Industrial Control and Monitoring
|
|
- Job Richardson
- 5 years ago
- Views:
Transcription
1 Internatonal Book Seres "Informaton Scence and Comutng" 89 Industral Control and Montorng APPLICATION OF GENETIC ALGORITHMS TO VECTOR OPTIMIZATION OF THE AUTOMATIC CONTROL SYSTEMS Valery Severn Abstract: Methods for calculaton of qualty ndexes for automatc control systems are resented. For the otmzaton of qualty ndexes defned only n a stablty doman a vector objectve functon of vared arameters of the system s roosed. The stewse rncle of successve satsfacton of constrants for the assage nto the defnton doman of qualty ndexes s consdered as well as a ratonal mechansm of ts realzaton n the form of the rorty otmzaton of the vector objectve functon. For the otmzaton of the vector objectve functons genetc algorthms as vector otmzaton methods are resented. Ther alcaton allows one to steer the otmzaton rocess from any ntal ont of the sace of vared arameters nto the stablty doman of the system and to fnd the otmum of the qualty ndexes n ths doman. The effcency of the roosed alcaton of vector genetc algorthms for the qualty ndexes otmzaton s confrmed by comutatonal exerments. Keywords: genetc algorthms vector otmzaton methods automatc control systems qualty ndexes. ACM Classfcaton Keywords: G..6 Otmzaton - Nonlnear rogrammng Introducton For the synthess of automatc control systems (ACS) qualty of ther functonng can be resented by dfferent crtera [Besekersky Poov 004]. There are many dffcultes even at the synthess of the lnear control systems and the results of synthess substantally deend on the aled crtera [Poljak Scherbako 005]. Yet the task of synthess of the nonlnear systems s even more dffcult. Qualty crtera for both lnear and nonlnear ACS can be reflected by the drect qualty ndexes (DQI) and mroved ntegral quadratc estmatons (IQE) [Severn Nkulna 004] [Severn 004] [Severn 005]. The otmzaton tasks of these crtera have an dentcal feature ther objectve functons doman s lmted by stablty condtons [Severn 008]. Therefore the standard otmzaton methods can not be effectvely used for the otmzaton of ACS qualty ndexes. For the synthess of the lnear control systems by means of DQI and mroved IQE otmzaton the vector objectve functons are offered and for ther otmzaton the drect methods of unconstraned mnmzaton are modfed [Severn 005]. The methods otmzaton laboratory OPTLAB s develoed n MATLAB system [Severn 009]. However the offered vector otmzaton methods do not allow to fnd global extremes. The decsons search of otmzaton tasks n very large and dffcult domans s executed by genetc algorthms whch are evolutonary comutatons varety and behave to heurstc search methods [Voronovsky Makhotlo Petrashev Sergeev 997] [Setlak 004]. Genetc algorthms are used for otmzaton tasks decson based on the rncles and mechansms remndng bologcal evoluton [Panchenko 007] [Wese 008].
2 90 No:3 Intellgent Informaton and Engneerng Systems The urose of ths aer conssts of conceton develoment of synthess for lnear and nonlnear ACS on the bass of DQI mroved IQE and modfcatons of genetc algorthms for vector otmzaton. The methods of DQI and mroved IQE calculaton are consdered for lnear and nonlnear systems. Statements of systems otmzaton tasks are resented wth usng vector objectve functons. Modfcaton of genetc algorthms s offered for vector otmzaton of ACS qualty ndexes. Qualty Indexes Calculaton of Lnear Automatc Control Systems Let lnear model of ACS deendng on a vector of vared arameters x R n state sace looks lke: t A( + B( u( y ( C( () where t ) s a state vector wth an ntal condton X 0 0 ; u ( s entrance nfluence y ( s control outut co-ordnate; A ( B ( C ( are matrces of the control system arameters. For the stable watchng system at standard nut ste sgnal u ( ( the matrx of outut C ( s set so that the condton of outut coordnate scalng was executed: y (. At the fxed arameters vector value x wll buld transent rocesses n model () on the quantum of tme [ 0 T f ]. For ths urose at L ntegraton stes of constant length h T f L wth numbers k L wll enter denotatons: We wll desgnate matrx exonent and t s ntegral: t k kh X k ( tk ) yk ( C( X k (. () h A( τ A( h ϕ ( e Φ( e dτ g( Φ ( B(. (3) 0 Then at an nut sgnal u ( ( transent rocess n ACS wth model () t s ossble to buld on the recurrent formulas of matrx method [Severn 008]: X ( ϕ( X k ( g( k L. (4) k + For a devaton z ( y( y( there are ts values and ther ncrements: u zk ( yk ( y( k 0 L (5) zk ( zk ( urk ( zk ( zk ( k L. (6) lk ( If the followng condton meanng that both successve ncrements are of the same sgn s met then wth usng of quadratc nterolaton the extreme value s calculated e ( : d uk ulk ( urk ( > 0 (7) ( [ ulk ( urk ( ] suk ( ulk ( + urk ( ruk ( duk ( suk ( (8) e ( zk ( duk ( ruk ( (9) where ne ( n e ( s extreme s number on segment [ 0 T f ]. By extreme s values of transent rocess the drect qualty ndexes are calculated: overshoot σ ( vbratons scoe ζ ( vbratons damng ndex λ (. Let ( v ) + max{ v0} s a cuttng functon of otonal varable v. For watchng system wth y ( drect ndexes are determned on formulas:
3 Internatonal Book Seres "Informaton Scence and Comutng" 9 0 σ( [max e ( ] n ( 0 e + ne ( > 0 (0) 0 ζ( max e ( e ne ( 0 ( n ( ) > e x 0 λ( max{ e ( e ne ( 0 ( } n ( ) > e x. For the stablzaton system wth y ( 0 a rocess n whch has even one extreme e ( () σ( max e ( () and at a calculaton ζ ( and λ ( n formulas () not taken nto account e (. For the calculaton of ACS control tme the entry tmes of devaton z ( t ) n the set segment [ δ z δ z ] of the steady-state value z ( 0 are determned by verfcaton of entrance condton: z k ( δ z zk ( < δ z. (3) At mlementaton of ths condton takng nto account denotatons (5) (8) auxlary values are calculated: u ( uk + δ zsgn zk ( zk ( v0 ( ruk ( h (4) s ( h r ( u ( s ( uk v0 ( + s ( v ( 0 v ( v0 ( s ( v ( > 0. (5) The moment of tme roer entrance of devaton functon z ( t ) n area of steady-state value s determned: Control tme t c ( and ts relatve value τ ( are calculated on formulas: t ( tk ( + v (. (6) t ( max t ( c τ ( x ) t ( T. (7) c f On formulas (3) (7) for calculaton of DQI σ ( ζ ( λ ( t c ( τ ( the algorthms are obtaned. For the synthess of watchng ACS n lace of few drect qualty ndexes t s ossble to use ther summarzng sngle ndex mroved IQE. On the model of knd () one can buld a transfer functon (TF) n 0 n m W ( β( α( α( α ( s β( β ( s. (8) For the watchng systems a method s offered for formng of mroved IQE I ( of error e ( : [ e( ] 0 l k 0 ( l k) I ( dt e( w z ( (9) k t m 0 where l s an order of estmaton l < n m ; w k are weghtng coeffcents: wk μ l k γ k s l k 0 l k l k k 0 l ; μ t e ts γ( ) γ ( s ) w k s. (0) k s w l k 0 Here t e and t s are control tmes of etalon and standard rocesses γ ( and w ( are standard and weghtng olynomals. On TF (8) Lalace reresentaton of error s formed E( δ( α( where δ ( x [ α( β( w( ] [Severn 005]. s. On the bass of ths reresentaton IQE calculaton algorthm s develoed
4 9 No:3 Intellgent Informaton and Engneerng Systems Otmzaton Tasks of Lnear Automatc Control Systems Takng nto account the hgh scoe values σ m ζ m λ m for DQI σ ( ζ ( λ ( and requrements of maxmal ACS resonse seed the system otmzaton task can be formulated as task of the constraned otmzaton whch requres mnmzaton of control tme at mlementaton of lmts on the other ndexes: mn τ( x σ ( σ ζ ( ζ m λ ( λ m. () m Usng the mroved ntegral estmaton the task of control system otmzaton conssts n mnmzaton IQE: mn I( x. () However statements of otmzaton control system tasks () and () take nto account nether rorty of drect ndexes nor lmtaton of ther defntonal doman and defntonal doman of ntegral estmaton. The analyss of automatc control system requrements allows to set the followng reference order of drect qualty ndexes: σ ( ζ ( λ ( τ (. The feature of these ndexes as rvate qualty crtera of the automatc control systems s the lmtaton of ther defntonal doman by stablty condtons. On Routh crteron for stablty of lnear ACS wth transfer functon (8) there are necessary and suffcent condtons: α ( > 0 0 n ; ρk ( > 0 k n (3) where ρ k ( are elements of the frst column of Routh table. The analyss of Routh crteron and research of roertes of functons ρ k ( justfy the stewse scheme of assage to the stablty doman: f some from elements ρ k ( s not ostve t s suggested to ncrease frst of them to the ostve value by the change of arameters values vector x and then to ncrease subsequent elements. To smlfy the scheme of assng to the stablty doman and to meet the condtons of drect qualty ndexes () the arameter sace R s dvded nto three doman sequences. The nequaltes (3) and () are satsfed on the followng domans of lmtatons: Ω { x α ( > 0 0 } Ωk { x ρk ( > 0 } k n (4) n Ω n { x σ( σm } Ω n + { x ζ( ζ m } Ω n + { x λ( λ m }. (5) On these m n + domans the derved ntersecton domans D k and domans of lmtatons levels H k are formed: D Ω ; Dk D k Ωk k m ; (6) \ + H 0 R \ D ; H k Dk Dk k m ; H m Dm. (7) The domans of levels dvde arameters sace nto the sequence of dsjont domans. The degree of volaton of the frst grou of nequaltes (3) s resented by enalty functon ( ) n x [ α ( 0 x P )]. (8) Stewse rncle of transferrng to the stablty doman and satsfacton of all lmtatons of drect qualty ndexes s based on the followng: from any ont x of arameters sace R t s necessary to ass consstently to the level doman wth greater ndex by mnmzng n the current level doman usng ts corresondng enalty functon. Takng nto account the amount of levels domans there wll be no more such stes of transton than the number of lmtatons m. For realzaton of stewse rncle of satsfacton of lmtatons n the task of ACS synthess wth otmzaton of drect qualty ndexes on the bass of levels domans a vector objectve functon s ntroduced +
5 Internatonal Book Seres "Informaton Scence and Comutng" 93 (0; P( ) x H 0; ( k; ρk+ ( ) x H k k n ; ( n ; σ( σ m ) x H n ; F ( ( n; ζ( ζ m ) x H ; (9) n ( n + ; λ( λ m ) x H n+ ; ( n + ; τ( ) x H n+. Denote the frst coordnate of ths functon as the functon of level F ( and the second coordnate as the functon of enalty F (. The vector objectve functon (9) can be calculated algorthmcally. Algorthm for calculaton of the vector objectve functon for drect qualty ndexes otmzaton. Inut arameters: x s a vector of varable arameters T f s the uer lmt of ntegraton nterval L s a number of stes of ntegraton σ m ζ m and λ m maxmum accetable values of DQI. Outut arameter: F s a value of vector objectve functon.. On model () calculate TF (8) wth the characterstc olynomal α ( α( of degree n.. If the necessary stablty condtons are volated calculate enalty functon (8) let F ( 0; P ) and go to. 3. Let k. 4. On Routh chart calculate ρ k + ρk+ (. 5. If ρ k + 0 let F ( k ; ρk+ ) and go to. 6. If k < n let k k + and go to On formulas () (7) by numercal ntegraton wth quadratc nterolaton calculate values of DQI ζ ζ( λ λ( tc tc ( τ τ(. 8. If σ > σm let F ( n ; σ σm ) and go to. 9. If ζ > ζm let F ( n; ζ ζ m ) and go to. 0. If λ > λm let F ( n + ; λ λ m ) and go to.. Let F ( n + ; τ).. Ext the algorthm. Lke functon (9) a vector objectve functon s bult for mnmzaton of the mroved IQE (9): (0; P( ) x H 0; F ( ( k ; ρk+ ( ) x H k k n ; (30) ( n ; I( ) x H n. The goal of control systems otmzaton usng vector objectve functons (9) and (30) can be resented as mnmzaton of the functon of enalty F ( wth the rorty condton of maxmzaton of functon of level F ( whch n turn can be resented as a sngle task of vector otmzaton: mn F( x. (3) Unlke the tasks of scalar otmzaton () and () the task of vector otmzaton (3) takes nto account the stablty condtons and order of reference of lmtatons. The rocess of otmal synthess of ACS s grounded by mnmzaton F ( wth rorty maxmzaton F ( as otmzaton of vector functons (9) and (30) on the bass of comarson of ther two arbtrary values U ( U ; U ) and V ( V ; V ) by the bnary oeratons: U < V 0 U V 0 U U U U > V < V > V < V U U U U V V V V U U U U < V U V > U U < V U V U > V U > V 0 U > V U V U U (3) U < V U V U V U V 0 U > V U V U < U. (33) These oeratons allowng to determne whch of the two values of vector objectve functon s «better» «worse» «not worse» or «not better» can be used n the numercal methods of unconstraned otmzaton.
6 94 No:3 Intellgent Informaton and Engneerng Systems Calculaton of Qualty Indexes of Nonlnear Control Systems For nonlnear models the state vector and control coordnate wll deend nonlnearly on the value of nut nfluence u u(. Unlke the lnear model of ACS n state sace () the nonlnear model can be resented as: u t f [ u u t] y ( u C( u. (34) For the stable watchng system at an nut ste sgnal u( us( wth magntude u s [ u mn ; umax ] the outut matrx C ( u ) scales an outut coordnate y ( u. At a fxed value of arameters vector x let s buld transent rocesses n model (34) on the quantum of tme [ 0 T f ] and calculate the Jacoban matrx of vector functon of equaton (34) by dfferentatng t on state vector coordnates: A ( f [ u u t] X ( u x 0 u 0 t 0. (35) Let s ntroduce notaton smlar to () and (3) but takng nto account system nonlnearty: h A( τ Φ( e dτ. (36) 0 Transent rocess n the control system on a model (34) t s ossble to buld on recurrent formulas for k L : X k ( X k ( + Φ( f [ X k ( u tk ]. (37) As a result of alcaton of formulas smlar to formulas (4) (7) but wth functons deendng both on x and u we can calculate the drect ndexes of qualty σ ( ζ ( λ ( t c ( τ (. Unlke lnear ACS for the nonlnear systems an ntegral estmaton (9) can be calculated only by numercal ntegraton of the nonlnear system of dfferental equatons (34) together wth dfferental equaton of estmaton: l k 0 ( l k) I ( u t w z ( u. (38) For the extended system Jacoban matrx (35) and ntegral of matrx exonent (36) are calculated. The mroved IQE I ( u T f ) wll be a result of ntegraton of such system of dfferental equatons usng formula (37) on the san of tme [ 0 T f ] requred for the convergence of mroer ntegral. Otmzaton Tasks of Nonlnear Control Systems In the frst aroachng stablty of the nonlnear control system can be defned on a lnearzed model. For ths urose we dfferentate the vector functon of equaton (34) on nut acton: k t B ( f [ u u t] u x 0 u 0 t 0. (39) Takng nto account matrx (35) let s resent the lnearzed model of the nonlnear system (34): u t A( u + B( u y ( u C( u. (40) On ths model let s buld a transfer functon n 0 n m W ( u β( u α( u α( u α ( s β( u β ( s. (4) On a characterstc olynomal α ( u let s defne the enalty functon P ( of knd (8) and elements of the frst column of Routh table ρ k (. Vector objectve functons for qualty crtera otmzaton (9) and (30) also wll deend both on the vector of the vared arameters x and on nut acton u. Let s desgnate these m 0
7 Internatonal Book Seres "Informaton Scence and Comutng" 95 functons through F ( u ) and ntroduce n u nut ste sgnals u ( us( nu wth magntudes u s [ u mn ; umax ]. Changng the value of nut acton u s at the fxed value of vector x we wll get dfferent ( ) values of vector functon F ( F[ u ( ] and usng comarson oeratons (3) fnd the worst value s G( max F ( ) (. (4) By analogy wth task (3) for lnear ACS the task of otmzaton of the nonlnear systems can be resented as: mn G( x. (43) The soluton of ths task gves the otmal vector of the vared arameters resultng to the best qualty of transent rocesses for the secfed set of nut actons. Modfcaton of Genetc Algorthms for Vector Otmzaton of Control Systems For otmzaton of vector objectve functons we offer modfcatons of genetc algorthms. Intal oulaton from M ndvduals s generated by ntroducng a set of random vectors x j M wth real coordnates n the sace of arameters R of the control system or vectors of bnary values. In the second case t s necessary to ( j) reresent every bnary vector n sace R and convert them to the vectors x j M. Usually for ths urose a bnary-to-decmal code or Gray code s used. The values of vector objectve functons (9) (30) or (4) ( j) j F F( x ) j M are calculated for all ndvduals usng systems models equatons () (34) (35) (39) (4) qualty ndexes calculaton formulas () (0) (36) (38) and defnng exressons of vector functons (3) (8). To rank ndvduals by the degree of ftness t s suggested to use the vector objectve functon sortng algorthms on the bass of oeratons of comarson of ts values (3) (33). The ftness level of ndvduals s subsequently scaled by the nverse square root j of ther rank j n the sorted sequence. The scaled ftness level s used n the casual mechansm of selecton. Alcaton of genetc oerators to the aternal ndvduals and generaton of descendants s made as well as n scalar genetc algorthms wth the use of dfferent tyes of crossover mutaton nverson. For all got descendants the values of vector objectve functon are calculated and ther ranks are obtaned smlarly to the stage of formng the ntal oulaton. The new oulaton s formed based on the results of sortng. Concluson The researches results allow to formulate next conclusons.. The calculaton methods of drect qualty ndexes and mroved ntegral quadratc estmatons have been studed for the lnear automatc control systems. These qualty ndexes are defned only n stablty doman of the systems.. The otmzaton tasks of qualty ndexes of the lnear automatc control systems are resented as the tasks of otmzaton of vector objectve functons takng nto account the condtons of stablty of the systems requrements to the qualty ndexes and rorty of system requrements. For modfcaton of otmzaton methods the set of comarson oeratons for vector objectve functons s ntroduced. 3. The methods of qualty ndexes calculaton have been also consdered for the nonlnear automatc control systems. These qualty ndexes are the functons of not only varyng arameters but also nut acton of control system. ( j)
8 96 No:3 Intellgent Informaton and Engneerng Systems 4. Through deendence of qualty ndexes on nut acton of nonlnear control systems for one value of vector of varyng arameters the several vector functons values are calculated at dfferent values of nut acton. By the choce from these vector values the worst value of the vector objectve functon of nonlnear system s determned. 5. Vector modfcatons of genetc algorthms for otmzaton of vector objectve functons allowng to solve the tasks of synthess for the lnear and nonlnear control systems have been develoed. The effcency of the roosed alcaton of genetc algorthms for the vector otmzaton of qualty ndexes of control systems has been confrmed by comutatonal exerments on the test and aled tasks. Bblograhy [Besekersky Poov 004] V. A. Besekersky E. P. Poov Teorja system avtomatcheskogo uravlenja St. Petersburg Professja 004 (n Rus.) 75. [Poljak Scherbakov 005] B. T. Poljak P. S. Scherbakov. Trudne zadach lnejnoj theor uravlenja. Nekotore odhod k reshenju // Automatka telemehanka (n Rus.) [Severn Nkulna 004] V. P.Severn E. N. Nkulna. Algortm vchslenja rjamh okazatelej kachestva hunkzj vesa sstem avtomatcheskogo uravlenja // Radoelectronca nformatca 004 (n Rus.) [Severn 004] V. P. Severn. Mnmzaton of Integral Square Estmates of Automatc Control Systems. Part II. Ste by Ste Aroach // Journal of Automaton and Informaton Scences 004 Vol. 36; N [Severn 005] V. P. Severn. Vector Otmzaton of the Integral Quadratc Estmates for Automatc Control Systems // Journal of Comuter and Systems Scences Internatonal 005 Vol. 44 N [Severn 008] V. P. Severn. Parametrcheskj synthes sstem automatcheskogo uravlenja methodam vectornoj otmzac // Tehncheskaja elektrodnamka 008 Vol. 4 (n Rus.) [Severn 009] Severn V. P. Struktura laborator methodov otmzac OPTLAB v systeme MATLAB // Trud IV Vserossjskoj nauchnoj konferenc «Proektrovane ngenernh nauchnh rlogenj v srede MATLAB» Astrakhan Izdatelskj dom «Astrakhanskj unverstet» 009 (n Rus.) [Voronovsky Makhotlo Petrashev Sergeev 997] G. K. Voronovsky K. V. Makhotlo S. N. Petrashev S. A. Sergeev. Kharkov. Genetcheske algortm skusstvenne nejronne set roblem vrtualnoj realnost / Bass 997 (n Rus.). [Setlak 004] G. Setlak. Intellgent Decson Suort System Kev LOGOS 004 (n Rus.) 5. [Panchenko 007] T. V. Panchenko. Genetcheske algortm. Uchebnoe osobe / Pod red. J. J. Tarasevcha Astrakhan Izdatelskj dom «Astrakhanskj unverstet» 007 (n Rus.) 88. [Wese 008] T. Wese. Global Otmzaton Algorthms Theory and Alcaton Authors' Informaton Valery Severn Professor Deartment of Comuter Scence and Control Natonal Techncal Unversty Kharkov Polytechncal Insttute ul. Frunze 300 Kharkov Ukrane; e-mal: severnv@mal.ru
Fuzzy approach to solve multi-objective capacitated transportation problem
Internatonal Journal of Bonformatcs Research, ISSN: 0975 087, Volume, Issue, 00, -0-4 Fuzzy aroach to solve mult-objectve caactated transortaton roblem Lohgaonkar M. H. and Bajaj V. H.* * Deartment of
More informationAdvanced Topics in Optimization. Piecewise Linear Approximation of a Nonlinear Function
Advanced Tocs n Otmzaton Pecewse Lnear Aroxmaton of a Nonlnear Functon Otmzaton Methods: M8L Introducton and Objectves Introducton There exsts no general algorthm for nonlnear rogrammng due to ts rregular
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationThe Study of Teaching-learning-based Optimization Algorithm
Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute
More informationUsing Genetic Algorithms in System Identification
Usng Genetc Algorthms n System Identfcaton Ecaterna Vladu Deartment of Electrcal Engneerng and Informaton Technology, Unversty of Oradea, Unverstat, 410087 Oradea, Româna Phone: +40259408435, Fax: +40259408408,
More informationPriority Queuing with Finite Buffer Size and Randomized Push-out Mechanism
ICN 00 Prorty Queung wth Fnte Buffer Sze and Randomzed Push-out Mechansm Vladmr Zaborovsy, Oleg Zayats, Vladmr Muluha Polytechncal Unversty, Sant-Petersburg, Russa Arl 4, 00 Content I. Introducton II.
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationTopology optimization of plate structures subject to initial excitations for minimum dynamic performance index
th World Congress on Structural and Multdsclnary Otmsaton 7 th -2 th, June 25, Sydney Australa oology otmzaton of late structures subject to ntal exctatons for mnmum dynamc erformance ndex Kun Yan, Gengdong
More informationLesson 16: Basic Control Modes
0/8/05 Lesson 6: Basc Control Modes ET 438a Automatc Control Systems Technology lesson6et438a.tx Learnng Objectves Ater ths resentaton you wll be able to: Descrbe the common control modes used n analog
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationDigital PI Controller Equations
Ver. 4, 9 th March 7 Dgtal PI Controller Equatons Probably the most common tye of controller n ndustral ower electroncs s the PI (Proortonal - Integral) controller. In feld orented motor control, PI controllers
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationAlgorithms for factoring
CSA E0 235: Crytograhy Arl 9,2015 Instructor: Arta Patra Algorthms for factorng Submtted by: Jay Oza, Nranjan Sngh Introducton Factorsaton of large ntegers has been a wdely studed toc manly because of
More information( ) 2 ( ) ( ) Problem Set 4 Suggested Solutions. Problem 1
Problem Set 4 Suggested Solutons Problem (A) The market demand functon s the soluton to the followng utlty-maxmzaton roblem (UMP): The Lagrangean: ( x, x, x ) = + max U x, x, x x x x st.. x + x + x y x,
More information6. Hamilton s Equations
6. Hamlton s Equatons Mchael Fowler A Dynamcal System s Path n Confguraton Sace and n State Sace The story so far: For a mechancal system wth n degrees of freedom, the satal confguraton at some nstant
More information2-Adic Complexity of a Sequence Obtained from a Periodic Binary Sequence by Either Inserting or Deleting k Symbols within One Period
-Adc Comlexty of a Seuence Obtaned from a Perodc Bnary Seuence by Ether Insertng or Deletng Symbols wthn One Perod ZHAO Lu, WEN Qao-yan (State Key Laboratory of Networng and Swtchng echnology, Bejng Unversty
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationHidden Markov Model Cheat Sheet
Hdden Markov Model Cheat Sheet (GIT ID: dc2f391536d67ed5847290d5250d4baae103487e) Ths document s a cheat sheet on Hdden Markov Models (HMMs). It resembles lecture notes, excet that t cuts to the chase
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationManaging Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration
Managng Caacty Through eward Programs on-lne comanon age Byung-Do Km Seoul Natonal Unversty College of Busness Admnstraton Mengze Sh Unversty of Toronto otman School of Management Toronto ON M5S E6 Canada
More informationConfidence intervals for weighted polynomial calibrations
Confdence ntervals for weghted olynomal calbratons Sergey Maltsev, Amersand Ltd., Moscow, Russa; ur Kalambet, Amersand Internatonal, Inc., Beachwood, OH e-mal: kalambet@amersand-ntl.com htt://www.chromandsec.com
More informationQUANTITATIVE RISK MANAGEMENT TECHNIQUES USING INTERVAL ANALYSIS, WITH APPLICATIONS TO FINANCE AND INSURANCE
QANTITATIVE RISK MANAGEMENT TECHNIQES SING INTERVA ANAYSIS WITH APPICATIONS TO FINANCE AND INSRANCE Slva DED Ph.D. Bucharest nversty of Economc Studes Deartment of Aled Mathematcs; Romanan Academy Insttute
More informationThe Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationNeuro-Adaptive Design - I:
Lecture 36 Neuro-Adaptve Desgn - I: A Robustfyng ool for Dynamc Inverson Desgn Dr. Radhakant Padh Asst. Professor Dept. of Aerospace Engneerng Indan Insttute of Scence - Bangalore Motvaton Perfect system
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationFeature Selection: Part 1
CSE 546: Machne Learnng Lecture 5 Feature Selecton: Part 1 Instructor: Sham Kakade 1 Regresson n the hgh dmensonal settng How do we learn when the number of features d s greater than the sample sze n?
More informationCHARACTERISTICS OF COMPLEX SEPARATION SCHEMES AND AN ERROR OF SEPARATION PRODUCTS OUTPUT DETERMINATION
Górnctwo Geonżynera Rok 0 Zeszyt / 006 Igor Konstantnovch Mladetskj * Petr Ivanovch Plov * Ekaterna Nkolaevna Kobets * Tasya Igorevna Markova * CHARACTERISTICS OF COMPLEX SEPARATION SCHEMES AND AN ERROR
More informationModel Reference Adaptive Temperature Control of the Electromagnetic Oven Process in Manufacturing Process
RECENT ADVANCES n SIGNAL PROCESSING, ROBOTICS and AUTOMATION Model Reference Adatve Temerature Control of the Electromagnetc Oven Process n Manufacturng Process JIRAPHON SRISERTPOL SUPOT PHUNGPHIMAI School
More informationA New Refinement of Jacobi Method for Solution of Linear System Equations AX=b
Int J Contemp Math Scences, Vol 3, 28, no 17, 819-827 A New Refnement of Jacob Method for Soluton of Lnear System Equatons AX=b F Naem Dafchah Department of Mathematcs, Faculty of Scences Unversty of Gulan,
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More informationFuzzy Set Approach to Solve Multi-objective Linear plus Fractional Programming Problem
Internatonal Journal of Oeratons Research Vol.8, o. 3, 5-3 () Internatonal Journal of Oeratons Research Fuzzy Set Aroach to Solve Mult-objectve Lnear lus Fractonal Programmng Problem Sanjay Jan Kalash
More information1 Convex Optimization
Convex Optmzaton We wll consder convex optmzaton problems. Namely, mnmzaton problems where the objectve s convex (we assume no constrants for now). Such problems often arse n machne learnng. For example,
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationNotes on Frequency Estimation in Data Streams
Notes on Frequency Estmaton n Data Streams In (one of) the data streamng model(s), the data s a sequence of arrvals a 1, a 2,..., a m of the form a j = (, v) where s the dentty of the tem and belongs to
More informationA Linear Programming Approach to the Train Timetabling Problem
A Lnear Programmng Aroach to the Tran Tmetablng Problem V. Cacchan, A. Carara, P. Toth DEIS, Unversty of Bologna (Italy) e-mal (vcacchan, acarara, toth @des.unbo.t) The Tran Tmetablng Problem (on a sngle
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationStudy on Demand Response of Residential Power Customer
Journal of Power and Energy Engneerng 06 4-7 Publshed Onlne July 06 n ScRes. htt://www.scr.org/journal/jee htt://dx.do.org/0.46/jee.06.4700 Study on Demand Resonse of Resdental Power Customer Xu Cao Hayong
More information9 Characteristic classes
THEODORE VORONOV DIFFERENTIAL GEOMETRY. Sprng 2009 [under constructon] 9 Characterstc classes 9.1 The frst Chern class of a lne bundle Consder a complex vector bundle E B of rank p. We shall construct
More informationMathematical Preparations
1 Introducton Mathematcal Preparatons The theory of relatvty was developed to explan experments whch studed the propagaton of electromagnetc radaton n movng coordnate systems. Wthn expermental error the
More informationLOW BIAS INTEGRATED PATH ESTIMATORS. James M. Calvin
Proceedngs of the 007 Wnter Smulaton Conference S G Henderson, B Bller, M-H Hseh, J Shortle, J D Tew, and R R Barton, eds LOW BIAS INTEGRATED PATH ESTIMATORS James M Calvn Department of Computer Scence
More informationHongyi Miao, College of Science, Nanjing Forestry University, Nanjing ,China. (Received 20 June 2013, accepted 11 March 2014) I)ϕ (k)
ISSN 1749-3889 (prnt), 1749-3897 (onlne) Internatonal Journal of Nonlnear Scence Vol.17(2014) No.2,pp.188-192 Modfed Block Jacob-Davdson Method for Solvng Large Sparse Egenproblems Hongy Mao, College of
More information4DVAR, according to the name, is a four-dimensional variational method.
4D-Varatonal Data Assmlaton (4D-Var) 4DVAR, accordng to the name, s a four-dmensonal varatonal method. 4D-Var s actually a drect generalzaton of 3D-Var to handle observatons that are dstrbuted n tme. The
More informationAN EXTENDED MPC CONVERGENCE CONDITION
Latn Amercan Aled esearch 36:57-6 (6 AN EXENDED MPC CONVEGENCE CONDIION A. H. GONZÁLEZ and. L. MACHEI Insttuto de Desarrollo ecnológco ara la Industra uímca, INEC (UNL - CONICE alegon@cerde.gov.ar lmarch@cerde.gov.ar
More informationn α j x j = 0 j=1 has a nontrivial solution. Here A is the n k matrix whose jth column is the vector for all t j=0
MODULE 2 Topcs: Lnear ndependence, bass and dmenson We have seen that f n a set of vectors one vector s a lnear combnaton of the remanng vectors n the set then the span of the set s unchanged f that vector
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationA total variation approach
Denosng n dgtal radograhy: A total varaton aroach I. Froso M. Lucchese. A. Borghese htt://as-lab.ds.unm.t / 46 I. Froso, M. Lucchese,. A. Borghese Images are corruted by nose ) When measurement of some
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationOn the Multicriteria Integer Network Flow Problem
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 5, No 2 Sofa 2005 On the Multcrtera Integer Network Flow Problem Vassl Vasslev, Marana Nkolova, Maryana Vassleva Insttute of
More informationA Quadratic Cumulative Production Model for the Material Balance of Abnormally-Pressured Gas Reservoirs F.E. Gonzalez M.S.
Natural as Engneerng A Quadratc Cumulatve Producton Model for the Materal Balance of Abnormally-Pressured as Reservors F.E. onale M.S. Thess (2003) T.A. Blasngame, Texas A&M U. Deartment of Petroleum Engneerng
More information6.3.4 Modified Euler s method of integration
6.3.4 Modfed Euler s method of ntegraton Before dscussng the applcaton of Euler s method for solvng the swng equatons, let us frst revew the basc Euler s method of numercal ntegraton. Let the general from
More informationOn a direct solver for linear least squares problems
ISSN 2066-6594 Ann. Acad. Rom. Sc. Ser. Math. Appl. Vol. 8, No. 2/2016 On a drect solver for lnear least squares problems Constantn Popa Abstract The Null Space (NS) algorthm s a drect solver for lnear
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationA Quadratic Cumulative Production Model for the Material Balance of Abnormally-Pressured Gas Reservoirs F.E. Gonzalez M.S.
Formaton Evaluaton and the Analyss of Reservor Performance A Quadratc Cumulatve Producton Model for the Materal Balance of Abnormally-Pressured as Reservors F.E. onale M.S. Thess (2003) T.A. Blasngame,
More informationPredictive Control of a Boiler-turbine System
Recent Researches n Crcuts and Systems Predctve Control of a Boler-turbne System JAKUB NOVAK, PR CHALUPA aculty of Aled Informatcs omas Bata Unversty n Zln Nam.G.Masaryka 5555, Zln CZCH RPUBLIC jnovak@fa.utb.cz
More informationOn the Connectedness of the Solution Set for the Weak Vector Variational Inequality 1
Journal of Mathematcal Analyss and Alcatons 260, 15 2001 do:10.1006jmaa.2000.7389, avalable onlne at htt:.dealbrary.com on On the Connectedness of the Soluton Set for the Weak Vector Varatonal Inequalty
More informationCombinational Circuit Design
Combnatonal Crcut Desgn Part I: Desgn Procedure and Examles Part II : Arthmetc Crcuts Part III : Multlexer, Decoder, Encoder, Hammng Code Combnatonal Crcuts n nuts Combnatonal Crcuts m oututs A combnatonal
More informationClassification as a Regression Problem
Target varable y C C, C,, ; Classfcaton as a Regresson Problem { }, 3 L C K To treat classfcaton as a regresson problem we should transform the target y nto numercal values; The choce of numercal class
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More informationEEE 241: Linear Systems
EEE : Lnear Systems Summary #: Backpropagaton BACKPROPAGATION The perceptron rule as well as the Wdrow Hoff learnng were desgned to tran sngle layer networks. They suffer from the same dsadvantage: they
More informationSELECTION OF MIXED SAMPLING PLANS WITH CONDITIONAL DOUBLE SAMPLING PLAN AS ATTRIBUTE PLAN INDEXED THROUGH MAPD AND LQL USING IRPD
R. Samath Kumar, R. Vaya Kumar, R. Radhakrshnan /Internatonal Journal Of Comutatonal Engneerng Research / ISSN: 50 005 SELECTION OF MIXED SAMPLING PLANS WITH CONDITIONAL DOUBLE SAMPLING PLAN AS ATTRIBUTE
More informationSolving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions
ISSN 746-7659 England UK Journal of Informaton and Computng Scence Vol. 9 No. 3 4 pp. 69-8 Solvng Fractonal Nonlnear Fredholm Integro-dfferental Equatons va Hybrd of Ratonalzed Haar Functons Yadollah Ordokhan
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationConsistency & Convergence
/9/007 CHE 374 Computatonal Methods n Engneerng Ordnary Dfferental Equatons Consstency, Convergence, Stablty, Stffness and Adaptve and Implct Methods ODE s n MATLAB, etc Consstency & Convergence Consstency
More informationPoisson brackets and canonical transformations
rof O B Wrght Mechancs Notes osson brackets and canoncal transformatons osson Brackets Consder an arbtrary functon f f ( qp t) df f f f q p q p t But q p p where ( qp ) pq q df f f f p q q p t In order
More informationACTM State Calculus Competition Saturday April 30, 2011
ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationThe equation of motion of a dynamical system is given by a set of differential equations. That is (1)
Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence
More information= z 20 z n. (k 20) + 4 z k = 4
Problem Set #7 solutons 7.2.. (a Fnd the coeffcent of z k n (z + z 5 + z 6 + z 7 + 5, k 20. We use the known seres expanson ( n+l ( z l l z n below: (z + z 5 + z 6 + z 7 + 5 (z 5 ( + z + z 2 + z + 5 5
More informationConservative Surrogate Model using Weighted Kriging Variance for Sampling-based RBDO
9 th World Congress on Structural and Multdsclnary Otmzaton June 13-17, 011, Shzuoka, Jaan Conservatve Surrogate Model usng Weghted Krgng Varance for Samlng-based RBDO Lang Zhao 1, K.K. Cho, Ikn Lee 3,
More informationInexact Newton Methods for Inverse Eigenvalue Problems
Inexact Newton Methods for Inverse Egenvalue Problems Zheng-jan Ba Abstract In ths paper, we survey some of the latest development n usng nexact Newton-lke methods for solvng nverse egenvalue problems.
More informationALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION
ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII AL.I. CUZA DIN IAŞI (S.N.) MATEMATICĂ, Tomul LIX, 013, f.1 DOI: 10.478/v10157-01-00-y ALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION BY ION
More informationAN IMPROVED METHOD OF HIERARCHIC ANALYSIS FOR CHOOSING OPTIMAL INFORMATION PROTECTION SYSTEM IN COMPUTER NETWORKS
S. M. Kusemko, Cand. Sc. (Eng.), Ass. Prof.; V. M. Melnchuk AN IMPROVED METHOD OF HIERARCHIC ANALYSIS FOR CHOOSING OPTIMAL INFORMATION PROTECTION SYSTEM IN COMPUTER NETWORKS An mproved herarchc analyss
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationComposite Hypotheses testing
Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter
More informationStanford University CS359G: Graph Partitioning and Expanders Handout 4 Luca Trevisan January 13, 2011
Stanford Unversty CS359G: Graph Parttonng and Expanders Handout 4 Luca Trevsan January 3, 0 Lecture 4 In whch we prove the dffcult drecton of Cheeger s nequalty. As n the past lectures, consder an undrected
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE II LECTURE - GENERAL LINEAR HYPOTHESIS AND ANALYSIS OF VARIANCE Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 3.
More informationPower-sum problem, Bernoulli Numbers and Bernoulli Polynomials.
Power-sum roblem, Bernoull Numbers and Bernoull Polynomals. Arady M. Alt Defnton 1 Power um Problem Fnd the sum n : 1... n where, n N or, usng sum notaton, n n n closed form. Recurrence for n Exercse Usng
More informationNaïve Bayes Classifier
9/8/07 MIST.6060 Busness Intellgence and Data Mnng Naïve Bayes Classfer Termnology Predctors: the attrbutes (varables) whose values are used for redcton and classfcaton. Predctors are also called nut varables,
More informationSL n (F ) Equals its Own Derived Group
Internatonal Journal of Algebra, Vol. 2, 2008, no. 12, 585-594 SL n (F ) Equals ts Own Derved Group Jorge Macel BMCC-The Cty Unversty of New York, CUNY 199 Chambers street, New York, NY 10007, USA macel@cms.nyu.edu
More informationRemarks on the Properties of a Quasi-Fibonacci-like Polynomial Sequence
Remarks on the Propertes of a Quas-Fbonacc-lke Polynomal Sequence Brce Merwne LIU Brooklyn Ilan Wenschelbaum Wesleyan Unversty Abstract Consder the Quas-Fbonacc-lke Polynomal Sequence gven by F 0 = 1,
More informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationComparing two Quantiles: the Burr Type X and Weibull Cases
IOSR Journal of Mathematcs (IOSR-JM) e-issn: 78-578, -ISSN: 39-765X. Volume, Issue 5 Ver. VII (Se. - Oct.06), PP 8-40 www.osrjournals.org Comarng two Quantles: the Burr Tye X and Webull Cases Mohammed
More informationLecture 21: Numerical methods for pricing American type derivatives
Lecture 21: Numercal methods for prcng Amercan type dervatves Xaoguang Wang STAT 598W Aprl 10th, 2014 (STAT 598W) Lecture 21 1 / 26 Outlne 1 Fnte Dfference Method Explct Method Penalty Method (STAT 598W)
More informationSupplementary Material for Spectral Clustering based on the graph p-laplacian
Sulementary Materal for Sectral Clusterng based on the grah -Lalacan Thomas Bühler and Matthas Hen Saarland Unversty, Saarbrücken, Germany {tb,hen}@csun-sbde May 009 Corrected verson, June 00 Abstract
More informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationThe internal structure of natural numbers and one method for the definition of large prime numbers
The nternal structure of natural numbers and one method for the defnton of large prme numbers Emmanul Manousos APM Insttute for the Advancement of Physcs and Mathematcs 3 Poulou str. 53 Athens Greece Abstract
More informationA Bayes Algorithm for the Multitask Pattern Recognition Problem Direct Approach
A Bayes Algorthm for the Multtask Pattern Recognton Problem Drect Approach Edward Puchala Wroclaw Unversty of Technology, Char of Systems and Computer etworks, Wybrzeze Wyspanskego 7, 50-370 Wroclaw, Poland
More informationNTRU Modulo p Flaw. Anas Ibrahim, Alexander Chefranov Computer Engineering Department Eastern Mediterranean University Famagusta, North Cyprus.
Internatonal Journal for Informaton Securty Research (IJISR), Volume 6, Issue 3, Setember 016 TRU Modulo Flaw Anas Ibrahm, Alexander Chefranov Comuter Engneerng Deartment Eastern Medterranean Unversty
More informationAssessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion
Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,
More informationHans-Joachim Kretzschmar and Katja Knobloch
Sulementary Backward Equatons for the Industral Formulaton IAPWS-IF of Water and Steam for Fast Calculatons of Heat Cycles, Bolers, and Steam Turbnes Hans-Joachm Kretzschmar and Katja Knobloch Deartment
More informationBinomial transforms of the modified k-fibonacci-like sequence
Internatonal Journal of Mathematcs and Computer Scence, 14(2019, no. 1, 47 59 M CS Bnomal transforms of the modfed k-fbonacc-lke sequence Youngwoo Kwon Department of mathematcs Korea Unversty Seoul, Republc
More informationChapter 2 A Class of Robust Solution for Linear Bilevel Programming
Chapter 2 A Class of Robust Soluton for Lnear Blevel Programmng Bo Lu, Bo L and Yan L Abstract Under the way of the centralzed decson-makng, the lnear b-level programmng (BLP) whose coeffcents are supposed
More information2.29 Numerical Fluid Mechanics Fall 2011 Lecture 12
REVIEW Lecture 11: 2.29 Numercal Flud Mechancs Fall 2011 Lecture 12 End of (Lnear) Algebrac Systems Gradent Methods Krylov Subspace Methods Precondtonng of Ax=b FINITE DIFFERENCES Classfcaton of Partal
More informationPID Controller Design Based on Second Order Model Approximation by Using Stability Boundary Locus Fitting
PID Controller Desgn Based on Second Order Model Aroxmaton by Usng Stablty Boundary Locus Fttng Furkan Nur Denz, Bars Baykant Alagoz and Nusret Tan Inonu Unversty, Deartment of Electrcal and Electroncs
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationAn Efficient Least-Squares Trilateration Algorithm for Mobile Robot Localization
he IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems October -5, St. Lous, USA An Effcent Least-Squares rlateraton Algorthm for Moble Robot Localzaton Yu Zhou, Member, IEEE Abstract A novel
More information