2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016)
|
|
- Moses Bridges
- 5 years ago
- Views:
Transcription
1 nd Internatonal Conference on Electroncs, Network and Computer Engneerng (ICENCE 6) Postve solutons of the fourth-order boundary value problem wth dependence on the frst order dervatve YuanJan Ln, a, Fe Yang,b Nanchang Insttute of Scence and Technology, Nanchang 338, Jangx Nanchang Insttute of Scence and Technology, Nanchang 338, Jangx a lnyuanzhou@6.com, bfexu6@6.com Keywords: The frst order dervatve; Fourth-order boundary value problem; Postve soluton bstract: In ths paper, By the use of a new fxed pont theorem and the Green functon. The exstence of at least one postve solutons for the fourth-order boundary value problem wth the frst order dervatve u () (t ) + u (t ) = λ f (t, u (t ), u (t )) () u= () u= () u= () u= < t < s consdered, where f s a nonnegatve contnuous functon and λ >, < < π. Introducton Recently, there has been much attenton focused on the queston of postve soluton of fourth-order dfferental equaton wth one or two parameters. For example, astronomy, bology, physcs, chemcal engneerng and nformaton scence and other felds. So, the fourth-order boundary value problems has very mportant n real lfe applcatons, see for example [-, 6-9 ]. L [6] nvestgated the exstence of postve solutons for the fourth-order boundaryvalue problem. ll the above works were done under the assumpton that the frst order dervatve u s not nvolved explctly n the nonlnear term f. In ths paper, we are concerned wth the exstence of postve solutons for the fourth-order boundary value problem u () (t ) + u (t ) = λ f (t, u (t ), u (t )) () u= () u= () u= () u= < t < () The followng condtons are satsfed throughout ths paper: (H ) λ >, < < π ; (H ) f :[,] [, ) R [, ) s contnuous. The prelmnary lemmas Suppose Y = C[,] be the Banach space equpped wth the norm u = max u (t ). t [,] 6. The authors - Publshed by tlants Press 75
2 Let λ, λ be the roots of the polynomal P( λ) = λ + λ, namely, λ =, λ =. By (H ) t s easy to see that π < λ <. Let G ( ts, )( =, ) be the Green s functon of the lnear boundary value problem: u () t + λ ut () =, u() = u() =. Then, carefully calculaton yeld: s( t), s t G (, ts) = t( s), t s sn ssn ( t), s t sn G (, ts) = sn t sn ( s), t s sn Lemma.: Suppose (H ) (H ) hold. Then for any gt C[,], BVP () u t + u t = g t < t < () () (), u() = u() = u () = u () = () the unque soluton where ut = G( tsg, ) ( s, t) g( t)dtds. (3) s( t), s t G (, ts) =, t( s), t s sn τ sn ( s), τ s sn G (, s τ ) = sn ssn ( τ ), s τ sn Lemma. [5] : ssume (H ) (H ) hold. Then one has: () G( ts, ), ts, [,] ; () G( ts, ) CG( ss, ), ts, [,]; () G(, ts) δ G(,) ttg( ss, ), ts, [,]. Where: C =, δ = ; C =, δ = sn. sn Lemma.3: ssume (H ) (H ) hold and are gven as above, Then one has: mn ut du 3 t 76
3 sn CG where: d =, M C = G(,) ssg(,)d s, Proof: By(3)and () of Lemma.,we get: Therefore, M = G( ss, )ds, G = mn G 3 ( tt, ). u( t) CC G( s, s) G ( tt, ) g( t)dtd s CC M G ( tt, ) g( t)dt u CC M G ( ττ, ) g( τ)dτ By ()of Lemma., we have: ut dd G( ttg, ) ( ssg, ) ( ssg, ) ( t, t) g( t)dtds = dd CG( tt, ) G( t, t) g( t)dt δδ C G (,) tt u CC M Let G = mn G 3 ( tt, ), we have: t [, ] t [, ] δδ CG mn ut t [ 3, ] CC M u = sn CG u M = du Theorem. [] : Let r > r >, L > be constants and { α β } Ω = u X : ( u) < r, ( u) < L, =, two bounded open sets n X. Set { α } D = u X : ( u) = r,, =, ; ssume T : K K s a completely contnuous operator satsfyng: ( ) α α ( Tu) < r, u D K; ( Tu) > r, u D K; ( ) β ( Tu) < L, u K; ( 3 )there s p ( K)\ { } Ω, such that α( p) and α( u+ λp) α( u),for all u K, λ. Then T has at least one fxed pont n ( Ω \ Ω) K. 77
4 3. The man results Let X = C [,] be the Banach space equpped wth the norm { :, mn t [ } 3, ] K= u X u ut du s a cone n X. max max t [,] t [,] u = ut + u t, and Defne functonals a( u) = max ut, β ( u) = max u ( t), u X. t [,] t [,] then, u max { a( u), β( u) }, α( λu) = λα( u), βλ ( u) = λβ( u), u X, λ R, α( u) α( v), uv, Ku, v. ssume (H ) hold, the greens functon of the problem () G (, ts). let gt () =, we have t + t t t sn sn sn (, ) (, t)dtd = + G tsg s s we denote: t [,] M max G ( tsg, ) ( s, t )d t d s =, sn Q = [6 ( cos ) 3sn ] = t [, 3 ] 3 m max G ( tsg, ) ( s, t )d t d s We wll suppose that there are L > b > db > c >, such that f(, tuv, ) f(, tuv, ) satsfes the followng growth condtons: c (H 3 ) f( tuv,, ) <, ( tuv,, ) [,] [, c] [ LL, ]; λm b 3 (H ) f(, tuv, ), (, tuv, ) [, ] [ dbb, ] [ LL, ]; λm L (H 5 ) f( tuv,, ) <, ( tuv,, ) [,] [, b] [ LL, ]. λq Let f( tuv,, ),( tuv,, ) [,] [, b] (, ) f (, tuv, ) = f(, tbv, ),(, tuv, ) [,] ( b, ) (, ) f ( tuv,, ),( tuv,, ) [,] [, ) [ LL, ] f(, tuv, ) = f (, tu, L),(, tuv, ) [,] [, ) (, L] f ( tul,, ),( tuv,, ) [,] [, ) [ L, ) Defne: λ (, ) (, t) ( t, ( t), ( t))dtd Tu t = G t s G s f u u s () = t t (5) ( Tu) ( t) λ[ G ( s, t) f ( t, u( t), u ( t))dtd s sg ( s, t) f ( t, u( t), u ( t))dtd s] Lemma 3.: Suppose (H ) (H ) hold, then T : K K s completely contnuous. Proof:For u K, by (5) and Lemma.,there s Tu. 78
5 so, = max λ (, ) (, t) ( t, ( t), ( t))dtd t [,] Tu G t s G s f u u s we have : λ CCG s s G ττ f τuτ u τ τ s (, ) (, ) (,, )d d (, ) (,, )d λcc M G ττ f τuτ u τ τ mn = mn (, ) (, ) (,, )d 3 3 t [, ] t [, ] Tu t λ G t s G s t f t u t u t tds (, ) (, ) (, ) (, ) (,, )d d λd d G ttg ssg ssg t t f t ut u t t s CG ( tt, ) G (, ) f(, u, u)d λd d t t t t t t CG G (, ) f(, u, u)d λd d τ τ τ τ τ τ λδ δ CG CC M = d Tu Tu Therefore, we get T( K) K. So we can get T( K) K.Let B K s bounded, t s clear that T( B ) s bounded. Usng f, G(, ts), G(, tss ) contnuous, we show that T( Bs ) equcontnuous. By the rzela-scol theorem, a standard proof yelds T : K K s completely contnuous. Theorem 3.: Suppose condton (H ) (H 5 ) hold, Then BVP () has at least one postve soluton ut () satsfyng: c< α( u) < b, u () t < L Proof : Take Ω = { u X: ut () < c, u() t < L}, Ω = { u X: ut () < b, u() t < L} two bounded open sets n X and D = { u X α u = c}, D = { u X α u = b} : : such that α( u+ λp) α( u), u K, λ, u D K, α( u) = c, From (H 3 ) we have: = max (, ) (, ) (,, )d d t [,] a Tu λ G t s G s t f t u t u t t s max (, ) (, ) c < λ G d d tsg st t s t [,] λm c = max G (, ) (, )d d tsg st t s M t [,] = c 3 u D K, α( u) = b. From Lemma.3, we have u() t dα( u) = db, t [, ], so, from (H ) we get: = max (, ) (, ) (,, )d d t [,] a Tu λ G t s G s t f t u t u t t s max 3 (, ) (, ) b λ G d d tsg st t s λm > t [, 3 ] 79
6 3 b = max G ( 3 tsg, ) ( s, t )d t d s m t [, ] = b u K, from (H 5 ) we get: = max (, ) (,, )d d t [,] t β Tu λ G s t f t u t u t t s λ (, ) (, τ) ( τ, ( τ), ( τ))dτd d Q ssq s f u u s < 6 ( cos ) 3sn L = = L Q sn λ sg s τ f τ u τ u τ τ s (, ) (,, )d d Theorem. mples there s u Ω ( \ Ω) K, such that u = Tu. for BVP(), satsfyng : c< α( u) < b, u () t < L so, ut () s a postve soluton Thus, Theorem 3. s completed. References [] R. M, H.WNG. On the Exstence of Postve Solutons of Fourth-Order Ordnary Dfferental Equatons. ppl. nal. 995, 59: 5 3 [] B. LIU. Postve Solutons of Fourth-Order Two-Pont Boundary Value Problems. ppl. Math. Comput,, 8: 7 [3] R.Y. M. Exstence of Postve Solutons of a Fourth-Order Boundary Value Problem. ppl. Math. Comput, 5,68: 9 3 [] Z.B. BI, H.Y. Wang. On the Postve Solutons of Some Nonlnear Fourth-Order Beam Equatons. J. Math. nal. ppl., 7: [5] Y.X. LI. Postve Solutons of Fourth-Order Boundary Value Problems wth Two Parameters. J. Math. nal. ppl, 3, 8:77 8 [6] Q.L. YO. Local Exstence of Multple Postve Solutons to a Sngular Cantlever Beam Equaton. J. Math. nal. ppl., 363: 38 5 [7] H.Y. FENG, D.H. JI, W.G. GE. Exstence and Unqueness of Solutons for a Fourth-Order Boundary Value Problem. Nonlnear nal, 9, 7: [8] G. Q. CHI. Exstence of Postve Solutons for Fourth-Order Boundary Value Problem wth Varable Parameters. Nonlnear nal, 7, 66:87 88 [9] J. f. Xu, Z. l. Yang. Postve Solutons for a Fourth order p-laplacan Boundary Value Problem. Nonlnear nal,, 7: 6-63 [] Y. P. GUO, W. G. GE. Postve Solutons for Three-Pont Boundary Value Problems wth Dependence on the Frst Order Dervatves. Journal of Mathematcal nalyss and pplcatons,, 9:
Existence results for a fourth order multipoint boundary value problem at resonance
Avalable onlne at www.scencedrect.com ScenceDrect Journal of the Ngeran Mathematcal Socety xx (xxxx) xxx xxx www.elsever.com/locate/jnnms Exstence results for a fourth order multpont boundary value problem
More informationUniqueness of Weak Solutions to the 3D Ginzburg- Landau Model for Superconductivity
Int. Journal of Math. Analyss, Vol. 6, 212, no. 22, 195-114 Unqueness of Weak Solutons to the 3D Gnzburg- Landau Model for Superconductvty Jshan Fan Department of Appled Mathematcs Nanjng Forestry Unversty
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationModelli Clamfim Equazioni differenziali 7 ottobre 2013
CLAMFIM Bologna Modell 1 @ Clamfm Equazon dfferenzal 7 ottobre 2013 professor Danele Rtell danele.rtell@unbo.t 1/18? Ordnary Dfferental Equatons A dfferental equaton s an equaton that defnes a relatonshp
More informationApplication of B-Spline to Numerical Solution of a System of Singularly Perturbed Problems
Mathematca Aeterna, Vol. 1, 011, no. 06, 405 415 Applcaton of B-Splne to Numercal Soluton of a System of Sngularly Perturbed Problems Yogesh Gupta Department of Mathematcs Unted College of Engneerng &
More informationn α j x j = 0 j=1 has a nontrivial solution. Here A is the n k matrix whose jth column is the vector for all t j=0
MODULE 2 Topcs: Lnear ndependence, bass and dmenson We have seen that f n a set of vectors one vector s a lnear combnaton of the remanng vectors n the set then the span of the set s unchanged f that vector
More informationPerron Vectors of an Irreducible Nonnegative Interval Matrix
Perron Vectors of an Irreducble Nonnegatve Interval Matrx Jr Rohn August 4 2005 Abstract As s well known an rreducble nonnegatve matrx possesses a unquely determned Perron vector. As the man result of
More informationProjective change between two Special (α, β)- Finsler Metrics
Internatonal Journal of Trend n Research and Development, Volume 2(6), ISSN 2394-9333 www.jtrd.com Projectve change between two Specal (, β)- Fnsler Metrcs Gayathr.K 1 and Narasmhamurthy.S.K 2 1 Assstant
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationModelli Clamfim Equazioni differenziali 22 settembre 2016
CLAMFIM Bologna Modell 1 @ Clamfm Equazon dfferenzal 22 settembre 2016 professor Danele Rtell danele.rtell@unbo.t 1/22? Ordnary Dfferental Equatons A dfferental equaton s an equaton that defnes a relatonshp
More informationThe equation of motion of a dynamical system is given by a set of differential equations. That is (1)
Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence
More informationAPPENDIX A Some Linear Algebra
APPENDIX A Some Lnear Algebra The collecton of m, n matrces A.1 Matrces a 1,1,..., a 1,n A = a m,1,..., a m,n wth real elements a,j s denoted by R m,n. If n = 1 then A s called a column vector. Smlarly,
More informationA CHARACTERIZATION OF ADDITIVE DERIVATIONS ON VON NEUMANN ALGEBRAS
Journal of Mathematcal Scences: Advances and Applcatons Volume 25, 2014, Pages 1-12 A CHARACTERIZATION OF ADDITIVE DERIVATIONS ON VON NEUMANN ALGEBRAS JIA JI, WEN ZHANG and XIAOFEI QI Department of Mathematcs
More informationGeneral viscosity iterative method for a sequence of quasi-nonexpansive mappings
Avalable onlne at www.tjnsa.com J. Nonlnear Sc. Appl. 9 (2016), 5672 5682 Research Artcle General vscosty teratve method for a sequence of quas-nonexpansve mappngs Cuje Zhang, Ynan Wang College of Scence,
More informationPolynomial Regression Models
LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance
More informationThe Analytical Solution of a System of Nonlinear Differential Equations
Int. Journal of Math. Analyss, Vol. 1, 007, no. 10, 451-46 The Analytcal Soluton of a System of Nonlnear Dfferental Equatons Yunhu L a, Fazhan Geng b and Mnggen Cu b1 a Dept. of Math., Harbn Unversty Harbn,
More informationTHE CHINESE REMAINDER THEOREM. We should thank the Chinese for their wonderful remainder theorem. Glenn Stevens
THE CHINESE REMAINDER THEOREM KEITH CONRAD We should thank the Chnese for ther wonderful remander theorem. Glenn Stevens 1. Introducton The Chnese remander theorem says we can unquely solve any par of
More informationSome modelling aspects for the Matlab implementation of MMA
Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton
More informationY. Guo. A. Liu, T. Liu, Q. Ma UDC
UDC 517. 9 OSCILLATION OF A CLASS OF NONLINEAR PARTIAL DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLES* ОСЦИЛЯЦIЯ КЛАСУ НЕЛIНIЙНИХ ЧАСТКОВО РIЗНИЦЕВИХ РIВНЯНЬ З НЕПЕРЕРВНИМИ ЗМIННИМИ Y. Guo Graduate School
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationContinuous Time Markov Chain
Contnuous Tme Markov Chan Hu Jn Department of Electroncs and Communcaton Engneerng Hanyang Unversty ERICA Campus Contents Contnuous tme Markov Chan (CTMC) Propertes of sojourn tme Relatons Transton probablty
More informationMath1110 (Spring 2009) Prelim 3 - Solutions
Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.
More informationGroup Analysis of Ordinary Differential Equations of the Order n>2
Symmetry n Nonlnear Mathematcal Physcs 997, V., 64 7. Group Analyss of Ordnary Dfferental Equatons of the Order n> L.M. BERKOVICH and S.Y. POPOV Samara State Unversty, 4430, Samara, Russa E-mal: berk@nfo.ssu.samara.ru
More informationHomogenization of reaction-diffusion processes in a two-component porous medium with a non-linear flux-condition on the interface
Homogenzaton of reacton-dffuson processes n a two-component porous medum wth a non-lnear flux-condton on the nterface Internatonal Conference on Numercal and Mathematcal Modelng of Flow and Transport n
More informationChapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary
More informationYong Joon Ryang. 1. Introduction Consider the multicommodity transportation problem with convex quadratic cost function. 1 2 (x x0 ) T Q(x x 0 )
Kangweon-Kyungk Math. Jour. 4 1996), No. 1, pp. 7 16 AN ITERATIVE ROW-ACTION METHOD FOR MULTICOMMODITY TRANSPORTATION PROBLEMS Yong Joon Ryang Abstract. The optmzaton problems wth quadratc constrants often
More informationIntegrals and Invariants of Euler-Lagrange Equations
Lecture 16 Integrals and Invarants of Euler-Lagrange Equatons ME 256 at the Indan Insttute of Scence, Bengaluru Varatonal Methods and Structural Optmzaton G. K. Ananthasuresh Professor, Mechancal Engneerng,
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationAsymptotics of the Solution of a Boundary Value. Problem for One-Characteristic Differential. Equation Degenerating into a Parabolic Equation
Nonl. Analyss and Dfferental Equatons, ol., 4, no., 5 - HIKARI Ltd, www.m-har.com http://dx.do.org/.988/nade.4.456 Asymptotcs of the Soluton of a Boundary alue Problem for One-Characterstc Dfferental Equaton
More informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationBeyond Zudilin s Conjectured q-analog of Schmidt s problem
Beyond Zudln s Conectured q-analog of Schmdt s problem Thotsaporn Ae Thanatpanonda thotsaporn@gmalcom Mathematcs Subect Classfcaton: 11B65 33B99 Abstract Usng the methodology of (rgorous expermental mathematcs
More informationIntroduction. - The Second Lyapunov Method. - The First Lyapunov Method
Stablty Analyss A. Khak Sedgh Control Systems Group Faculty of Electrcal and Computer Engneerng K. N. Toos Unversty of Technology February 2009 1 Introducton Stablty s the most promnent characterstc of
More informationMMA and GCMMA two methods for nonlinear optimization
MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons
More informationMechanics Physics 151
Mechancs Physcs 151 Lecture 3 Lagrange s Equatons (Goldsten Chapter 1) Hamlton s Prncple (Chapter 2) What We Dd Last Tme! Dscussed mult-partcle systems! Internal and external forces! Laws of acton and
More informationResearch Article The Solution of Two-Point Boundary Value Problem of a Class of Duffing-Type Systems with Non-C 1 Perturbation Term
Hndaw Publshng Corporaton Boundary Value Problems Volume 9, Artcle ID 87834, 1 pages do:1.1155/9/87834 Research Artcle The Soluton of Two-Pont Boundary Value Problem of a Class of Duffng-Type Systems wth
More informationFixed point method and its improvement for the system of Volterra-Fredholm integral equations of the second kind
MATEMATIKA, 217, Volume 33, Number 2, 191 26 c Penerbt UTM Press. All rghts reserved Fxed pont method and ts mprovement for the system of Volterra-Fredholm ntegral equatons of the second knd 1 Talaat I.
More informationarxiv: v1 [math.co] 1 Mar 2014
Unon-ntersectng set systems Gyula O.H. Katona and Dánel T. Nagy March 4, 014 arxv:1403.0088v1 [math.co] 1 Mar 014 Abstract Three ntersecton theorems are proved. Frst, we determne the sze of the largest
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationIntegrals and Invariants of
Lecture 16 Integrals and Invarants of Euler Lagrange Equatons NPTEL Course Varatonal Methods and Structural Optmzaton G. K. Ananthasuresh Professor, Mechancal Engneerng, Indan Insttute of Scence, Banagalore
More informationModelli Clamfim Equazione del Calore Lezione ottobre 2014
CLAMFIM Bologna Modell 1 @ Clamfm Equazone del Calore Lezone 17 15 ottobre 2014 professor Danele Rtell danele.rtell@unbo.t 1/24? Convoluton The convoluton of two functons g(t) and f(t) s the functon (g
More information( ) [ ( k) ( k) ( x) ( ) ( ) ( ) [ ] ξ [ ] [ ] [ ] ( )( ) i ( ) ( )( ) 2! ( ) = ( ) 3 Interpolation. Polynomial Approximation.
3 Interpolaton {( y } Gven:,,,,,, [ ] Fnd: y for some Mn, Ma Polynomal Appromaton Theorem (Weerstrass Appromaton Theorem --- estence ε [ ab] f( P( , then there ests a polynomal
More informationFACTORIZATION IN KRULL MONOIDS WITH INFINITE CLASS GROUP
C O L L O Q U I U M M A T H E M A T I C U M VOL. 80 1999 NO. 1 FACTORIZATION IN KRULL MONOIDS WITH INFINITE CLASS GROUP BY FLORIAN K A I N R A T H (GRAZ) Abstract. Let H be a Krull monod wth nfnte class
More informationResearch Article A Generalized Sum-Difference Inequality and Applications to Partial Difference Equations
Hndaw Publshng Corporaton Advances n Dfference Equatons Volume 008, Artcle ID 695495, pages do:0.55/008/695495 Research Artcle A Generalzed Sum-Dfference Inequalty and Applcatons to Partal Dfference Equatons
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationMultiple non-trivial solutions of the Neumann problem for p-laplacian systems
Complex Varables and Ellptc Equatons Vol. 55, Nos. 5 6, May June 2010, 573 579 Multple non-trval solutons of the Neumann problem for p-laplacan systems Sad El Manoun a and Kanshka Perera b * a Department
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationCase Study of Markov Chains Ray-Knight Compactification
Internatonal Journal of Contemporary Mathematcal Scences Vol. 9, 24, no. 6, 753-76 HIKAI Ltd, www.m-har.com http://dx.do.org/.2988/cms.24.46 Case Study of Marov Chans ay-knght Compactfcaton HaXa Du and
More informationSharp integral inequalities involving high-order partial derivatives. Journal Of Inequalities And Applications, 2008, v. 2008, article no.
Ttle Sharp ntegral nequaltes nvolvng hgh-order partal dervatves Authors Zhao, CJ; Cheung, WS Ctaton Journal Of Inequaltes And Applcatons, 008, v. 008, artcle no. 5747 Issued Date 008 URL http://hdl.handle.net/07/569
More informationAppendix for Causal Interaction in Factorial Experiments: Application to Conjoint Analysis
A Appendx for Causal Interacton n Factoral Experments: Applcaton to Conjont Analyss Mathematcal Appendx: Proofs of Theorems A. Lemmas Below, we descrbe all the lemmas, whch are used to prove the man theorems
More informationPerfect Competition and the Nash Bargaining Solution
Perfect Competton and the Nash Barganng Soluton Renhard John Department of Economcs Unversty of Bonn Adenauerallee 24-42 53113 Bonn, Germany emal: rohn@un-bonn.de May 2005 Abstract For a lnear exchange
More informationPETER HENR IC I TECHNICAL REPORT NO. CS 137 JULY COMPUTER SCIENCE DEPARTMENT School of Humanities and Sciences STANFORD UN IVERS ITY
cs 137 j FXED PONTS OF ANAYTC FUNCTONS BY * PETER HENR C TECHNCA REPORT NO. CS 137 JUY 1969 COMPUTER SCENCE DEPARTMENT School of Humantes and Scences STANFORD UN VERS TY FXED POXNTS QF ANAZYTC.FUNCTQNS*..
More informationThe Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method
Journal of Electromagnetc Analyss and Applcatons, 04, 6, 0-08 Publshed Onlne September 04 n ScRes. http://www.scrp.org/journal/jemaa http://dx.do.org/0.46/jemaa.04.6000 The Exact Formulaton of the Inverse
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationChapter 2 Transformations and Expectations. , and define f
Revew for the prevous lecture Defnton: support set of a ranom varable, the monotone functon; Theorem: How to obtan a cf, pf (or pmf) of functons of a ranom varable; Eamples: several eamples Chapter Transformatons
More informationInternational Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013) equation. E. M. E. Zayed and S. A.
Internatonal Conference on Advanced Computer Scence and Electroncs Informaton (ICACSEI ) The two varable (G'/G/G) -expanson method for fndng exact travelng wave solutons of the (+) dmensonal nonlnear potental
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationA note on almost sure behavior of randomly weighted sums of φ-mixing random variables with φ-mixing weights
ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA Volume 7, Number 2, December 203 Avalable onlne at http://acutm.math.ut.ee A note on almost sure behavor of randomly weghted sums of φ-mxng
More informationAppendix B. Criterion of Riemann-Stieltjes Integrability
Appendx B. Crteron of Remann-Steltes Integrablty Ths note s complementary to [R, Ch. 6] and [T, Sec. 3.5]. The man result of ths note s Theorem B.3, whch provdes the necessary and suffcent condtons for
More informationSelf-complementing permutations of k-uniform hypergraphs
Dscrete Mathematcs Theoretcal Computer Scence DMTCS vol. 11:1, 2009, 117 124 Self-complementng permutatons of k-unform hypergraphs Artur Szymańsk A. Paweł Wojda Faculty of Appled Mathematcs, AGH Unversty
More informationMaejo International Journal of Science and Technology
Maejo Int. J. Sc. Technol. () - Full Paper Maejo Internatonal Journal of Scence and Technology ISSN - Avalable onlne at www.mjst.mju.ac.th Fourth-order method for sngularly perturbed sngular boundary value
More information8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS
SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 493 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces you have studed thus far n the text are real vector spaces because the scalars
More informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationLecture 17 : Stochastic Processes II
: Stochastc Processes II 1 Contnuous-tme stochastc process So far we have studed dscrete-tme stochastc processes. We studed the concept of Makov chans and martngales, tme seres analyss, and regresson analyss
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationSTEINHAUS PROPERTY IN BANACH LATTICES
DEPARTMENT OF MATHEMATICS TECHNICAL REPORT STEINHAUS PROPERTY IN BANACH LATTICES DAMIAN KUBIAK AND DAVID TIDWELL SPRING 2015 No. 2015-1 TENNESSEE TECHNOLOGICAL UNIVERSITY Cookevlle, TN 38505 STEINHAUS
More informationA New Refinement of Jacobi Method for Solution of Linear System Equations AX=b
Int J Contemp Math Scences, Vol 3, 28, no 17, 819-827 A New Refnement of Jacob Method for Soluton of Lnear System Equatons AX=b F Naem Dafchah Department of Mathematcs, Faculty of Scences Unversty of Gulan,
More informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More informationON THE JACOBIAN CONJECTURE
v v v Far East Journal of Mathematcal Scences (FJMS) 17 Pushpa Publshng House, Allahabad, Inda http://www.pphm.com http://dx.do.org/1.17654/ms1111565 Volume 11, Number 11, 17, Pages 565-574 ISSN: 97-871
More information6.3.4 Modified Euler s method of integration
6.3.4 Modfed Euler s method of ntegraton Before dscussng the applcaton of Euler s method for solvng the swng equatons, let us frst revew the basc Euler s method of numercal ntegraton. Let the general from
More informationLecture 16 Statistical Analysis in Biomaterials Research (Part II)
3.051J/0.340J 1 Lecture 16 Statstcal Analyss n Bomaterals Research (Part II) C. F Dstrbuton Allows comparson of varablty of behavor between populatons usng test of hypothess: σ x = σ x amed for Brtsh statstcan
More informationFirst day August 1, Problems and Solutions
FOURTH INTERNATIONAL COMPETITION FOR UNIVERSITY STUDENTS IN MATHEMATICS July 30 August 4, 997, Plovdv, BULGARIA Frst day August, 997 Problems and Solutons Problem. Let {ε n } n= be a sequence of postve
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics
ECOOMICS 35*-A Md-Term Exam -- Fall Term 000 Page of 3 pages QUEE'S UIVERSITY AT KIGSTO Department of Economcs ECOOMICS 35* - Secton A Introductory Econometrcs Fall Term 000 MID-TERM EAM ASWERS MG Abbott
More informationThe lower and upper bounds on Perron root of nonnegative irreducible matrices
Journal of Computatonal Appled Mathematcs 217 (2008) 259 267 wwwelsevercom/locate/cam The lower upper bounds on Perron root of nonnegatve rreducble matrces Guang-Xn Huang a,, Feng Yn b,keguo a a College
More informationMath 217 Fall 2013 Homework 2 Solutions
Math 17 Fall 013 Homework Solutons Due Thursday Sept. 6, 013 5pm Ths homework conssts of 6 problems of 5 ponts each. The total s 30. You need to fully justfy your answer prove that your functon ndeed has
More information8.022 (E&M) Lecture 4
Topcs: 8.0 (E&M) Lecture 4 More applcatons of vector calculus to electrostatcs: Laplacan: Posson and Laplace equaton url: concept and applcatons to electrostatcs Introducton to conductors Last tme Electrc
More informationALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION
ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII AL.I. CUZA DIN IAŞI (S.N.) MATEMATICĂ, Tomul LIX, 013, f.1 DOI: 10.478/v10157-01-00-y ALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION BY ION
More informationarxiv: v1 [math.co] 12 Sep 2014
arxv:1409.3707v1 [math.co] 12 Sep 2014 On the bnomal sums of Horadam sequence Nazmye Ylmaz and Necat Taskara Department of Mathematcs, Scence Faculty, Selcuk Unversty, 42075, Campus, Konya, Turkey March
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationLecture. Polymer Thermodynamics 0331 L Chemical Potential
Prof. Dr. rer. nat. habl. S. Enders Faculty III for Process Scence Insttute of Chemcal Engneerng Department of Thermodynamcs Lecture Polymer Thermodynamcs 033 L 337 3. Chemcal Potental Polymer Thermodynamcs
More informationComparative Studies of Law of Conservation of Energy. and Law Clusters of Conservation of Generalized Energy
Comparatve Studes of Law of Conservaton of Energy and Law Clusters of Conservaton of Generalzed Energy No.3 of Comparatve Physcs Seres Papers Fu Yuhua (CNOOC Research Insttute, E-mal:fuyh1945@sna.com)
More informationLecture 5.8 Flux Vector Splitting
Lecture 5.8 Flux Vector Splttng 1 Flux Vector Splttng The vector E n (5.7.) can be rewrtten as E = AU (5.8.1) (wth A as gven n (5.7.4) or (5.7.6) ) whenever, the equaton of state s of the separable form
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationThe Study of Teaching-learning-based Optimization Algorithm
Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute
More informationGeneralized Linear Methods
Generalzed Lnear Methods 1 Introducton In the Ensemble Methods the general dea s that usng a combnaton of several weak learner one could make a better learner. More formally, assume that we have a set
More informationThe binomial transforms of the generalized (s, t )-Jacobsthal matrix sequence
Int. J. Adv. Appl. Math. and Mech. 6(3 (2019 14 20 (ISSN: 2347-2529 Journal homepage: www.jaamm.com IJAAMM Internatonal Journal of Advances n Appled Mathematcs and Mechancs The bnomal transforms of the
More informationMaximizing the number of nonnegative subsets
Maxmzng the number of nonnegatve subsets Noga Alon Hao Huang December 1, 213 Abstract Gven a set of n real numbers, f the sum of elements of every subset of sze larger than k s negatve, what s the maxmum
More informationSUCCESSIVE MINIMA AND LATTICE POINTS (AFTER HENK, GILLET AND SOULÉ) M(B) := # ( B Z N)
SUCCESSIVE MINIMA AND LATTICE POINTS (AFTER HENK, GILLET AND SOULÉ) S.BOUCKSOM Abstract. The goal of ths note s to present a remarably smple proof, due to Hen, of a result prevously obtaned by Gllet-Soulé,
More informationNew Exact Traveling Wave Solutions for Two Nonlinear Evolution Equations
Internatonal Conference on Computer Technology and Scence (ICCTS ) IPCSIT vol. 47 () () IACSIT Press, Sngapore DOI:.7763/IPCSIT..V47.66 New Exact Travelng Wave Solutons for Two Nonlnear Evoluton Equatons
More informationAppendix B. The Finite Difference Scheme
140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton
More informationCubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two
World Academy of Scence Engneerng and echnology Internatonal Journal of Mathematcal and omputatonal Scences Vol: No:0 00 ubc rgonometrc B-Splne Appled to Lnear wo-pont Boundary Value Problems of Order
More informationTR/95 February Splines G. H. BEHFOROOZ* & N. PAPAMICHAEL
TR/9 February 980 End Condtons for Interpolatory Quntc Splnes by G. H. BEHFOROOZ* & N. PAPAMICHAEL *Present address: Dept of Matematcs Unversty of Tabrz Tabrz Iran. W9609 A B S T R A C T Accurate end condtons
More informationOptimal Pursuit Time in Differential Game for an Infinite System of Differential Equations
Malaysan Journal of Mathematcal Scences 1(S) August: 267 277 (216) Specal Issue: The 7 th Internatonal Conference on Research and Educaton n Mathematcs (ICREM7) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES
More informationCALCULUS CLASSROOM CAPSULES
CALCULUS CLASSROOM CAPSULES SESSION S86 Dr. Sham Alfred Rartan Valley Communty College salfred@rartanval.edu 38th AMATYC Annual Conference Jacksonvlle, Florda November 8-, 202 2 Calculus Classroom Capsules
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More information