Observation on the Bi-quadratic Equation with Five Unknowns
|
|
- Myron Walters
- 5 years ago
- Views:
Transcription
1 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org Oservtion on the Bi-qudrtic Eqution ith Five Unnons 1 1 R.Anuselvi 1 nd N.Ahil * 1 Deprtment of Mthemtics A.D.M. College for Women Autonomous Ngpttinm Tmil Ndu Indi. Deprtment of Mthemtics Thiru.Vi.K. Govt. Arts College Tiruvrur Tmil Ndu Indi Astrct: In this pper e find sustntill mn non-ero numerl quintuples pqdet fulfilling the iqudrtic eqution ith five unnons 1 1 different ttrctive delings mong the solutions nd out of the ordinr numers octhedrl numers centered multilterl & prmidl numers re ehiited. Ke ords: Bi-Qudrtic eqution ith five unnons essentil solutions multilterl numer Prmidl numers Centered multilterl. 010 Mthemtics suject clssifiction: 11D5. Nottions Used: - Polgonl numer of rn n ith sie m. n Pm - Prmidl numer of rn n ith sie m. - Pronic numer of rn n. - Octhedrl numer of rn n. 1. INTRODUCTION Bi-qudrtic Diophntine Equtions uniform nd ununiform hve roused the ttention of mn Mthemticins since uncertint s cn e seen from [117-19]. In the cground one m refer [-1] for vrieties of prolems on the Diophntine equtions ith to three nd four vriles. This communiqué concerns ith the prolems of determining non-ero fundmentl solutions of i-qudrtic eqution in the si unnons represented 1 1. solutions nd prticulr multilterl numers re offered.. METHOD OF ANALSIS The Diophntine eqution representing the i-qudrtic eqution ith si unnons elo deliertion is 1 1 Introducing the liner trnsformtions A smll numer of ttrctive reltions eteen the u v u v u v u v in 1 it simplifies to 1 50
2 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org u 1v 1 1 The ove eqution is solved through diverse methods nd thus one otins different sets of integer solutions to eqution 1. Set.1 Let 1 Sustituting in nd using method of fctorition define u i v 1 i i 5 Equting rel nd imginr prts e hve u v 1 1 Sustituting the vlues of u nd v in eqution the non-ero distinct integrl solutions of 1 re given Properties: i ii t 8t mod t 1 8Pr 0 iii OH 8t 7t 1 0 iv 1 1 t t SO 1 t 1t 1SO 1 0 v 1 1 t t 7t 1 t 8 1 mod9 vi 1 1 8t 19t5 vii 8 mod 88 t10 t 9 0 Note: In 5 replce 1 i 1 i 505
3 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org u i v 1 i i 8 Folloing the process offered in set. 1 diverse solution is given Set. cn e ritten s u 1v Write 1 s 1 i i 1 11 Using 11 in 10 nd emploing the method of fctorition delinete i u i v 1 i i 1 Equting rel nd imginr prts & replcing nd e hve u 8 v Using 1 & e get the integrl solutions of 1 to e Properties: i t 8t 1SO 1 17t 1t ii 1 1 5t 78 Pr 1mod 1SO 0 50
4 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org iii 1 1 t OH 8t 7t OH 0 iv Ol 11t 1 Ol t 0 5 v P t 1t t 1t 1 19 mod 8 vi 1 vii t viii t Note : 1 1 8t GnO t 9 7t t 171t t 1 88mod mod 880 i In 1 replce i u i v 1 i i i 15 Folloing the process offered in set. diverse solution is given Cse 1: u 1v Insted of 11 rite 1 s 1 i 1 i 1 c 17 9 Using 17 in 10 nd emploing the method of fctorition define 1 i u i v 1 i i 18 7 Equting rel nd imginr prts nd replcing 7 nd 7 507
5 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org u 7 v Using 19 & e get the integrl solutions of 1 to e Note 1 i In 18 replce 7 1 i 7 u i v 1 i i Folloing the procedure presented in cse 1 different solution is given i Cse : u 1v As n lterntive of 17 rite 1 s 8 i8 1 8 i8 5 Using 17 in 10 nd emploing the method of fctorition define 8 i8 u i v 1 i i 1 Equting rel nd imginr prts nd replcing 1 nd 1 508
6 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org u 18 v Using 5 & e get the integrl solutions of 1 to e Note 8 i8 In replce 1 8 i8 1 u i v 1 i i Folloing the prllel process s in cse the equivlent numerl solutions of 1 re given i Set.III Rerite e get u 1 v 9 Choice: I u v v u 0 0 Using method of cross rtio e get u v 1 509
7 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org Hence in oservtion of the prllel non-ero numerl solutions of 1 re Properties i ii iii 1 1 t iv t 1 t 1 8t v 9t vi t vii 8t viii 1 1 t 1t Pr t 7 8t t t 8t 10 9t 7OH 1t t 8 Pr 8 8SO SO 1Pr 8 0 1t 7 79t mod t t 9 0mod In ddition to 0 9 m lso e uttered in the form of rtios in three diverse choices tht re otinle elo Choice: II u v v u Choice: III u v v u Choice: IV u v v u S1O Solving ech of the eceeding sstem of eqution the susequent process s offered in set.iii the prllel integer solution to 1 re estlish to e s given elo Solution for choice II: 0 510
8 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org Solution for choice III: Solution for choice IV: CONCLUSION: In this pper e hve offered distinct choices of integrl solutions to homogeneous iqudrtic eqution ith si unnons 1 1.To terminte s iqudrtic equtions re rich in multiplicit one m regrd s other forms of iqudrtic equtions nd rummge round for nlogous properties. REFERENCES [1] Crmichel R.D 1959 The theor of numers nd Diophntine nlsis Dover Pulictions Ne or. [] Dicson.I.E. 195 Histor of theor of numers Vol. Chelsi Pulishing Co. Ne or. [] Gopln.M.A. nd Anuselvi.R. 009 Integrl solutions of inr qurtic eqution reflections des ERA- JMS Vol.Issue pp [] Gopln.M.A. nd Jni.G. 009 Oservtion on Act cienci Indic Vol.VM No.5 [5] Gopln.M.A. Vidhlshmi.S nd Devil.S 010 Ternr Qurtic Diophntine Eqution n [] Gopln M.A. Vijsnr.A nd Mnju Somnth 010 Integrl solutions of Impct journl of Science nd Technolog Vol. No [7] Gopln.M.A.nd Shnmugnndhm.P. 010 On the Biqudrtic eqution Impct journl of Science nd Technolog Vol. No [8] Gopln M.A. Sngeeth.G.011 Integrl solutions of ternr non-homogeneous iqudrtic eqution Act cienci indic Vol.VII M No [9] Gopln.M.A..Vidhlshmi.S. Sumthi.G01 On the ternr iqudrtic non-homogeneous eqution 1 Indin journl of EngineeringVol1 No.1. [10] Gopln.M.A..Vidhlshmi.S. Sumthi.G01 Integrl solutions of ternr iqudrtic non-homogeneous eqution
9 Interntionl Journl of Reserch in Advent Technolog Vol. No.9 Septemer 018 E-ISSN: 1-97 Aville online t.ijrt.org 1 1 JRACE Vol.No [11] Gopln.M.A..Vidhlshmi.S. Sumthi.G01 Integer solutions of ternr iqudrtic non-homogeneous eqution 1 1 Archimeds J.Mth [1] Gopln.M.A.Geeth.V01Integrl solurtions of ternr iqudrtic eqution 1 IJLRSTVol. Issue [1] Gopln.M.A..Vidhlshmi.S. Sumthi.G01 On the ternr iqudrtic non-homogeneous eqution [1] Gopln.M.A. Vidhlshmi.S. Kvith.A. 01Integrl points on the iqudrtic eqution IJMSEAVol.7No [15] Gopln.M.A. Vidhlshmi. S. Mlli.S01Integrl solutions of 7 IJMIEVol. No [1] Gopln M.A nd Sivmi. B01Integrl solutions of qudrtic eqution ith four unnons Antrctic JMth [17] Mordell L.J 1970 Diophntine EqutionsAcdemic Press Ne or [18] NigelSmrt.P1999 The Algorithmic Resolutoins of Diophntine Equtions Cmridge Universit Presslondon [19] Telng S.G. 199 Numer TheorTt Mcgr Hill Pulishing compn Ne Delhi n 51
Homogeneous Bi-Quadratic Equation With Five Unknowns
Interntionl Journl of Mthemtics Reserch. ISSN 0976-580 Volume 6, Number (01), pp. 5-51 Interntionl Reserch Publiction House http://www.irphouse.com Homogeneous Bi-Qudrtic Eqution With Five y p q Unknowns
More informationOBSERVATIONS ON TERNARY QUADRATIC EQUATION z 82 x
Interntionl Reserch Journl of Engineering nd Technology IRJET) e-issn: 395-0056 Volume: 04 Issue: 03 Mr -017 www.irjet.net p-issn: 395-007 OBSERVATIONS ON TERNARY UADRATIC EUATION z 8 x y G. Jnki 1 nd
More informationON THE TERNARY QUADRATIC DIOPHANTINE EQUATION
Interntionl Reserch Journl of Engineering nd echnology IRJE) e-issn: 395-56 Volume: Issue: 4 July-15 www.irjet.net p-issn: 395-7 ON HE ERNARY QUADRAIC DIOPHANINE EQUAION 4x y ) 3xy 16 M.A.Gopln 1 *, S.Vidhylkshmi,
More informationOn rational Diophantine Triples and Quadruples
Interntionl Journl of Scientific nd Reserch Pulictions, Volume 4, Issue 9, Septemer 014 1 ISSN 50-3153 On rtionl Diophntine riples nd Qudruples M.A.Gopln *, K.Geeth **, Mnju Somnth *** * Professor,Dept.of
More informationScience and Technology RMUTT Journal
Science nd Technolog RMUTT Journl Vol7 No (017) : 00 05 wwwscirmuttcth/stj Online ISSN 9-1547 Possile Solutions of the Diophntine Eqution x Pinut Pungjump Deprtment of Mthemtics nd Sttistics, Fcult of
More informationHamiltonian Cycle in Complete Multipartite Graphs
Annls of Pure nd Applied Mthemtics Vol 13, No 2, 2017, 223-228 ISSN: 2279-087X (P), 2279-0888(online) Pulished on 18 April 2017 wwwreserchmthsciorg DOI: http://dxdoiorg/1022457/pmv13n28 Annls of Hmiltonin
More informationThe Existence of the Moments of the Cauchy Distribution under a Simple Transformation of Dividing with a Constant
Theoreticl Mthemtics & Applictions, vol., no., 0, 7-5 ISSN: 79-9687 (print), 79-9709 (online) Interntionl Scientific Press, 0 The Eistence of the Moments of the Cuch Distriution under Simple Trnsformtion
More informationThe Shortest Confidence Interval for the Mean of a Normal Distribution
Interntionl Journl of Sttistics nd Proility; Vol. 7, No. 2; Mrch 208 ISSN 927-7032 E-ISSN 927-7040 Pulished y Cndin Center of Science nd Eduction The Shortest Confidence Intervl for the Men of Norml Distriution
More informationNecessary and sufficient conditions for some two variable orthogonal designs in order 44
University of Wollongong Reserch Online Fculty of Informtics - Ppers (Archive) Fculty of Engineering n Informtion Sciences 1998 Necessry n sufficient conitions for some two vrile orthogonl esigns in orer
More informationINTEGRAL SOLUTIONS OF THE TERNARY CUBIC EQUATION
Itertiol Reserch Jourl of Egieerig d Techology IRJET) e-issn: 9-006 Volume: 04 Issue: Mr -017 www.irjet.et p-issn: 9-007 INTEGRL SOLUTIONS OF THE TERNRY CUBIC EQUTION y ) 4y y ) 97z G.Jki 1, C.Sry,* ssistt
More informationRectangular group congruences on an epigroup
cholrs Journl of Engineering nd Technology (JET) ch J Eng Tech, 015; 3(9):73-736 cholrs Acdemic nd cientific Pulisher (An Interntionl Pulisher for Acdemic nd cientific Resources) wwwsspulishercom IN 31-435X
More informationOPEN NEWTON - COTES QUADRATURE WITH MIDPOINT DERIVATIVE FOR INTEGRATION OF ALGEBRAIC FUNCTIONS
IJRET: Interntionl Journl of Reserch in Engineering nd Technology eissn: 9-6 pissn: -78 OPEN NEWTON - COTES QUADRATURE WITH MIDPOINT DERIVATIVE FOR INTEGRATION OF ALGEBRAIC FUNCTIONS T. Rmchndrn R.Priml
More informationBailey [1] established a simple but very useful identity: If
itlin journl of pure nd pplied mthemtics n 7 010 (179 190) 179 CERTAIN TRANSFORMATION AND SUMMATION FORMULAE FOR q-series Remy Y Denis Deprtment of Mthemtics University of Gorkhpur Gorkhpur-73009 Indi
More informationAN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS. I. Fedotov and S. S. Dragomir
RGMIA Reserch Report Collection, Vol., No., 999 http://sci.vu.edu.u/ rgmi AN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS I. Fedotov nd S. S. Drgomir Astrct. An
More informationOn the Non-Homogeneous Quintic Equation with Five Unknowns X 4 -Y 4 =10 p 3 (Z 2 -W 2 )
Journal of Mathematics and Informatics Vol. 0 07-6 ISSN: 49-06 (P) 49-0640 (online) Pulished Decemer 07 www.researchmathsci.org DOI: http://d.doi.org/0.457/jmi.v0a4 Journal of On the Non-Homogeneous Quintic
More informationHarmonic Mean Derivative - Based Closed Newton Cotes Quadrature
IOSR Journl of Mthemtics (IOSR-JM) e-issn: - p-issn: 9-X. Volume Issue Ver. IV (My. - Jun. 0) PP - www.iosrjournls.org Hrmonic Men Derivtive - Bsed Closed Newton Cotes Qudrture T. Rmchndrn D.Udykumr nd
More informationSome circular summation formulas for theta functions
Ci et l. Boundr Vlue Prolems 013, 013:59 R E S E A R C H Open Access Some circulr summtion formuls for thet functions Yi Ci, Si Chen nd Qiu-Ming Luo * * Correspondence: luomth007@163.com Deprtment of Mthemtics,
More informationSeptember 13 Homework Solutions
College of Engineering nd Computer Science Mechnicl Engineering Deprtment Mechnicl Engineering 5A Seminr in Engineering Anlysis Fll Ticket: 5966 Instructor: Lrry Cretto Septemer Homework Solutions. Are
More informationINEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV FUNCTIONAL. Mohammad Masjed-Jamei
Fculty of Sciences nd Mthemtics University of Niš Seri Aville t: http://www.pmf.ni.c.rs/filomt Filomt 25:4 20) 53 63 DOI: 0.2298/FIL0453M INEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV
More informationA Brief Note on Quasi Static Thermal Stresses In A Thin Rectangular Plate With Internal Heat Generation
Americn Journl of Engineering Reserch (AJER) 13 Americn Journl of Engineering Reserch (AJER) e-issn : 3-847 p-issn : 3-936 Volume-, Issue-1, pp-388-393 www.jer.org Reserch Pper Open Access A Brief Note
More informationJim Lambers MAT 169 Fall Semester Lecture 4 Notes
Jim Lmbers MAT 169 Fll Semester 2009-10 Lecture 4 Notes These notes correspond to Section 8.2 in the text. Series Wht is Series? An infinte series, usully referred to simply s series, is n sum of ll of
More informationCalculus of variations with fractional derivatives and fractional integrals
Anis do CNMAC v.2 ISSN 1984-820X Clculus of vritions with frctionl derivtives nd frctionl integrls Ricrdo Almeid, Delfim F. M. Torres Deprtment of Mthemtics, University of Aveiro 3810-193 Aveiro, Portugl
More informationGeneralized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral
DOI 763/s4956-6-4- Moroccn J Pure nd Appl AnlMJPAA) Volume ), 6, Pges 34 46 ISSN: 35-87 RESEARCH ARTICLE Generlized Hermite-Hdmrd-Fejer type inequlities for GA-conve functions vi Frctionl integrl I mdt
More informationBULLETIN OF MATHEMATICS AND STATISTICS RESEARCH
Vol..Issue.1.14 BULLETIN OF MATHEMATICS AND STATISTICS RESEARCH A eer Reviewed Itertiol Reserch Jourl http://www.bomsr.com RESEARCH ARTICLE INTEGRAL SOLUTIONS OF TERNARY QUADRATIC DIOHANTINE EQUATIONS
More informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationAn Alternative Approach to Estimating the Bounds of the Denominators of Egyptian Fractions
Leonrdo Journl of Sciences ISSN 58-0 Issue, Jnury-June 0 p. -0 An Alterntive Approch to Estimting the Bounds of the Denomintors of Egyptin Frctions School of Humn Life Sciences, University of Tsmni, Locked
More informationLINEAR ALGEBRA APPLIED
5.5 Applictions of Inner Product Spces 5.5 Applictions of Inner Product Spces 7 Find the cross product of two vectors in R. Find the liner or qudrtic lest squres pproimtion of function. Find the nth-order
More informationTorsion in Groups of Integral Triangles
Advnces in Pure Mthemtics, 01,, 116-10 http://dxdoiorg/1046/pm011015 Pulished Online Jnury 01 (http://wwwscirporg/journl/pm) Torsion in Groups of Integrl Tringles Will Murry Deprtment of Mthemtics nd Sttistics,
More informationGEOMETRIC PROOFS OF POLYNOMIAL RECIPROCITY LAWS OF CARLITZ, BERNDT, AND DIETER
GEOMETRIC PROOFS OF POLYNOMIAL RECIPROCITY LAWS OF CARLITZ, BERNDT, AND DIETER MATTHIAS BECK Dedicted to Iet Shiow on the occsion of his 65th irthdy nd retirement Astrct We study higher-dimensionl nlogs
More informationLOGARITHMIC INEQUALITIES FOR TWO POSITIVE NUMBERS VIA TAYLOR S EXPANSION WITH INTEGRAL REMAINDER
LOGARITHMIC INEQUALITIES FOR TWO POSITIVE NUMBERS VIA TAYLOR S EXPANSION WITH INTEGRAL REMAINDER S. S. DRAGOMIR ;2 Astrct. In this pper we otin severl new logrithmic inequlities for two numers ; minly
More informationComposite Mendeleev s Quadratures for Solving a Linear Fredholm Integral Equation of The Second Kind
Globl Journl of Pure nd Applied Mthemtics. ISSN 0973-1768 Volume 12, Number (2016), pp. 393 398 Reserch Indi Publictions http://www.ripubliction.com/gjpm.htm Composite Mendeleev s Qudrtures for Solving
More informationThe contact stress problem for a piecewisely defined punch indenting an elastic half space. Jacques Woirgard
The contct stress prolem for pieceisely defined punch indenting n elstic hlf spce Jcques Woirgrd 5 Rue du Châteu de l Arceu 8633 Notre Dme d Or FRANC Astrct A solution for the contct stress prolem of n
More informationCzechoslovak Mathematical Journal, 55 (130) (2005), , Abbotsford. 1. Introduction
Czechoslovk Mthemticl Journl, 55 (130) (2005), 933 940 ESTIMATES OF THE REMAINDER IN TAYLOR S THEOREM USING THE HENSTOCK-KURZWEIL INTEGRAL, Abbotsford (Received Jnury 22, 2003) Abstrct. When rel-vlued
More informationResearch Article Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions
Hindwi Pulishing Corportion Journl of Applied Mthemtics Volume 4, Article ID 38686, 6 pges http://dx.doi.org/.55/4/38686 Reserch Article Fejér nd Hermite-Hdmrd Type Inequlities for Hrmoniclly Convex Functions
More informationResearch Article Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method
Hindwi Compleity Volume 7, Article ID 457589, 6 pges https://doi.org/.55/7/457589 Reserch Article Anlyticl Solution of the Frctionl Fredholm Integrodifferentil Eqution Using the Frctionl Residul Power
More informationA Study on the Properties of Rational Triangles
Interntionl Journl of Mthemtis Reserh. ISSN 0976-5840 Volume 6, Numer (04), pp. 8-9 Interntionl Reserh Pulition House http://www.irphouse.om Study on the Properties of Rtionl Tringles M. Q. lm, M.R. Hssn
More informationChapter 6 Techniques of Integration
MA Techniques of Integrtion Asst.Prof.Dr.Suprnee Liswdi Chpter 6 Techniques of Integrtion Recll: Some importnt integrls tht we hve lernt so fr. Tle of Integrls n+ n d = + C n + e d = e + C ( n ) d = ln
More informationA Companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications
Filomt 30:3 06, 360 36 DOI 0.9/FIL6360Q Pulished y Fculty of Sciences nd Mthemtics, University of Niš, Seri Aville t: http://www.pmf.ni.c.rs/filomt A Compnion of Ostrowski Type Integrl Inequlity Using
More informationORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD
Author Nme et. l. / Interntionl Journl of New Technologies in Science nd Engineering Vol., Issue., 7, ISSN 9-78 ORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD A Chinn Nidu* G Dileep**
More informationNetwork Analysis and Synthesis. Chapter 5 Two port networks
Network Anlsis nd Snthesis hpter 5 Two port networks . ntroduction A one port network is completel specified when the voltge current reltionship t the terminls of the port is given. A generl two port on
More informationAQA Further Pure 1. Complex Numbers. Section 1: Introduction to Complex Numbers. The number system
Complex Numbers Section 1: Introduction to Complex Numbers Notes nd Exmples These notes contin subsections on The number system Adding nd subtrcting complex numbers Multiplying complex numbers Complex
More informationON THE EXCEPTIONAL SET IN THE PROBLEM OF DIOPHANTUS AND DAVENPORT
ON THE EXCEPTIONAL SET IN THE PROBLEM OF DIOPHANTUS AND DAVENPORT Andrej Dujell Deprtment of Mthemtics, University of Zgreb, 10000 Zgreb, CROATIA The Greek mthemticin Diophntus of Alexndri noted tht the
More informationFundamental Theorem of Calculus
Fundmentl Theorem of Clculus Recll tht if f is nonnegtive nd continuous on [, ], then the re under its grph etween nd is the definite integrl A= f() d Now, for in the intervl [, ], let A() e the re under
More informationMath 259 Winter Solutions to Homework #9
Mth 59 Winter 9 Solutions to Homework #9 Prolems from Pges 658-659 (Section.8). Given f(, y, z) = + y + z nd the constrint g(, y, z) = + y + z =, the three equtions tht we get y setting up the Lgrnge multiplier
More informationMathematics Number: Logarithms
plce of mind F A C U L T Y O F E D U C A T I O N Deprtment of Curriculum nd Pedgogy Mthemtics Numer: Logrithms Science nd Mthemtics Eduction Reserch Group Supported y UBC Teching nd Lerning Enhncement
More informationI. INTEGRAL THEOREMS. A. Introduction
1 U Deprtment of Physics 301A Mechnics - I. INTEGRAL THEOREM A. Introduction The integrl theorems of mthemticl physics ll hve their origin in the ordinry fundmentl theorem of clculus, i.e. xb x df dx dx
More informationON ALTERNATING POWER SUMS OF ARITHMETIC PROGRESSIONS
ON ALTERNATING POWER SUMS OF ARITHMETIC PROGRESSIONS A. BAZSÓ Astrct. Depending on the prity of the positive integer n the lternting power sum T k n = k + k + + k...+ 1 n 1 n 1 + k. cn e extended to polynomil
More informationCalculus Module C21. Areas by Integration. Copyright This publication The Northern Alberta Institute of Technology All Rights Reserved.
Clculus Module C Ares Integrtion Copright This puliction The Northern Alert Institute of Technolog 7. All Rights Reserved. LAST REVISED Mrch, 9 Introduction to Ares Integrtion Sttement of Prerequisite
More information1.9 C 2 inner variations
46 CHAPTER 1. INDIRECT METHODS 1.9 C 2 inner vritions So fr, we hve restricted ttention to liner vritions. These re vritions of the form vx; ǫ = ux + ǫφx where φ is in some liner perturbtion clss P, for
More information1. Twelve less than five times a number is thirty three. What is the number
Alger 00 Midterm Review Nme: Dte: Directions: For the following prolems, on SEPARATE PIECE OF PAPER; Define the unknown vrile Set up n eqution (Include sketch/chrt if necessr) Solve nd show work Answer
More informationAn iterative method for solving nonlinear functional equations
J. Mth. Anl. Appl. 316 (26) 753 763 www.elsevier.com/locte/jm An itertive method for solving nonliner functionl equtions Vrsh Dftrdr-Gejji, Hossein Jfri Deprtment of Mthemtics, University of Pune, Gneshkhind,
More informationNORMALS. a y a y. Therefore, the slope of the normal is. a y1. b x1. b x. a b. x y a b. x y
LOCUS 50 Section - 4 NORMALS Consider n ellipse. We need to find the eqution of the norml to this ellipse t given point P on it. In generl, we lso need to find wht condition must e stisfied if m c is to
More informationThe margin is too narrow to contain a truly remarkable proof.
The mrgin is too nrrow to contin trul remrkble proof. Pierre de Fermt B For HP & KP Abstrct. The im of this pper is to tr for Fermt s lost proof. Introduction In bout 637 Pierre de Fermt, French mthemticin,
More informationJoint Distribution of any Record Value and an Order Statistics
Interntionl Mthemticl Forum, 4, 2009, no. 22, 09-03 Joint Distribution of ny Record Vlue nd n Order Sttistics Cihn Aksop Gzi University, Deprtment of Sttistics 06500 Teknikokullr, Ankr, Turkey entelpi@yhoo.com
More informationThe Modified Heinz s Inequality
Journl of Applied Mthemtics nd Physics, 03,, 65-70 Pulished Online Novemer 03 (http://wwwscirporg/journl/jmp) http://dxdoiorg/0436/jmp03500 The Modified Heinz s Inequlity Tkshi Yoshino Mthemticl Institute,
More informationFarey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
More informationCOEXISTENCE OF POINT, PERIODIC AND STRANGE ATTRACTORS
Interntionl Journl of Bifurction nd Chos, Vol., No. 5 () 59 (5 pges) c World Scientific Publishing Compn DOI:./S8759 COEISTENCE OF POINT, PERIODIC AND STRANGE ATTRACTORS JULIEN CLINTON SPROTT Deprtment
More informationSTRAND J: TRANSFORMATIONS, VECTORS and MATRICES
Mthemtics SKE: STRN J STRN J: TRNSFORMTIONS, VETORS nd MTRIES J3 Vectors Text ontents Section J3.1 Vectors nd Sclrs * J3. Vectors nd Geometry Mthemtics SKE: STRN J J3 Vectors J3.1 Vectors nd Sclrs Vectors
More informationSection 6.1 INTRO to LAPLACE TRANSFORMS
Section 6. INTRO to LAPLACE TRANSFORMS Key terms: Improper Integrl; diverge, converge A A f(t)dt lim f(t)dt Piecewise Continuous Function; jump discontinuity Function of Exponentil Order Lplce Trnsform
More informationSome Hermite-Hadamard type inequalities for functions whose exponentials are convex
Stud. Univ. Beş-Bolyi Mth. 6005, No. 4, 57 534 Some Hermite-Hdmrd type inequlities for functions whose exponentils re convex Silvestru Sever Drgomir nd In Gomm Astrct. Some inequlities of Hermite-Hdmrd
More informationSolving the (3+1)-dimensional potential YTSF equation with Exp-function method
Journl of Physics: Conference Series Solving the (3+-dimensionl potentil YTSF eqution with Exp-function method To cite this rticle: Y-P Wng 8 J. Phys.: Conf. Ser. 96 86 View the rticle online for updtes
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationAbsolute values of real numbers. Rational Numbers vs Real Numbers. 1. Definition. Absolute value α of a real
Rtionl Numbers vs Rel Numbers 1. Wht is? Answer. is rel number such tht ( ) =. R [ ( ) = ].. Prove tht (i) 1; (ii). Proof. (i) For ny rel numbers x, y, we hve x = y. This is necessry condition, but not
More informationPolynomials and Division Theory
Higher Checklist (Unit ) Higher Checklist (Unit ) Polynomils nd Division Theory Skill Achieved? Know tht polynomil (expression) is of the form: n x + n x n + n x n + + n x + x + 0 where the i R re the
More informationA Note on Feng Qi Type Integral Inequalities
Int Journl of Mth Anlysis, Vol 1, 2007, no 25, 1243-1247 A Note on Feng Qi Type Integrl Inequlities Hong Yong Deprtment of Mthemtics Gungdong Business College Gungzhou City, Gungdong 510320, P R Chin hongyong59@sohucom
More informationNote 12. Introduction to Digital Control Systems
Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the
More informationSolutions of Klein - Gordan equations, using Finite Fourier Sine Transform
IOSR Journl of Mthemtics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 13, Issue 6 Ver. IV (Nov. - Dec. 2017), PP 19-24 www.iosrjournls.org Solutions of Klein - Gordn equtions, using Finite Fourier
More informationCHAPTER 6b. NUMERICAL INTERPOLATION
CHAPTER 6. NUMERICAL INTERPOLATION A. J. Clrk School o Engineering Deprtment o Civil nd Environmentl Engineering y Dr. Irhim A. Asskk Spring ENCE - Computtion s in Civil Engineering II Deprtment o Civil
More informationAM1 Mathematical Analysis 1 Oct Feb Exercises Lecture 3. sin(x + h) sin x h cos(x + h) cos x h
AM Mthemticl Anlysis Oct. Feb. Dte: October Exercises Lecture Exercise.. If h, prove the following identities hold for ll x: sin(x + h) sin x h cos(x + h) cos x h = sin γ γ = sin γ γ cos(x + γ) (.) sin(x
More informationA Generalized Inequality of Ostrowski Type for Twice Differentiable Bounded Mappings and Applications
Applied Mthemticl Sciences, Vol. 8, 04, no. 38, 889-90 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.988/ms.04.4 A Generlized Inequlity of Ostrowski Type for Twice Differentile Bounded Mppings nd Applictions
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More informationLecture 6. Notes. Notes. Notes. Representations Z A B and A B R. BTE Electronics Fundamentals August Bern University of Applied Sciences
Lecture 6 epresenttions epresenttions TE52 - Electronics Fundmentls ugust 24 ern University of pplied ciences ev. c2d5c88 6. Integers () sign-nd-mgnitude representtion The set of integers contins the Nturl
More informationarxiv:solv-int/ v1 4 Aug 1997
Two-dimensionl soliton cellulr utomton of deutonomized Tod-type A. Ngi 1,2, T. Tokihiro 1, J. Stsum 1, R. Willox 1,3 nd K. Kiwr 4 1 Grdute School of Mthemticl Sciences, University of Tokyo, rxiv:solv-int/9708001v1
More informationarxiv: v2 [math.nt] 2 Feb 2015
rxiv:407666v [mthnt] Fe 05 Integer Powers of Complex Tridigonl Anti-Tridigonl Mtrices Htice Kür Duru &Durmuş Bozkurt Deprtment of Mthemtics, Science Fculty of Selçuk University Jnury, 08 Astrct In this
More informationNUMERICAL INTEGRATION
NUMERICAL INTEGRATION How do we evlute I = f (x) dx By the fundmentl theorem of clculus, if F (x) is n ntiderivtive of f (x), then I = f (x) dx = F (x) b = F (b) F () However, in prctice most integrls
More informationMath 100 Review Sheet
Mth 100 Review Sheet Joseph H. Silvermn December 2010 This outline of Mth 100 is summry of the mteril covered in the course. It is designed to be study id, but it is only n outline nd should be used s
More informationad = cb (1) cf = ed (2) adf = cbf (3) cf b = edb (4)
10 Most proofs re left s reding exercises. Definition 10.1. Z = Z {0}. Definition 10.2. Let be the binry reltion defined on Z Z by, b c, d iff d = cb. Theorem 10.3. is n equivlence reltion on Z Z. Proof.
More informationModification Adomian Decomposition Method for solving Seventh OrderIntegro-Differential Equations
IOSR Journl of Mthemtics (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X. Volume, Issue 5 Ver. V (Sep-Oct. 24), PP 72-77 www.iosrjournls.org Modifiction Adomin Decomposition Method for solving Seventh OrderIntegro-Differentil
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics GENERALIZATIONS OF THE TRAPEZOID INEQUALITIES BASED ON A NEW MEAN VALUE THEOREM FOR THE REMAINDER IN TAYLOR S FORMULA volume 7, issue 3, rticle 90, 006.
More informationThe Trapezoidal Rule
_.qd // : PM Pge 9 SECTION. Numericl Integrtion 9 f Section. The re of the region cn e pproimted using four trpezoids. Figure. = f( ) f( ) n The re of the first trpezoid is f f n. Figure. = Numericl Integrtion
More informationQUADRATURE is an old-fashioned word that refers to
World Acdemy of Science Engineering nd Technology Interntionl Journl of Mthemticl nd Computtionl Sciences Vol:5 No:7 011 A New Qudrture Rule Derived from Spline Interpoltion with Error Anlysis Hdi Tghvfrd
More informationImprovement of Grüss and Ostrowski Type Inequalities
Filomt 9:9 (05), 07 035 DOI 098/FIL50907A Pulished y Fculty of Sciences nd Mthemtics, University of Niš, Seri Aville t: http://wwwpmfnicrs/filomt Improvement of Grüss nd Ostrowski Type Inequlities An Mri
More informationMT Integral equations
MT58 - Integrl equtions Introduction Integrl equtions occur in vriety of pplictions, often eing otined from differentil eqution. The reson for doing this is tht it my mke solution of the prolem esier or,
More informationZero-Sum Magic Graphs and Their Null Sets
Zero-Sum Mgic Grphs nd Their Null Sets Ebrhim Slehi Deprtment of Mthemticl Sciences University of Nevd Ls Vegs Ls Vegs, NV 89154-4020. ebrhim.slehi@unlv.edu Abstrct For ny h N, grph G = (V, E) is sid to
More information4.6 Numerical Integration
.6 Numericl Integrtion 5.6 Numericl Integrtion Approimte definite integrl using the Trpezoidl Rule. Approimte definite integrl using Simpson s Rule. Anlze the pproimte errors in the Trpezoidl Rule nd Simpson
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics ON LANDAU TYPE INEQUALITIES FOR FUNCTIONS WIT ÖLDER CONTINUOUS DERIVATIVES LJ. MARANGUNIĆ AND J. PEČARIĆ Deprtment of Applied Mthemtics Fculty of Electricl
More informationOBSERVATIONS ON THE NON- HOMOGENEOUS SEXTIC EQUATION WITH FOUR UNKNOWNS
ISSN: 1-87 Itertiol Jourl of Iovtive Reerch i Sciece, Egieerig d Techology Vol., Iue, My 01 OSERVTIONS ON THE NON- HOMOGENEOUS SEXTIC EQUTION WITH FOUR UNKNOWNS y ( k z S.Vidhylkhmi 1,M..Gopl,.Kvith Profeor,
More informationSelberg s integral and linear forms in zeta values
Journl of Computtionl nd Applied Mthemtics 160 (2003 265 270 www.elsevier.com/locte/cm Selberg s integrl nd liner forms in zet vlues Tnguy Rivol Lbortoire de Mthemtiques Nicols Oresme, CNRS UMR 6139, Universite
More informationChapter 2. Random Variables and Probability Distributions
Rndom Vriles nd Proilit Distriutions- 6 Chpter. Rndom Vriles nd Proilit Distriutions.. Introduction In the previous chpter, we introduced common topics of proilit. In this chpter, we trnslte those concepts
More informationChapter 8: Methods of Integration
Chpter 8: Methods of Integrtion Bsic Integrls 8. Note: We hve the following list of Bsic Integrls p p+ + c, for p sec tn + c p + ln + c sec tn sec + c e e + c tn ln sec + c ln + c sec ln sec + tn + c ln
More informationInvention of the plane geometrical formulae - Part II
IOSR Journl of Mthemtics (IOSR-JM) e-issn: 78-578,p-ISSN: 319-765X, Volume 6, Issue 3 (My. - Jun. 013), PP 10-15 Invention of the plne geometricl formule - Prt II Mr. Stish M. Kple sst. Techer Mhtm Phule
More informationSome basic concepts of fluid dynamics derived from ECE theory
Some sic concepts of fluid dynmics 363 Journl of Foundtions of Physics nd Chemistry, 2, vol. (4) 363 374 Some sic concepts of fluid dynmics derived from ECE theory M.W. Evns Alph Institute for Advnced
More informationWENJUN LIU AND QUÔ C ANH NGÔ
AN OSTROWSKI-GRÜSS TYPE INEQUALITY ON TIME SCALES WENJUN LIU AND QUÔ C ANH NGÔ Astrct. In this pper we derive new inequlity of Ostrowski-Grüss type on time scles nd thus unify corresponding continuous
More informationR(3, 8) P( 3, 0) Q( 2, 2) S(5, 3) Q(2, 32) P(0, 8) Higher Mathematics Objective Test Practice Book. 1 The diagram shows a sketch of part of
Higher Mthemtics Ojective Test Prctice ook The digrm shows sketch of prt of the grph of f ( ). The digrm shows sketch of the cuic f ( ). R(, 8) f ( ) f ( ) P(, ) Q(, ) S(, ) Wht re the domin nd rnge of
More informationM344 - ADVANCED ENGINEERING MATHEMATICS
M3 - ADVANCED ENGINEERING MATHEMATICS Lecture 18: Lplce s Eqution, Anltic nd Numericl Solution Our emple of n elliptic prtil differentil eqution is Lplce s eqution, lso clled the Diffusion Eqution. If
More informationNumerical Linear Algebra Assignment 008
Numericl Liner Algebr Assignment 008 Nguyen Qun B Hong Students t Fculty of Mth nd Computer Science, Ho Chi Minh University of Science, Vietnm emil. nguyenqunbhong@gmil.com blog. http://hongnguyenqunb.wordpress.com
More informationADAPTIVE CONTROL AND SYNCHRONIZATION OF RÖSSLER PROTOTYPE-4 SYSTEM
ADAPTIVE CONTROL AND SYNCHRONIZATION OF RÖSSLER PROTOTYPE-4 SYSTEM Sundrpndin Vidynthn 1 1 Reserch nd Development Centre, Vel Tech Dr. RR & Dr. SR Technicl University Avdi, Chenni-600 06, Tmil Ndu, INDIA
More informationENGI 3424 Engineering Mathematics Five Tutorial Examples of Partial Fractions
ENGI 44 Engineering Mthemtics Five Tutoril Exmples o Prtil Frctions 1. Express x in prtil rctions: x 4 x 4 x 4 b x x x x Both denomintors re liner non-repeted ctors. The cover-up rule my be used: 4 4 4
More informationSOME INTEGRAL INEQUALITIES OF GRÜSS TYPE
RGMIA Reserch Report Collection, Vol., No., 998 http://sci.vut.edu.u/ rgmi SOME INTEGRAL INEQUALITIES OF GRÜSS TYPE S.S. DRAGOMIR Astrct. Some clssicl nd new integrl inequlities of Grüss type re presented.
More information50 AMC Lectures Problem Book 2 (36) Substitution Method
0 AMC Letures Prolem Book Sustitution Metho PROBLEMS Prolem : Solve for rel : 9 + 99 + 9 = Prolem : Solve for rel : 0 9 8 8 Prolem : Show tht if 8 Prolem : Show tht + + if rel numers,, n stisf + + = Prolem
More information