Advances in Mathematics and Statistical Sciences. On Positive Definite Solution of the Nonlinear Matrix Equation
|
|
- Samantha Newton
- 6 years ago
- Views:
Transcription
1 Advace i Mathematic ad Statitical Sciece O Poitive Defiite Solutio of the Noliea * Matix Equatio A A I SANA'A A. ZAREA Mathematical Sciece Depatmet Pice Nouah Bit Abdul Rahma Uiveity B.O.Box 9Riyad 6 SAUDI ARABIA azaea@pu.edu.a _zaea@yahoo.com Abtact: - I thi pape a efficiet iteative method i peeted to olve a ew oliea matix equatio * A A I with eal matice ad. Some popetie of the poitive defiite olutio fo the oliea matix equatio ae deived. Moeove eceay ad ufficiet coditio fo the exitece of the poitive defiite olutio ae deived. The eo etimatio of the iteative method i alo give. Fially two umeical example ae give to demotate the efficiecy of the algoithm. Key-Wod: - : Noliea matix equatio poitive defiite olutio exitece iteative method fixed-poit theoem. Itoductio The oliea matix equatio aie i a wide vaiety of applicatio ad eeach aea icludig automatic cotol ladde etwo dyamic pogammig tochatic filteig tatitic ad othe field of pue ad applied mathematic [6]. Fo example coide the oliea matix equatio of the fom * A A Q () whee A i a quae eal matix ad Q i a poitive defiite matix. whe i a pecial cae of algebaic dicete type Riccati equatio []. Equatio () ha bee ivetigated by may autho [-]. Some umeical method uch a fixed poit iteatio [67]. Newto method [7] SDA algoithm [] LR algoithm [] ad Buttefly SZ algoithm [] have bee popoed to compute the poitive defiite olutio. Baed o the fixed-poit theoem the ufficiet ad eceay coditio fo the exitece of a poitive defiite olutio of the matix () have bee give whe i egative itege []. Recetly fo i poitive itege equatio ( ) ha bee tudied i [7]. I thi pape we coide ew oliea matix equatio of the fom * A A I () R whee i eal umbe i uow matix I i the idetity matix ad A R i oigula matix. The matix equatio () could be viewed a a pecial cae of the ymmetic liea matix equatio [6]. Thi pape i ogaized a follow. I Sectio ome popetie of poitive defiite olutio of the matix equatio () ae give. I Sectio a iteative method i cotucted to compute the uique poitive defiite olutio. The eo etimatio of thi iteative method i alo give. Fially Sectio iclude two umeical example to illutate the theoetical eult. I thi pape we will ue mathematical iductio techique i the mot poof. The aim of thi pape i to fid the poitive defiite olutio of equatio (). Thoughout thi pape we wite A ( A ) mea that A i poitive emidefiite (poitive defiite) A * deote the tapoe of A ad I i the idetity matix. Moeove A B( A B ) i ued a a diffeet otatio fo A B A B ( ) deote the equece.... We deote by (A) A the pectal adiu of A. The om ued i thi pape i the pectal om of the matix A ule othewie oted. ISBN:
2 Advace i Mathematic ad Statitical Sciece Some Popetie of the Solutio I thi ectio we'll dicu ome popetie of poitive defiite olutio of the matix equatio (). Theoem.. If m ad M ae the mallet ad the laget eigevalue of a olutio of equatio () epectively ad i a eigevalue of A the m M. m M Poof. Let v be a eigevecto coepodig to a eigevalue of the matix A ad v. Sice the olutio of equatio () i a poitive defiite matix the m v v v v v v m m v v v v v v v v v v v v v v m m m m Theoem. If equatio () ha a poitive defiite olutio the ad.. Poof. Sice be a poitive defiite olutio of equatio () ad ad. The Iteative Method I thi ectio the iteative method fo obtaiig a poitive defiite olutio of equatio () i etablihed. A iteative method to compute the uique poitive defiite olutio i popoed the two lemma ae biefly eviewed ad the ued to etablih eceay ad ufficiet coditio fo the exitece of a poitive defiite olutio of Equatio ().. Algoithm. Tae. Fo... compute * B ( )B () whee B B * *. Lemma. [] Let f be a opeato mootoe fuctio o ( ) ad let AB be two poitive opeato that ae bouded below by a;i.e.a ai ad B ai fo the poitive umbe a. The fo evey pectal om f ( A ) f ( B ) f ( a) A B. Lemma. [](Lowe-Heiz iequality) p The fuctio t i ode-peevig fo p p p i.e. A B A B. The ext theoem give the eceay ad ufficiet coditio fo the exitece of a olutio of equatio (). Theoem. Let the equece be detemied by the Algoithm. I B B I ad if equatio () ha a poitive defiite olutio the covege to poitive defiite olutio Moeove if fo evey ad I B B I the equatio () ha a poitive defiite olutio. Poof. Let equatio () ha a poitive defiite olutio. We pove the cocluio by iductio. Fom algoithm. we have * B B by uig Lemma. (Lowe-Heiz iequality) we get B ( I )B B ( )B * *. Aume that the cocluio hold fo... that i the fo = + by uig Lowe-Heiz iequality we have B ( I )B B ( )B * *. The equece i iceaig. To pove it i bouded fom above let I i.e. * B B I I ad I. ISBN:
3 Advace i Mathematic ad Statitical Sciece To pove that I.... Let the cocluio I hold fo the fo * * I B ( I ) B B B I I thu I... i mootoic iceaig ad bouded fom above by I. Moeove it limit exit that i lim. The equece by taig the limit of () we get A A I ad the olutio atifie Equatio (). Suppoe fo evey we poved that the limit of exit. Let A A I by taig the limit of both ided a we have A A I Coequetly equatio () ha poitive defiite olutio. Theoem. Let be the iteate i Algoithm. ad I B B I. If q. The q whee i a poitive defiite olutio of equatio (). Poof. Fom Theoem. it follow that the equece () i coveget to a poitive defiite olutio of equatio (). We compute the pectal om of the matix we obtai * * B ( I ) B B ( I ) B R P * whee R B ( I ) B P B * ( I ) B. By uig lemma. with a mootoe opeato f ( x) x ; ad fo * *... the R B ( I ) B B B I povided a R ai ad by the ame mae we get P ai. Sice f ( a) a f ( ) B let q we have q afte -tep q q. Coollay.. Aume that Equatio () ha a olutio. If q the covege to with at leat the liea covegece ate. Poof. A we have q. The chooe a eal umbe that atifie q. Sice thee exit a N uch that fo ay N q. Hece. Theoem. If equatio () ha a poitive defiite olutio ad afte iteative tep of Algoithm. ad we have the i-. ad ii- whee i the iteate i Algoithm.. Poof. i- Fom algoithm. ad lemma. the tae the om of both ide * * B ( I )B B ( I )B B. I Sice ad a. Coequetly ad ISBN:
4 Advace i Mathematic ad Statitical Sciece I a the. ii- the tae the om of both ide <. Numeical Expeimet I thi ectio we give two umeical example to illutate that the matix equece geeated by iteative method (.) covege to the uique poitive defiite olutio of equatio (). The uique olutio i computed fo diffeet matice A. All pogam ae witte i MATHAMATICA. Fo the followig example the pactical toppig citeio ae ad the olutio i.. Example Example Coide the oliea matix equatio * A A I whee... A A Fo..8 Afte 6 iteatio we get epectively. See Table. Example Coide the oliea matix equatio * A A I whee A Fo Afte 999 iteatio we get epectively. See Table. ISBN:
5 Advace i Mathematic ad Statitical Sciece. Table I the followig table we deote * A A I. Table : Eo aalyi fo Example fo diffeet value of.87e-6.987e E-.68E-6.7E-6.6E-8.89E-.9E E-6.8E-8. 6E-9.9E E-.699E E E-9. 79E-.789E E-6.E E E-.8E E-8.E-8.9E-..9.7E-.96E-6.676E-8.88E E-.87E-.8E-8.87E-8.86E- Table : Eo aalyi fo Example fo diffeet value of K E-.7E-7.8E-9.696E E-.E-7.89E E E-.9888E-7.987E-9 9.E E E-9.96E E-.7E-6.6E E E-.9 E-6.8 E-6.769E-8.9 E E-.E E-.76E-.96E-6.898E-6.779E-8.777E E-.8E- Cocluio I thi pape a ew fom of oliea matix equatio () wa coideed. Some popetie of a poitive defiite olutio equatio () have bee tudied. Baed o the fixed poit theoem a iteative method i popoed to compute the uique poitive defiite olutio. Alo the eceay ad ufficiet coditio fo the covegece to poitive defiite olutio wee deduced. Fially umeical example how that the iteative method i feaible to compute the uique poitive defiite olutio. Refeece: [] W.N. Adeo J. T.D. Moley ad G.E. * Tapp Poitive Solutio to A B B Liea Algeba ad It Applicatio Vol. 99 pp. 6. [] P. Bee ad H. Fabede O the Solutio of the Ratioal Matix Equatio Q L* L EURASIP Joual o Advace i Sigal Poceig Vol.7 7 pp.. [] R. Bhatia Matix Aalyi Gaduate Text i Mathematic 69 Spige Velag 997. [] S. M. El-Sayed ad A. M. Al-Dbiba O Poitive Defiite Solutio of Noliea Matix Equatio A A I Applied Mathematic ad Computatio Vol. pp. -. [] J. Egweda O the Exitece of A Poitive Defiite Solutio of the Matix Equatio T A A I Liea Algeba ad it Applicatio Vol.999 pp [6] S. Fital ad C.H. Guo A Note o the Fixed Poit Iteatio fo the Matix Eqatio A* A I Liea Algeba ad it Applicatio. Vol.9 8 pp. 98. [7] C. H. Guo ad W. W. LiThe Matix Equatio A* A Q ad it Applicatio i Nao Reeach SIAM Joual o Scietific Computig Vol. No. pp. -8. [8] C.H. Guo ad P. Lacate Iteative Solutio of Two Matix Equatio Mathematic of Computatio Vol pp [9] V.I. Haaov ad I.G. Ivaov O Two Petubatio Etimate of the Exteme Solutio to the Equatio A* A Q Liea Algeba ad it Applicatio Vol. 6 pp [] I.G. Ivaov V.I. Haaov ad F. Ulig Impoved Method ad Statig Value to Solve the Matix Equatio A* A I Iteatively Mathematic of Computatio Vol. 7 pp ISBN:
6 Advace i Mathematic ad Statitical Sciece [] P. Lacate ad L. Rodma Algebaic Riccati Equatio Oxfod Sciece Oxfod 99. [] W.W. Li ad S.F. u Covegece Aalyi of Stuctue-Peevig Doublig Algoithm fo Riccati-Type Matix Equatio SIAM Joual o Matix Aalyi ad Applicatio Vol. 8 6 pp [] B. Meii Efficiet Computatio of the Exteme Solutio of A* A Q ad Mathematic of Computa- A* A Q tio Vol. 7 pp. 89. [] B. Meii Matix Equatio ad Stuctue: Efficiet Solutio of Special Dicete Algebaic Riccati Equatio Poceedig of the WLSS- COO Bulgaia. [] G.K. Pedee Some Opeato Mootoe Fuctio Poceedig of the Ameica Mathematical Society Vol pp.9. [6] A. RaM. C. Reuig The Symmetic Liea Matix Equatio The Electoic Joual of Liea Algeba Vol.9 pp.9-7. [7] S. A. Zaea S. M. El-Sayed O Poitive Defiite Solutio of the Noliea Matix Equatio A A I Applied Mathematical Sciece Vol. 9 No. pp. 7-. ISBN:
Applied Mathematical Sciences, Vol. 9, 2015, no. 3, HIKARI Ltd,
Applied Mathematical Sciece Vol 9 5 o 3 7 - HIKARI Ltd wwwm-hiaricom http://dxdoiorg/988/am54884 O Poitive Defiite Solutio of the Noliear Matrix Equatio * A A I Saa'a A Zarea* Mathematical Sciece Departmet
More informationA two-sided Iterative Method for Solving
NTERNATONAL JOURNAL OF MATHEMATCS AND COMPUTERS N SMULATON Volume 9 0 A two-sided teative Method fo Solvig * A Noliea Matix Equatio X= AX A Saa'a A Zaea Abstact A efficiet ad umeical algoithm is suggested
More informationInternational Journal of Mathematical Archive-5(3), 2014, Available online through ISSN
Iteatioal Joual of Mathematical Achive-5(3, 04, 7-75 Available olie though www.ijma.ifo ISSN 9 5046 ON THE OSCILLATOY BEHAVIO FO A CETAIN CLASS OF SECOND ODE DELAY DIFFEENCE EQUATIONS P. Mohakuma ad A.
More informationSome characterizations for Legendre curves in the 3-Dimensional Sasakian space
IJST (05) 9A4: 5-54 Iaia Joual of Sciece & Techology http://ijthiazuaci Some chaacteizatio fo Legede cuve i the -Dimeioal Saakia pace H Kocayigit* ad M Ode Depatmet of Mathematic, Faculty of At ad Sciece,
More information( ) 1 Comparison Functions. α is strictly increasing since ( r) ( r ) α = for any positive real number c. = 0. It is said to belong to
Compaiso Fuctios I this lesso, we study stability popeties of the oautoomous system = f t, x The difficulty is that ay solutio of this system statig at x( t ) depeds o both t ad t = x Thee ae thee special
More informationUnified Mittag-Leffler Function and Extended Riemann-Liouville Fractional Derivative Operator
Iteatioal Joual of Mathematic Reeach. ISSN 0976-5840 Volume 9, Numbe 2 (2017), pp. 135-148 Iteatioal Reeach Publicatio Houe http://www.iphoue.com Uified Mittag-Leffle Fuctio ad Exteded Riema-Liouville
More informationSTRONG DEVIATION THEOREMS FOR THE SEQUENCE OF CONTINUOUS RANDOM VARIABLES AND THE APPROACH OF LAPLACE TRANSFORM
Joural of Statitic: Advace i Theory ad Applicatio Volume, Number, 9, Page 35-47 STRONG DEVIATION THEORES FOR THE SEQUENCE OF CONTINUOUS RANDO VARIABLES AND THE APPROACH OF LAPLACE TRANSFOR School of athematic
More informationOPTIMAL ESTIMATORS FOR THE FINITE POPULATION PARAMETERS IN A SINGLE STAGE SAMPLING. Detailed Outline
OPTIMAL ESTIMATORS FOR THE FIITE POPULATIO PARAMETERS I A SIGLE STAGE SAMPLIG Detailed Outlie ITRODUCTIO Focu o implet poblem: We ae lookig fo a etimato fo the paamete of a fiite populatio i a igle adom
More informationSums of Involving the Harmonic Numbers and the Binomial Coefficients
Ameica Joual of Computatioal Mathematics 5 5 96-5 Published Olie Jue 5 i SciRes. http://www.scip.og/oual/acm http://dx.doi.og/.46/acm.5.58 Sums of Ivolvig the amoic Numbes ad the Biomial Coefficiets Wuyugaowa
More informationLesson 5. Chapter 7. Wiener Filters. Bengt Mandersson. r x k We assume uncorrelated noise v(n). LTH. September 2010
Optimal Sigal Poceig Leo 5 Chapte 7 Wiee Filte I thi chapte we will ue the model how below. The igal ito the eceive i ( ( iga. Nomally, thi igal i ditubed by additive white oie v(. The ifomatio i i (.
More informationOn the Positive Definite Solutions of the Matrix Equation X S + A * X S A = Q
The Ope Applied Mathematic Joural 011 5 19-5 19 Ope Acce O the Poitive Defiite Solutio of the Matrix Equatio X S + A * X S A = Q Maria Adam * Departmet of Computer Sciece ad Biomedical Iformatic Uiverity
More informationFIXED POINT AND HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN BANACH SPACES
IJRRAS 6 () July 0 www.apapess.com/volumes/vol6issue/ijrras_6.pdf FIXED POINT AND HYERS-UAM-RASSIAS STABIITY OF A QUADRATIC FUNCTIONA EQUATION IN BANACH SPACES E. Movahedia Behbaha Khatam Al-Abia Uivesity
More informationCHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method
CHAPTER 5 : SERIES 5.1 Seies 5. The Sum of a Seies 5..1 Sum of Powe of Positive Iteges 5.. Sum of Seies of Patial Factio 5..3 Diffeece Method 5.3 Test of covegece 5.3.1 Divegece Test 5.3. Itegal Test 5.3.3
More informationEVALUATION OF SUMS INVOLVING GAUSSIAN q-binomial COEFFICIENTS WITH RATIONAL WEIGHT FUNCTIONS
EVALUATION OF SUMS INVOLVING GAUSSIAN -BINOMIAL COEFFICIENTS WITH RATIONAL WEIGHT FUNCTIONS EMRAH KILIÇ AND HELMUT PRODINGER Abstact We coside sums of the Gaussia -biomial coefficiets with a paametic atioal
More informationON CERTAIN CLASS OF ANALYTIC FUNCTIONS
ON CERTAIN CLASS OF ANALYTIC FUNCTIONS Nailah Abdul Rahma Al Diha Mathematics Depatmet Gils College of Educatio PO Box 60 Riyadh 567 Saudi Aabia Received Febuay 005 accepted Septembe 005 Commuicated by
More informationu t u 0 ( 7) Intuitively, the maximum principles can be explained by the following observation. Recall
Oct. Heat Equatio M aximum priciple I thi lecture we will dicu the maximum priciple ad uiquee of olutio for the heat equatio.. Maximum priciple. The heat equatio alo ejoy maximum priciple a the Laplace
More informationUsing Difference Equations to Generalize Results for Periodic Nested Radicals
Usig Diffeece Equatios to Geealize Results fo Peiodic Nested Radicals Chis Lyd Uivesity of Rhode Islad, Depatmet of Mathematics South Kigsto, Rhode Islad 2 2 2 2 2 2 2 π = + + +... Vieta (593) 2 2 2 =
More informationConditional Convergence of Infinite Products
Coditioal Covegece of Ifiite Poducts William F. Tech Ameica Mathematical Mothly 106 1999), 646-651 I this aticle we evisit the classical subject of ifiite poducts. Fo stadad defiitios ad theoems o this
More informationGeneralized Fibonacci-Lucas Sequence
Tuish Joual of Aalysis ad Numbe Theoy, 4, Vol, No 6, -7 Available olie at http://pubssciepubcom/tjat//6/ Sciece ad Educatio Publishig DOI:6/tjat--6- Geealized Fiboacci-Lucas Sequece Bijeda Sigh, Ompaash
More informationStrong Result for Level Crossings of Random Polynomials
IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh
More informationSome Properties of the K-Jacobsthal Lucas Sequence
Deepia Jhala et. al. /Iteatioal Joual of Mode Scieces ad Egieeig Techology (IJMSET) ISSN 349-3755; Available at https://www.imset.com Volume Issue 3 04 pp.87-9; Some Popeties of the K-Jacobsthal Lucas
More informationBayesian and Maximum Likelihood Estimation for Kumaraswamy Distribution Based on Ranked Set Sampling
Ameica Joual of Mathematic ad Statitic 04 4(): 0-7 DOI: 0.59/j.ajm.04040.05 Bayeia ad Maximum Lielihood Etimatio fo Kumaawamy Ditibutio Baed o Raed Set Samplig Mohamed A. Huia Depatmet of Mathematical
More informationMinimal order perfect functional observers for singular linear systems
Miimal ode efect fuctioal obseves fo sigula liea systems Tadeusz aczoek Istitute of Cotol Idustial lectoics Wasaw Uivesity of Techology, -66 Waszawa, oszykowa 75, POLAND Abstact. A ew method fo desigig
More informationMinimization of the quadratic test function
Miimizatio of the quadatic test fuctio A quadatic fom is a scala quadatic fuctio of a vecto with the fom f ( ) A b c with b R A R whee A is assumed to be SPD ad c is a scala costat Note: A symmetic mati
More informationOn the Explicit Determinants and Singularities of r-circulant and Left r-circulant Matrices with Some Famous Numbers
O the Explicit Detemiats Sigulaities of -ciculat Left -ciculat Matices with Some Famous Numbes ZHAOLIN JIANG Depatmet of Mathematics Liyi Uivesity Shuaglig Road Liyi city CHINA jzh08@siacom JUAN LI Depatmet
More informationON EUCLID S AND EULER S PROOF THAT THE NUMBER OF PRIMES IS INFINITE AND SOME APPLICATIONS
Joual of Pue ad Alied Mathematics: Advaces ad Alicatios Volume 0 Numbe 03 Pages 5-58 ON EUCLID S AND EULER S PROOF THAT THE NUMBER OF PRIMES IS INFINITE AND SOME APPLICATIONS ALI H HAKAMI Deatmet of Mathematics
More informationDANIEL YAQUBI, MADJID MIRZAVAZIRI AND YASIN SAEEDNEZHAD
MIXED -STIRLING NUMERS OF THE SEOND KIND DANIEL YAQUI, MADJID MIRZAVAZIRI AND YASIN SAEEDNEZHAD Abstact The Stilig umbe of the secod id { } couts the umbe of ways to patitio a set of labeled balls ito
More informationAuchmuty High School Mathematics Department Sequences & Series Notes Teacher Version
equeces ad eies Auchmuty High chool Mathematics Depatmet equeces & eies Notes Teache Vesio A sequece takes the fom,,7,0,, while 7 0 is a seies. Thee ae two types of sequece/seies aithmetic ad geometic.
More informationOn composite conformal mapping of an annulus to a plane with two holes
O composite cofomal mappig of a aulus to a plae with two holes Mila Batista (July 07) Abstact I the aticle we coside the composite cofomal map which maps aulus to ifiite egio with symmetic hole ad ealy
More informationINVERSE CAUCHY PROBLEMS FOR NONLINEAR FRACTIONAL PARABOLIC EQUATIONS IN HILBERT SPACE
IJAS 6 (3 Febuay www.apapess.com/volumes/vol6issue3/ijas_6_3_.pdf INVESE CAUCH POBLEMS FO NONLINEA FACTIONAL PAABOLIC EQUATIONS IN HILBET SPACE Mahmoud M. El-Boai Faculty of Sciece Aleadia Uivesit Aleadia
More informationA NOTE ON DOMINATION PARAMETERS IN RANDOM GRAPHS
Discussioes Mathematicae Gaph Theoy 28 (2008 335 343 A NOTE ON DOMINATION PARAMETERS IN RANDOM GRAPHS Athoy Boato Depatmet of Mathematics Wilfid Lauie Uivesity Wateloo, ON, Caada, N2L 3C5 e-mail: aboato@oges.com
More informationBound states solution of Klein-Gordon Equation with type - I equal vector and Scalar Poschl-Teller potential for Arbitray l State
AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH Sciece Huβ http://www.cihub.og/ajsir ISSN: 5-649X doi:.55/aji...79.8 Boud tate olutio of Klei-Godo Equatio with type - I equal vecto ad Scala Pochl-Telle
More informationDerivation of a Single-Step Hybrid Block Method with Generalized Two Off-Step Points for Solving Second Order Ordinary Differential Equation Directly.
INTENATIONAL JOUNAL OF MATHEMATICS AND COMPUTES IN SIMULATION Volume, 6 Deivatio o a Sigle-Step Hybid Block Metod wit Geealized Two O-Step Poit o Solvig Secod Ode Odiay Dieetial Equatio Diectly. a t. Abdelaim.
More informationSOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES
#A17 INTEGERS 9 2009), 181-190 SOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES Deick M. Keiste Depatmet of Mathematics, Pe State Uivesity, Uivesity Pak, PA 16802 dmk5075@psu.edu James A. Selles Depatmet
More informationCongruences for sequences similar to Euler numbers
Coguece fo equece iila to Eule ube Zhi-Hog Su School of Matheatical Sciece, Huaiyi Noal Uiveity, Huaia, Jiagu 00, Peole Reublic of Chia Received July 00 Revied 5 Augut 0 Couicated by David Go Abtact a
More information= 5! 3! 2! = 5! 3! (5 3)!. In general, the number of different groups of r items out of n items (when the order is ignored) is given by n!
0 Combiatoial Aalysis Copyight by Deiz Kalı 4 Combiatios Questio 4 What is the diffeece betwee the followig questio i How may 3-lette wods ca you wite usig the lettes A, B, C, D, E ii How may 3-elemet
More informationSome Integral Mean Estimates for Polynomials
Iteatioal Mathematical Foum, Vol. 8, 23, o., 5-5 HIKARI Ltd, www.m-hikai.com Some Itegal Mea Estimates fo Polyomials Abdullah Mi, Bilal Ahmad Da ad Q. M. Dawood Depatmet of Mathematics, Uivesity of Kashmi
More informationStructure and Some Geometric Properties of Nakano Difference Sequence Space
Stuctue ad Soe Geoetic Poeties of Naao Diffeece Sequece Sace N Faied ad AA Baey Deatet of Matheatics, Faculty of Sciece, Ai Shas Uivesity, Caio, Egyt awad_baey@yahooco Abstact: I this ae, we exted the
More informationAdvanced Physical Geodesy
Supplemetal Notes Review of g Tems i Moitz s Aalytic Cotiuatio Method. Advaced hysical Geodesy GS887 Chistophe Jekeli Geodetic Sciece The Ohio State Uivesity 5 South Oval Mall Columbus, OH 4 7 The followig
More informationHeat Equation: Maximum Principles
Heat Equatio: Maximum Priciple Nov. 9, 0 I thi lecture we will dicu the maximum priciple ad uiquee of olutio for the heat equatio.. Maximum priciple. The heat equatio alo ejoy maximum priciple a the Laplace
More informationOn a Problem of Littlewood
Ž. JOURAL OF MATHEMATICAL AALYSIS AD APPLICATIOS 199, 403 408 1996 ARTICLE O. 0149 O a Poblem of Littlewood Host Alze Mosbache Stasse 10, 51545 Waldbol, Gemay Submitted by J. L. Bee Received May 19, 1995
More informationBy the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences
Chapte : Theoy of Modula Aithmetic 8 Sectio D Chiese Remaide Theoem By the ed of this sectio you will be able to pove the Chiese Remaide Theoem apply this theoem to solve simultaeous liea cogueces The
More informationTHE ANALYTIC LARGE SIEVE
THE ANALYTIC LAGE SIEVE 1. The aalytic lage sieve I the last lectue we saw how to apply the aalytic lage sieve to deive a aithmetic fomulatio of the lage sieve, which we applied to the poblem of boudig
More informationStrong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA
Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics
More informationRange Symmetric Matrices in Minkowski Space
BULLETIN of the Bull. alaysia ath. Sc. Soc. (Secod Seies) 3 (000) 45-5 LYSIN THETICL SCIENCES SOCIETY Rae Symmetic atices i ikowski Space.R. EENKSHI Depatmet of athematics, amalai Uivesity, amalaiaa 608
More informationComplementary Dual Subfield Linear Codes Over Finite Fields
1 Complemetay Dual Subfield Liea Codes Ove Fiite Fields Kiagai Booiyoma ad Somphog Jitma,1 Depatmet of Mathematics, Faculty of Sciece, Silpao Uivesity, Naho Pathom 73000, hailad e-mail : ai_b_555@hotmail.com
More informationOn the Circulant Matrices with. Arithmetic Sequence
It J Cotep Math Scieces Vol 5 o 5 3 - O the Ciculat Matices with Aithetic Sequece Mustafa Bahsi ad Süleya Solak * Depatet of Matheatics Educatio Selçuk Uivesity Mea Yeiyol 499 Koya-Tukey Ftly we have defied
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.265/15.070J Fall 2013 Lecture 16 11/04/2013. Ito integral. Properties
MASSACHUSES INSIUE OF ECHNOLOGY 6.65/15.7J Fall 13 Lecture 16 11/4/13 Ito itegral. Propertie Cotet. 1. Defiitio of Ito itegral. Propertie of Ito itegral 1 Ito itegral. Exitece We cotiue with the cotructio
More informationUniversity of Pavia, Pavia, Italy. North Andover MA 01845, USA
Iteatoal Joual of Optmzato: heoy, Method ad Applcato 27-5565(Pt) 27-6839(Ole) wwwgph/otma 29 Global Ifomato Publhe (HK) Co, Ltd 29, Vol, No 2, 55-59 η -Peudoleaty ad Effcecy Gogo Gog, Noma G Rueda 2 *
More informationLast time: Completed solution to the optimum linear filter in real-time operation
6.3 tochatic Etimatio ad Cotrol, Fall 4 ecture at time: Completed olutio to the oimum liear filter i real-time operatio emi-free cofiguratio: t D( p) F( p) i( p) dte dp e π F( ) F( ) ( ) F( p) ( p) 4444443
More informationIntegral Problems of Trigonometric Functions
06 IJSRST Volume Issue Pit ISSN: 395-60 Olie ISSN: 395-60X Themed Sectio: Sciece ad Techology Itegal Poblems of Tigoometic Fuctios Chii-Huei Yu Depatmet of Ifomatio Techology Na Jeo Uivesity of Sciece
More informationLecture 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
More informationA Statistical Integral of Bohner Type. on Banach Space
Applied Mathematical cieces, Vol. 6, 202, o. 38, 6857-6870 A tatistical Itegal of Bohe Type o Baach pace Aita Caushi aita_caushi@yahoo.com Ago Tato agtato@gmail.com Depatmet of Mathematics Polytechic Uivesity
More informationOn ARMA(1,q) models with bounded and periodically correlated solutions
Reseach Repot HSC/03/3 O ARMA(,q) models with bouded ad peiodically coelated solutios Aleksade Weo,2 ad Agieszka Wy oma ska,2 Hugo Steihaus Cete, Woc aw Uivesity of Techology 2 Istitute of Mathematics,
More informationGreatest term (numerically) in the expansion of (1 + x) Method 1 Let T
BINOMIAL THEOREM_SYNOPSIS Geatest tem (umeically) i the epasio of ( + ) Method Let T ( The th tem) be the geatest tem. Fid T, T, T fom the give epasio. Put T T T ad. Th will give a iequality fom whee value
More informationWe will look for series solutions to (1) around (at most) regular singular points, which without
ENM 511 J. L. Baai April, 1 Frobeiu Solutio to a d order ODE ear a regular igular poit Coider the ODE y 16 + P16 y 16 + Q1616 y (1) We will look for erie olutio to (1) aroud (at mot) regular igular poit,
More informationTaylor Transformations into G 2
Iteatioal Mathematical Foum, 5,, o. 43, - 3 Taylo Tasfomatios ito Mulatu Lemma Savaah State Uivesity Savaah, a 344, USA Lemmam@savstate.edu Abstact. Though out this pape, we assume that
More information-statistical convergence in intuitionistic fuzzy normed linear space
Soglaaai J. Sci. Techol. 40 (3), 540-549, Ma - Ju. 2018 Oigial Aticle Geealized I -tatitical covegece i ituitioitic fuzz omed liea pace Nabaita Kowa ad Padip Debath* Depatmet of Mathematic, Noth Eate Regioal
More informationChapter 9. Key Ideas Hypothesis Test (Two Populations)
Chapter 9 Key Idea Hypothei Tet (Two Populatio) Sectio 9-: Overview I Chapter 8, dicuio cetered aroud hypothei tet for the proportio, mea, ad tadard deviatio/variace of a igle populatio. However, ofte
More informationPositive solutions of singular (k,n-k) conjugate boundary value problem
Joural of Applied Mathematic & Bioiformatic vol5 o 25-2 ISSN: 792-662 prit 792-699 olie Sciepre Ltd 25 Poitive olutio of igular - cojugate boudar value problem Ligbi Kog ad Tao Lu 2 Abtract Poitive olutio
More informationLacunary Almost Summability in Certain Linear Topological Spaces
BULLETIN of te MLYSİN MTHEMTİCL SCİENCES SOCİETY Bull. Malays. Mat. Sci. Soc. (2) 27 (2004), 27 223 Lacuay lost Suability i Cetai Liea Topological Spaces BÜNYMIN YDIN Cuuiyet Uivesity, Facutly of Educatio,
More informationGeneralizations and analogues of the Nesbitt s inequality
OCTOGON MATHEMATICAL MAGAZINE Vol 17, No1, Apil 2009, pp 215-220 ISSN 1222-5657, ISBN 978-973-88255-5-0, wwwhetfaluo/octogo 215 Geealiatios ad aalogues of the Nesbitt s iequalit Fuhua Wei ad Shahe Wu 19
More information10-716: Advanced Machine Learning Spring Lecture 13: March 5
10-716: Advaced Machie Learig Sprig 019 Lecture 13: March 5 Lecturer: Pradeep Ravikumar Scribe: Charvi Ratogi, Hele Zhou, Nicholay opi Note: Lae template courtey of UC Berkeley EECS dept. Diclaimer: hee
More informationLower Bounds for Cover-Free Families
Loe Bouds fo Cove-Fee Families Ali Z. Abdi Covet of Nazaeth High School Gade, Abas 7, Haifa Nade H. Bshouty Dept. of Compute Sciece Techio, Haifa, 3000 Apil, 05 Abstact Let F be a set of blocks of a t-set
More informationTechnical Report: Bessel Filter Analysis
Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we
More informationA note on random minimum length spanning trees
A ote o adom miimum legth spaig tees Ala Fieze Miklós Ruszikó Lubos Thoma Depatmet of Mathematical Scieces Caegie Mello Uivesity Pittsbugh PA15213, USA ala@adom.math.cmu.edu, usziko@luta.sztaki.hu, thoma@qwes.math.cmu.edu
More informationLesson 5. Chapter 7. Wiener Filters. Bengt Mandersson. r k s r x LTH. September Prediction Error Filter PEF (second order) from chapter 4
Optimal Sigal oceig Leo 5 Capte 7 Wiee Filte I ti capte we will ue te model ow below. Te igal ito te eceie i ( ( iga. Nomally, ti igal i ditubed by additie wite oie (. Te ifomatio i i (. Alo, we ofte ued
More informationLECTURE 13 SIMULTANEOUS EQUATIONS
NOVEMBER 5, 26 Demad-upply ytem LETURE 3 SIMULTNEOUS EQUTIONS I thi lecture, we dicu edogeeity problem that arie due to imultaeity, i.e. the left-had ide variable ad ome of the right-had ide variable are
More informationGeneralized k-normal Matrices
Iteatioal Joual of Computatioal Sciece ad Mathematics ISSN 0974-389 Volume 3, Numbe 4 (0), pp 4-40 Iteatioal Reseach Publicatio House http://wwwiphousecom Geealized k-omal Matices S Kishamoothy ad R Subash
More informationMapping Radius of Regular Function and Center of Convex Region. Duan Wenxi
d Iteatioal Cofeece o Electical Compute Egieeig ad Electoics (ICECEE 5 Mappig adius of egula Fuctio ad Cete of Covex egio Dua Wexi School of Applied Mathematics Beijig Nomal Uivesity Zhuhai Chia 363463@qqcom
More informationOn the Signed Domination Number of the Cartesian Product of Two Directed Cycles
Ope Joural of Dicrete Mathematic, 205, 5, 54-64 Publihed Olie July 205 i SciRe http://wwwcirporg/oural/odm http://dxdoiorg/0426/odm2055005 O the Siged Domiatio Number of the Carteia Product of Two Directed
More informationEffect of Graph Structures on Selection for a Model of a Population on an Undirected Graph
Effect of Gah Stuctue o Selectio fo a Model of a Poulatio o a Udiected Gah Watig Che Advio: Jao Schweibeg May 0, 206 Abtact Thi eeach focue o aalyzig electio amlifie i oulatio geetic. Sice the tuctue of
More informationActa Scientiarum. Technology ISSN: Universidade Estadual de Maringá Brasil
Acta cietiau Techology IN: 806-2563 edue@ueb Uiveidade Etadual de Maigá Bail Dutta, Hee; uede Reddy, Boa; Hazah Jebil, Iqbal O two ew type of tatitical covegece ad a uability ethod Acta cietiau Techology,
More informationSTA 4032 Final Exam Formula Sheet
Chapter 2. Probability STA 4032 Fial Eam Formula Sheet Some Baic Probability Formula: (1) P (A B) = P (A) + P (B) P (A B). (2) P (A ) = 1 P (A) ( A i the complemet of A). (3) If S i a fiite ample pace
More informationFibonacci Congruences and Applications
Ameica Ope Joual of Statitic 8-38 doi:436/oj5 Publihed Olie July (http://wwwscirpog/joual/oj) Fiboacci Coguece ad Applicatio Abtact Reé Blache Laboatoy LJK Uiveité Joeph Fouie Geoble Face E-mail: eeblache@aliceadlf
More information2012 GCE A Level H2 Maths Solution Paper Let x,
GCE A Level H Maths Solutio Pape. Let, y ad z be the cost of a ticet fo ude yeas, betwee ad 5 yeas, ad ove 5 yeas categoies espectively. 9 + y + 4z =. 7 + 5y + z = 8. + 4y + 5z = 58.5 Fo ude, ticet costs
More informationOn the 2-Domination Number of Complete Grid Graphs
Ope Joural of Dicrete Mathematic, 0,, -0 http://wwwcirporg/oural/odm ISSN Olie: - ISSN Prit: - O the -Domiatio Number of Complete Grid Graph Ramy Shahee, Suhail Mahfud, Khame Almaea Departmet of Mathematic,
More informationp-adic Invariant Integral on Z p Associated with the Changhee s q-bernoulli Polynomials
It. Joual of Math. Aalysis, Vol. 7, 2013, o. 43, 2117-2128 HIKARI Ltd, www.m-hiai.com htt://dx.doi.og/10.12988/ima.2013.36166 -Adic Ivaiat Itegal o Z Associated with the Chaghee s -Beoulli Polyomials J.
More informationThe Multivariate-t distribution and the Simes Inequality. Abstract. Sarkar (1998) showed that certain positively dependent (MTP 2 ) random variables
The Multivaiate-t distibutio ad the Simes Iequality by Hey W. Block 1, Saat K. Saka 2, Thomas H. Savits 1 ad Jie Wag 3 Uivesity of ittsbugh 1,Temple Uivesity 2,Gad Valley State Uivesity 3 Abstact. Saka
More informationMATH Midterm Solutions
MATH 2113 - Midtem Solutios Febuay 18 1. A bag of mables cotais 4 which ae ed, 4 which ae blue ad 4 which ae gee. a How may mables must be chose fom the bag to guaatee that thee ae the same colou? We ca
More informationRECIPROCAL POWER SUMS. Anthony Sofo Victoria University, Melbourne City, Australia.
#A39 INTEGERS () RECIPROCAL POWER SUMS Athoy Sofo Victoia Uivesity, Melboue City, Austalia. athoy.sofo@vu.edu.au Received: /8/, Acceted: 6//, Published: 6/5/ Abstact I this ae we give a alteative oof ad
More informationKEY. Math 334 Midterm II Fall 2007 section 004 Instructor: Scott Glasgow
KEY Math 334 Midtem II Fall 7 sectio 4 Istucto: Scott Glasgow Please do NOT wite o this exam. No cedit will be give fo such wok. Rathe wite i a blue book, o o you ow pape, pefeably egieeig pape. Wite you
More informationMultivector Functions
I: J. Math. Aal. ad Appl., ol. 24, No. 3, c Academic Pess (968) 467 473. Multivecto Fuctios David Hestees I a pevious pape [], the fudametals of diffeetial ad itegal calculus o Euclidea -space wee expessed
More informationFinite q-identities related to well-known theorems of Euler and Gauss. Johann Cigler
Fiite -idetities elated to well-ow theoems of Eule ad Gauss Joha Cigle Faultät fü Mathemati Uivesität Wie A-9 Wie, Nodbegstaße 5 email: oha.cigle@uivie.ac.at Abstact We give geealizatios of a fiite vesio
More informationThe Pigeonhole Principle 3.4 Binomial Coefficients
Discete M athematic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Ageda Ch 3. The Pigeohole Piciple
More informationTheorem 2: Proof: Note 1: Proof: Note 2:
A New 3-Dimenional Polynomial Intepolation Method: An Algoithmic Appoach Amitava Chattejee* and Rupak Bhattachayya** A new 3-dimenional intepolation method i intoduced in thi pape. Coeponding to the method
More informationAt the end of this topic, students should be able to understand the meaning of finite and infinite sequences and series, and use the notation u
Natioal Jio College Mathematics Depatmet 00 Natioal Jio College 00 H Mathematics (Seio High ) Seqeces ad Seies (Lecte Notes) Topic : Seqeces ad Seies Objectives: At the ed of this topic, stdets shold be
More informationOn the quadratic support of strongly convex functions
Int. J. Nonlinea Anal. Appl. 7 2016 No. 1, 15-20 ISSN: 2008-6822 electonic http://dx.doi.og/10.22075/ijnaa.2015.273 On the quadatic uppot of tongly convex function S. Abbazadeh a,b,, M. Ehaghi Godji a
More informationCOUNTING SUBSET SUMS OF FINITE ABELIAN GROUPS
COUNTING SUBSET SUMS OF FINITE ABELIAN GROUPS JIYOU LI AND DAQING WAN Abstact I this pape, we obtai a explicit fomula fo the umbe of zeo-sum -elemet subsets i ay fiite abelia goup 1 Itoductio Let A be
More information[Dhayabaran*, 5(1): January, 2016] ISSN: (I2OR), Publication Impact Factor: 3.785
[Dhayabaa* 5(): Jauay 206] ISSN: 2277-9655 (I2OR) Publicatio Impact Facto: 3.785 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY SOLVING FUZZY DIFFERENTIAL EQUATIONS USING RUNGE-KUTTA
More informationProof of Analytic Extension Theorem for Zeta Function Using Abel Transformation and Euler Product
Joual of athematic ad Statitic 6 (3): 294-299, 200 ISSN 549-3644 200 Sciece Publicatio Poof of Aalytic Eteio Theoem fo Zeta Fuctio Uig Abel Tafomatio ad Eule Poduct baitiga Zachaie Deatmet of edia Ifomatio
More information12.6 Sequential LMMSE Estimation
12.6 Sequetial LMMSE Estimatio Same kid if settig as fo Sequetial LS Fied umbe of paametes (but hee they ae modeled as adom) Iceasig umbe of data samples Data Model: [ H[ θ + w[ (+1) 1 p 1 [ [[0] [] ukow
More informationSTUDENT S t-distribution AND CONFIDENCE INTERVALS OF THE MEAN ( )
STUDENT S t-distribution AND CONFIDENCE INTERVALS OF THE MEAN Suppoe that we have a ample of meaured value x1, x, x3,, x of a igle uow quatity. Aumig that the meauremet are draw from a ormal ditributio
More informationChapter 8 Complex Numbers
Chapte 8 Complex Numbes Motivatio: The ae used i a umbe of diffeet scietific aeas icludig: sigal aalsis, quatum mechaics, elativit, fluid damics, civil egieeig, ad chaos theo (factals. 8.1 Cocepts - Defiitio
More informationNon-Orthogonal Tensor Diagonalization Based on Successive Rotations and LU Decomposition
o-othogoal Teo Diagoalizatio Baed o Succeive Rotatio ad LU Decompoitio Yig-Liag Liu Xiao-eg Gog ad Qiu-ua Li School of Ifomatio ad ommuicatio Egieeig Dalia Uiveity of Techology Dalia 11603 hia E-mail:
More informationSIMPLE LOW-ORDER AND INTEGRAL-ACTION CONTROLLER SYNTHESIS FOR MIMO SYSTEMS WITH TIME DELAYS
Appl. Comput. Math., V.10, N.2, 2011, pp.242-249 SIMPLE LOW-ORDER AND INTEGRAL-ACTION CONTROLLER SYNTHESIS FOR MIMO SYSTEMS WITH TIME DELAYS A.N. GÜNDEŞ1, A.N. METE 2 Abtact. A imple finite-dimenional
More informationA smoothing Newton method for the minimum norm solution of linear program
ISSN 746-7659, Eglad, UK Joual of Ifoatio ad Coputig Sciece Vol. 9, No. 4, 04, pp. 67-76 A soothig Newto ethod fo the iiu o solutio of liea poga Lia Zhag, Zhesheg Yu, Yaya Zhu Uivesity of Shaghai fo Sciece
More informationMATHS FOR ENGINEERS ALGEBRA TUTORIAL 8 MATHEMATICAL PROGRESSIONS AND SERIES
MATHS FOR ENGINEERS ALGEBRA TUTORIAL 8 MATHEMATICAL PROGRESSIONS AND SERIES O completio of this ttoial yo shold be able to do the followig. Eplai aithmetical ad geometic pogessios. Eplai factoial otatio
More informationGeneralized Fibonacci Like Sequence Associated with Fibonacci and Lucas Sequences
Turkih Joural of Aalyi ad Number Theory, 4, Vol., No. 6, 33-38 Available olie at http://pub.ciepub.com/tjat//6/9 Sciece ad Educatio Publihig DOI:.69/tjat--6-9 Geeralized Fiboacci Like Sequece Aociated
More informationReceived 17 August 2015; accepted 22 September 2015; published 25 September 2015
Ameica Joual of Computatioal Mathematics, 05, 5, 393 404 Published Olie Septembe 05 i SciRes. http://www.scip.og/joual/ajcm http://d.doi.og/0.436/ajcm.05.53034 A Compaative Stud o Numeical Solutios of
More information