PROBLEMS
VOL. 5 NO. JULY ISSN 89-8 RN Joul of Egeeg d ppled Sceces - s Resech ulshg Netok RN. ll ghts eseved..pouls.com SETIC -SLINE COLLOCTION METHOD FOR SIXTH ORDER OUNDRY VLUE ROLEMS K.N.S. Ks Vsdhm d. Mul Ksh
such that for 1 From the definition of the k-fibonacci numbers, the firsts of them are presented in Table 1. Table 1: First k-fibonacci numbers F 1
Scholas Joual of Egeeg ad Techology (SJET) Sch. J. Eg. Tech. 0; (C):669-67 Scholas Academc ad Scetfc Publshe (A Iteatoal Publshe fo Academc ad Scetfc Resouces) www.saspublshe.com ISSN -X (Ole) ISSN 7-9
On EPr Bimatrices II. ON EP BIMATRICES A1 A Hence x. is said to be EP if it satisfies the condition ABx
Iteatoal Joual of Mathematcs ad Statstcs Iveto (IJMSI) E-ISSN: 3 4767 P-ISSN: 3-4759 www.jms.og Volume Issue 5 May. 4 PP-44-5 O EP matces.ramesh, N.baas ssocate Pofesso of Mathematcs, ovt. ts College(utoomous),Kumbakoam.
Simultaneous Estimation of Adjusted Rate of Two Factors Using Method of Direct Standardization
Biometics & Biosttistics Itetiol Joul Simulteous Estimtio of Adjusted Rte of Two Fctos Usig Method of Diect Stddiztio Astct This ppe pesets the use of stddiztio o djustmet of tes d tios i compig two popultios
Lecture 24: Observability and Constructibility
ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio
Noncommutative Solitons and Quasideterminants
Nocommutatve Soltos ad Quasdetemats asas HNK Nagoya Uvesty ept. o at. Teoetcal Pyscs Sema Haove o eb.8t ased o H ``NC ad's cojectue ad tegable systems NP74 6 368 ep-t/69 H ``Notes o eact mult-solto solutos
KEB INVERTER L1 L2 L3 FLC - RELAY 1 COMMON I1 - APPROACH CLOSE 0V - DIGITAL COMMON FLA - RELAY 1 N.O. AN1+ - ANALOG 1 (+) CRF - +10V OUTPUT
XT SSMLY MOL 00 (O FS) 00 (I- PT) 00 (SIGL SLI) WG O 0 0-0 0-0-0 0.0. 0 0-0 0-0-0 0 0-0 0-0-0 VOLTG F.L...0..0..0.0..0 IIG POW FOM US SUPPLI ISOT (S TL) US OP OUTOS T T 0 O HIGH H IUIT POTTIO OT: H IUIT
Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks
T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt
Complete Classification of BKM Lie Superalgebras Possessing Strictly Imaginary Property
Appled Mthemtcs 4: -5 DOI: 59/m4 Complete Clssfcto of BKM Le Supelges Possessg Stctly Imgy Popety N Sthumoothy K Pydhs Rmu Isttute fo Advced study Mthemtcs Uvesty of Mds Che 6 5 Id Astct I ths ppe complete
XII. Addition of many identical spins
XII. Addto of may detcal sps XII.. ymmetc goup ymmetc goup s the goup of all possble pemutatos of obects. I total! elemets cludg detty opeato. Each pemutato s a poduct of a ceta fte umbe of pawse taspostos.
A Public-Key Black-Box Traitor Tracing Scheme with Sublinear Ciphertext Size against Self-Defensive Pirates
A Public-Key Blc-Box Tito Tcin Sceme wit Subline Cipetext Size inst Self-Defensive Pites T. Mtsusit nd H. Imi TOSHIBA Copotion Univesity of Toyo Copyit 004 Tosib Copotion. All its eseved. Content distibution
ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY)
ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) Floet Smdche, Ph D Aocte Pofeo Ch of Deptmet of Mth & Scece Uvety of New Mexco 2 College Rod Gllup, NM 873, USA E-ml: md@um.edu
12781 Velp Avenue. West County B Rural Residential Development
U PL & EET E 28 Vel ee eded 2 P.. ) LL EET T E 2) PPVE E ) ET E ) e e e e eded eebe 2 Plg & g eeg b) Bldg Pe e: eebe ) PUBL FU ( -E TE): g be bg bee e Plg & g eel ll be de ll be e. 5) UEETFEEBK: ) be ll
MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER
MATHEMATICS II PUC VECTOR ALGEBRA QUESTIONS & ANSWER I One M Queston Fnd the unt veto n the deton of Let ˆ ˆ 9 Let & If Ae the vetos & equl? But vetos e not equl sne the oespondng omponents e dstnt e detons
Generalisation on the Zeros of a Family of Complex Polynomials
Ieol Joul of hemcs esech. ISSN 976-584 Volume 6 Numbe 4. 93-97 Ieol esech Publco House h://www.house.com Geelso o he Zeos of Fmly of Comlex Polyomls Aee sgh Neh d S.K.Shu Deme of hemcs Lgys Uvesy Fdbd-
CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find
BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,
Studying the Problems of Multiple Integrals with Maple Chii-Huei Yu
Itetol Joul of Resech (IJR) e-issn: 2348-6848, - ISSN: 2348-795X Volume 3, Issue 5, Mch 26 Avlble t htt://tetoljoulofesechog Studyg the Poblems of Multle Itegls wth Mle Ch-Hue Yu Detmet of Ifomto Techology,
5 - Determinants. r r. r r. r r. r s r = + det det det
5 - Detemts Assote wth y sque mtx A thee s ume lle the etemt of A eote A o et A. Oe wy to efe the etemt, ths futo fom the set of ll mtes to the set of el umes, s y the followg thee popetes. All mtes elow
SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz
STAT UIU Pctice Poblems # SOLUTIONS Stepov Dlpiz The followig e umbe of pctice poblems tht my be helpful fo completig the homewo, d will liely be vey useful fo studyig fo ems...-.-.- Pove (show) tht. (
Chapter 2 Intro to Math Techniques for Quantum Mechanics
Wter 3 Chem 356: Itroductory Qutum Mechcs Chpter Itro to Mth Techques for Qutum Mechcs... Itro to dfferetl equtos... Boudry Codtos... 5 Prtl dfferetl equtos d seprto of vrbles... 5 Itroducto to Sttstcs...
RECAPITULATION & CONDITIONAL PROBABILITY. Number of favourable events n E Total number of elementary events n S
Fomulae Fo u Pobablty By OP Gupta [Ida Awad We, +91-9650 350 480] Impotat Tems, Deftos & Fomulae 01 Bascs Of Pobablty: Let S ad E be the sample space ad a evet a expemet espectvely Numbe of favouable evets
T h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION
AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o
Integration by Parts for D K
Itertol OPEN ACCESS Jourl Of Moder Egeerg Reserc IJMER Itegrto y Prts for D K Itegrl T K Gr, S Ry 2 Deprtmet of Mtemtcs, Rgutpur College, Rgutpur-72333, Purul, West Begl, Id 2 Deprtmet of Mtemtcs, Ss Bv,
Phys 2310 Fri. Oct. 23, 2017 Today s Topics. Begin Chapter 6: More on Geometric Optics Reading for Next Time
Py F. Oct., 7 Today Topc Beg Capte 6: Moe o Geometc Optc eadg fo Next Tme Homewok t Week HW # Homewok t week due Mo., Oct. : Capte 4: #47, 57, 59, 6, 6, 6, 6, 67, 7 Supplemetal: Tck ee ad e Sytem Pcple
Nonquadratic Lyapunov Functions for Nonlinear Takagi-Sugeno Discrete Time Uncertain Systems Analysis and Control
(JACSA) ntentonl Jounl of Advnced Compute Scence nd Applctons, Vol. 7, No., 6 Nonqudtc Lypunov unctons fo Nonlne g-sugeno Dscete me Uncetn Systems Anlyss nd Contol Al Bouyhy Unvesty of uns El Mn, Ntonl
Elastic-Plastic Transition of Transversely. Isotropic Thin Rotating Disc
otempoy Egeeg Sceces, Vol., 9, o. 9, 4-44 Elstc-Plstc sto o svesely Isotopc h ottg Dsc Sjeev Shm d Moj Sh Deptmet o Mthemtcs JII Uvesty, -, Secto 6 Nod-7, UP, Id sjt@edml.com, moj_sh7@edml.com stct Elstc-plstc
The formulae in this booklet have been arranged according to the unit in which they are first
Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule
Electric Potential and Energy
Electic Potential and Enegy Te polem: A solid spee of te adius R is omogeneously caged wit te cage Q and put inside an infinite ollow cylinde. Te cylinde inne and oute adii ae a and, R < a
GREEN S FUNCTION FOR HEAT CONDUCTION PROBLEMS IN A MULTI-LAYERED HOLLOW CYLINDER
Joual of ppled Mathematcs ad Computatoal Mechacs 4, 3(3), 5- GREE S FUCTIO FOR HET CODUCTIO PROBLEMS I MULTI-LYERED HOLLOW CYLIDER Stasław Kukla, Uszula Sedlecka Isttute of Mathematcs, Czestochowa Uvesty
176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
U>, and is negative. Electric Potential Energy
Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When
2. Elementary Linear Algebra Problems
. Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )
Application of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Homogeneous Systems
Poceedgs of the Itetol MultCofeece of Egees d Comute Scetsts 009 Vol II IMECS 009, Mch 8-0, 009, Hog Kog Alcto of Hghe Ode Detes of Lyuo Fuctos Stblty Alyss of Nole Homogeeous Systems Vhd Megol, d S. K.
General Method for Calculating Chemical Equilibrium Composition
AE 6766/Setzma Sprg 004 Geeral Metod for Calculatg Cemcal Equlbrum Composto For gve tal codtos (e.g., for gve reactats, coose te speces to be cluded te products. As a example, for combusto of ydroge wt
AS and A Level Further Mathematics B (MEI)
fod Cmbdge d RSA *3369600* AS d A evel Futhe Mthemtcs B (MEI) The fomto ths booklet s fo the use of cddtes followg the Advced Subsd Futhe Mthemtcs B (MEI)(H635) o the Advced GCE Futhe Mthemtcs B (MEI)
Technical Appendix for Inventory Management for an Assembly System with Product or Component Returns, DeCroix and Zipkin, Management Science 2005.
Techc Appedx fo Iveoy geme fo Assemy Sysem wh Poduc o Compoe eus ecox d Zp geme Scece 2005 Lemm µ µ s c Poof If J d µ > µ he ˆ 0 µ µ µ µ µ µ µ µ Sm gumes essh he esu f µ ˆ > µ > µ > µ o K ˆ If J he so
Lecture 10: Condensed matter systems
Lectue 0: Codesed matte systems Itoducg matte ts codesed state.! Ams: " Idstgushable patcles ad the quatum atue of matte: # Cosequeces # Revew of deal gas etopy # Femos ad Bosos " Quatum statstcs. # Occupato
SUBSEQUENCE 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
Inequalities for Dual Orlicz Mixed Quermassintegrals.
Advaces Pue Mathematcs 206 6 894-902 http://wwwscpog/joual/apm IN Ole: 260-0384 IN Pt: 260-0368 Iequaltes fo Dual Olcz Mxed Quemasstegals jua u chool of Mathematcs ad Computatoal cece Hua Uvesty of cece
Induction. Induction and Recursion. Induction is a very useful proof technique
Iductio Iductio is vey useul poo techique Iductio d Recusio CSC-59 Discete Stuctues I compute sciece, iductio is used to pove popeties o lgoithms Iductio d ecusio e closely elted Recusio is desciptio method
Mathematical Statistics
7 75 Ode Sttistics The ode sttistics e the items o the dom smple ed o odeed i mitude om the smllest to the lest Recetl the impotce o ode sttistics hs icesed owi to the moe equet use o opmetic ieeces d
Available online through
Avlble ole through wwwmfo FIXED POINTS FOR NON-SELF MAPPINGS ON CONEX ECTOR METRIC SPACES Susht Kumr Moht* Deprtmet of Mthemtcs West Begl Stte Uverst Brst 4 PrgsNorth) Kolt 76 West Begl Id E-ml: smwbes@yhoo
Lattice planes. Lattice planes are usually specified by giving their Miller indices in parentheses: (h,k,l)
Ltte ples Se the epol ltte of smple u ltte s g smple u ltte d the Mlle des e the oodtes of eto oml to the ples, the use s ey smple lttes wth u symmety. Ltte ples e usully spefed y gg the Mlle des petheses:
Hyper-wiener index of gear fan and gear wheel related graph
Iteatoal Joual of Chemcal Studes 015; (5): 5-58 P-ISSN 49 858 E-ISSN 1 490 IJCS 015; (5): 5-58 014 JEZS Receed: 1-0-015 Accepted: 15-0-015 We Gao School of Ifomato Scece ad Techology, Yua Nomal Uesty,
14.2 Line Integrals. determines a partition P of the curve by points Pi ( xi, y
4. Le Itegrls I ths secto we defe tegrl tht s smlr to sgle tegrl except tht sted of tegrtg over tervl [ ] we tegrte over curve. Such tegrls re clled le tegrls lthough curve tegrls would e etter termology.
Non-axial symmetric loading on axial symmetric. Final Report of AFEM
No-axal symmetc loadg o axal symmetc body Fal Repot of AFEM Ths poject does hamoc aalyss of o-axal symmetc loadg o axal symmetc body. Shuagxg Da, Musket Kamtokat 5//009 No-axal symmetc loadg o axal symmetc
--- Deceased Information. A1ry't (Ay't olll n5. F\ease turn page ) lslamic Community Center of Tempe. Please print all information clearly.
A1y't (Ay't lll l uty ete ee lese t ll t lely. Deese t st e Mle e s t\e Lee De Bth Age Dte Seultv t\ube h :;;"' :;...".::.."'t ' ' ue uetttte ube use Deth Heste Als ( y); he t vle hve lll be use t etg
THE WEIGHTED POSSIBILISTIC MEAN VARIANCE AND COVARIANCE OF FUZZY NUMBERS
Quattatve Methos Iques THE WEIGHTED POSSIBILISTIC MEAN VARIANCE AND COVARIANCE OF FUZZY NUMBERS Supa SUDRADJAT PhD Depatmet of Mathematcs Faculty of Mathematcs a Natual Sceces Paaaa Uvesty Jl Raya Baug-Sumeag
Objectives. Learning Outcome. 7.1 Centre of Gravity (C.G.) 7. Statics. Determine the C.G of a lamina (Experimental method)
Ojectves 7 Statcs 7. Cete of Gavty 7. Equlum of patcles 7.3 Equlum of g oes y Lew Sau oh Leag Outcome (a) efe cete of gavty () state the coto whch the cete of mass s the cete of gavty (c) state the coto
An Unconstrained Q - G Programming Problem and its Application
Joual of Ifomato Egeeg ad Applcatos ISS 4-578 (pt) ISS 5-0506 (ole) Vol.5, o., 05 www.ste.og A Ucostaed Q - G Pogammg Poblem ad ts Applcato M. He Dosh D. Chag Tved.Assocate Pofesso, H L College of Commece,
FIBONACCI-LIKE SEQUENCE ASSOCIATED WITH K-PELL, K-PELL-LUCAS AND MODIFIED K-PELL SEQUENCES
Joual of Appled Matheatcs ad Coputatoal Mechacs 7, 6(), 59-7 www.ac.pcz.pl p-issn 99-9965 DOI:.75/jac.7..3 e-issn 353-588 FIBONACCI-LIKE SEQUENCE ASSOCIATED WITH K-PELL, K-PELL-LUCAS AND MODIFIED K-PELL
A Brief Introduction to Olympiad Inequalities
Ev Che Aprl 0, 04 The gol of ths documet s to provde eser troducto to olympd equltes th the stdrd exposto Olympd Iequltes, by Thoms Mldorf I ws motvted to wrte t by feelg gulty for gettg free 7 s o problems
1 4 6 is symmetric 3 SPECIAL MATRICES 3.1 SYMMETRIC MATRICES. Defn: A matrix A is symmetric if and only if A = A, i.e., a ij =a ji i, j. Example 3.1.
SPECIAL MATRICES SYMMETRIC MATRICES Def: A mtr A s symmetr f d oly f A A, e,, Emple A s symmetr Def: A mtr A s skew symmetr f d oly f A A, e,, Emple A s skew symmetr Remrks: If A s symmetr or skew symmetr,
Physics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
Piecewise Quadratic Stability of Closed-loop Takagi-Sugeno Fuzzy Systems
7 Poceedgs of the Iteatoal Cofeece o Ifoato Autoato Decebe -8 Colobo S Laa Pecewse Quadatc Stablty of Closed-loop aag-sugeo Fuzzy Systes Pet Huše Mguel Beal Depatet of Cotol geeeg Faculty of lectcal geeg
RANDOM SYSTEMS WITH COMPLETE CONNECTIONS AND THE GAUSS PROBLEM FOR THE REGULAR CONTINUED FRACTIONS
RNDOM SYSTEMS WTH COMPETE CONNECTONS ND THE GUSS PROBEM FOR THE REGUR CONTNUED FRCTONS BSTRCT Da ascu o Coltescu Naval cademy Mcea cel Bata Costata lascuda@gmalcom coltescu@yahoocom Ths pape peset the
Chapter Simpson s 1/3 Rule of Integration. ( x)
Cper 7. Smpso s / Rule o Iegro Aer redg s per, you sould e le o. derve e ormul or Smpso s / rule o egro,. use Smpso s / rule o solve egrls,. develop e ormul or mulple-segme Smpso s / rule o egro,. use
The Area of a Triangle
The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest
Variance Estimation After Imputation
Suve Metodolog, Jue 00 75 Vol 7, o, pp 75 83 Sttstcs Cd, Ctlogue o 00 Vce Estmto Afte mputto Je Kwg Km Abstct mputto s commol used to compeste fo tem oespose Vce estmto fte mputto s geeted cosdeble dscusso
Solutions to Homework 3
Solutions to Homework 3 Section 3.4, Repeated Roots; Reduction of Order Q 1). Find the general solution to 2y + y = 0. Answer: The charactertic equation : r 2 2r + 1 = 0, solving it we get r = 1 as a repeated
The Exponentiated Lomax Distribution: Different Estimation Methods
Ameca Joual of Appled Mathematcs ad Statstcs 4 Vol. No. 6 364-368 Avalable ole at http://pubs.scepub.com/ajams//6/ Scece ad Educato Publshg DOI:.69/ajams--6- The Expoetated Lomax Dstbuto: Dffeet Estmato
The z-transform. LTI System description. Prof. Siripong Potisuk
The -Trsform Prof. Srpog Potsuk LTI System descrpto Prevous bss fucto: ut smple or DT mpulse The put sequece s represeted s ler combto of shfted DT mpulses. The respose s gve by covoluto sum of the put
The Mathematical Appendix
The Mathematcal Appedx Defto A: If ( Λ, Ω, where ( λ λ λ whch the probablty dstrbutos,,..., Defto A. uppose that ( Λ,,..., s a expermet type, the σ-algebra o λ λ λ are defed s deoted by ( (,,...,, σ Ω.
Bayes (Naïve or not) Classifiers: Generative Approach
Logstc regresso Bayes (Naïve or ot) Classfers: Geeratve Approach What do we mea by Geeratve approach: Lear p(y), p(x y) ad the apply bayes rule to compute p(y x) for makg predctos Ths s essetally makg
P a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
Insurance Risk EC for XL contracts with an inflation stability clause
suce Rs E fo L cotcts wth flto stlt cluse 40 th t. AT oll. Mdd Jue 9-0 opght 008 FR Belgum V "FRGlol". Aged upemposed flto / stlt cluse suce Rs olutos o-lfe Rs / tdd ppoch o-lfe Rs / tochstc ppoch goss
4. Runge-Kutta Formula For Differential Equations. A. Euler Formula B. Runge-Kutta Formula C. An Example for Fourth-Order Runge-Kutta Formula
NCTU Deprme o Elecrcl d Compuer Egeerg Seor Course By Pro. Yo-Pg Ce. Ruge-Ku Formul For Derel Equos A. Euler Formul B. Ruge-Ku Formul C. A Emple or Four-Order Ruge-Ku Formul