THE EXISTENCE OF SOLUTIONS FOR A CLASS OF IMPULSIVE FRACTIONAL Q-DIFFERENCE EQUATIONS
|
|
- Imogene Richards
- 5 years ago
- Views:
Transcription
1 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN THE EXSTENCE OF SOLUTONS FOR A CLASS OF MPULSVE FRACTONAL Q-DFFERENCE EQUATONS Shuyun Wn, Yu Tng, Q GE Deprmen of Mhemcs, Ynbn Unversy, Yn, Jln, CHNA Correspondence should be ddressed o Q GE, ge9688@6com ABSTRACT n hs pper, we prove he exsence nd unueness of soluons for clss of nl vlue problem for mpulsve frconl -dfference euon of order by pplyng some well-nown fxed pon heorems Some exmples re presened o llusre he mn resuls MSC: 6A; 9A; 4A7 Keywords: -clculus ; mpulsve frconl -dfference euons; exsence; unueness NTRODUCTON n recen yers, he opc of -clculus hs rced he enon of severl reserchers nd vrey of new resuls on -dfference nd frconl -dfference euons cn be found n he ppers [-] nd he references ced heren n [4] he noons of -dervve nd - negrl of funcon f : J : [, ] R hve been nroduced nd her bsc properes ws proved As pplcons exsence nd unueness resuls for nl vlue problems for frs nd second order mpulsve -dfference euons re proved n [5], he uhors ppled he conceps of unum clculus developed n [4] o sudy clss of boundry vlue problem of ordnry mpulsve -negro-dfference euons, some exsence nd unueness resuls for hs problem were proved by usng vrey of fxed pon heorems n [6] he uhors used he -shfng operor o develop he new conceps of frconl unum clculus such s he Remnn Louvlle frconl dervve nd negrl nd her properes They lso formuled he exsence nd unueness resuls for some clsses of frs nd second orders mpulsve frconl -dfference euons nspred by[6], n hs pper, we sudy he exsence nd unueness of soluons for he followng nl vlue problem for mpulsve frconl -dffer- ence euon of order he form D ( (, (,, x f x J Δ x( ( x(,,,, m, ( Δ x( ( x(,,,, m, x(, D x( (, D x where J T m m T J J nd [, ],, [, ], (, ],,,, m D respecvely re he Remnn-Louvlle frconl -dfference of order nd on nervl J, for,,, m, f : JRR s connuous funcon,, ( RR, for,,, m The noon Δ x ( nd Δ x ( re defned by C where nd Δ x( x( x(,,,, m, Δ x( x( x(,,,, m, ( respecvely re he Remnn-Louvlle frconl -negrl of order nd on J R, {,,, m}, (, ] D Progressve Acdemc Publshng, UK Pge 6 wwwdpublconsorg
2 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN Prelmnres Ths secon s devoed o some bsc conceps such s -shfng operor, Remnn Louvlle frconl -negrl nd -dfference on gven nervl The presenon here cn be found n, for exmple, [6,7] We defne -shfng operor s Φ ( m m ( The power of -shfng operor s defned s More generlly, f R, hen ( ( ( n m, ( n m ( n Φ ( m, { } Φ ( mn Φ ( mn ( ( n ( n m n n N, Defnon The frconl -dervve of Remnn Louvlle ype of order v on nervl [ b, ] s defned by ( D f ( f ( nd ( v ( ( l l D f D v f (, v, where l s he smlles neger greer hn or eul o ν Defnon Le nd f be funcon defned on [ b, ] The frconl -negrl of Remnn Louvlle ype s gven by ( f ( f ( nd ( ( f ( ( Φ ( s f ( s ds,, [, b] ( From [6], we hve he followng formuls for [, b],, R : ( ( D ( (, ( ( ( ( Lemm Le, R nd f be connuous funcon on[, b], The Remnn Louvlle frconl -negrl hs he followng sem-group propery f ( f ( f ( Lemm 4 Le f be -negrble funcon on[ b, ] Then he followng euly holds D f ( f ( For, [, b] Lemm 5 Le nd p be posve neger Then for [, b] he followng euly holds p p p p ( D f ( D f ( D f ( ( p Lemm 6 ([8]Le E be Bnch spce Assume h s n open bounded subse of E wh nd le T: E be compleely connuous operor such h Tu u, u Then T hs fxed pon n Lemm 7 ([8] Le E be Bnch spce Assume h T : E E s compleely connuous operor nd he se V { ue u Tu, } s bounded Then T hs fxed pon n E Le PC( J, R { x : J R: x( s connuous everywhere excep for some whch x ( nd x ( Progressve Acdemc Publshng, UK Pge 7 wwwdpublconsorg
3 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN exs nd x( = x(,,,,, m} For R, we nroduce he spce C, ( J, R { x : J R: : ( x( C( J, R } wh he norm for ech J nd x sup J ( x( nd PC ( J, R { x : J R: : C, ( x( C( J, R,,,, m} wh he norm x mx{sup ( x( :,,, m} Clerly PC ( J, R s Bnch spce Lemm8 f xpc( J, R s soluon of (, hen for ny J,,,, m, m( m( x( = (, ( f x, ( ( ( Where m [ f ( s, x( s( f ( s, x( s( ( x( ] PC J, ( f ( s, x( s( ( x( + f ( s, x( s( ( x( ( m [ f ( s, x( s( f ( s, x( s( ( x( ] f ( s, x( s( ( x(, ( Wh ( < Proof For J, ng he Remnn-Louvlle frconl -negrl of order for he frs euon of ( nd usng Defnon wh Lemm 5, we ge x( = C C f (, x( (4 ( ( where C= x( nd C = x( The frs nl condon of ( mples h C = Tng he Remnn-Louvlle frconl -dervve of order for (4 on J, we hve D x( C f (, x(, And D x( C Therefore, (4 cn be wren s x( = C f (, x( (5 ( Applyng he Remnn-Louvlle frconl -dervve of orders nd =, we hve x( C f ( s, x( s(, x( C f ( s, x( s(, (6 For J =(, ], Remnn-Louvlle frconl -negrng (, we obn ( ( for (5 ( ( x( = x( x( f (, x(, (7 Usng he ump condons of euon ( wh (6-(7 for J, we ge ( ( x( = [ C f ( s, x( s( ( x( ] [ C f ( s, x( s( ( x( ] f (, x( ( ( Repeng he bove process, for J =(, ], we obn Progressve Acdemc Publshng, UK Pge 8 wwwdpublconsorg
4 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN ( x( = [ C ( f ( s, x( s( ( x( ( ( + f ( s, x( s( ( x( ] [ C ( (, ( ( ( ( ] (, ( f s x s x f x, Tng he Remnn-Louvlle frconl -dervve of order (, follows h D x( = C f ( s, x( s( ( x( f (, x( (8 for (8 nd usng For {,,, m}, (, ], we hve D ( = (, ( ( ( ( (, ( ( x C f s x s x f s x s The nl condon D x( ( D x leds o C = [ (, ( ( ( ( (, ( ( ] f s x s x f s x s Subsung he vlue of C n (8, we obn ( Conversely, ssume h x s soluon of he mpulsve frconl negrl euon (, hen by drec compuon, follows h he soluon gven by(ssfes euon ( Ths complees he proof Mn resuls Ths secon dels wh he exsence nd unueness of soluons for he euon ( n vew of Lemm 8, we defne n operor A: PC( J, R PC( J, R by where m, m re gven by ( nd ( m( m( ( Ax( = (, ( f x, ( ( f (, x ( x ( x Theorem Le lm,lm nd lm (,,, m, hen euon x x x x x x ( hs les one soluon Proof To show h Ax PC ( J, R for xpc ( J, R, we suppose, J, nd, hen ( Ax( ( Ax( m ( m ( = ( [ (, ( ( ] f s x s ( ( Progressve Acdemc Publshng, UK Pge 9 wwwdpublconsorg
5 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN m ( m ( ( [ (, ( ( ] f s x s ( ( ( ( { [ f ( s, x( s ( f ( s, x( s ( ( x( ] ( ( f ( s, x( s ( ( x( + f ( s, x( s ( ( x( } ( ( { [ f ( s, x( s ( f ( s, x( s ( ( x( ] ( f ( s, x( s ( ( x( } ( ( Φ ( s f ( s, x( s d s ( ( ( ( ( [( ( Φ ( s ( ( Φ ( s ] f ( s, x( s d s As, we hve ( Ax( ( Ax( for ech,,,, m Therefore, we ge Ax PC ( J, R Now we show h he operor A: PC ( J, R PC ( J, R s compleely connuous Noe h A s connuous n vew of connuy of f, nd Le B PC ( J, R be bounded Then, here exs posve consns L (,, such h f (, x L, ( x L, ( x L, x B Thus, x B, We hve m [ L ( f ( s, x( s ( ( x( ] f s x s x f s x s x ( ( (, ( ( ( ( + ( (, ( ( ( ( T ( L L L ( L ( ( L L m ( L L ( L L, Therefore, ( L f (, x( ( (, ( T ( ( ( Ax( [ ( L L L ( whch mples h ( L ( ( L L ] ( L ( [ ( L L L L ] ( ( T T m TL [ ( ] L ml ml LmT ( T LT ( (, [ ( L ml LT ml ] ( Progressve Acdemc Publshng, UK Pge wwwdpublconsorg
6 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN T T m TL ( Ax( [ ( L ml ml L mt ] ( T LT L ml L T ml L ( ( [ ( ] : On he oher hnd, for ny, J,wh, m,we hve ( ( Ax( ( ( Ax( ( ( TL [ ( ] T L L L L T ( ( ( [ ( L L LT L ] ( ( f ( s, x( s( ( f ( s, x( s( (, Ths mples h A s euconnuous on ll he subnervls J,,,,, m Thus, by Arzel Ascol Theorem, follows h A: PC ( J, R PC ( J, R s compleely connuous f (, x ( x ( x Now, n vew of lm,lm nd lm (,,, m, here exss x x x x x x consn r such h f (, x x, ( x x, ( x x, for x r, where (,, ssfy T T m T [ ( m m mt ] ( T T [ ( m T m ] ( ( Defne ={ x PC ( J, R : x r} nd e xpc ( J, R such h x = rso h x Then, by he process used o obn (, we hve T T mt ( ( Ax( { [ ( m m mt ] ( T T m T m x x, ( ( [ ( ] } whch mples h ( Ax( x, x Therefore, by Lemm 6, he operor A hs les one fxed pon, whch n urn mples h ( hs les one soluon x Ths complees he proof Theorem Assume h (H here exs posve consns L ( =,, such h f (, x L, ( x L, ( x L for J, xr nd,,, m Then euon ( hs les one soluon Proof As shown n Theorem, he operor A: PC( J, R PC( J, R s compleely connuous Now, we show he se V { xpc ( J, R x Ax, } s bounded Le x V, hen x Ax, For ny J, we hve m( m( x( = (, ( f x, ( ( ( where m, m re gven by ( nd ( Combnng (H nd (, we obn Progressve Acdemc Publshng, UK Pge wwwdpublconsorg
7 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN m ( m ( ( x( ( f (, x( ( ( T T m TL [ ( L ml ml LmT ] ( LT L ml LT ml L ( ( :=, T [ ( ] Thus, for ny J, follows h x L So, he se V s bounded Therefore, by he concluson of Lemm 7, he operor A hs les one fxed pon Ths mplesh ( hs les one soluon Ths complees he proof Theorem Assume h (H here exs posve consns N ( =,, such h f (, x f (, y N x y, ( x ( y N x y, ( x ( y N x y for J, xr nd,,, m Then euon ( hs unue soluon f T m T = [ ( N mn ( T mn N( T mt N( m ], ( Where T =mx{ T, T, T } = mn{ (, (, ( } Proof For x, ypc ( J, R, we hve ( T ( ( Ax( ( Ay( { [ f ( s, x( s f ( s, y( s ( ( (, ( (, ( ( ( ( ( ( ] f s x s f s y s x y ( f ( s, x( s f ( s, y( s ( ( ( ( ( x y + f ( s, x( s f ( s, y( s ( ( x( ( y( } ( { [ (, ( (, ( ( f s x s f s y s ( f s x s f s y s x y (, ( (, ( ( ( ( ( ( ] f s x s f s y s x y (, ( (, ( ( ( ( ( ( } ( f ( s, x( s f ( s, y( s ( ( T TN { [ ( N N N NT ] ( ( + [ ( N N N T N ] } x y ( ( NT PC Progressve Acdemc Publshng, UK Pge wwwdpublconsorg
8 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN T T [ ( N N( T N N( T T N( ] x y T m T [ ( N mn( T mn N( T mt N( m ] x y x y PC where s gven by ( Thus, Ax Ay x y As, herefore, A s PC PC conrcon Hence, by he conrcon mppng prncple, euon ( hs unue soluon Exmples Exmple 4 Consder he followng mpulsve frconl -dfference nl vlue problem: D x( rcn x( e x (, [, ],, Δ x( cos x(,,,,,, Δ x( sn x(,,,,,, x(, D7 x( D x(, Here, ( 7 ( 8,,,,, m, T,,, 4, f (, x( rcn x( e x (, ( x( cos x(, ( x( sn x(, Clerly, ll he ssumpons of Theorem re ssfed Thus, by he concluson of Theorem, he mpulsve frconl -dfference nl vlue problem 4 hs les one soluon Exmple 4 Consder he followng mpulsve frconl -dfference nl vlue problem: e sn x( D x(, [,],, ( x 4 8 Δ x( cos x(,,,,9,, x ( Δ x( sn(4 e,,,,9,, x(, D7 x( D x(, Here, ( 7 ( 8,,,,9, m 9, T,,, 4, f (, x( e 5 sn x( 4 x (, x x ( ( ( cos (, x ( x( sn(4 e, Clerly L e, L 6, L 9 nd he condons of Theorem cn redly be verfed Therefore, he concluson of Theorem pples o he mpulsve frconl -dfference nl vlue problem 4 REFERENCES []Jcson, FH: -Dfference euons Am J Mh, 5-4 (9 PC PC Progressve Acdemc Publshng, UK Pge wwwdpublconsorg
9 Europen Journl of Mhemcs nd Compuer Scence Vol 4 No, 7 SSN [] Al-Slm, WA: Some frconl -negrls nd -dervves Proc Ednb Mh Soc 5(, 5-4 (966/967 [] Agrwl, RP: Cern frconl -negrls nd -dervves Proc Cmb Phlos Soc 66, 65-7 (969 [4] Bngerezo, G: Vronl -clculus J Mh Anl Appl 89, (4 [5] Dobrogows, A, Odzewcz, A: Second order -dfference euons solvble by fcorzon mehod J CompuAppl Mh 9, 9-46 (6 [6]Gsper, G, Rhmn, M: Some sysems of mulvrble orhogonl -Rch polynomls Rmnun J, 89-45(7 [7]sml, MEH, Smeonov, P: -Dfference operors for orhogonl polynomls J Compu Appl Mh, (9 [8] Bohner, M, Gusenov, GS: The h-lplce nd -Lplce rnsforms J Mh Anl Appl 65, 75-9 ( [9]El-Shhed, M, Hssn, HA: Posve soluons of -dfference euon Proc Am Mh Soc 8,7-78 ( []Ahmd, B: Boundry-vlue problems for nonlner hrd-order -dfference euons Elecron J Dffer Eu, 94( [] Ahmd, B, Alsed, A, Nouys, SK: A sudy of second-order -dfference euons wh boundry condons AdvDffer Eu, 5 ( []Ahmd, B, Neo, JJ: On nonlocl boundry vlue problems of nonlner -dfference euons Adv Dffer Eu, 8 ( []Yu, C, Wng, J: Exsence of soluons for nonlner second-order -dfference euons wh frs-order -dervves Adv Dffer Eu, 4 ( [4]Trboon, J, Nouys, SK: Qunum clculus on fne nervls nd pplcons o mpulsve dfference euons Adv Dffer Eu, 8 ( [5] C Thpryoon, J Trboon, SK Nouys: Sepred boundry vlue problems for second-order mpulsve -negro-dfference euons, Adv Dffer Eu 4,88 (4 [6]J Trboon, SK Nouys, P Agrwl: New conceps of frconl unum clculus nd pplcons o mpulsve frconl -dfference euons Adv Dffer Eu 5,8 (5 [7]Bshr Ahmd, Sors K Nouys, Jessd Trboon, Ahmed Alsed, Hmed H Alsulm: mpulsve frconl -negro-dfference euons wh sepred boundry condons Appled Mhemcs nd Compuon, 8,99 (6 [8]JX Sun:Nonlner Funconl Anlyss nd s Applcon, Scence Press, Beng, 8 Progressve Acdemc Publshng, UK Pge 4 wwwdpublconsorg
Research Article Oscillatory Criteria for Higher Order Functional Differential Equations with Damping
Journl of Funcon Spces nd Applcons Volume 2013, Arcle ID 968356, 5 pges hp://dx.do.org/10.1155/2013/968356 Reserch Arcle Oscllory Crer for Hgher Order Funconl Dfferenl Equons wh Dmpng Pegung Wng 1 nd H
More informationExistence and Uniqueness Results for Random Impulsive Integro-Differential Equation
Global Journal of Pure and Appled Mahemacs. ISSN 973-768 Volume 4, Number 6 (8), pp. 89-87 Research Inda Publcaons hp://www.rpublcaon.com Exsence and Unqueness Resuls for Random Impulsve Inegro-Dfferenal
More informationA NEW INTERPRETATION OF INTERVAL-VALUED FUZZY INTERIOR IDEALS OF ORDERED SEMIGROUPS
ScInLhore),7),9-37,4 ISSN 3-536; CODEN: SINTE 8 9 A NEW INTERPRETATION O INTERVAL-VALUED UZZY INTERIOR IDEALS O ORDERED SEMIGROUPS Hdy Ullh Khn, b, Nor Hnz Srmn, Asghr Khn c nd z Muhmmd Khn d Deprmen of
More informationSupporting information How to concatenate the local attractors of subnetworks in the HPFP
n Effcen lgorh for Idenfyng Prry Phenoype rcors of Lrge-Scle Boolen Newor Sng-Mo Choo nd Kwng-Hyun Cho Depren of Mhecs Unversy of Ulsn Ulsn 446 Republc of Kore Depren of Bo nd Brn Engneerng Kore dvnced
More informationThe Characterization of Jones Polynomial. for Some Knots
Inernon Mhemc Forum,, 8, no, 9 - The Chrceron of Jones Poynom for Some Knos Mur Cncn Yuuncu Y Ünversy, Fcuy of rs nd Scences Mhemcs Deprmen, 8, n, Turkey m_cencen@yhoocom İsm Yr Non Educon Mnsry, 8, n,
More informationJordan Journal of Physics
Volume, Number, 00. pp. 47-54 RTICLE Jordn Journl of Physcs Frconl Cnoncl Qunzon of he Free Elecromgnec Lgrngn ensy E. K. Jrd, R. S. w b nd J. M. Khlfeh eprmen of Physcs, Unversy of Jordn, 94 mmn, Jordn.
More informationII The Z Transform. Topics to be covered. 1. Introduction. 2. The Z transform. 3. Z transforms of elementary functions
II The Z Trnsfor Tocs o e covered. Inroducon. The Z rnsfor 3. Z rnsfors of eleenry funcons 4. Proeres nd Theory of rnsfor 5. The nverse rnsfor 6. Z rnsfor for solvng dfference equons II. Inroducon The
More informationPositive and negative solutions of a boundary value problem for a
Invenion Journl of Reerch Technology in Engineering & Mngemen (IJRTEM) ISSN: 2455-3689 www.ijrem.com Volume 2 Iue 9 ǁ Sepemer 28 ǁ PP 73-83 Poiive nd negive oluion of oundry vlue prolem for frcionl, -difference
More informationResearch Article The General Solution of Impulsive Systems with Caputo-Hadamard Fractional Derivative of Order
Hndw Publhng Corporon Mhemcl Problem n Engneerng Volume 06, Arcle ID 8080, 0 pge hp://dx.do.org/0.55/06/8080 Reerch Arcle The Generl Soluon of Impulve Syem wh Cpuo-Hdmrd Frconl Dervve of Order q C (R(q)
More informationEXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECOND-ORDER ITERATIVE BOUNDARY-VALUE PROBLEM
Elecronic Journl of Differenil Equions, Vol. 208 (208), No. 50, pp. 6. ISSN: 072-669. URL: hp://ejde.mh.xse.edu or hp://ejde.mh.un.edu EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECOND-ORDER ITERATIVE
More informationCalculus 241, section 12.2 Limits/Continuity & 12.3 Derivatives/Integrals notes by Tim Pilachowski r r r =, with a domain of real ( )
Clculu 4, econ Lm/Connuy & Devve/Inel noe y Tm Plchow, wh domn o el Wh we hve o : veco-vlued uncon, ( ) ( ) ( ) j ( ) nume nd ne o veco The uncon, nd A w done wh eul uncon ( x) nd connuy e he componen
More informationOn One Analytic Method of. Constructing Program Controls
Appled Mahemacal Scences, Vol. 9, 05, no. 8, 409-407 HIKARI Ld, www.m-hkar.com hp://dx.do.org/0.988/ams.05.54349 On One Analyc Mehod of Consrucng Program Conrols A. N. Kvko, S. V. Chsyakov and Yu. E. Balyna
More informationPower Series Solutions for Nonlinear Systems. of Partial Differential Equations
Appled Mhemcl Scences, Vol. 6, 1, no. 14, 5147-5159 Power Seres Soluons for Nonlner Sysems of Prl Dfferenl Equons Amen S. Nuser Jordn Unversy of Scence nd Technology P. O. Bo 33, Irbd, 11, Jordn nuser@us.edu.o
More informationExistence Of Solutions For Nonlinear Fractional Differential Equation With Integral Boundary Conditions
Reserch Ivey: Ieriol Jourl Of Egieerig Ad Sciece Vol., Issue (April 3), Pp 8- Iss(e): 78-47, Iss(p):39-6483, Www.Reserchivey.Com Exisece Of Soluios For Nolier Frciol Differeil Equio Wih Iegrl Boudry Codiios,
More informationMethod of upper lower solutions for nonlinear system of fractional differential equations and applications
Malaya Journal of Maemak, Vol. 6, No. 3, 467-472, 218 hps://do.org/1.26637/mjm63/1 Mehod of upper lower soluons for nonlnear sysem of fraconal dfferenal equaons and applcaons D.B. Dhagude1 *, N.B. Jadhav2
More informationRelative controllability of nonlinear systems with delays in control
Relave conrollably o nonlnear sysems wh delays n conrol Jerzy Klamka Insue o Conrol Engneerng, Slesan Techncal Unversy, 44- Glwce, Poland. phone/ax : 48 32 37227, {jklamka}@a.polsl.glwce.pl Keywor: Conrollably.
More information90 S.S. Drgomr nd (t b)du(t) =u()(b ) u(t)dt: If we dd the bove two equltes, we get (.) u()(b ) u(t)dt = p(; t)du(t) where p(; t) := for ll ; t [; b]:
RGMIA Reserch Report Collecton, Vol., No. 1, 1999 http://sc.vu.edu.u/οrgm ON THE OSTROWSKI INTEGRAL INEQUALITY FOR LIPSCHITZIAN MAPPINGS AND APPLICATIONS S.S. Drgomr Abstrct. A generlzton of Ostrowsk's
More informationOnline Supplement for Dynamic Multi-Technology. Production-Inventory Problem with Emissions Trading
Onlne Supplemen for Dynamc Mul-Technology Producon-Invenory Problem wh Emssons Tradng by We Zhang Zhongsheng Hua Yu Xa and Baofeng Huo Proof of Lemma For any ( qr ) Θ s easy o verfy ha he lnear programmng
More informationContraction Mapping Principle Approach to Differential Equations
epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of
More informationON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX.
ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX. MEHMET ZEKI SARIKAYA?, ERHAN. SET, AND M. EMIN OZDEMIR Asrc. In his noe, we oin new some ineuliies
More informationApproximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy
Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae
More informationON THE WEAK LIMITS OF SMOOTH MAPS FOR THE DIRICHLET ENERGY BETWEEN MANIFOLDS
ON THE WEA LIMITS OF SMOOTH MAPS FOR THE DIRICHLET ENERGY BETWEEN MANIFOLDS FENGBO HANG Absrac. We denfy all he weak sequenal lms of smooh maps n W (M N). In parcular, hs mples a necessary su cen opologcal
More informationGreen s Functions and Comparison Theorems for Differential Equations on Measure Chains
Green s Funcions nd Comprison Theorems for Differenil Equions on Mesure Chins Lynn Erbe nd Alln Peerson Deprmen of Mhemics nd Sisics, Universiy of Nebrsk-Lincoln Lincoln,NE 68588-0323 lerbe@@mh.unl.edu
More informationGENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS. Youngwoo Ahn and Kitae Kim
Korean J. Mah. 19 (2011), No. 3, pp. 263 272 GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS Youngwoo Ahn and Kae Km Absrac. In he paper [1], an explc correspondence beween ceran
More informationHEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More informationNUMERICAL SOLUTION OF THIN FILM EQUATION IN A CLASS OF DISCONTINUOUS FUNCTIONS
Eropen Scenfc Jornl Ags 5 /SPECAL/ eon SSN: 857 788 Prn e - SSN 857-74 NMERCAL SOLON OF HN FLM EQAON N A CLASS OF DSCONNOS FNCONS Bn Snsoysl Assoc Prof Mr Rslov Prof Beyen nversy Deprmen of Memcs n Compng
More informationHidden Markov Model. a ij. Observation : O1,O2,... States in time : q1, q2,... All states : s1, s2,..., sn
Hdden Mrkov Model S S servon : 2... Ses n me : 2... All ses : s s2... s 2 3 2 3 2 Hdden Mrkov Model Con d Dscree Mrkov Model 2 z k s s s s s s Degree Mrkov Model Hdden Mrkov Model Con d : rnson roly from
More informationANOTHER CATEGORY OF THE STOCHASTIC DEPENDENCE FOR ECONOMETRIC MODELING OF TIME SERIES DATA
Tn Corn DOSESCU Ph D Dre Cner Chrsn Unversy Buchres Consnn RAISCHI PhD Depren of Mhecs The Buchres Acdey of Econoc Sudes ANOTHER CATEGORY OF THE STOCHASTIC DEPENDENCE FOR ECONOMETRIC MODELING OF TIME SERIES
More informationON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX
Journl of Applied Mhemics, Sisics nd Informics JAMSI), 9 ), No. ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX MEHMET ZEKI SARIKAYA, ERHAN. SET
More informationHermite-Hadamard-Fejér type inequalities for convex functions via fractional integrals
Sud. Univ. Beş-Bolyi Mh. 6(5, No. 3, 355 366 Hermie-Hdmrd-Fejér ype inequliies for convex funcions vi frcionl inegrls İmd İşcn Asrc. In his pper, firsly we hve eslished Hermie Hdmrd-Fejér inequliy for
More informationMultiple Positive Solutions for the System of Higher Order Two-Point Boundary Value Problems on Time Scales
Electronic Journl of Qulittive Theory of Differentil Equtions 2009, No. 32, -3; http://www.mth.u-szeged.hu/ejqtde/ Multiple Positive Solutions for the System of Higher Order Two-Point Boundry Vlue Problems
More informationTrack Properities of Normal Chain
In. J. Conemp. Mah. Scences, Vol. 8, 213, no. 4, 163-171 HIKARI Ld, www.m-har.com rac Propes of Normal Chan L Chen School of Mahemacs and Sascs, Zhengzhou Normal Unversy Zhengzhou Cy, Hennan Provnce, 4544,
More informationComparison of Differences between Power Means 1
In. Journal of Mah. Analyss, Vol. 7, 203, no., 5-55 Comparson of Dfferences beween Power Means Chang-An Tan, Guanghua Sh and Fe Zuo College of Mahemacs and Informaon Scence Henan Normal Unversy, 453007,
More information@FMI c Kyung Moon Sa Co.
Annals of Fuzzy Mahemacs and Informacs Volume 8, No. 2, (Augus 2014), pp. 245 257 ISSN: 2093 9310 (prn verson) ISSN: 2287 6235 (elecronc verson) hp://www.afm.or.kr @FMI c Kyung Moon Sa Co. hp://www.kyungmoon.com
More informationSome estimates on the Hermite-Hadamard inequality through quasi-convex functions
Annls of University of Criov, Mth. Comp. Sci. Ser. Volume 3, 7, Pges 8 87 ISSN: 13-693 Some estimtes on the Hermite-Hdmrd inequlity through qusi-convex functions Dniel Alexndru Ion Abstrct. In this pper
More informationAttribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method GAO Jing1,a, Ma Hui1, Han Zhidong2,b
Inernaonal Indusral Informacs and Compuer Engneerng Conference (IIICEC 05) Arbue educon Algorhm Based on Dscernbly Marx wh Algebrac Mehod GAO Jng,a, Ma Hu, Han Zhdong,b Informaon School, Capal Unversy
More informationEpistemic Game Theory: Online Appendix
Epsemc Game Theory: Onlne Appendx Edde Dekel Lucano Pomao Marcano Snscalch July 18, 2014 Prelmnares Fx a fne ype srucure T I, S, T, β I and a probably µ S T. Le T µ I, S, T µ, βµ I be a ype srucure ha
More informationApplication on Inner Product Space with. Fixed Point Theorem in Probabilistic
Journl of Applied Mhemics & Bioinformics, vol.2, no.2, 2012, 1-10 ISSN: 1792-6602 prin, 1792-6939 online Scienpress Ld, 2012 Applicion on Inner Produc Spce wih Fixed Poin Theorem in Probbilisic Rjesh Shrivsv
More informationPositive Solutions of Operator Equations on Half-Line
Int. Journl of Mth. Anlysis, Vol. 3, 29, no. 5, 211-22 Positive Solutions of Opertor Equtions on Hlf-Line Bohe Wng 1 School of Mthemtics Shndong Administrtion Institute Jinn, 2514, P.R. Chin sdusuh@163.com
More informationHERMITE SERIES SOLUTIONS OF LINEAR FREDHOLM INTEGRAL EQUATIONS
Mhemcl nd Compuonl Applcons, Vol 6, o, pp 97-56, Assocon fo Scenfc Resech ERMITE SERIES SOLUTIOS OF LIEAR FREDOLM ITEGRAL EQUATIOS Slh Ylçınbş nd Müge Angül Depmen of Mhemcs, Fcul of Scence nd As, Cell
More informationThe Number of Rows which Equal Certain Row
Interntonl Journl of Algebr, Vol 5, 011, no 30, 1481-1488 he Number of Rows whch Equl Certn Row Ahmd Hbl Deprtment of mthemtcs Fcult of Scences Dmscus unverst Dmscus, Sr hblhmd1@gmlcom Abstrct Let be X
More informationVolatility Interpolation
Volaly Inerpolaon Prelmnary Verson March 00 Jesper Andreasen and Bran Huge Danse Mares, Copenhagen wan.daddy@danseban.com brno@danseban.com Elecronc copy avalable a: hp://ssrn.com/absrac=69497 Inro Local
More informationCH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
More informationRank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
More informationConvergence of Singular Integral Operators in Weighted Lebesgue Spaces
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 10, No. 2, 2017, 335-347 ISSN 1307-5543 www.ejpm.com Published by New York Business Globl Convergence of Singulr Inegrl Operors in Weighed Lebesgue
More informationCALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION
Avilble online hp://scik.org Eng. Mh. Le. 15, 15:4 ISSN: 49-9337 CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION PANDEY, C. P. 1, RAKESH MOHAN AND BHAIRAW NATH TRIPATHI 3 1 Deprmen o Mhemics, Ajy
More informationSurvival Analysis and Reliability. A Note on the Mean Residual Life Function of a Parallel System
Communcaons n Sascs Theory and Mehods, 34: 475 484, 2005 Copyrgh Taylor & Francs, Inc. ISSN: 0361-0926 prn/1532-415x onlne DOI: 10.1081/STA-200047430 Survval Analyss and Relably A Noe on he Mean Resdual
More information4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
More informationA Deza Frankl type theorem for set partitions
A Deza Frankl ype heorem for se parons Cheng Yeaw Ku Deparmen of Mahemacs Naonal Unversy of Sngapore Sngapore 117543 makcy@nus.edu.sg Kok Bn Wong Insue of Mahemacal Scences Unversy of Malaya 50603 Kuala
More informationUNIVERSAL BOUNDS FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR ON DOMAINS IN COMPLEX PROJECTIVE SPACES
wwwrresscom/volmes/vol7isse/ijrras_7 df UNIVERSAL BOUNDS FOR EIGENVALUES OF FOURTH-ORDER WEIGHTED POLYNOIAL OPERATOR ON DOAINS IN COPLEX PROJECTIVE SPACES D Feng & L Ynl * Scool of emcs nd Pyscs Scence
More informationINTEGRALS. Exercise 1. Let f : [a, b] R be bounded, and let P and Q be partitions of [a, b]. Prove that if P Q then U(P ) U(Q) and L(P ) L(Q).
INTEGRALS JOHN QUIGG Eercise. Le f : [, b] R be bounded, nd le P nd Q be priions of [, b]. Prove h if P Q hen U(P ) U(Q) nd L(P ) L(Q). Soluion: Le P = {,..., n }. Since Q is obined from P by dding finiely
More information1.B Appendix to Chapter 1
Secon.B.B Append o Chper.B. The Ordnr Clcl Here re led ome mporn concep rom he ordnr clcl. The Dervve Conder ncon o one ndependen vrble. The dervve o dened b d d lm lm.b. where he ncremen n de o n ncremen
More informationON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS
Hceepe Journl of Mhemics nd Sisics Volume 45) 0), 65 655 ON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS M Emin Özdemir, Ahme Ock Akdemir nd Erhn Se Received 6:06:0 : Acceped
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 informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More informationChapter Lagrangian Interpolation
Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and
More informationQuery Data With Fuzzy Information In Object- Oriented Databases An Approach The Semantic Neighborhood Of Hedge Algebras
(IJCSIS) Inernonl Journl of Compuer Scence nd Informon Secury, Vol 9, No 5, My 20 Query D Wh Fuzzy Informon In Obec- Orened Dbses An Approch The Semnc Neghborhood Of edge Algebrs Don Vn Thng Kore-VeNm
More informationOn computing differential transform of nonlinear non-autonomous functions and its applications
On compung dfferenal ransform of nonlnear non-auonomous funcons and s applcaons Essam. R. El-Zahar, and Abdelhalm Ebad Deparmen of Mahemacs, Faculy of Scences and Humanes, Prnce Saam Bn Abdulazz Unversy,
More informationResearch Article Boltzmann s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions
Hndw Publshng Corporon Journl of Appled Mhemcs Volume 216, Arcle ID 583462, 8 pges hp://dx.do.org/1.1155/216/583462 Reserch Arcle Bolzmnn s Sx-Momen One-Dmensonl Nonlner Sysem Equons wh he Mxwell-Auzhn
More informationA New Generalized Gronwall-Bellman Type Inequality
22 Inernaonal Conference on Image, Vson and Comung (ICIVC 22) IPCSIT vol. 5 (22) (22) IACSIT Press, Sngaore DOI:.7763/IPCSIT.22.V5.46 A New Generalzed Gronwall-Bellman Tye Ineualy Qnghua Feng School of
More informationComb Filters. Comb Filters
The smple flers dscussed so far are characered eher by a sngle passband and/or a sngle sopband There are applcaons where flers wh mulple passbands and sopbands are requred Thecomb fler s an example of
More informationAppendix H: Rarefaction and extrapolation of Hill numbers for incidence data
Anne Chao Ncholas J Goell C seh lzabeh L ander K Ma Rober K Colwell and Aaron M llson 03 Rarefacon and erapolaon wh ll numbers: a framewor for samplng and esmaon n speces dversy sudes cology Monographs
More informationSOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β
SARAJEVO JOURNAL OF MATHEMATICS Vol.3 (15) (2007), 137 143 SOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β M. A. K. BAIG AND RAYEES AHMAD DAR Absrac. In hs paper, we propose
More informationW. B. Vasantha Kandasamy Florentin Smarandache NEUTROSOPHIC BILINEAR ALGEBRAS AND THEIR GENERALIZATIONS
W. B. Vsnh Kndsmy Florenn Smrndche NEUTROSOPHIC BILINEAR ALGEBRAS AND THEIR GENERALIZATIONS Svensk fyskrkve Sockholm, Sweden 00 Svensk fyskrkve (Swedsh physcs rchve) s publsher regsered wh he Royl Nonl
More informationExistence of Time Periodic Solutions for the Ginzburg-Landau Equations. model of superconductivity
Journal of Mahemacal Analyss and Applcaons 3, 3944 999 Arcle ID jmaa.999.683, avalable onlne a hp:www.dealbrary.com on Exsence of me Perodc Soluons for he Gnzburg-Landau Equaons of Superconducvy Bxang
More informationCubic Bezier Homotopy Function for Solving Exponential Equations
Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.
More informationRotations.
oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse
More informationINTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY
[Mjuh, : Jury, 0] ISSN: -96 Scefc Jourl Impc Fcr: 9 ISRA, Impc Fcr: IJESRT INTERNATIONAL JOURNAL OF ENINEERIN SCIENCES & RESEARCH TECHNOLOY HAMILTONIAN LACEABILITY IN MIDDLE RAPHS Mjuh*, MurlR, B Shmukh
More informationIntegral Transform. Definitions. Function Space. Linear Mapping. Integral Transform
Inegrl Trnsform Definiions Funcion Spce funcion spce A funcion spce is liner spce of funcions defined on he sme domins & rnges. Liner Mpping liner mpping Le VF, WF e liner spces over he field F. A mpping
More informationON BERNOULLI BOUNDARY VALUE PROBLEM
LE MATEMATICHE Vol. LXII (2007) Fsc. II, pp. 163 173 ON BERNOULLI BOUNDARY VALUE PROBLEM FRANCESCO A. COSTABILE - ANNAROSA SERPE We consider the boundry vlue problem: x (m) (t) = f (t,x(t)), t b, m > 1
More informationV.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS
R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon
More informationTo Possibilities of Solution of Differential Equation of Logistic Function
Arnold Dávd, Frnše Peller, Rená Vooroosová To Possbles of Soluon of Dfferenl Equon of Logsc Funcon Arcle Info: Receved 6 My Acceped June UDC 7 Recommended con: Dávd, A., Peller, F., Vooroosová, R. ().
More informationLOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN FRACTAL HEAT TRANSFER
Yn, S.-P.: Locl Frctonl Lplce Seres Expnson Method for Dffuson THERMAL SCIENCE, Yer 25, Vol. 9, Suppl., pp. S3-S35 S3 LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN
More informationLecture 3 ( ) (translated and slightly adapted from lecture notes by Martin Klazar)
Lecture 3 (5.3.2018) (trnslted nd slightly dpted from lecture notes by Mrtin Klzr) Riemnn integrl Now we define precisely the concept of the re, in prticulr, the re of figure U(, b, f) under the grph of
More informationISSN 075-7 : (7) 0 007 C ( ), E-l: ssolos@glco FPGA LUT FPGA EM : FPGA, LUT, EM,,, () FPGA (feldprogrble ge rrs) [, ] () [], () [] () [5] [6] FPGA LUT (Look-Up-Tbles) EM (Ebedded Meor locks) [7, 8] LUT
More information5.1-The Initial-Value Problems For Ordinary Differential Equations
5.-The Iniil-Vlue Problems For Ordinry Differenil Equions Consider solving iniil-vlue problems for ordinry differenil equions: (*) y f, y, b, y. If we know he generl soluion y of he ordinry differenil
More information[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5
TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres
More informationLAPLACE TRANSFORM SOLUTION OF THE PROBLEM OF TIME-FRACTIONAL HEAT CONDUCTION IN A TWO-LAYERED SLAB
Journl of Appled Mthemtcs nd Computtonl Mechncs 5, 4(4), 5-3 www.mcm.pcz.pl p-issn 99-9965 DOI:.75/jmcm.5.4. e-issn 353-588 LAPLACE TRANSFORM SOLUTION OF THE PROBLEM OF TIME-FRACTIONAL HEAT CONDUCTION
More informationPart II CONTINUOUS TIME STOCHASTIC PROCESSES
Par II CONTINUOUS TIME STOCHASTIC PROCESSES 4 Chaper 4 For an advanced analyss of he properes of he Wener process, see: Revus D and Yor M: Connuous marngales and Brownan Moon Karazas I and Shreve S E:
More information( ) [ ] MAP Decision Rule
Announcemens Bayes Decson Theory wh Normal Dsrbuons HW0 due oday HW o be assgned soon Proec descrpon posed Bomercs CSE 90 Lecure 4 CSE90, Sprng 04 CSE90, Sprng 04 Key Probables 4 ω class label X feaure
More informationM. Y. Adamu Mathematical Sciences Programme, AbubakarTafawaBalewa University, Bauchi, Nigeria
IOSR Journal of Mahemacs (IOSR-JM e-issn: 78-578, p-issn: 9-765X. Volume 0, Issue 4 Ver. IV (Jul-Aug. 04, PP 40-44 Mulple SolonSoluons for a (+-dmensonalhroa-sasuma shallow waer wave equaon UsngPanlevé-Bӓclund
More informationResearch Article On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation
Journl of Applied Mthemtics Volume 2011, Article ID 743923, 7 pges doi:10.1155/2011/743923 Reserch Article On Existence nd Uniqueness of Solutions of Nonliner Integrl Eqution M. Eshghi Gordji, 1 H. Bghni,
More informationA DECOMPOSITION METHOD FOR SOLVING DIFFUSION EQUATIONS VIA LOCAL FRACTIONAL TIME DERIVATIVE
S13 A DECOMPOSITION METHOD FOR SOLVING DIFFUSION EQUATIONS VIA LOCAL FRACTIONAL TIME DERIVATIVE by Hossen JAFARI a,b, Haleh TAJADODI c, and Sarah Jane JOHNSTON a a Deparen of Maheacal Scences, Unversy
More informationNotes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
More informationA LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR IAN KNOWLES
A LIMIT-POINT CRITERION FOR A SECOND-ORDER LINEAR DIFFERENTIAL OPERATOR j IAN KNOWLES 1. Inroducion Consider he forml differenil operor T defined by el, (1) where he funcion q{) is rel-vlued nd loclly
More informationJens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
More informationTwo Coefficients of the Dyson Product
Two Coeffcents of the Dyson Product rxv:07.460v mth.co 7 Nov 007 Lun Lv, Guoce Xn, nd Yue Zhou 3,,3 Center for Combntorcs, LPMC TJKLC Nnk Unversty, Tnjn 30007, P.R. Chn lvlun@cfc.nnk.edu.cn gn@nnk.edu.cn
More informationLecture 18: The Laplace Transform (See Sections and 14.7 in Boas)
Lecure 8: The Lalace Transform (See Secons 88- and 47 n Boas) Recall ha our bg-cure goal s he analyss of he dfferenal equaon, ax bx cx F, where we emloy varous exansons for he drvng funcon F deendng on
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationCS286.2 Lecture 14: Quantum de Finetti Theorems II
CS286.2 Lecure 14: Quanum de Fne Theorems II Scrbe: Mara Okounkova 1 Saemen of he heorem Recall he las saemen of he quanum de Fne heorem from he prevous lecure. Theorem 1 Quanum de Fne). Le ρ Dens C 2
More informationFURTHER GENERALIZATIONS. QI Feng. The value of the integral of f(x) over [a; b] can be estimated in a variety ofways. b a. 2(M m)
Univ. Beogrd. Pul. Elekroehn. Fk. Ser. M. 8 (997), 79{83 FUTHE GENEALIZATIONS OF INEQUALITIES FO AN INTEGAL QI Feng Using he Tylor's formul we prove wo inegrl inequliies, h generlize K. S. K. Iyengr's
More information1. On some properties of definite integrals. We prove
This short collection of notes is intended to complement the textbook Anlisi Mtemtic 2 by Crl Mdern, published by Città Studi Editore, [M]. We refer to [M] for nottion nd the logicl stremline of the rguments.
More informationDynamic Team Decision Theory. EECS 558 Project Shrutivandana Sharma and David Shuman December 10, 2005
Dynamc Team Decson Theory EECS 558 Proec Shruvandana Sharma and Davd Shuman December 0, 005 Oulne Inroducon o Team Decson Theory Decomposon of he Dynamc Team Decson Problem Equvalence of Sac and Dynamc
More informationResearch Article On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order
Hndw Publshng Corporton Interntonl Journl of Dfferentl Equtons Volume 0, Artcle ID 7703, pges do:055/0/7703 Reserch Artcle On the Upper Bounds of Egenvlues for Clss of Systems of Ordnry Dfferentl Equtons
More informationON A GENERALIZED STURM-LIOUVILLE PROBLEM
Foli Mthemtic Vol. 17, No. 1, pp. 17 22 Act Universittis Lodziensis c 2010 for University of Łódź Press ON A GENERALIZED STURM-LIOUVILLE PROBLEM GRZEGORZ ANDRZEJCZAK AND TADEUSZ POREDA Abstrct. Bsic results
More information1. Introduction. 1 b b
Journl of Mhemicl Inequliies Volume, Number 3 (007), 45 436 SOME IMPROVEMENTS OF GRÜSS TYPE INEQUALITY N. ELEZOVIĆ, LJ. MARANGUNIĆ AND J. PEČARIĆ (communiced b A. Čižmešij) Absrc. In his pper some inequliies
More informationTHE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR
REVUE D ANALYSE NUMÉRIQUE ET DE THÉORIE DE L APPROXIMATION Tome 32, N o 1, 2003, pp 11 20 THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR TEODORA CĂTINAŞ Abstrct We extend the Sheprd opertor by
More informationTight results for Next Fit and Worst Fit with resource augmentation
Tgh resuls for Nex F and Wors F wh resource augmenaon Joan Boyar Leah Epsen Asaf Levn Asrac I s well known ha he wo smple algorhms for he classc n packng prolem, NF and WF oh have an approxmaon rao of
More informationAn improved statistical disclosure attack
In J Grnulr Compung, Rough Ses nd Inellgen Sysems, Vol X, No Y, xxxx An mproved sscl dsclosure c Bn Tng* Deprmen of Compuer Scence, Clforn Se Unversy Domnguez Hlls, Crson, CA, USA Eml: bng@csudhedu *Correspondng
More informationA Simple Method to Solve Quartic Equations. Key words: Polynomials, Quartics, Equations of the Fourth Degree INTRODUCTION
Ausrlin Journl of Bsic nd Applied Sciences, 6(6): -6, 0 ISSN 99-878 A Simple Mehod o Solve Quric Equions Amir Fhi, Poo Mobdersn, Rhim Fhi Deprmen of Elecricl Engineering, Urmi brnch, Islmic Ad Universi,
More information