New Results on Oscillation of even Order Neutral Differential Equations with Deviating Arguments
|
|
- Poppy Norton
- 6 years ago
- Views:
Transcription
1 Advace i Pue Maheaic 9-53 doi: 36/ap3 Pubihed Oie May (hp://wwwscirpog/oua/ap) New Reu o Ociaio of eve Ode Neua Diffeeia Equaio wih Deviaig Ague Abac Liahog Li Fawei Meg Schoo of Maheaica Sye Sciece aiha Coege ai a Chia Schoo of Maheaica Sciece Qufu Noa Uiveiy Qufu Chia E-ai: 397@63co fweg@qfueduc Received Jauay 9 ; evied Mach 5 ; acceped Mach I hi pape we poi ou oe a iae i [6] evie he we obai oe ew ociaio eu fo ceai eve ode eua diffeeia equaio wih deviaig ague Ou eu exed ipove ay ow ociaio cieia becaue he aice u geeaie Meg Xu eu Keywo: Ociaio Neua Diffeeia Equaio Deviaig Ague Ioducio Ociaio of oe eve ode diffeeia equaio have bee udied by ay auho Fo iace ee [-7] he efeece heei We dea wih he ociaoy behavio of he eve ode eua diffeeia equaio wih deviaig ague of he fo x pi x i i q f x () whee i eve houghou hi pape i i aued ha: (A ) pi q C R f CR R uf u fo u f u i o-deceaig o R i ; (A ) i C R i i i i ; C R i (A 3 ) ; (A ) hee exi a coa M uch ha f xg x M x fo x ; (A 5 ) pi p p hee exi a fuc- i io q C R uch ha q q i : By a ouio of Equaio () we ea a fucio aifie Equa- We eic ou aeio o hoe x of Equaio () which exi o oe haf-ie x wih fo ay x A oivia ouio of Equaio () i caed ociaoy if i ha abiaiy age eo ohewie i i aid o be oociaoy Equaio () i aid o be ociaoy if a of i oivia ouio ae ociaoy Recey Meg Xu [6] udied Equaio () obaied oe ufficie codiio fo ociaio of he Equaio () we i he ai eu of [6] a foow Foowig Phio [5] we ay ha a fucio x which ha he popey ha x pi x i i C x R fo oe x io () o x ouio up x : H H beog o a fucio ca W deoe by H W if H CD R whee D : which aifie: (H ) H H fo ; (H ) H ha a coiuou o-poiive H paia deivaive aifyig he codiio: S H hh S fo oe h Loc D R C i a o-deceaig fucio heoe A ([6 heoe ]) Aue ha (A ) - (A 5 ) hod e he fucio H haify (H ) (H ) uppoe iup CF C G () Copyigh SciRe
2 5 L Z LI E AL ho fo evey C C whee F H q d H h G H H p he evey ouio of Equaio () i ociaoy heoe B ([6 heoe ]) Aue ha (A )-(A 5 ) hod H h ae he ae a i heoe A uppoe ha H if i if H i up G If hee exi a fucio (3) () C R uch ha fo a i if CF G (5) C i up d (6) whee ax he evey ouio of Equaio () i ociaoy I heoe A B fucio G houd be G o each of he codiio () () (5) (6) ha a ay a codiio Meawhie he Riccai fucio i o we-defied hee exi oe a eo i he poof of he heoe he pupoe of hi pape i fuhe o eghe ociaio eu obaied fo Equaio () by Meg Xu [6] I ou pape we edefie he fucio F G povide oe ew ociaio cieia fo ociaio of Equaio () Mai Reu I he eque we eed he foowig ea: Lea ([]) Le x be a ie diffeeiabe fucio o of oe ig x o which ( ) aifie x x he: (I ) hee exi a uch ha i x i ae of oe ig o ; (I ) hee exi a ube h 3 5 whe h 6 whe i odd i eve o uch ha i i i x x xx fo i h ; fo i h h Lea ([]) If x i a i Lea x x fo he fo evey hee exi a coa N uch ha x N X fo a age Lea 3([7]) Suppoe ha x i a eveuay poiive ouio of Equaio () e x pi x i i he hee exi a ube uch ha heoe Aue ha (A ) - (A 5 ) hod e he fucio H h aify (H ) (H ) uppoe iup MF G N (7) ho fo evey fo oe whee F H q H h G H H p he evey ouio of Equaio () i ociaoy Poof Suppoe o he coay ha x i a oociaoy ouio of Equaio () ha x i eve- uay poiive (whe x i eveuay egaive he poof i iia) Le be defied a i Lea 3 he foowig he poof of heoe i [6] wihou o of geeaiy aue hee exi a uch ha x ( ) N (by ea ) M q fo a Le he we have (o a [6]) Copyigh SciRe
3 L Z LI E AL 5 N M q Muipyig he above equaio wih epaced by H iegaig i fo o fo a by h (o a [6]) fo oe we obai M H q d H h N H NH H NH NH h H NH Hece we have MF G N fo a hi give i up MF N G which coadic (7) hi copee he poof of he heoe he aupio (7) i heoe ca fai coequey heoe doe o appy he foowig eu povide oe eeiay ew ociaio cieia fo Equaio () heoe Aue ha (A )-(A 5 ) hod he fucio H hf G be he ae a i heoe uppoe ha H if i if H If hee exi a fucio fo a fo oe NH (8) C R uch ha i up MF N G (9) h () i up whee ax he evey ouio of Equaio () i ociaoy Poof Aue o he coay ha () i o-ociaoy Foowig he poof of heoe wihou o of geeaiy aue fo a fo oe we obai M H q d H h NH NH So we ge MF G NB N whee B H H d Copyigh SciRe
4 5 L Z LI E AL he iup MF N G Niif B Fo a fo ay by (9) we have So epeciay N i if B () i if B ( ) N () Now we cai ha i up (3) Suppoe o he coay ha i up () By (8) hee i a poiive coa aifyig H if iif H (5) Le be ay abiay poiive ube fo () hee exi a uch ha fo a he fo we have B v v H d vdv H v v v H vdv H v H H By (5) hee exi a uch ha fo a H which ipie B fo a H Sice i abiay we have B i if B i which coadic () hu (3) ho he by () (3) we ge i up i up d which coadic () hi copee he poof Rea Le i heoe heoe educe o heoe A [6]; we obai he ae eu i heoe i which we oi he aupio () i heoe B [6] heefoe heoe ae geeaiaio ipovee of he eu obaied i [6] Rea Wih a appopiae choice of he fucio H h oe ca deive a ube of ociaio cieia fo Equaio () fo ou heoe Le () i a coa H h we have H i i H fo ay Coequey e uig heoe we have: Cooay Aue ha (A )-(A 5 ) (8) hod uppoe ha hee exi a fucio C R uch ha fo oe i up M q N (6) () (wih ) hod he evey ouio of Equaio () i ociaoy Exape Le coide he foowig ecod ode eua diffeeia equaio x p x q x (7) Copyigh SciRe
5 L Z LI E AL 53 p q ax i f x x i i hi cae M Le whee N by diec cacuaio we ge i up M q N i up i i co i co I i eay o veify ha () ho heefoe Equaio (7) i ociaoy by Cooay Howeve we ca eaiy fid ha i upg i up i o codiio () i heoe B i o aified hee how ha heoe B cao be appied o Equaio (7) Obviouy ou eu ae upeio o he eu obaied befoe 3 Acowedege he auho ae vey gaefu o he efeee fo hi/he vauabe uggeio Refeece [] R P Agawa S R Gace D ORega Ociaio heoy fo Diffeeia Equaio Kuwe Acadeic Dodech [] R P Agawa S R Gace he Ociaio of Highe Ode Diffeeia Equaio wih Deviaig Ague Copue & Maheaic wih Appicaio Vo 38 No pp doi:6/s898-(99)93-5 [3] Y Boa O Ai Ociaoy Behavio of Highe Ode Neua ype Noiea Foced Diffeeia Equaio wih Ociaig Coefficie Joua of Maheaica Aayi Appicaio Vo 9 No pp 3-39 doi:6/aa396 [] W N Li Ociaio of Highe Ode Deay Diffeeia Equaio of Neua ype he Geogia Maheaica Joua Vo 7 No pp [5] Ch G Phio Ociaio heoe fo Liea Diffeeia Equaio of Secod Ode Achiv de Maheai Vo 53 No p 83 doi:7/bf373 [6] F Meg R Xu Kaeev-ype Ociaio Cieia fo Eve Ode Neua Diffeeia Equaio wih Deviaig Ague Appied Maheaic Copuaio Vo 9 No 7 pp -8 doi:6/ac77 [7] Yu V Rogovcheo F ucay Ociaio Cieia Fo Secod-Ode Noiea Diffeeia Equaio wih Dapig Noiea Aayi: heoy Meho & Appicaio Vo 69 No 8 pp 8- doi:6/a75 Copyigh SciRe
The Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues
Alied Maheaical Sciece Vol. 8 o. 5 747-75 The No-Tucaed Bul Aival Queue M x /M/ wih Reei Bali Sae-Deede ad a Addiioal Seve fo Loe Queue A. A. EL Shebiy aculy of Sciece Meofia Uiveiy Ey elhebiy@yahoo.co
More informationOn Interval Valued Generalized Difference Classes Defined by Orlicz Function
Tuih oua of Aayi ad Numbe Theoy, 03, Vo., No., 48-53 Avaiabe oie a hp://pub.ciepub.com/ja///0 Sciece ad ducaio Pubihig DOI:0.69/ja---0 O Ieva Vaued Geeaized Diffeece Cae Defied by Oicz Fucio Ayha i, Bipa
More informationSpectrum of The Direct Sum of Operators. 1. Introduction
Specu of The Diec Su of Opeaos by E.OTKUN ÇEVİK ad Z.I.ISMILOV Kaadeiz Techical Uivesiy, Faculy of Scieces, Depae of Maheaics 6080 Tabzo, TURKEY e-ail adess : zaeddi@yahoo.co bsac: I his wok, a coecio
More informationTypes Ideals on IS-Algebras
Ieraioal Joural of Maheaical Aalyi Vol. 07 o. 3 635-646 IARI Ld www.-hikari.co hp://doi.org/0.988/ija.07.7466 Type Ideal o IS-Algebra Sudu Najah Jabir Faculy of Educaio ufa Uiveriy Iraq Copyrigh 07 Sudu
More informationOn Probability Density Function of the Quotient of Generalized Order Statistics from the Weibull Distribution
ISSN 684-843 Joua of Sac Voue 5 8 pp. 7-5 O Pobaby Dey Fuco of he Quoe of Geeaed Ode Sac fo he Webu Dbuo Abac The pobaby dey fuco of Muhaad Aee X k Y k Z whee k X ad Y k ae h ad h geeaed ode ac fo Webu
More informationABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES
Available olie a h://sciog Egieeig Maheaics Lees 2 (23) No 56-66 ISSN 249-9337 ABSLUE INDEED SUMMABILIY FACR F AN INFINIE SERIES USING QUASI-F-WER INCREASING SEQUENCES SKAIKRAY * RKJAI 2 UKMISRA 3 NCSAH
More informationMeromorphic Functions Sharing Three Values *
Alied Maheaic 11 718-74 doi:1436/a11695 Pulihed Olie Jue 11 (h://wwwscirporg/joural/a) Meroorhic Fucio Sharig Three Value * Arac Chagju Li Liei Wag School o Maheaical Sciece Ocea Uiveriy o Chia Qigdao
More informationCHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE
Fameal Joal of Mahemaic a Mahemaical Sciece Vol. 7 Ie 07 Page 5- Thi pape i aailable olie a hp://.fi.com/ Pblihe olie Jaa 0 07 CHATTERJEA CONTRACTION MAPPING THEOREM IN CONE HEPTAGONAL METRIC SPACE Caolo
More informationResearch Article On Pointwise Approximation of Conjugate Functions by Some Hump Matrix Means of Conjugate Fourier Series
Hidawi Publishig Copoaio Joual of Fucio Spaces Volue 5, Aicle ID 475, 9 pages hp://dx.doi.og/.55/5/475 Reseach Aicle O Poiwise Appoxiaio of Cojugae Fucios by Soe Hup Maix Meas of Cojugae Fouie Seies W.
More informationON THE EXTENSION OF WEAK ARMENDARIZ RINGS RELATIVE TO A MONOID
wwweo/voue/vo9iue/ijas_9 9f ON THE EXTENSION OF WEAK AENDAIZ INGS ELATIVE TO A ONOID Eye A & Ayou Eoy Dee of e Nowe No Uvey Lzou 77 C Dee of e Uvey of Kou Ou Su E-: eye76@o; you975@yooo ABSTACT Fo oo we
More informationI t n e a r ti o o J r n eri R s r e c m t n ( I u - ss e u -, A li I E D R F A T C IO U O F THE E I E D H TZ- T ION
eaioa Joua o Egieeig each A Maagee (JERM) SSN : 2349-258, Voue-3, ue- 4, Api 26 GENERALZE FRATONAL ALULUS OF TE GENERALZE URWTZ- L ER ZETA FUNTON J iea aiya, Jea R a A bac Thi pape ea wih he eivaio o he
More informationInternational Journal of Mathematical Archive-5(3), 2014, Available online through ISSN
Iteatioal Joual of Mathematical Achive-5(3, 04, 7-75 Available olie though www.ijma.ifo ISSN 9 5046 ON THE OSCILLATOY BEHAVIO FO A CETAIN CLASS OF SECOND ODE DELAY DIFFEENCE EQUATIONS P. Mohakuma ad A.
More informationAvailable online at J. Math. Comput. Sci. 2 (2012), No. 4, ISSN:
Available olie a h://scik.og J. Mah. Comu. Sci. 2 (22), No. 4, 83-835 ISSN: 927-537 UNBIASED ESTIMATION IN BURR DISTRIBUTION YASHBIR SINGH * Deame of Saisics, School of Mahemaics, Saisics ad Comuaioal
More informationEXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D. S. Palimkar
Ieraioal Joural of Scieific ad Research Publicaios, Volue 2, Issue 7, July 22 ISSN 225-353 EXISTENCE THEORY OF RANDOM DIFFERENTIAL EQUATIONS D S Palikar Depare of Maheaics, Vasarao Naik College, Naded
More informationON POINTWISE APPROXIMATION OF FUNCTIONS BY SOME MATRIX MEANS OF FOURIER SERIES
M aheaical I equaliies & A pplicaios Volue 19, Nube 1 (216), 287 296 doi:1.7153/ia-19-21 ON POINTWISE APPROXIMATION OF FUNCTIONS BY SOME MATRIX MEANS OF FOURIER SERIES W. ŁENSKI AND B. SZAL (Couicaed by
More informationBINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =
wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em
More informationM-ary Detection Problem. Lecture Notes 2: Detection Theory. Example 1: Additve White Gaussian Noise
Hi ue Hi ue -ay Deecio Pole Coide he ole of decidig which of hyohei i ue aed o oevig a ado vaiale (veco). he efoace cieia we coide i he aveage eo oailiy. ha i he oailiy of decidig ayhig ece hyohei H whe
More informationGENERALIZED FRACTIONAL INTEGRAL OPERATORS AND THEIR MODIFIED VERSIONS
GENERALIZED FRACTIONAL INTEGRAL OPERATORS AND THEIR MODIFIED VERSIONS HENDRA GUNAWAN Absac. Associaed o a fucio ρ :(, ) (, ), le T ρ be he opeao defied o a suiable fucio space by T ρ f(x) := f(y) dy, R
More informationRuled surfaces are one of the most important topics of differential geometry. The
CONSTANT ANGLE RULED SURFACES IN EUCLIDEAN SPACES Yuuf YAYLI Ere ZIPLAR Deparme of Mahemaic Faculy of Sciece Uieriy of Aara Tadoğa Aara Turey yayli@cieceaaraedur Deparme of Mahemaic Faculy of Sciece Uieriy
More informationStrong Result for Level Crossings of Random Polynomials
IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh
More informationComparing Different Estimators for Parameters of Kumaraswamy Distribution
Compaig Diffee Esimaos fo Paamees of Kumaaswamy Disibuio ا.م.د نذير عباس ابراهيم الشمري جامعة النهرين/بغداد-العراق أ.م.د نشات جاسم محمد الجامعة التقنية الوسطى/بغداد- العراق Absac: This pape deals wih compaig
More informationSLOW INCREASING FUNCTIONS AND THEIR APPLICATIONS TO SOME PROBLEMS IN NUMBER THEORY
VOL. 8, NO. 7, JULY 03 ISSN 89-6608 ARPN Jourl of Egieerig d Applied Sciece 006-03 Ai Reerch Publihig Nework (ARPN). All righ reerved. www.rpjourl.com SLOW INCREASING FUNCTIONS AND THEIR APPLICATIONS TO
More informationStability of Quadratic and Cubic Functional Equations in Paranormed Spaces
IOSR Joua o Matheatics IOSR-JM e-issn 8-578, p-issn 9-765. Voue, Issue Ve. IV Ju - Aug. 05, - www.iosouas.og Stabiit o uadatic ad ubic Fuctioa Equatios i aaoed Spaces Muiappa, Raa S Depatet o Matheatics,
More informationGeneralized Fibonacci-Type Sequence and its Properties
Geelized Fibocci-Type Sequece d is Popeies Ompsh Sihwl shw Vys Devshi Tuoil Keshv Kuj Mdsu (MP Idi Resech Schol Fculy of Sciece Pcific Acdemy of Highe Educio d Resech Uivesiy Udipu (Rj Absc: The Fibocci
More informationThe Nehari Manifold for a Class of Elliptic Equations of P-laplacian Type. S. Khademloo and H. Mohammadnia. afrouzi
Wold Alied cieces Joal (8): 898-95 IN 88-495 IDOI Pblicaios = h x g x x = x N i W whee is a eal aamee is a boded domai wih smooh boday i R N 3 ad< < INTRODUCTION Whee s ha is s = I his ae we ove he exisece
More informationPRIMARY DECOMPOSITION, ASSOCIATED PRIME IDEALS AND GABRIEL TOPOLOGY
Orietal J. ath., Volue 1, Nuber, 009, Page 101-108 009 Orietal Acadeic Publiher PRIARY DECOPOSITION, ASSOCIATED PRIE IDEALS AND GABRIEL TOPOLOGY. EL HAJOUI, A. IRI ad A. ZOGLAT Uiverité ohaed V aculté
More informationGenerating Function for Partitions with Parts in A.P
Geetig Fuctio fo Ptitio wi Pt i AP Hum Reddy K # K Jkmm * # Detmet of Memtic Hidu Coege Gutu 50 AP Idi * Detmet of Memtic 8 Mi AECS Lyout B BLOCK Sigd Bgoe 5604 Idi Abtct: I i e we deive e geetig fuctio
More informationCameras and World Geometry
Caeas ad Wold Geoe How all is his woa? How high is he caea? Wha is he caea oaio w. wold? Which ball is close? Jaes Has Thigs o eebe Has Pihole caea odel ad caea (pojecio) ai Hoogeeous coodiaes allow pojecio
More informationState-Space Model. In general, the dynamic equations of a lumped-parameter continuous system may be represented by
Sae-Space Model I geeral, he dyaic equaio of a luped-paraeer coiuou ye ay be repreeed by x & f x, u, y g x, u, ae equaio oupu equaio where f ad g are oliear vecor-valued fucio Uig a liearized echique,
More informationThe Central Limit Theorems for Sums of Powers of Function of Independent Random Variables
ScieceAsia 8 () : 55-6 The Ceal Limi Theoems fo Sums of Poes of Fucio of Idepede Radom Vaiables K Laipapo a ad K Neammaee b a Depame of Mahemaics Walailak Uivesiy Nakho Si Thammaa 86 Thailad b Depame of
More informationS, we call the base curve and the director curve. The straight lines
Developable Ruled Sufaces wih Daboux Fame i iowsi -Space Sezai KIZILTUĞ, Ali ÇAKAK ahemaics Depame, Faculy of As ad Sciece, Ezica Uivesiy, Ezica, Tuey ahemaics Depame, Faculy of Sciece, Aau Uivesiy, Ezuum,
More informationarxiv:math/ v1 [math.fa] 1 Feb 1994
arxiv:mah/944v [mah.fa] Feb 994 ON THE EMBEDDING OF -CONCAVE ORLICZ SPACES INTO L Care Schü Abrac. I [K S ] i wa how ha Ave ( i a π(i) ) π i equivale o a Orlicz orm whoe Orlicz fucio i -cocave. Here we
More informationCalculus Limits. Limit of a function.. 1. One-Sided Limits...1. Infinite limits 2. Vertical Asymptotes...3. Calculating Limits Using the Limit Laws.
Limi of a fucio.. Oe-Sided..... Ifiie limis Verical Asympoes... Calculaig Usig he Limi Laws.5 The Squeeze Theorem.6 The Precise Defiiio of a Limi......7 Coiuiy.8 Iermediae Value Theorem..9 Refereces..
More informationDegree of Approximation of a Class of Function by (C, 1) (E, q) Means of Fourier Series
IAENG Inenaional Jounal of Applied Mahemaic, 4:, IJAM_4 7 Degee of Appoximaion of a Cla of Funcion by C, E, q Mean of Fouie Seie Hae Kihna Nigam and Kuum Shama Abac In hi pape, fo he fi ime, we inoduce
More informationMoment Generating Function
1 Mome Geeraig Fucio m h mome m m m E[ ] x f ( x) dx m h ceral mome m m m E[( ) ] ( ) ( x ) f ( x) dx Mome Geeraig Fucio For a real, M () E[ e ] e k x k e p ( x ) discree x k e f ( x) dx coiuous Example
More informationOn Almost Increasing Sequences For Generalized Absolute Summability
Joul of Applied Mthetic & Bioifotic, ol., o., 0, 43-50 ISSN: 79-660 (pit), 79-6939 (olie) Itetiol Scietific Pe, 0 O Alot Iceig Sequece Fo Geelized Abolute Subility W.. Suli Abtct A geel eult coceig bolute
More informationExercise: Show that. Remarks: (i) Fc(l) is not continuous at l=c. (ii) In general, we have. yn ¾¾. Solution:
Exercie: Show ha Soluio: y ¾ y ¾¾ L c Þ y ¾¾ p c. ¾ L c Þ F y (l Fc (l I[c,(l "l¹c Þ P( y c
More informationOn Approximation of Conjugate of Signals (Functions) Belonging to the Generalized Weighted. of Conjugate Series of Fourier Series
I Joual of Mah Aalyi, Vol 6,, o 35, 73-75 O Aoximaio of ojugae of Sigal (Fucio Belogig o he Geealized Weighed ( x W L, (, ( ³ -la y Poduc Summailiy Mea of ojugae Seie of Fouie Seie Vihu Naaya Miha, Huzoo
More informationIn this section we will study periodic signals in terms of their frequency f t is said to be periodic if (4.1)
Fourier Series Iroducio I his secio we will sudy periodic sigals i ers o heir requecy is said o be periodic i coe Reid ha a sigal ( ) ( ) ( ) () or every, where is a uber Fro his deiiio i ollows ha ( )
More information( ) ( ) ( ) ( ) ( ) t ( ) ( ) ( ) ( ) [ ) Abstract. Keywords. 1. Introduction. Yunlong Gao, Yuting Sun, Guoguang Lin
Ieraioal Joural of Moder Noliear Theory ad Applicaio 6 5 85- hp://wwwcirporg/oural/ia ISSN Olie: 67-9487 ISSN Pri: 67-9479 The Global Aracor ad Their Haudorff ad Fracal Dieio Eiaio for he Higher-Order
More informationBy the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences
Chapte : Theoy of Modula Aithmetic 8 Sectio D Chiese Remaide Theoem By the ed of this sectio you will be able to pove the Chiese Remaide Theoem apply this theoem to solve simultaeous liea cogueces The
More informationLecture 4. Electrons and Holes in Semiconductors
ecue 4 lec ad Hle i Semicduc I hi lecue yu will lea: eeai-ecmbiai i emicduc i me deail The baic e f euai gveig he behavi f elec ad hle i emicduc Shcley uai Quai-eualiy i cducive maeial C 35 Sig 2005 Faha
More informationSome Properties of Semi-E-Convex Function and Semi-E-Convex Programming*
The Eighh Ieraioal Symposium o Operaios esearch ad Is Applicaios (ISOA 9) Zhagjiajie Chia Sepember 2 22 29 Copyrigh 29 OSC & APOC pp 33 39 Some Properies of Semi-E-Covex Fucio ad Semi-E-Covex Programmig*
More informationUnion-Find Partition Structures Goodrich, Tamassia Union-Find 1
Uio-Fid Pariio Srucures 004 Goodrich, Tamassia Uio-Fid Pariios wih Uio-Fid Operaios makesex: Creae a sileo se coaii he eleme x ad reur he posiio sori x i his se uioa,b : Reur he se A U B, desroyi he old
More informationDegree of Approximation of Fourier Series
Ieaioal Mahemaical Foum Vol. 9 4 o. 9 49-47 HIARI Ld www.m-hiai.com h://d.doi.og/.988/im.4.49 Degee o Aoimaio o Fouie Seies by N E Meas B. P. Padhy U.. Misa Maheda Misa 3 ad Saosh uma Naya 4 Deame o Mahemaics
More informationEffect of Weight Function in Nonlinear Part on Global Solvability of Cauchy Problem for Semi-Linear Hyperbolic Equations
Ieraioa Jora of Moder Noiear Theory ad Aicaio -6 h://ddoiorg/46/ijmaa Pbihed Oie March (h://wwwcirorg/jora/ijma) Effec of Weigh Fcio i Noiear Par o Goba Sovabiiy of Cachy Probem for Semi-Liear Hyerboic
More informationRelations on the Apostol Type (p, q)-frobenius-euler Polynomials and Generalizations of the Srivastava-Pintér Addition Theorems
Tish Joal of Aalysis ad Nmbe Theoy 27 Vol 5 No 4 26-3 Available olie a hp://pbssciepbcom/ja/5/4/2 Sciece ad Edcaio Pblishig DOI:269/ja-5-4-2 Relaios o he Aposol Type (p -Fobeis-Ele Polyomials ad Geealizaios
More informationComparison between Fourier and Corrected Fourier Series Methods
Malaysia Joural of Mahemaical Scieces 7(): 73-8 (13) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES Joural homepage: hp://eispem.upm.edu.my/oural Compariso bewee Fourier ad Correced Fourier Series Mehods 1
More informationStrong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA
Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics
More informationX-Ray Notes, Part III
oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel
More informationMathematical Models and the Soil Hydraulic Properties
Bullei UASVM Hoiculue 66/9 Pi ISSN 843-554; Elecoic ISSN 843-5394 Maeaical Model ad e Soil Hydaulic Popeie Floica MATEI Macel IRJA Ioaa POP Vioel BUIU Maia MICULA Faculy of Hoiculue Uiveiy of Agiculual
More informationMATH Midterm Solutions
MATH 2113 - Midtem Solutios Febuay 18 1. A bag of mables cotais 4 which ae ed, 4 which ae blue ad 4 which ae gee. a How may mables must be chose fom the bag to guaatee that thee ae the same colou? We ca
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationEconomics 8723 Macroeconomic Theory Problem Set 3 Sketch of Solutions Professor Sanjay Chugh Spring 2017
Deparme of Ecoomic The Ohio Sae Uiveriy Ecoomic 8723 Macroecoomic Theory Problem Se 3 Skech of Soluio Profeor Sajay Chugh Sprig 27 Taylor Saggered Nomial Price-Seig Model There are wo group of moopoliically-compeiive
More informationON GENERALIZED FRACTIONAL INTEGRAL OPERATORS. ( ρ( x y ) T ρ f(x) := f(y) R x y n dy, R x y n ρ( y )(1 χ )
Scieiae Mahemaicae Japoicae Olie, Vol., 24), 37 38 37 ON GENERALIZED FRACTIONAL INTEGRAL OPERATORS ERIDANI, HENDRA GUNAWAN 2 AND EIICHI NAKAI 3 Received Augus 29, 23; evised Apil 7, 24 Absac. We pove he
More informationECSE Partial fraction expansion (m<n) 3 types of poles Simple Real poles Real Equal poles
ECSE- Lecue. Paial facio expasio (m
More informationUnion-Find Partition Structures
Uio-Fid //4 : Preseaio for use wih he exbook Daa Srucures ad Alorihms i Java, h ediio, by M. T. Goodrich, R. Tamassia, ad M. H. Goldwasser, Wiley, 04 Uio-Fid Pariio Srucures 04 Goodrich, Tamassia, Goldwasser
More informationComplementary Dual Subfield Linear Codes Over Finite Fields
1 Complemetay Dual Subfield Liea Codes Ove Fiite Fields Kiagai Booiyoma ad Somphog Jitma,1 Depatmet of Mathematics, Faculty of Sciece, Silpao Uivesity, Naho Pathom 73000, hailad e-mail : ai_b_555@hotmail.com
More informationxp (X = x) = P (X = 1) = θ. Hence, the method of moments estimator of θ is
Exercise 7 / page 356 Noe ha X i are ii from Beroulli(θ where 0 θ a Meho of momes: Sice here is oly oe parameer o be esimae we ee oly oe equaio where we equae he rs sample mome wih he rs populaio mome,
More information. Since P-U I= P+ (p-l)} Aap Since pn for every GF(pn) we have A pn A Therefore. As As. A,Ap. (Zp,+,.) ON FUNDAMENTAL SETS OVER A FINITE FIELD
Ie J Mh & Mh Sci Vol 8 No 2 (1985) 373-388 373 ON FUNDAMENTAL SETS OVER A FINITE FIELD YOUSEF ABBAS d JOSEH J LIANG Dee of Mheic Uiveiy of Souh Floid T, Floid 33620 USA (Received Mch 3, 1983) ABSTRACT
More informationSOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE
Faulty of Siees ad Matheatis, Uivesity of Niš, Sebia Available at: http://www.pf.i.a.yu/filoat Filoat 22:2 (28), 59 64 SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE Saee Ahad Gupai Abstat. The sequee
More informationME 321 Kinematics and Dynamics of Machines S. Lambert Winter 2002
ME 31 Kiemaic ad Dyamic o Machie S. Lamber Wier 6.. Forced Vibraio wih Dampig Coider ow he cae o orced vibraio wih dampig. Recall ha he goverig diereial equaio i: m && c& k F() ad ha we will aume ha he
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationAngle Modulation: NB (Sinusoid)
gle Moulaio: NB Siuoi I uay, i he eage igal i a pue iuoi, ha i, a a i o o PM o FM The, i whee a p a o PM o FM : pea equey eviaio Noe ha i ow a oulaio ie o agle oulaio a i he aiu value o phae eviaio o boh
More informationCongruences for sequences similar to Euler numbers
Coguece fo equece iila to Eule ube Zhi-Hog Su School of Matheatical Sciece, Huaiyi Noal Uiveity, Huaia, Jiagu 00, Peole Reublic of Chia Received July 00 Revied 5 Augut 0 Couicated by David Go Abtact a
More information1. Solve by the method of undetermined coefficients and by the method of variation of parameters. (4)
7 Differeial equaios Review Solve by he mehod of udeermied coefficies ad by he mehod of variaio of parameers (4) y y = si Soluio; we firs solve he homogeeous equaio (4) y y = 4 The correspodig characerisic
More informationAdvanced Physical Geodesy
Supplemetal Notes Review of g Tems i Moitz s Aalytic Cotiuatio Method. Advaced hysical Geodesy GS887 Chistophe Jekeli Geodetic Sciece The Ohio State Uivesity 5 South Oval Mall Columbus, OH 4 7 The followig
More informationHadamard matrices from the Multiplication Table of the Finite Fields
adamard marice from he Muliplicaio Table of he Fiie Field 신민호 송홍엽 노종선 * Iroducio adamard mari biary m-equece New Corucio Coe Theorem. Corucio wih caoical bai Theorem. Corucio wih ay bai Remark adamard
More informationExtremal graph theory II: K t and K t,t
Exremal graph heory II: K ad K, Lecure Graph Theory 06 EPFL Frak de Zeeuw I his lecure, we geeralize he wo mai heorems from he las lecure, from riagles K 3 o complee graphs K, ad from squares K, o complee
More informationSpectral Simulation of Turbulence. and Tracking of Small Particles
Specra Siuaio of Turbuece ad Trackig of Sa Parices Hoogeeous Turbuece Saisica ie average properies RMS veociy fucuaios dissipaio rae are idepede of posiio. Hoogeeous urbuece ca be odeed wih radoy sirred
More informationMODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecure 9, Sae Space Repreeaio Emam Fahy Deparme of Elecrical ad Corol Egieerig email: emfmz@aa.edu hp://www.aa.edu/cv.php?dip_ui=346&er=6855 Trafer Fucio Limiaio TF = O/P I/P ZIC
More informationOn a Z-Transformation Approach to a Continuous-Time Markov Process with Nonfixed Transition Rates
Ge. Mah. Noes, Vol. 24, No. 2, Ocobe 24, pp. 85-96 ISSN 229-784; Copyigh ICSRS Publicaio, 24 www.i-css.og Available fee olie a hp://www.gema.i O a Z-Tasfomaio Appoach o a Coiuous-Time Maov Pocess wih Nofixed
More informationLecture 4. Electrons and Holes in Semiconductors
Lecue 4 lec ad Hle i Semicduc I hi lecue yu will lea: Geeai-ecmbiai i emicduc i me deail The baic e f euai gveig he behavi f elec ad hle i emicduc Shckley uai Quai-eualiy i cducive maeial C 35 Sig 2005
More informationExistence and Smoothness of Solution of Navier-Stokes Equation on R 3
Ieaioal Joual of Mode Noliea Theoy ad Applicaio, 5, 4, 7-6 Published Olie Jue 5 i SciRes. hp://www.scip.og/joual/ijma hp://dx.doi.og/.436/ijma.5.48 Exisece ad Smoohess of Soluio of Navie-Sokes Equaio o
More informationAfrican Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS
Af Joul of See Tehology (AJST) See Egeeg See Vol. 4, No.,. 7-79 GENERALISED DELETION DESIGNS Mhel Ku Gh Joh Wylff Ohbo Dee of Mhe, Uvey of Nob, P. O. Bo 3097, Nob, Key ABSTRACT:- I h e yel gle ele fol
More informationOptical flow equation
Opical Flow Sall oio: ( ad ae le ha piel) H() I(++) Be foce o poible ppoe we ake he Talo eie epaio of I: (Sei) Opical flow eqaio Cobiig hee wo eqaio I he lii a ad go o eo hi becoe eac (Sei) Opical flow
More information-HYBRID LAPLACE TRANSFORM AND APPLICATIONS TO MULTIDIMENSIONAL HYBRID SYSTEMS. PART II: DETERMINING THE ORIGINAL
UPB Sc B See A Vo 72 I 3 2 ISSN 223-727 MUTIPE -HYBRID APACE TRANSORM AND APPICATIONS TO MUTIDIMENSIONA HYBRID SYSTEMS PART II: DETERMININ THE ORIINA Ve PREPEIŢĂ Te VASIACHE 2 Ace co copeeă oă - pce he
More informationGeodesic Lightlike Submanifolds of Indefinite Sasakian Manifolds *
Advance in Pure Mahemaic 2011 1 378-383 doi:104236/apm201116067 Pubihed Onine November 2011 (hp://wwwscirporg/journa/apm) Geodeic Lighike Submanifod of Indefinie Saakian Manifod * Abrac Junhong Dong 1
More informationA New Result On A,p n,δ k -Summabilty
OSR Joual of Matheatics (OSR-JM) e-ssn: 2278-5728, p-ssn:239-765x. Volue 0, ssue Ve. V. (Feb. 204), PP 56-62 www.iosjouals.og A New Result O A,p,δ -Suabilty Ripeda Kua &Aditya Kua Raghuashi Depatet of
More informationConditional Convergence of Infinite Products
Coditioal Covegece of Ifiite Poducts William F. Tech Ameica Mathematical Mothly 106 1999), 646-651 I this aticle we evisit the classical subject of ifiite poducts. Fo stadad defiitios ad theoems o this
More informationExistence of Nonoscillatory Solution of High Order Linear Neutral Delay Difference Equation
oder Appied Sciece ovember, 008 Existece of oosciatory Soutio of High Order Liear eutra Deay Differece Equatio Shasha Zhag, Xiaozhu Zhog, Pig Yu, Wexia Zhag & ig Li Departmet of athematics Yasha Uiversity
More informationStructure and Some Geometric Properties of Nakano Difference Sequence Space
Stuctue ad Soe Geoetic Poeties of Naao Diffeece Sequece Sace N Faied ad AA Baey Deatet of Matheatics, Faculty of Sciece, Ai Shas Uivesity, Caio, Egyt awad_baey@yahooco Abstact: I this ae, we exted the
More informationFIXED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE
Mohia & Samaa, Vol. 1, No. II, December, 016, pp 34-49. ORIGINAL RESEARCH ARTICLE OPEN ACCESS FIED FUZZY POINT THEOREMS IN FUZZY METRIC SPACE 1 Mohia S. *, Samaa T. K. 1 Deparme of Mahemaics, Sudhir Memorial
More informationLecture 24: Observability and Constructibility
ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio
More informationS n. = n. Sum of first n terms of an A. P is
PROGREION I his secio we discuss hree impora series amely ) Arihmeic Progressio (A.P), ) Geomeric Progressio (G.P), ad 3) Harmoic Progressio (H.P) Which are very widely used i biological scieces ad humaiies.
More informationFermat Numbers in Multinomial Coefficients
1 3 47 6 3 11 Joural of Ieger Sequeces, Vol. 17 (014, Aricle 14.3. Ferma Numbers i Muliomial Coefficies Shae Cher Deparme of Mahemaics Zhejiag Uiversiy Hagzhou, 31007 Chia chexiaohag9@gmail.com Absrac
More information( F, ρ )-Convexity in Nonsmooth Vector Optimization over Cones
Appied Maheaics, 25, 6, 7-9 Pubished Oie Jauary 25 i SciRes hp://wwwscirporg/joura/a hp://dxdoiorg/4236/a2562 Higher-Order Miiizers ad Geeraized ( F, ρ )-Covexiy i Nosooh Vecor Opiizaio over Coes S K Sueja,
More informationTIME RESPONSE Introduction
TIME RESPONSE Iroducio Time repoe of a corol yem i a udy o how he oupu variable chage whe a ypical e ipu igal i give o he yem. The commoly e ipu igal are hoe of ep fucio, impule fucio, ramp fucio ad iuoidal
More informationSupplementary Information
Supplemeay Ifomaio No-ivasive, asie deemiaio of he coe empeaue of a hea-geeaig solid body Dea Ahoy, Daipaya Saka, Aku Jai * Mechaical ad Aeospace Egieeig Depame Uivesiy of Texas a Aligo, Aligo, TX, USA.
More information( ) 1 Comparison Functions. α is strictly increasing since ( r) ( r ) α = for any positive real number c. = 0. It is said to belong to
Compaiso Fuctios I this lesso, we study stability popeties of the oautoomous system = f t, x The difficulty is that ay solutio of this system statig at x( t ) depeds o both t ad t = x Thee ae thee special
More informationLIMITS OF FUNCTIONS (I)
LIMITS OF FUNCTIO (I ELEMENTARY FUNCTIO: (Elemeary fucios are NOT piecewise fucios Cosa Fucios: f(x k, where k R Polyomials: f(x a + a x + a x + a x + + a x, where a, a,..., a R Raioal Fucios: f(x P (x,
More informationA note on characterization related to distributional properties of random translation, contraction and dilation of generalized order statistics
PobSa Foum, Volume 6, July 213, Pages 35 41 ISSN 974-3235 PobSa Foum is an e-jounal. Fo eails please visi www.pobsa.og.in A noe on chaaceizaion elae o isibuional popeies of anom anslaion, conacion an ilaion
More informationSome Identities Relating to Degenerate Bernoulli Polynomials
Fioma 30:4 2016), 905 912 DOI 10.2298/FIL1604905K Pubishe by Facuy of Scieces a Mahemaics, Uiversiy of Niš, Serbia Avaiabe a: hp://www.pmf.i.ac.rs/fioma Some Ieiies Reaig o Degeerae Beroui Poyomias Taekyu
More informationECE-314 Fall 2012 Review Questions
ECE-34 Fall 0 Review Quesios. A liear ime-ivaria sysem has he ipu-oupu characerisics show i he firs row of he diagram below. Deermie he oupu for he ipu show o he secod row of he diagram. Jusify your aswer.
More informationIt is often useful to approximate complicated functions using simpler ones. We consider the task of approximating a function by a polynomial.
Taylor Polyomials ad Taylor Series It is ofte useful to approximate complicated fuctios usig simpler oes We cosider the task of approximatig a fuctio by a polyomial If f is at least -times differetiable
More informationReview - Week 10. There are two types of errors one can make when performing significance tests:
Review - Week Read: Chaper -3 Review: There are wo ype of error oe ca make whe performig igificace e: Type I error The ull hypohei i rue, bu we miakely rejec i (Fale poiive) Type II error The ull hypohei
More informationهقارنت طرائق تقذير هعلواث توزيع كاها ري املعلوتني
هقارنت طرائق تقذير هعلواث توزيع كاها ري املعلوتني يف حالت البياناث املفقودة باستخذام احملاكاة د أ. الباحثة ظافر حسين رشيد جامعة بغداد- كمية االدارة واالقتصاد قسم االحصاء آوات سردار وادي املستخلص Maxiu
More informationTwo-Pion Exchange Currents in Photodisintegration of the Deuteron
Two-Pion Exchange Cuens in Phoodisinegaion of he Deueon Dagaa Rozędzik and Jacek Goak Jagieonian Univesiy Kaków MENU00 3 May 00 Wiiasbug Conen Chia Effecive Fied Theoy ChEFT Eecoagneic cuen oeaos wihin
More informationStability. Outline Stability Sab Stability of Digital Systems. Stability for Continuous-time Systems. system is its stability:
Oulie Sabiliy Sab Sabiliy of Digial Syem Ieral Sabiliy Exeral Sabiliy Example Roo Locu v ime Repoe Fir Orer Seco Orer Sabiliy e Jury e Rouh Crierio Example Sabiliy A very impora propery of a yamic yem
More informationODEs II, Supplement to Lectures 6 & 7: The Jordan Normal Form: Solving Autonomous, Homogeneous Linear Systems. April 2, 2003
ODEs II, Suppleme o Lecures 6 & 7: The Jorda Normal Form: Solvig Auoomous, Homogeeous Liear Sysems April 2, 23 I his oe, we describe he Jorda ormal form of a marix ad use i o solve a geeral homogeeous
More information