EXTERNALLY AND INTERNALLY POSITIVE TIME- VARYING LINEAR SYSTEMS
|
|
|
- Amberly Hancock
- 5 years ago
- Views:
Transcription
1 Coyrigh IFAC 5h Trieial World Cogress Barceloa Sai EXTERNALLY AND INTERNALLY POSITIVE TIME- VARYING LINEAR SYSTEMS Tadeusz Kaczorek Warsaw Uiversiy o Techology Faculy o Elecrical Egieerig Isiue o Corol ad Idusrial Elecroics -66 Warszawa Koszykowa 75 Polad e-ail: kaczorek@isewedul Absrac The oios o eerally osiive ad ierally osiive ie-varyig liear syses are iroduced Necessary ad suicie codiios or he eeral osiiviy ad ieral osiiviy o ie-varyig liear syses are esablished Suicie codiios or he reachabiliy o ierally osiive ie-varyig liear syses are reseed INTRODUCTION Roughly seakig osiive syses are syses whose rajecories are eirely i he oegaive orha R wheever he iiial sae ad iu are oegaive Posiive syses arise i odellig o syses i egieerig ecooics social scieces biology edicie ad oher areas (Faria ad Rialdi ; d Alessadro de Sais 994; Bera Neua ad Ser 989; Bera ad Pleos 994; Kaczorek ; Ruchev Jaes 99; Ruchev Jaes 995 The sigle-iu sigle-ouu eerally osiive ad ierally osiive liear ie-ivaria syses have bee ivesigaed i (Faria ad Rialdi ; Bera Neua ad Ser 989; Bera ad Pleos 994 The oios o eerally osiive ad ierally osiive syses have bee eeded or sigular coiuous-ie ad discree-ie ad wodiesioal liear syses i (Kaczorek The reachabiliy ad corollabiliy o sadard ad sigular ierally osiive liear syses have bee aalysed i (Fai Maioe ad Turchsao 99; Klaka 998; Oha Madea ad Kodaa 984; Valcher 996 The oios o weakly osiive discree-ie ad coiuous-ie liear syses have bee iroduced i (Kaczorek ; 998 Recely he osiive wo-diesioal (D liear syses have bee eesively ivesigaed by Forasii ad Valcher (Forasii ad Valcher 997; Valcher 996; 997 ad i (Kaczorek PRELIMINARIES R be he se o q q Le real arices ad R : R The se o q real arices wih oegaive eries will be deoed by R : R Cosider he liear ie-varyig syse &( A( ( B( u( ( ( C( ( D(( u q R ad (a y (b ( & ( d where ( d R is he sae
2 vecor u( R is he iu vecor y( R is he ouu vecor ad A ( B ( C ( D ( are real arices o aroriae diesios wih coiuous-ie eries Soluio ( o he equaio saisyig he iiial codiio ( is give by (Gaacher 959 ( ( ( B( u( d ( where ( is he udaeal ari deied by g ( C( ( B( D( δ ( ad ( or δ is he Dirac iulse (6 Theore The syse ( is eerally osiive i ad oly i g ( R or (7 Proo The ecessiy ollows iediaely ro deiiio ad he deiiio o iulse resose To show he suiciecy le us assue ha (7 holds The ro (5 or u ( R we have ( R or y ( I A( A( A( K where I is he ideiy ari I ( A( A( A( he (3 akes he or (Gaacher 959 A or [ ( (3 e A( (3a The udaeal ari ( diereial equaio saisies he ari ( A( ( & (4 ad he iiial codiio ( I 4 INTERNALLY POSITIVE SYSTEMS Deiiio The syse ( is called ierally osiive i or every R ad all u ( R he sae vecor ( R ad y ( R or Fro coariso o he deiiios ad i ollows ha every ierally osiive syse ( is always eerally osiive Lea The udaeal ari ( R or (8 i ad oly i he o-diagoal eries a i j i j K o he ari A ( saisy he codiio ( a or i j i j K (9 3 EXTERNALLY POSITIVE SYSTEMS Deiiio The syse ( is called eerally osiive i or all u ( R ad zero iiial codiios ( he ouu vecor ( y R or Le g( R be he ari iulse resose o he syse ( I is well-kow ha he ouu vecor y ( o he syse ( wih zero iiial codiios or a iu vecor u ( is give by he orula Proo Firs we shall show ha (9 ilies (8 Le i ( ( z i ( be he i-h cooe o he z ad vecor ( ( ( ( ( ( i zi e a ii i K ( Subsiuio o ( io he equaio (a or u ( yields (Raajczak 967 z & A z ( ( ( ( where y ( g( ( u d (5 where A( a ( [ ] R
3 a ( a Fro ( i ollows ha ( ( i [ ] ( e a ( a ( jj ii zi or i K i Usig ( or ( obai where or i j or i j ( R (3 u ad (3 or ( we z ( ( z (4 ( I A( A( A( K (5 Fro ( i ollows ha i (9 holds he A( R ad by (5 his ilies ( R ad z ( R or ay z R Hece by ( ad (3 ( R or ay R Thereore (9 ilies (8 Necessiy ollows iediaely ro (3a ad he ac ha ( R oly i ( ari or ay A d (Kaczorek 998 is a Mezler Reark I he ari A ( is ideede o ie A ( A [ a ] ad a or i j he A is he Mezler ari (Faria d Rialdi ; Kaczorek ad ( e( A( Theore The syse ( is ierally osiive i ad oly i i he o-diagoal eries o A ( saisy he codiio (9 ii B( R C R D( R or ( Proo Necessiy Le ( u or ad e j The rajecory does o leave he orha A e R oly i ( ( & j ad his ilies (9 For he sae reasos or we have & ( Bu( ad his ilies B( R sice u ( R ay be arbirary Fro (b or u ( we have ( C( R C R y R ad ( sice ay be arbirary Siilarly ro (b or we obai y ( D( u( R ad D( R or sice u ( R ay be arbirary Suiciecy I he codiio (9 is saisied he by Lea (8 holds ad ro ( we obai ( R or ay R ad u ( R sice B( R I C( R ad D( R or he ro (b we obai y ( R sice ( R ad u ( R or 5 REACHABILITY Deiiio 3 The sae ( R o he syse ( is called reachable i ie i here eis a iu vecor u ( R or [ ] which seers he sae o he syse ro o Deiiio 4 I every sae ( R o he syse ( is reachable i ie he he syse is called reachable i ie Deiiio 5 I or every sae ( R here eis > such ha he sae is reachable i ie he he syse ( is called reachable A ari A R is called ooial (or he geeralised eruaio ari i i each row ad i each colu oly oe ery is osiive ad he reaiig eries are zero Theore 3 The ierally osiive syse ( is reachable i ie i he ari ( : ( B( B ( ( R ( T deoes he rasose (6 is a ooial ari
4 The iu vecor which seers he sae vecor o ( ro o is give by u ( B ( ( R ( (7 or ] [ Proo I ( iverse ari ( R is a ooial ari he he R R ad u ( R or ] We shall show ha (7 seers he sae [ o ( ro o Subsiuig (7 io ( or ad we obai ( ( B( B ( ( R ( ( B( B ( ( R ( Thereore i (6 is a ooial ari he he osiive syse ( is reachable i ie Theore 4 The ierally osiive syse ( is reachable i ie i A ( [ a ( a ( a ( ] diag K (8 ( a i ( i K is coiuous-ie ucio ad B( R is a ooial coiuous-ie ari Proo I is well-kow (Gaacher 959 ha i A ( has he or (8 he A A A ad A ( ( ( ( or [ ( ( e A is also diagoal oegaive ari or Hece he ari ( B( R is a ooial ari ad he ari is also a ooial ari The by Theore 3 he syse ( is reachable i ie Reark I he diagoal ari (8 ad B ( are ideede o he ro heores 3 ad 4 we obai he corresodig heores 3 ad 3 i (Kaczorek Siilar resuls ca be obaied or he corollabiliy o ie-varyig liear syses 6 EXAMPLE Cosider he syse ( wih ad A( e ( B (9 By heore 4 he syse is reachable i ie Thereore here eis iu u ( which seers he sae o he syse ro o i ie Usig (3a (6 ad (7 we obai ( e A( e ( ( e ( ( R( ( B( B ( ( R 4 - ( e e ( e - ( B ( ( R ( u ( ( B( B ( ( R T ( B( [ ( B( ] 4 e e ( e e - (
5 7 CONCLUDING REMARKS The oios o eerally osiive ad ierally osiive ie-varyig liear syses have bee iroduced Necessary ad suicie codiios or he eeral ad ieral osiiviy o ie-varyig liear syses have bee esablished The coce o reachabiliy has bee eeded or ierally osiive ie-varyig liear syses ad suicie codiios or he reachabiliy o ierally osiive ievaryig liear syses have bee esablished Wih sligh odiicaios he cosideraio ca be eeded or discree-ie varyig liear syses A eesio o hese cosideraios or D liear syses wih variable coeicies is also ossible A oe roble is a eesio o hese cosideraios or sigular ie-varyig liear syses REFERENCES P d'alessadro E de Sais (994 Posiivess o dyaic syses wih o osiive coeicies arices IEEE Tras Auo Cor vol AC A Berra M Neua ad R Ser (989 Noegaive Marices i Dyaic Syses New York A Bera ad RJ Pleos (994 Noegaive Marices i Maheaical Scieces SIAM Press Philadelhia MP Fai B Maioe ad B Turchsao (99 Corollabiliy o uli-iu osiive discreeie syses I J Corol vol 5 No L Faria ad S Rialdi ( Posiive Liear Syses Theory ad Alicaios J Wiley New York E Forasii ad ME Valcher (997 Rece develoes i D osiive syses heory J o Alied Mah ad Couer Sciece 7-3 FR Gaacher (959 The heory o Marices Chelsea New York T Kaczorek ( Posiive D ad D Syses Sriger-Verlag T Kaczorek (998 Weakly osiive coiuousie liear syses Bull Pol Acad Tech Sci vol 46 No T Kaczorek (998 Posiive descrior discree-ie liear syses Probles o Noliear Aalysis i Egieerig Syses No ( J Klaka (998 Cosraied corollabiliy o osiive D syses Bull Pol Acad Tech Sci vol 46 No 93- Y Oha H Madea ad S Kodaa (984 Reachabiliy observabiliy ad realizabiliy o coiuous-ie osiive syses SIAM J Corol ad Oiisaio vol No 7-8 VG Ruchev ad DJG Jaes (995 Secral Characerisaio ad ole assige or osiive liear discree-ie syses I J Syses Sci vol 6 No 95-3 Z Raajczak (967 O soluios o he syse o hoogeous diereial liear equaios Zeszyy Naukowe Poliechiki Pozaskiej Maeayka Nr (i Polish VG Ruchev DJG Jaes (99 The role o oegaive arices i discree-ie aheaical odellig I J Mah Educ Sci Techol vol 69-8 ME Valcher (996 Corollabiliy ad reachabiliy crieria or discree-ie osiive syses I J Corol vol ME Valcher (997 O he ieral sabiliy ad asyoic behaviour o D osiive syses IEEE Tras Cir ad Sys Par I vol
VISCOSITY APPROXIMATION TO COMMON FIXED POINTS OF kn- LIPSCHITZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES
Joral o Maheaical Scieces: Advaces ad Alicaios Vole Nber 9 Pages -35 VISCOSIY APPROXIMAION O COMMON FIXED POINS OF - LIPSCHIZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES HONGLIANG ZUO ad MIN YANG Deare o
Guaranteed cost finite-time control for positive switched delay systems with ADT
Ieraioal Joural o dvaced Research i Comuer Egieerig & echology (IJRCE) Volume 6 Issue 9 Seember 7 ISSN: 78 33 Guaraeed cos iie-ime corol or osiive swiched delay sysems wih D Xiagyag Cao Migliag Ma Hao
EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D. S. Palimkar
Ieraioal Joural of Scieific ad Research Publicaios, Volue 2, Issue 7, July 22 ISSN 225-353 EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D S Palikar Depare of Maheaics, Vasarao Naik College, Naded
ASYMPTOTIC STABILITY OF POSITIVE FRACTIONAL 2D LINEAR SYSTEMS WITH DELAYS
ASYMPTOTIC STABILITY OF POSITIVE FRACTIONAL D LINEAR SYSTEMS WITH DELAYS Tadeusz Kaczorek Faculty of Electrical Egieerig Bialystok Techical Uiversity Wiejska 45D 5-35 Bialystok Polad kaczorek@isep.pw.edu.pl
E will be denoted by n
JASEM ISSN 9-8362 All rigs reserved Full-ex Available Olie a p:// wwwbiolieorgbr/ja J Appl Sci Eviro Mg 25 Vol 9 3) 3-36 Corollabiliy ad Null Corollabiliy of Liear Syses * DAVIES, I; 2 JACKREECE, P Depare
In this section we will study periodic signals in terms of their frequency f t is said to be periodic if (4.1)
Fourier Series Iroducio I his secio we will sudy periodic sigals i ers o heir requecy is said o be periodic i coe Reid ha a sigal ( ) ( ) ( ) () or every, where is a uber Fro his deiiio i ollows ha ( )
CHARACTERIZATIONS OF THE NON-UNIFORM IN TIME ISS PROPERTY AND APPLICATIONS
CHARACTERIZATIONS OF THE NON-UNIFORM IN TIME ISS PROPERTY AND APPLICATIONS I. Karafyllis ad J. Tsiias Depare of Maheaics, Naioal Techical Uiversiy of Ahes, Zografou Capus 578, Ahes, Greece Eail: jsi@ceral.ua.gr.
Linear System Theory
Naioal Tsig Hua Uiversiy Dearme of Power Mechaical Egieerig Mid-Term Eamiaio 3 November 11.5 Hours Liear Sysem Theory (Secio B o Secio E) [11PME 51] This aer coais eigh quesios You may aswer he quesios
EXTERNALLY AND INTERNALLY POSITIVE TIME-VARYING LINEAR SYSTEMS
Int. J. Appl. Math. Comput. Sci., 1, Vol.11, No.4, 957 964 EXTERNALLY AND INTERNALLY POSITIVE TIME-VARYING LINEAR SYSTEMS Tadeusz KACZOREK The notions of externally and internally positive time-varying
A TAUBERIAN THEOREM FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY
U.P.B. Sci. Bull., Series A, Vol. 78, Iss. 2, 206 ISSN 223-7027 A TAUBERIAN THEOREM FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY İbrahim Çaak I his paper we obai a Tauberia codiio i erms of he weighed classical
MODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecure 9, Sae Space Repreeaio Emam Fahy Deparme of Elecrical ad Corol Egieerig email: emfmz@aa.edu hp://www.aa.edu/cv.php?dip_ui=346&er=6855 Trafer Fucio Limiaio TF = O/P I/P ZIC
Comparison between Fourier and Corrected Fourier Series Methods
Malaysia Joural of Mahemaical Scieces 7(): 73-8 (13) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: hp://eispem.upm.edu.my/oural Compariso bewee Fourier ad Correced Fourier Series Mehods 1
LOCALLY POSITIVE NONLINEAR SYSTEMS
Int. J. Appl. Math. Comput. Sci. 3 Vol. 3 No. 4 55 59 LOCALLY POSITIVE NONLINEAR SYSTEMS TADEUSZ KACZOREK Institute of Control Industrial Electronics Warsaw University of Technology ul. Koszykowa 75 66
Fractional Fourier Series with Applications
Aeric Jourl o Couiol d Alied Mheics 4, 4(6): 87-9 DOI: 593/jjc446 Frciol Fourier Series wih Alicios Abu Hd I, Khlil R * Uiversiy o Jord, Jord Absrc I his er, we iroduce coorble rciol Fourier series We
FIXED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE
Mohia & Samaa, Vol. 1, No. II, December, 016, pp 34-49. ORIGINAL RESEARCH ARTICLE OPEN ACCESS FIED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE 1 Mohia S. *, Samaa T. K. 1 Deparme of Mahemaics, Sudhir Memorial
ODEs II, Supplement to Lectures 6 & 7: The Jordan Normal Form: Solving Autonomous, Homogeneous Linear Systems. April 2, 2003
ODEs II, Suppleme o Lecures 6 & 7: The Jorda Normal Form: Solvig Auoomous, Homogeeous Liear Sysems April 2, 23 I his oe, we describe he Jorda ormal form of a marix ad use i o solve a geeral homogeeous
Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space via Compatible Mappings of Type (K)
Ieraioal Joural of ahemaics Treds ad Techology (IJTT) Volume 35 umber 4- July 016 Commo Fixed Poi Theorem i Iuiioisic Fuzzy eric Sace via Comaible aigs of Tye (K) Dr. Ramaa Reddy Assisa Professor De. of
SUMMATION OF INFINITE SERIES REVISITED
SUMMATION OF INFINITE SERIES REVISITED I several aricles over he las decade o his web page we have show how o sum cerai iiie series icludig he geomeric series. We wa here o eed his discussio o he geeral
Sliding Mode Control for Robust Stabilization of Uncertain Input-Delay Systems
98 CSE: he siue of Corol, uoaio ad Syses Egieers, KORE Vol, No, Jue, Slidig Mode Corol for Robus Sabilizaio of Ucerai pu-delay Syses Youg-Hoo Roh ad Ju-Ho Oh bsrac: his paper is cocered wih a delay-depede
Journal of Quality Measurement and Analysis JQMA 12(1-2) 2016, Jurnal Pengukuran Kualiti dan Analisis
Joural o Qualiy Measureme ad alysis JQM - 6 89-95 Jural Peguura Kualii da alisis SOME RESLTS FOR THE LSS OF LYTI FTIOS IVOLVIG SLGE IFFERETIL OPERTOR Beberapa Sia uu Kelas Fugsi alisis Melibaa Pegoperasi
Stability of fractional positive nonlinear systems
Archives of Cotrol Scieces Volume 5(LXI), 15 No. 4, pages 491 496 Stability of fractioal positive oliear systems TADEUSZ KACZOREK The coditios for positivity ad stability of a class of fractioal oliear
Classifications of Ordered Semigroups in Terms of Bipolar Fuzzy Bi-Ideals
J l Eviro iol Sci 7034-4 07 07 TeRoad Publicaio ISSN: 090-474 Joural o lied Eviromeal ad iological Scieces wwweroadcom Classiicaios o Ordered Semigrous i Terms o iolar Fu i-ideals Tariq Mahmood M Ibrar
Common Solution of Nonlinear Functional Equations via Iterations
Proeedigs of he World Cogress o Egieerig Vol I WCE July 6-8 Lodo U.K. Coo Soluio of Noliear Fuioal Equaios via Ieraios Muhaad Arshad Akbar Aza ad Pasquale Vero Absra We obai oo fied ois ad ois of oiidee
A quadratic convergence method for the management equilibrium model
(IJACSA Ieraioal Joural of Advaced Copuer Sciece ad Applicaios Vol No 9 03 A quadraic covergece ehod for he aagee equilibriu odel Jiayi Zhag Feixia School Liyi Uiversiy Feixia Shadog PRChia Absrac i his
BE.430 Tutorial: Linear Operator Theory and Eigenfunction Expansion
BE.43 Tuorial: Liear Operaor Theory ad Eigefucio Expasio (adaped fro Douglas Lauffeburger) 9//4 Moivaig proble I class, we ecouered parial differeial equaios describig rasie syses wih cheical diffusio.
State and Parameter Estimation of The Lorenz System In Existence of Colored Noise
Sae ad Parameer Esimaio of he Lorez Sysem I Eisece of Colored Noise Mozhga Mombeii a Hamid Khaloozadeh b a Elecrical Corol ad Sysem Egieerig Researcher of Isiue for Research i Fudameal Scieces (IPM ehra
Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
Basic Results in Functional Analysis
Preared by: F.. ewis Udaed: Suday, Augus 7, 4 Basic Resuls i Fucioal Aalysis f ( ): X Y is coiuous o X if X, (, ) z f( z) f( ) f ( ): X Y is uiformly coiuous o X if i is coiuous ad ( ) does o deed o. f
Application of Fixed Point Theorem of Convex-power Operators to Nonlinear Volterra Type Integral Equations
Ieraioal Mahemaical Forum, Vol 9, 4, o 9, 47-47 HIKRI Ld, wwwm-hikaricom h://dxdoiorg/988/imf4333 licaio of Fixed Poi Theorem of Covex-ower Oeraors o Noliear Volerra Tye Iegral Equaios Ya Chao-dog Huaiyi
EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO-POINT BOUNDARY CONDITIONS
Advaced Mahemaical Models & Applicaios Vol3, No, 8, pp54-6 EXISENCE AND UNIQUENESS OF SOLUIONS FOR NONLINEAR FRACIONAL DIFFERENIAL EQUAIONS WIH WO-OIN BOUNDARY CONDIIONS YA Shariov *, FM Zeyally, SM Zeyally
Bernstein Direct Method for Solving. Variational Problems
Ieraioal Maheaical Foru, 5,, o. 48, 35-37 Bersei Direc Mehod for Solvig Variaioal Probles Sadeep Dixi*, Viee K. Sigh**, Ai K. Sigh*, O P. Sigh* *Depare of Applied Maheaics, Isiue of echology, Baaras Hidu
Approximating Solutions for Ginzburg Landau Equation by HPM and ADM
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 193-9466 Vol. 5, No. Issue (December 1), pp. 575 584 (Previously, Vol. 5, Issue 1, pp. 167 1681) Applicaios ad Applied Mahemaics: A Ieraioal Joural
Meromorphic Functions Sharing Three Values *
Alied Maheaic 11 718-74 doi:1436/a11695 Pulihed Olie Jue 11 (h://wwwscirporg/joural/a) Meroorhic Fucio Sharig Three Value * Arac Chagju Li Liei Wag School o Maheaical Sciece Ocea Uiveriy o Chia Qigdao
Actuarial Society of India
Acuarial Sociey of Idia EXAMINAIONS Jue 5 C4 (3) Models oal Marks - 5 Idicaive Soluio Q. (i) a) Le U deoe he process described by 3 ad V deoe he process described by 4. he 5 e 5 PU [ ] PV [ ] ( e ).538!
λiv Av = 0 or ( λi Av ) = 0. In order for a vector v to be an eigenvector, it must be in the kernel of λi
Liear lgebra Lecure #9 Noes This week s lecure focuses o wha migh be called he srucural aalysis of liear rasformaios Wha are he irisic properies of a liear rasformaio? re here ay fixed direcios? The discussio
Some Properties of Semi-E-Convex Function and Semi-E-Convex Programming*
The Eighh Ieraioal Symposium o Operaios esearch ad Is Applicaios (ISOA 9) Zhagjiajie Chia Sepember 2 22 29 Copyrigh 29 OSC & APOC pp 33 39 Some Properies of Semi-E-Covex Fucio ad Semi-E-Covex Programmig*
Reduced Differential Transform Method for Solving Klein Gordon Equations
Proceedigs of he World Cogress o Egieerig 0 Vol I WCE 0, July - 8, 0, Lodo, UK Reduced Differeial Trasfor Mehod for Solvig Klei Gordo Equaios Yıldıray Kesi, Sea Servi ad Gali Ouraç Absrac Reduced differeial
The Importance of Ordering the Number of Lattice Points Inside a Rational Polyhedron Using Generating Functions
Ieraioal Joural of Copuer Sciece ad Elecroics Egieerig (IJCSEE Volue Issue ( ISSN 48 (Olie he Iporace of Orderig he Nuber of Laice ois Iside a Raioal olyhedro Usig Geeraig Fucios Halil Sopce Absrac I pure
The Solution of the One Species Lotka-Volterra Equation Using Variational Iteration Method ABSTRACT INTRODUCTION
Malaysia Joural of Mahemaical Scieces 2(2): 55-6 (28) The Soluio of he Oe Species Loka-Volerra Equaio Usig Variaioal Ieraio Mehod B. Baiha, M.S.M. Noorai, I. Hashim School of Mahemaical Scieces, Uiversii
Lecture 15: Three-tank Mixing and Lead Poisoning
Lecure 15: Three-ak Miig ad Lead Poisoig Eigevalues ad eigevecors will be used o fid he soluio of a sysem for ukow fucios ha saisfy differeial equaios The ukow fucios will be wrie as a 1 colum vecor [
Online Supplement to Reactive Tabu Search in a Team-Learning Problem
Olie Suppleme o Reacive abu Search i a eam-learig Problem Yueli She School of Ieraioal Busiess Admiisraio, Shaghai Uiversiy of Fiace ad Ecoomics, Shaghai 00433, People s Republic of Chia, she.yueli@mail.shufe.edu.c
State-Space Model. In general, the dynamic equations of a lumped-parameter continuous system may be represented by
Sae-Space Model I geeral, he dyaic equaio of a luped-paraeer coiuou ye ay be repreeed by x & f x, u, y g x, u, ae equaio oupu equaio where f ad g are oliear vecor-valued fucio Uig a liearized echique,
Calculus Limits. Limit of a function.. 1. One-Sided Limits...1. Infinite limits 2. Vertical Asymptotes...3. Calculating Limits Using the Limit Laws.
Limi of a fucio.. Oe-Sided..... Ifiie limis Verical Asympoes... Calculaig Usig he Limi Laws.5 The Squeeze Theorem.6 The Precise Defiiio of a Limi......7 Coiuiy.8 Iermediae Value Theorem..9 Refereces..
L-functions and Class Numbers
L-fucios ad Class Numbers Sude Number Theory Semiar S. M.-C. 4 Sepember 05 We follow Romyar Sharifi s Noes o Iwasawa Theory, wih some help from Neukirch s Algebraic Number Theory. L-fucios of Dirichle
Samuel Sindayigaya 1, Nyongesa L. Kennedy 2, Adu A.M. Wasike 3
Ieraioal Joural of Saisics ad Aalysis. ISSN 48-9959 Volume 6, Number (6, pp. -8 Research Idia Publicaios hp://www.ripublicaio.com The Populaio Mea ad is Variace i he Presece of Geocide for a Simple Birh-Deah-
Inference of the Second Order Autoregressive. Model with Unit Roots
Ieraioal Mahemaical Forum Vol. 6 0 o. 5 595-604 Iferece of he Secod Order Auoregressive Model wih Ui Roos Ahmed H. Youssef Professor of Applied Saisics ad Ecoomerics Isiue of Saisical Sudies ad Research
1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
Notes 03 largely plagiarized by %khc
1 1 Discree-Time Covoluio Noes 03 largely plagiarized by %khc Le s begi our discussio of covoluio i discree-ime, sice life is somewha easier i ha domai. We sar wih a sigal x[] ha will be he ipu io our
Research Article A Generalized Nonlinear Sum-Difference Inequality of Product Form
Joural of Applied Mahemaics Volume 03, Aricle ID 47585, 7 pages hp://dx.doi.org/0.55/03/47585 Research Aricle A Geeralized Noliear Sum-Differece Iequaliy of Produc Form YogZhou Qi ad Wu-Sheg Wag School
Energy Density / Energy Flux / Total Energy in 1D. Key Mathematics: density, flux, and the continuity equation.
ecure Phys 375 Eergy Desiy / Eergy Flu / oal Eergy i D Overview ad Moivaio: Fro your sudy of waves i iroducory physics you should be aware ha waves ca raspor eergy fro oe place o aoher cosider he geeraio
An interesting result about subset sums. Nitu Kitchloo. Lior Pachter. November 27, Abstract
A ieresig resul abou subse sums Niu Kichloo Lior Pacher November 27, 1993 Absrac We cosider he problem of deermiig he umber of subses B f1; 2; : : :; g such ha P b2b b k mod, where k is a residue class
INVESTMENT PROJECT EFFICIENCY EVALUATION
368 Miljeko Crjac Domiika Crjac INVESTMENT PROJECT EFFICIENCY EVALUATION Miljeko Crjac Professor Faculy of Ecoomics Drsc Domiika Crjac Faculy of Elecrical Egieerig Osijek Summary Fiacial efficiecy of ivesme
ECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
Decoupling Zeros of Positive Discrete-Time Linear Systems*
Circuits ad Systems,,, 4-48 doi:.436/cs..7 Published Olie October (http://www.scirp.org/oural/cs) Decouplig Zeros of Positive Discrete-Time Liear Systems* bstract Tadeusz Kaczorek Faculty of Electrical
A NEW NUMERICAL TECHNIQUE FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
A NEW NUMERICAL TECHNIQUE FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS Oer Aca *, Duiru Baleau,3 Depare of Maheaics, Faculy of Ar ad Sciece, Siir Uiversiy, 56, Siir, Turey Depare of Maheaics ad
Prakash Chandra Rautaray 1, Ellipse 2
Prakash Chadra Rauara, Ellise / Ieraioal Joural of Egieerig Research ad Alicaios (IJERA) ISSN: 48-96 www.ijera.com Vol. 3, Issue, Jauar -Februar 3,.36-337 Degree Of Aroimaio Of Fucios B Modified Parial
Existence Of Solutions For Nonlinear Fractional Differential Equation With Integral Boundary Conditions
Reserch Ivey: Ieriol Jourl Of Egieerig Ad Sciece Vol., Issue (April 3), Pp 8- Iss(e): 78-47, Iss(p):39-6483, Www.Reserchivey.Com Exisece Of Soluios For Nolier Frciol Differeil Equio Wih Iegrl Boudry Codiios,
TAKA KUSANO. laculty of Science Hrosh tlnlersty 1982) (n-l) + + Pn(t)x 0, (n-l) + + Pn(t)Y f(t,y), XR R are continuous functions.
Iera. J. Mah. & Mah. Si. Vol. 6 No. 3 (1983) 559-566 559 ASYMPTOTIC RELATIOHIPS BETWEEN TWO HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS TAKA KUSANO laculy of Sciece Hrosh llersy 1982) ABSTRACT. Some asympoic
Spectrum of The Direct Sum of Operators. 1. Introduction
Specu of The Diec Su of Opeaos by E.OTKUN ÇEVİK ad Z.I.ISMILOV Kaadeiz Techical Uivesiy, Faculy of Scieces, Depae of Maheaics 6080 Tabzo, TURKEY e-ail adess : zaeddi@yahoo.co bsac: I his wok, a coecio
ECE 350 Matlab-Based Project #3
ECE 350 Malab-Based Projec #3 Due Dae: Nov. 26, 2008 Read he aached Malab uorial ad read he help files abou fucio i, subs, sem, bar, sum, aa2. he wrie a sigle Malab M file o complee he followig ask for
A Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix
4h Ieraioal Coferece o Sesors, Mecharoics ad Auomaio (ICSMA 06) A Complex Neural Newor Algorihm for Compuig he Larges eal Par Eigevalue ad he correspodig Eigevecor of a eal Marix HANG AN, a, XUESONG LIANG,
Math 6710, Fall 2016 Final Exam Solutions
Mah 67, Fall 6 Fial Exam Soluios. Firs, a sude poied ou a suble hig: if P (X i p >, he X + + X (X + + X / ( evaluaes o / wih probabiliy p >. This is roublesome because a radom variable is supposed o be
CLOSED FORM EVALUATION OF RESTRICTED SUMS CONTAINING SQUARES OF FIBONOMIAL COEFFICIENTS
PB Sci Bull, Series A, Vol 78, Iss 4, 2016 ISSN 1223-7027 CLOSED FORM EVALATION OF RESTRICTED SMS CONTAINING SQARES OF FIBONOMIAL COEFFICIENTS Emrah Kılıc 1, Helmu Prodiger 2 We give a sysemaic approach
K3 p K2 p Kp 0 p 2 p 3 p
Mah 80-00 Mo Ar 0 Chaer 9 Fourier Series ad alicaios o differeial equaios (ad arial differeial equaios) 9.-9. Fourier series defiiio ad covergece. The idea of Fourier series is relaed o he liear algebra
On Stability of Quintic Functional Equations in Random Normed Spaces
J. COMPUTATIONAL ANALYSIS AND APPLICATIONS, VOL. 3, NO.4, 07, COPYRIGHT 07 EUDOXUS PRESS, LLC O Sabiliy of Quiic Fucioal Equaios i Radom Normed Spaces Afrah A.N. Abdou, Y. J. Cho,,, Liaqa A. Kha ad S.
On The Generalized Type and Generalized Lower Type of Entire Function in Several Complex Variables With Index Pair (p, q)
O he eeralized ye ad eeralized Lower ye of Eire Fucio i Several Comlex Variables Wih Idex Pair, Aima Abdali Jaffar*, Mushaq Shakir A Hussei Dearme of Mahemaics, College of sciece, Al-Musasiriyah Uiversiy,
MAZUR-ORLICZ THEOREM IN CONCRETE SPACES AND INVERSE PROBLEMS RELATED TO THE MOMENT PROBLEM
U.P.B. Sci. Bull. Series Vol. 79 Iss. 3 7 ISSN 3-77 ZUR-ORLICZ THEORE IN CONCRETE SPCES ND INVERSE PROBLES RELTED TO THE OENT PROBLE Ocav OLTENU I he firs ar of his wor we derive soe ew alicaios of a versio
ABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES
Available olie a h://sciog Egieeig Maheaics Lees 2 (23) No 56-66 ISSN 249-9337 ABSLUE INDEED SUMMABILIY FACR F AN INFINIE SERIES USING QUASI-F-WER INCREASING SEQUENCES SKAIKRAY * RKJAI 2 UKMISRA 3 NCSAH
Math-303 Chapter 7 Linear systems of ODE November 16, Chapter 7. Systems of 1 st Order Linear Differential Equations.
Mah-33 Chaper 7 Liear sysems of ODE November 6, 7 Chaper 7 Sysems of s Order Liear Differeial Equaios saddle poi λ >, λ < Mah-33 Chaper 7 Liear sysems of ODE November 6, 7 Mah-33 Chaper 7 Liear sysems
Solutions to selected problems from the midterm exam Math 222 Winter 2015
Soluios o seleced problems from he miderm eam Mah Wier 5. Derive he Maclauri series for he followig fucios. (cf. Pracice Problem 4 log( + (a L( d. Soluio: We have he Maclauri series log( + + 3 3 4 4 +...,
Procedia - Social and Behavioral Sciences 230 ( 2016 ) Joint Probability Distribution and the Minimum of a Set of Normalized Random Variables
Available olie a wwwsciecedireccom ScieceDirec Procedia - Social ad Behavioral Scieces 30 ( 016 ) 35 39 3 rd Ieraioal Coferece o New Challeges i Maageme ad Orgaizaio: Orgaizaio ad Leadership, May 016,
New Class of Estimators of Population Mean. DECISION SCIENCES INSTITUTE New Class of Estimators of Population Mean Utilizing Median of Study Variable
New lass of Esiaors of Poulaio Mea DEISION SIENES INSTITUTE New lass of Esiaors of Poulaio Mea Uilizig Media of Sudy Variable S.K. Yadav Dr. RML Avadh Uiversiy drskysas@gail.co Diesh K. Shara Uiversiy
On Another Type of Transform Called Rangaig Transform
Ieraioal Joural of Parial Differeial Equaios ad Applicaios, 7, Vol 5, No, 4-48 Available olie a hp://pubssciepubcom/ijpdea/5//6 Sciece ad Educaio Publishig DOI:69/ijpdea-5--6 O Aoher Type of Trasform Called
A note on Generalized Hermite polynomials
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND INFORMATICS Volue 8 14 A oe o Geeralized Herie poloials Cleee Cesarao Absrac B sarig fro he geeral heor of he oevariable Herie poloials we will iroduce
BIBECHANA A Multidisciplinary Journal of Science, Technology and Mathematics
Biod Prasad Dhaal / BIBCHANA 9 (3 5-58 : BMHSS,.5 (Olie Publicaio: Nov., BIBCHANA A Mulidisciliary Joural of Sciece, Techology ad Mahemaics ISSN 9-76 (olie Joural homeage: h://ejol.ifo/idex.h/bibchana
A note on diagonalization of integral quadratic forms modulo p m
NNTDM 7 ( 3-36 A noe on diagonalizaion of inegral quadraic fors odulo Ali H Hakai Dearen of Maheaics King Khalid Universiy POo 94 Abha Posal Code: 643 Saudi Arabia E-ail: aalhakai@kkuedusa Absrac: Le be
arxiv: v1 [math.fa] 12 Jul 2012
![arxiv: v1 [math.fa] 12 Jul 2012](/thumbs/89/97554371.jpg "arxiv: v1 [math.fa] 12 Jul 2012")
AN EXTENSION OF THE LÖWNER HEINZ INEQUALITY MOHAMMAD SAL MOSLEHIAN AND HAMED NAJAFI arxiv:27.2864v [ah.fa] 2 Jul 22 Absrac. We exend he celebraed Löwner Heinz inequaliy by showing ha if A, B are Hilber
MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES. Boundary Value Problem for the Higher Order Equation with Fractional Derivative
Malaysia Joural of Maheaical Scieces 7(): 3-7 (3) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural hoepage: hp://eispe.up.edu.y/joural Boudary Value Proble for he Higher Order Equaio wih Fracioal Derivaive
Economics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017
Deparme of Ecoomics The Ohio Sae Uiversiy Ecoomics 8723 Macroecoomic Theory Problem Se 2 Professor Sajay Chugh Sprig 207 Labor Icome Taxes, Nash-Bargaied Wages, ad Proporioally-Bargaied Wages. I a ecoomy
Available online at J. Math. Comput. Sci. 4 (2014), No. 4, ISSN:
Available olie a hp://sci.org J. Mah. Compu. Sci. 4 (2014), No. 4, 716-727 ISSN: 1927-5307 ON ITERATIVE TECHNIQUES FOR NUMERICAL SOLUTIONS OF LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS S.O. EDEKI *, A.A.
Extended Laguerre Polynomials
I J Coemp Mah Scieces, Vol 7, 1, o, 189 194 Exeded Laguerre Polyomials Ada Kha Naioal College of Busiess Admiisraio ad Ecoomics Gulberg-III, Lahore, Pakisa adakhaariq@gmailcom G M Habibullah Naioal College
David Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
The Eigen Function of Linear Systems
1/25/211 The Eige Fucio of Liear Sysems.doc 1/7 The Eige Fucio of Liear Sysems Recall ha ha we ca express (expad) a ime-limied sigal wih a weighed summaio of basis fucios: v ( ) a ψ ( ) = where v ( ) =
Robust Dynamic Output Feedback Second-Order Sliding Mode Controller for Uncertain Systems
Ieraioal Joural of Corol, Auoaio, ad Syses (3 (5:878-884 DOI.7/s555--7-9 ISSN:598-6446 eissn:5-49 hp://www.spriger.co/555 Robus Dyaic Oupu Feedbac Secod-Order Slidig Mode Coroller for cerai Syses Jeag-Li
Moment Generating Function
1 Mome Geeraig Fucio m h mome m m m E[ ] x f ( x) dx m h ceral mome m m m E[( ) ] ( ) ( x ) f ( x) dx Mome Geeraig Fucio For a real, M () E[ e ] e k x k e p ( x ) discree x k e f ( x) dx coiuous Example
APPROXIMATE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH UNCERTAINTY
APPROXIMATE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH UNCERTAINTY ZHEN-GUO DENG ad GUO-CHENG WU 2, 3 * School of Mahemaics ad Iformaio Sciece, Guagi Uiversiy, Naig 534, PR Chia 2 Key Laboraory
A Note on Random k-sat for Moderately Growing k
A Noe o Radom k-sat for Moderaely Growig k Ju Liu LMIB ad School of Mahemaics ad Sysems Sciece, Beihag Uiversiy, Beijig, 100191, P.R. Chia juliu@smss.buaa.edu.c Zogsheg Gao LMIB ad School of Mahemaics
Numerical methods for ordinary differential equations
A Maser Scieiic copuig Nuerical ehos or oriar iereial equaios Oriar iereial equaios Le be a ocio o oe variable havig successive erivaives. A h orer oriar iereial equaio ODE is a equaio o he or: A s orer
Hybrid System Modeling Using Impulsive Differential Equations
Hybrid Syse Modelig Usig Ipulsive Differeial Equaios ENDRA JOELIANO Depare of Egieerig Physics Isiu eologi Badug Jl Gaesha 1, Badug 413 INDONESIA Absrac: Hybrid syses have eerged as a rapidly expadig field
Hedi LABIADH. ALMAS, 1135 Naassan TUNISIA Micahel DADA, O. Bamidele AWOJOYOGBE
DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES,8 reg P75 a 797 ISSN 87-7 h://wwwewaru/oural h://wwwahsburu/user/diffoural e-ail: odiff@ailru Alicaios o hysics, elecroechics, ad elecroics Esablishe of a ordiary
Inverse Heat Conduction Problem in a Semi-Infinite Circular Plate and its Thermal Deflection by Quasi-Static Approach
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 93-9466 Vol. 5 Issue ue pp. 7 Previously Vol. 5 No. Applicaios ad Applied Mahemaics: A Ieraioal oural AAM Iverse Hea Coducio Problem i a Semi-Ifiie
Fourier transform. Continuous-time Fourier transform (CTFT) ω ω
Fourier rasform Coiuous-ime Fourier rasform (CTFT P. Deoe ( he Fourier rasform of he sigal x(. Deermie he followig values, wihou compuig (. a (0 b ( d c ( si d ( d d e iverse Fourier rasform for Re { (
International Journal of Mathematical Archive-4(9), 2013, 1-5 Available online through ISSN
Iteratioal Joural o Matheatical Archive-4(9), 03, -5 Available olie through www.ija.io ISSN 9 5046 THE CUBIC RATE OF CONVERGENCE OF GENERALIZED EXTRAPOLATED NEWTON RAPHSON METHOD FOR SOLVING NONLINEAR
Approximate Solutions for the Coupled Nonlinear. Equations Using the Homotopy Analysis Method
Applied Maheaical Scieces, Vol. 5,, o. 37, 89-86 Approxiae Solios for he Copled Noliear Eqaios Usig he Hooopy Aalysis Mehod Spig Qia a, b a Facly of Sciece, Jiags Uiersiy, Zhejiag, Jiags 3, Chia b Depare
Suggested Solution for Pure Mathematics 2011 By Y.K. Ng (last update: 8/4/2011) Paper I. (b) (c)
per I. Le α 7 d β 7. The α d β re he roos o he equio, such h α α, β β, --- α β d αβ. For, α β For, α β α β αβ 66 The seme is rue or,. ssume Cosider, α β d α β y deiiio α α α α β or some posiive ieer.
NEWTON METHOD FOR DETERMINING THE OPTIMAL REPLENISHMENT POLICY FOR EPQ MODEL WITH PRESENT VALUE
Yugoslav Joural of Operaios Research 8 (2008, Number, 53-6 DOI: 02298/YUJOR080053W NEWTON METHOD FOR DETERMINING THE OPTIMAL REPLENISHMENT POLICY FOR EPQ MODEL WITH PRESENT VALUE Jeff Kuo-Jug WU, Hsui-Li
Fermat Numbers in Multinomial Coefficients
1 3 47 6 3 11 Joural of Ieger Sequeces, Vol. 17 (014, Aricle 14.3. Ferma Numbers i Muliomial Coefficies Shae Cher Deparme of Mahemaics Zhejiag Uiversiy Hagzhou, 31007 Chia chexiaohag9@gmail.com Absrac
Convergence Analysis of Multi-innovation Learning Algorithm Based on PID Neural Network
Sesors & rasducers, Vol., Secial Issue, May 03,. 4-46 Sesors & rasducers 03 by IFSA h://www.sesorsoral.com Coergece Aalysis of Muli-ioaio Learig Algorihm Based o PID Neural Nework Gag Re,, Pile Qi, Mimi
Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
America Joural of Compuaioal Mahemaics, 04, 4, 80-88 Published Olie Sepember 04 i SciRes. hp://www.scirp.org/joural/ajcm hp://dx.doi.org/0.436/ajcm.04.4404 Mea Square Coverge Fiie Differece Scheme for
A Robust H Filter Design for Uncertain Nonlinear Singular Systems
A Robus H Filer Desig for Ucerai Noliear Sigular Sysems Qi Si, Hai Qua Deparme of Maageme Ier Mogolia He ao College Lihe, Chia College of Mahemaics Sciece Ier Mogolia Normal Uiversiy Huhho, Chia Absrac