Think of the Relationship Between Time and Space Again


 Donald Douglas
 3 years ago
 Views:
Transcription
1 Repor nd Opinion, 1(3),009 hp://wwwsciencepubne Think of he Relionship Beween Time nd Spce Agin Yng Fcheng Compny of Ruid Cenre in Xinjing 15 Hongxing Sree, Klmyi, Xingjing , CHINA emil: ABSTRACT In his pper, he uhor pus forwrd mhemicl model, his model cn give cler relionship beween ime nd spce The uhors pu forwrd from he objecive reliy, he new ides nd mhemicl formul, le people know long he correc rod of lw reflecs reliy [Repor nd Opinion 009;(3): 5863](ISSN: ) Key words: ligh sphericl, wvefron, insnneous spceime, rnsmission ime 1 INTRODUCTION Time his concep hs been Newonin in Philosophic Nurlis Principle Mhemicl in Time clock is used for mesuring rel ime of kind of insrumen (iming is used o mesure ime clock of n insrumen) Auhors ssume wo reference frme S nd S in reference frme S (excep he source poin) hve rbirry spil poin ligh P, when he movemen of he reference frme S coincides wih sic sysem S compleely momens, poin P o lunch flsh In ech of he origin of he observer nd iming srs, ech frme of reference in differen ime o receive pulse respecively The uhor fer creful considerion, nd ry o esblish new relionship beween ime nd spce RELATIONSHIP BETWEEN TIME AND SPACE In he ps hs pu forwrd he heory of he ligh speed invrince, he speed nd no sy invribiliy of he phoon wih ny reference poin I refers o he mening iself : From he poin ligh shining pulse, he flsh o spred round he geomery is sphere The sphericl surfce in he vcuum diffusion speed remin unchnged We obined he sphericl equion h ech reference frme 1 Using Algebric Equions is Obined As Fig1 shown, uhors ssume wo reference frme S nd S long he X xil movemen speed reference frme S for V moves from poin J o A nd presenly coincides wih he reference frme S compleely A his momen, from he lighsource poin P shining pulse, in heir respecive reference frme origin he observer iming srs, he flsh o spred round he geomery is sphere Poin P is lwys he cener of sphericl rry, bll sphericl surfce(or wvefron)spred o he source of reference frme S, poin O Timer vlues for reding The spce locion in reference frme S poin P for (x, y, z), insn spceime s (x, y, z, ) In ime T 0 o T, pulse propgion disnce is he rdius of he bll[1] According o he Pyhgoren heorem we obin sphericl equion in he reference frme S : x + y + z (c) (1) Move long he X xis reference frme S, sphericl surfce coninued o spred in, he bll on he pursui of diffusion in fce of reference frme S observer A his momen, in reference frme S o red he clock is he spce locion in reference frme S poin P for (x y z ), insn spceime s x y z Figure 1 in nlysis, 58
2 Repor nd Opinion, 1(3),009 hp://wwwsciencepubne obviously, Ligh sphericl diffusion speed relive o he cener from poin of origin for finding C Due o he poin P is fixed in he reference frme S i is relive o he movemen of reference frme S vry wih ime So, insn spceime s x y z In ime T 0 o T, pulse propgion disnce is he rdius of he bll According o he Pyhgoren heorem we obin sphericl equion in he reference frme S : x + y + z ( c) () The x shf nd X xle lod, reference frme S long he X xis movemen, round he X xis roion does no Th is, y y, z z y y, z z, x xv Will formul (1) nd () join soluion formul we hve : y + z ( c) x, ( ) + [( c) x ] ( c) 0 x ( x V ) + [( c) x ] ( c) 0, ( c )( ) + Vx ( c) 0 Decomposiion of he unry qudric equions (1 ) + (Vx ) 0 V V (3) In order o fcilie he process wih V / C Tke equion is roo, we mus : (4) (1 ) + x x 1 Fig1 The reference frme S sphericl equion is Eq(1) The reference frme S sphericl equion is Eq() Derived Using he Geomeric Equions The x shf nd X xle lod [] nd y xis prllel xis wih y, z xis prllel xis wih z Therefore, poin P on reference frme, S nd S, y y, z z In he equion (1), sy flsh signl rnsmission ime vlue, from poin P o O In he equion (), sy flsh signl rnsmission ime vlue, from poin P o O Obviously, in Fig1, Is he 59
3 Repor nd Opinion, 1(3),009 hp://wwwsciencepubne signl propgion dely effec [3] In noher wy, he sme resuls When he movemen of he reference frme S coincides wih sic sysem S momen Compleely A flsh poin P, ligh blls for reference frme S in pursui of he movemen Figure 1 of righ ringle: righ ringle PKO in PKO plne pk + ko po pk + ko po b Type (b) minus () is po po ko ko ko x V ko x, po c nd po c generion of he soring ge ( x V c ) + [( c) x ] ( ) In order o ge on he sme fer he equion ( x V ) + [( c) x ] ( c ) In Fig1, if he negive direcion long he X xis reference frme S movemen, resuls wih he sme formul (3) From he perspecive of geomery discuss he dvnges of: Along he X xis movemen, reference frme S round he X xis roion my, don ssume y y z z h is y y z z If he vrible is long he X xis reference frme S movemen known s reference frme S speed chnging wih ime, he funcion h cn use he definie inegrl o nswer [4] 3 DISCUSS AND REVIEW Ligh source poin P is hypohesis in he y xis, by equion (4) h sme ime dilion nd Einsein formul Ligh source poin P is hypohesis in he X xis, ssume he ligh source is on he X xis, wo kinds of circumsnces, is in he posiive direcion of he X xis nd he opposiion upwrd, we hve series of formuls 31 Ligh Source Poin P In y  z Plne Use he formul (3) nd Fig1 nlysis: will be ligh source poin P moves o (y z ) plne, in he formul (3), x 0, we obin : (5) This formul is similr wih Einsein ype Fig Ligh source poin P in y  z plne Y nd z he sme ime is no zero 60
4 Repor nd Opinion, 1(3),009 hp://wwwsciencepubne 3 Ligh Source Poin In he X xis Will ligh source poin P moves o he X xis, h is in Fig1 X xis of negive direcion, x 0, x 0 y 0, z 0, hen we hve: c x, x Subsiue hese vlues ino formul (4) obined : x x 1 ± x V x 1, (6) If he ligh source poin P is moving o he Xxis direcion, x > 0 x V (1 ) c c x 1 (1 )(1 + ) c + V (7) Poin P on he X xis of he opposiion, x < 0 x V (1 + ) c c x (1 )(1 + ) c V (8) 33 The Relionship Beween Moving Phoonic nd Reference Frme Assuming he X xis symmeric poin O on wo poin ligh source of P 1 nd P, s Fig3 shown When he movemen of he reference frme S coincides wih sic sysems S compleely momens, wo poin ligh lso issued flsh ligh, reference frme S o wo poin ligh source of P 1 nd P, clock wih 1 respecively According o he formul (7) nd (8) vilble Reference frme S movemen owrd he ligh source poin : c+ V x/ 1 Th is U 1 c + V x/ 1 (9) Reference frme S movemen wy from ligh poin : c V x/ Th is c x/ U V (10) Anlysis he formul (9) nd (10) Source: P is in reference frme S on he movemen direcion, h sid, ineril sysems S is long he phoon rjecory line movemen Therefore, he phoons movemen speed by Glileo rnsformion (relive reference frme S ) From he formul (9) nd (10), movemen speed of reference frme S for ny vlue 61
5 Repor nd Opinion, 1(3),009 hp://wwwsciencepubne Fig3 Along he X xis movemen reference frme S, ligh source poin is fixed on he X xis 4 UNDER THE LIGHT OF THE RELATIONSHIP BETWEEN TIME AND SPACE MOVEMENT In lile ligh in reference frme, relive o heir source of phoon speed isoropic for C As Fig4 shown, source: P is sphericl of cener, bu he relive o heir reference frme ouside he ineril sysem is nisoropic When long he Xxis movemen sysems S nd sillness reference frme S compleely coincidence momens, send flsh poin P In heir respecive reference frme origin he observer iming srs, when he ineri ligh poin P speed is V O V C movemen o poin E, bll sphericl surfce or wveform spred o he source of reference frme S poin O, imer vlues for reding The spce locion in reference frme S poin P for [ X+V, y, z ], insn spceime s [ X+V, y, z, ] From poin A o B disnce is V According o he Pyhgoren heorem we obin sphericl surfce equion in he reference frme S : + y + z ( c ), x (11) Ligh sphericl coninued o spred, in he momen, sphericl surfce diffuse o poin A ble Ineril sysem poin P wih sic reference frme S poin G of superposiion, he ime, in he reference frme S poin P spceime is he cener of he bll in According o he Pyhgoren heorem we obin (1) ( x V c + ) + y + z ( ), Suppose y y, z z, y y, z z nd V /c combined he formul (11) wih he formul (1) o form simulneous equions nd o solve his equions We obined, he oneelemen qudric equion of n unknown number : (13) (1 V ) (Vx ) 0 We chose he posiive roo of such qudric equion s follows: 6
6 Repor nd Opinion, 1(3),009 hp://wwwsciencepubne (1 ) + x 1 + x (14) If we like his "discussion nd reviews" nlyicl formul 14 will ge he sme resul wih In Fig4, if he negive direcion long he X xis reference frme S movemen, resuls wih he sme formul (13) If he vrible is long he X xis reference frme S movemen known s reference frme S speed chnging wih ime, he funcion h cn use he definie inegrl o nswer [4,5] + ) + y + z ( x V ( c) x + y + z ( c ) Fig4 The reference frme sphericl equion is Eq(11) The reference frme S sphericl equion is Eq(1) 5 CONCLUSION The speed of ligh sphericl diffusion invrin In he vcuum, ligh sphericl diffusion speed relive o he cener from poin of origin for finding C The chnge of phoonic speed Ineril sysem is long he phoon rjecory line movemen, he speed of phoon nd ineril sysem se closely reled Therefore, he phoons movemen speed by Glileo rnsformion ( relively ll ineril sysem ) REFERENCES [1] Zhng Chong An Mer Regulriy 003, P07, 003 [] Yng F Cheng Mer Regulriy 003, P91, Journl of Xinjing Peroleum Educion College, 001, issue 4, P51 [3] C Kiel e l Berkeley Physies Course, Vol1, Science Press, 1979 [4] Xu Sho Zhi, The Mhemicl Fundion of he Specil Theory of Reliviy is Wrong, Invenion nd Innovion, 001(1) [5] Yng F Cheng, A New Mhemicl Model o Replce he Lorenz Trnsformion, he New probe of spceime Theory, A chief Edior, Ho Jin Yu, Beijing, Geology Press,005 4/15/009 63
Contraction Mapping Principle Approach to Differential Equations
epl Journl of Science echnology 0 (009) 4953 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 informationPhysics 2A HW #3 Solutions
Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 33 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen
More informationSeptember 20 Homework Solutions
College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum
More informationMotion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v  vo = Δv Δ ccelerion = = v  vo chnge of velociy elpsed ime Accelerion is vecor, lhough in onedimensionl
More information0 for t < 0 1 for t > 0
8.0 Sep nd del funcions Auhor: Jeremy Orloff The uni Sep Funcion We define he uni sep funcion by u() = 0 for < 0 for > 0 I is clled he uni sep funcion becuse i kes uni sep = 0. I is someimes clled he Heviside
More informationAverage & instantaneous velocity and acceleration Motion with constant acceleration
Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission
More informationA Kalman filtering simulation
A Klmn filering simulion The performnce of Klmn filering hs been esed on he bsis of wo differen dynmicl models, ssuming eiher moion wih consn elociy or wih consn ccelerion. The former is epeced o beer
More informationENGR 1990 Engineering Mathematics The Integral of a Function as a Function
ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under
More informatione t dt e t dt = lim e t dt T (1 e T ) = 1
Improper Inegrls There re wo ypes of improper inegrls  hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie
More informationSome Inequalities variations on a common theme Lecture I, UL 2007
Some Inequliies vriions on common heme Lecure I, UL 2007 Finbrr Hollnd, Deprmen of Mhemics, Universiy College Cork, fhollnd@uccie; July 2, 2007 Three Problems Problem Assume i, b i, c i, i =, 2, 3 re rel
More informationA 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m
PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl
More informationPHYSICS 1210 Exam 1 University of Wyoming 14 February points
PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is opennoe nd closedbook. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher
More information3 Motion with constant acceleration: Linear and projectile motion
3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr
More informationMATH 124 AND 125 FINAL EXAM REVIEW PACKET (Revised spring 2008)
MATH 14 AND 15 FINAL EXAM REVIEW PACKET (Revised spring 8) The following quesions cn be used s review for Mh 14/ 15 These quesions re no cul smples of quesions h will pper on he finl em, bu hey will provide
More informationChapter 2. Motion along a straight line. 9/9/2015 Physics 218
Chper Moion long srigh line 9/9/05 Physics 8 Gols for Chper How o describe srigh line moion in erms of displcemen nd erge elociy. The mening of insnneous elociy nd speed. Aerge elociy/insnneous elociy
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 informationGENERALIZATION OF SOME INEQUALITIES VIA RIEMANNLIOUVILLE FRACTIONAL CALCULUS
 TAMKANG JOURNAL OF MATHEMATICS Volume 5, Number, 75, June doi:5556/jkjm555 Avilble online hp://journlsmhkueduw/    GENERALIZATION OF SOME INEQUALITIES VIA RIEMANNLIOUVILLE FRACTIONAL CALCULUS MARCELA
More informationMTH 146 Class 11 Notes
8. Are of Surfce of Revoluion MTH 6 Clss Noes Suppose we wish o revolve curve C round n is nd find he surfce re of he resuling solid. Suppose f( ) is nonnegive funcion wih coninuous firs derivive on he
More informationChapter Direct Method of Interpolation
Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o
More informationConvergence of Singular Integral Operators in Weighted Lebesgue Spaces
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 10, No. 2, 2017, 335347 ISSN 13075543 www.ejpm.com Published by New York Business Globl Convergence of Singulr Inegrl Operors in Weighed Lebesgue
More informationf t f a f x dx By Lin McMullin f x dx= f b f a. 2
Accumulion: Thoughs On () By Lin McMullin f f f d = + The gols of he AP* Clculus progrm include he semen, Sudens should undersnd he definie inegrl s he ne ccumulion of chnge. 1 The Topicl Ouline includes
More informationEXERCISE  01 CHECK YOUR GRASP
UNIT # 09 PARABOLA, ELLIPSE & HYPERBOLA PARABOLA EXERCISE  0 CHECK YOUR GRASP. Hin : Disnce beween direcri nd focus is 5. Given (, be one end of focl chord hen oher end be, lengh of focl chord 6. Focus
More informationFM Applications of Integration 1.Centroid of Area
FM Applicions of Inegrion.Cenroid of Are The cenroid of ody is is geomeric cenre. For n ojec mde of uniform meril, he cenroid coincides wih he poin which he ody cn e suppored in perfecly lnced se ie, is
More informationSOME USEFUL MATHEMATICS
SOME USEFU MAHEMAICS SOME USEFU MAHEMAICS I is esy o mesure n preic he behvior of n elecricl circui h conins only c volges n currens. However, mos useful elecricl signls h crry informion vry wih ime. Since
More informationSolutions to Problems from Chapter 2
Soluions o Problems rom Chper Problem. The signls u() :5sgn(), u () :5sgn(), nd u h () :5sgn() re ploed respecively in Figures.,b,c. Noe h u h () :5sgn() :5; 8 including, bu u () :5sgn() is undeined..5
More information1. Consider a PSA initially at rest in the beginning of the lefthand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.
In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lefhnd
More information2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.
Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl
More informationEXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECONDORDER ITERATIVE BOUNDARYVALUE PROBLEM
Elecronic Journl of Differenil Equions, Vol. 208 (208), No. 50, pp. 6. ISSN: 072669. URL: hp://ejde.mh.xse.edu or hp://ejde.mh.un.edu EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A SECONDORDER ITERATIVE
More informationRESPONSE UNDER A GENERAL PERIODIC FORCE. When the external force F(t) is periodic with periodτ = 2π
RESPONSE UNDER A GENERAL PERIODIC FORCE When he exernl force F() is periodic wih periodτ / ω,i cn be expnded in Fourier series F( ) o α ω α b ω () where τ F( ) ω d, τ,,,... () nd b τ F( ) ω d, τ,,... (3)
More informationVersion 001 test1 swinney (57010) 1. is constant at m/s.
Version 001 es1 swinne (57010) 1 This prinou should hve 20 quesions. Muliplechoice quesions m coninue on he nex column or pge find ll choices before nswering. CubeUniVec1x76 001 10.0 poins Acubeis1.4fee
More informationME 141. Engineering Mechanics
ME 141 Engineeing Mechnics Lecue 13: Kinemics of igid bodies hmd Shhedi Shkil Lecue, ep. of Mechnicl Engg, UET Emil: sshkil@me.bue.c.bd, shkil6791@gmil.com Websie: eche.bue.c.bd/sshkil Couesy: Veco Mechnics
More informationPhys 110. Answers to even numbered problems on Midterm Map
Phys Answers o een numbered problems on Miderm Mp. REASONING The word per indices rio, so.35 mm per dy mens.35 mm/d, which is o be epressed s re in f/cenury. These unis differ from he gien unis in boh
More information2k 1. . And when n is odd number, ) The conclusion is when n is even number, an. ( 1) ( 2 1) ( k 0,1,2 L )
Scholrs Journl of Engineering d Technology SJET) Sch. J. Eng. Tech., ; A):86 Scholrs Acdemic d Scienific Publisher An Inernionl Publisher for Acdemic d Scienific Resources) www.sspublisher.com ISSN X
More informationPhysic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =
Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he
More information(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.
Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)
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 99878 A Simple Mehod o Solve Quric Equions Amir Fhi, Poo Mobdersn, Rhim Fhi Deprmen of Elecricl Engineering, Urmi brnch, Islmic Ad Universi,
More informationMagnetostatics Bar Magnet. Magnetostatics Oersted s Experiment
Mgneosics Br Mgne As fr bck s 4500 yers go, he Chinese discovered h cerin ypes of iron ore could rc ech oher nd cerin mels. Iron filings "mp" of br mgne s field Crefully suspended slivers of his mel were
More informationAsymptotic relationship between trajectories of nominal and uncertain nonlinear systems on time scales
Asympoic relionship beween rjecories of nominl nd uncerin nonliner sysems on ime scles Fim Zohr Tousser 1,2, Michel Defoor 1, Boudekhil Chfi 2 nd Mohmed Djemï 1 Absrc This pper sudies he relionship beween
More informationREAL ANALYSIS I HOMEWORK 3. Chapter 1
REAL ANALYSIS I HOMEWORK 3 CİHAN BAHRAN The quesions re from Sein nd Shkrchi s e. Chper 1 18. Prove he following sserion: Every mesurble funcion is he limi.e. of sequence of coninuous funcions. We firs
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 informationProcedia Computer Science
Procedi Compuer Science 00 (0) 000 000 Procedi Compuer Science www.elsevier.com/loce/procedi The Third Informion Sysems Inernionl Conference The Exisence of Polynomil Soluion of he Nonliner Dynmicl Sysems
More informationMotion in a Straight Line
Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in
More informationCollision Detection and Bouncing
Collision Deecion nd Bouncing Collisions re Hndled in Two Prs. Deecing he collision Mike Biley mj@cs.oregonse.edu. Hndling he physics of he collision collisionouncing.ppx If You re Lucky, You Cn Deec
More informationM r. d 2. R t a M. Structural Mechanics Section. Exam CT5141 Theory of Elasticity Friday 31 October 2003, 9:00 12:00 hours. Problem 1 (3 points)
Delf Universiy of Technology Fculy of Civil Engineering nd Geosciences Srucurl echnics Secion Wrie your nme nd sudy numer he op righhnd of your work. Exm CT5 Theory of Elsiciy Fridy Ocoer 00, 9:00 :00
More informationHORIZONTAL POSITION OPTIMAL SOLUTION DETERMINATION FOR THE SATELLITE LASER RANGING SLOPE MODEL
HOIZONAL POSIION OPIMAL SOLUION DEEMINAION FO HE SAELLIE LASE ANGING SLOPE MODEL Yu Wng,* Yu Ai b Yu Hu b enli Wng b Xi n Surveying nd Mpping Insiue, No. 1 Middle Yn od, Xi n, Chin, 710054640677@qq.com
More informationLecture 3: 1D Kinematics. This Week s Announcements: Class Webpage: visit regularly
Lecure 3: 1D Kinemics This Week s Announcemens: Clss Webpge: hp://kesrel.nm.edu/~dmeier/phys121/phys121.hml isi regulrly Our TA is Lorrine Bowmn Week 2 Reding: Chper 2  Gincoli Week 2 Assignmens: Due:
More informationON THE OSTROWSKIGRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS
Hceepe Journl of Mhemics nd Sisics Volume 45) 0), 65 655 ON THE OSTROWSKIGRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS M Emin Özdemir, Ahme Ock Akdemir nd Erhn Se Received 6:06:0 : Acceped
More informationMinimum Squared Error
Minimum Squred Error LDF: Minimum SquredError Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > for ll smples y i solve sysem of liner inequliies MSE procedure y i = i for ll smples
More informationThe solution is often represented as a vector: 2xI + 4X2 + 2X3 + 4X4 + 2X5 = 4 2xI + 4X2 + 3X3 + 3X4 + 3X5 = 4. 3xI + 6X2 + 6X3 + 3X4 + 6X5 = 6.
[~ o o : o o ill] i 1. Mrices, Vecors, nd GussJordn Eliminion 1 x y = =  z= The soluion is ofen represened s vecor: n his exmple, he process of eliminion works very smoohly. We cn elimine ll enries
More informationMinimum Squared Error
Minimum Squred Error LDF: Minimum SquredError Procedures Ide: conver o esier nd eer undersood prolem Percepron y i > 0 for ll smples y i solve sysem of liner inequliies MSE procedure y i i for ll smples
More informationAn object moving with speed v around a point at distance r, has an angular velocity. m/s m
Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor
More information1.0 Electrical Systems
. Elecricl Sysems The ypes of dynmicl sysems we will e sudying cn e modeled in erms of lgeric equions, differenil equions, or inegrl equions. We will egin y looking fmilir mhemicl models of idel resisors,
More information( ) ( ) ( ) ( ) ( ) ( y )
8. Lengh of Plne Curve The mos fmous heorem in ll of mhemics is he Pyhgoren Theorem. I s formulion s he disnce formul is used o find he lenghs of line segmens in he coordine plne. In his secion you ll
More informationCBSE 2014 ANNUAL EXAMINATION ALL INDIA
CBSE ANNUAL EXAMINATION ALL INDIA SET Wih Complee Eplnions M Mrks : SECTION A Q If R = {(, y) : + y = 8} is relion on N, wrie he rnge of R Sol Since + y = 8 h implies, y = (8 ) R = {(, ), (, ), (6, )}
More informationLocation is relative. Coordinate Systems. Which of the following can be described with vectors??
Locion is relive Coordine Sysems The posiion o hing is sed relive o noher hing (rel or virul) review o he physicl sis h governs mhemicl represenions Reerence oec mus e deined Disnce mus e nown Direcion
More informationAn integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples.
Improper Inegrls To his poin we hve only considered inegrls f(x) wih he is of inegrion nd b finie nd he inegrnd f(x) bounded (nd in fc coninuous excep possibly for finiely mny jump disconinuiies) An inegrl
More informationCHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS
Physics h Ediion Cunell Johnson Young Sdler Soluions Mnul Soluions Mnul, Answer keys, Insrucor's Resource Mnul for ll chpers re included. Compleed downlod links: hps://esbnkre.com/downlod/physicshediionsoluionsmnulcunelljohnsonyoungsdler/
More informationAvailable Online :
fo/u fopjr Hh# u] ugh vjehs de] foifr ns[ NsMs rqjr e/;e eu dj ';ea iq#" flg ldyi dj] lgrs foifr vusd] ^cu^ u NsMs /;s; ds] j?qcj j[s VsdAA jfpr% euo /ez iz.sr ln~xq# Jh j.nsmnlh egj STUDY PACKAGE Subjec
More informationSolutions from Chapter 9.1 and 9.2
Soluions from Chaper 9 and 92 Secion 9 Problem # This basically boils down o an exercise in he chain rule from calculus We are looking for soluions of he form: u( x) = f( k x c) where k x R 3 and k is
More informationPhysics 101 Lecture 4 Motion in 2D and 3D
Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd
More informationProperties of Logarithms. Solving Exponential and Logarithmic Equations. Properties of Logarithms. Properties of Logarithms. ( x)
Properies of Logrihms Solving Eponenil nd Logrihmic Equions Properies of Logrihms Produc Rule ( ) log mn = log m + log n ( ) log = log + log Properies of Logrihms Quoien Rule log m = logm logn n log7 =
More informationMathematics 805 Final Examination Answers
. 5 poins Se he Weiersrss Mes. Mhemics 85 Finl Eminion Answers Answer: Suppose h A R, nd f n : A R. Suppose furher h f n M n for ll A, nd h Mn converges. Then f n converges uniformly on A.. 5 poins Se
More informationD zone schemes
Ch. 5. Enegy Bnds in Cysls 5.. D zone schemes Fee elecons E k m h Fee elecons in cysl sinα P + cosα cosk α cos α cos k cos( k + π n α k + πn mv ob P 0 h cos α cos k n α k + π m h k E Enegy is peiodic
More informationApplication on Inner Product Space with. Fixed Point Theorem in Probabilistic
Journl of Applied Mhemics & Bioinformics, vol.2, no.2, 2012, 110 ISSN: 17926602 prin, 17926939 online Scienpress Ld, 2012 Applicion on Inner Produc Spce wih Fixed Poin Theorem in Probbilisic Rjesh Shrivsv
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl o Inequlities in Pure nd Applied Mthemtics http://jipm.vu.edu.u/ Volume 6, Issue 4, Article 6, 2005 MROMORPHIC UNCTION THAT SHARS ON SMALL UNCTION WITH ITS DRIVATIV QINCAI ZHAN SCHOOL O INORMATION
More informationName: Per: L o s A l t o s H i g h S c h o o l. Physics Unit 1 Workbook. 1D Kinematics. Mr. Randall Room 705
Nme: Per: L o s A l o s H i g h S c h o o l Physics Uni 1 Workbook 1D Kinemics Mr. Rndll Room 705 Adm.Rndll@ml.ne www.laphysics.com Uni 1  Objecies Te: Physics 6 h Ediion Cunel & Johnson The objecies
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 informationA Special Hour with Relativity
A Special Hour wih Relaiviy Kenneh Chu The Graduae Colloquium Deparmen of Mahemaics Universiy of Uah Oc 29, 2002 Absrac Wha promped Einsen: Incompaibiliies beween Newonian Mechanics and Maxwell s Elecromagneism.
More informationPhysics Worksheet Lesson 4: Linear Motion Section: Name:
Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.
More informationHow to prove the Riemann Hypothesis
Scholrs Journl of Phsics, Mhemics nd Sisics Sch. J. Phs. Mh. S. 5; (B:56 Scholrs Acdemic nd Scienific Publishers (SAS Publishers (An Inernionl Publisher for Acdemic nd Scienific Resources *Corresonding
More informationCALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION
Avilble online hp://scik.org Eng. Mh. Le. 15, 15:4 ISSN: 499337 CALDERON S REPRODUCING FORMULA FOR DUNKL CONVOLUTION PANDEY, C. P. 1, RAKESH MOHAN AND BHAIRAW NATH TRIPATHI 3 1 Deprmen o Mhemics, Ajy
More informationTMatch: Matching Techniques For Driving YagiUda Antennas: TMatch. 2a s. Z in. (Sections 9.5 & 9.7 of Balanis)
3/0/018 _mch.doc Pge 1 of 6 TMch: Mching Techniques For Driving YgiUd Anenns: TMch (Secions 9.5 & 9.7 of Blnis) l s l / l / in The TMch is shunmching echnique h cn be used o feed he driven elemen
More informationMath 2142 Exam 1 Review Problems. x 2 + f (0) 3! for the 3rd Taylor polynomial at x = 0. To calculate the various quantities:
Mah 4 Eam Review Problems Problem. Calculae he 3rd Taylor polynomial for arcsin a =. Soluion. Le f() = arcsin. For his problem, we use he formula f() + f () + f ()! + f () 3! for he 3rd Taylor polynomial
More informationProbability, Estimators, and Stationarity
Chper Probbiliy, Esimors, nd Sionriy Consider signl genered by dynmicl process, R, R. Considering s funcion of ime, we re opering in he ime domin. A fundmenl wy o chrcerize he dynmics using he ime domin
More informationS Radio transmission and network access Exercise 12
S7.330 Rdio rnsmission nd nework ccess Exercise 1  P1 In foursymbol digil sysem wih eqully probble symbols he pulses in he figure re used in rnsmission over AWGNchnnel. s () s () s () s () 1 3 4 )
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 informationSolutions for Nonlinear Partial Differential Equations By TanCot Method
IOSR Journl of Mhemics (IOSRJM) eissn: 78578. Volume 5, Issue 3 (Jn.  Feb. 13), PP 611 Soluions for Nonliner Pril Differenil Equions By TnCo Mehod Mhmood Jwd Abdul Rsool Abu AlSheer Al Rfidin Universiy
More informationHermiteHadamardFejér type inequalities for convex functions via fractional integrals
Sud. Univ. BeşBolyi Mh. 6(5, No. 3, 355 366 HermieHdmrdFejér ype inequliies for convex funcions vi frcionl inegrls İmd İşcn Asrc. In his pper, firsly we hve eslished Hermie HdmrdFejér inequliy for
More informationThe Finite Element Method for the Analysis of NonLinear and Dynamic Systems
Swiss Federl Insiue of Pge 1 The Finie Elemen Mehod for he Anlysis of NonLiner nd Dynmic Sysems Prof. Dr. Michel Hvbro Fber Dr. Nebojs Mojsilovic Swiss Federl Insiue of ETH Zurich, Swizerlnd Mehod of
More informationgraph of unit step function t
.5 Piecewie coninuou forcing funcion...e.g. urning he forcing on nd off. The following Lplce rnform meril i ueful in yem where we urn forcing funcion on nd off, nd when we hve righ hnd ide "forcing funcion"
More informationA LIMITPOINT CRITERION FOR A SECONDORDER LINEAR DIFFERENTIAL OPERATOR IAN KNOWLES
A LIMITPOINT CRITERION FOR A SECONDORDER LINEAR DIFFERENTIAL OPERATOR j IAN KNOWLES 1. Inroducion Consider he forml differenil operor T defined by el, (1) where he funcion q{) is relvlued nd loclly
More informationForms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics:
SPH4U: Inroducion o ork ork & Energy ork & Energy Discussion Definiion Do Produc ork of consn force ork/kineic energy heore ork of uliple consn forces Coens One of he os iporn conceps in physics Alernive
More informationECE Microwave Engineering
EE 537635 Microwve Engineering Adped from noes y Prof. Jeffery T. Willims Fll 8 Prof. Dvid R. Jcson Dep. of EE Noes Wveguiding Srucures Pr 7: Trnsverse Equivlen Newor (N) Wveguide Trnsmission Line Model
More informationHow to Prove the Riemann Hypothesis Author: Fayez Fok Al Adeh.
How o Prove he Riemnn Hohesis Auhor: Fez Fok Al Adeh. Presiden of he Srin Cosmologicl Socie P.O.Bo,387,Dmscus,Sri Tels:96377679,735 Emil:hf@scsne.org Commens: 3 ges SubjClss: Funcionl nlsis, comle
More informationThe Paradox of Twins Described in a Threedimensional Spacetime Frame
The Paradox of Twins Described in a Threedimensional Spaceime Frame Tower Chen E_mail: chen@uguam.uog.edu Division of Mahemaical Sciences Universiy of Guam, USA Zeon Chen E_mail: zeon_chen@yahoo.com
More informationAvailable online at Pelagia Research Library. Advances in Applied Science Research, 2011, 2 (3):
Avilble online www.pelgireserchlibrry.com Pelgi Reserch Librry Advnces in Applied Science Reserch 0 (): 565 ISSN: 0976860 CODEN (USA): AASRFC A Mhemicl Model of For Species SynEcosymbiosis Comprising
More informationUsing hypothesis one, energy of gravitational waves is directly proportional to its frequency,
ushl nd Grviy Prshn Shool of Siene nd ngineering, Universiy of Glsgow, GlsgowG18QQ, Unied ingdo. * orresponding uhor: : Prshn. Shool of Siene nd ngineering, Universiy of Glsgow, GlsgowG18QQ, Unied ingdo,
More informationChapter 2 PROBLEM SOLUTIONS
Chper PROBLEM SOLUTIONS. We ssume h you re pproximely m ll nd h he nere impulse rels uniform speed. The elpsed ime is hen Δ x m Δ = m s s. s.3 Disnces reled beween pirs of ciies re ( ) Δx = Δ = 8. km h.5
More informationMore on Magnetically C Coupled Coils and Ideal Transformers
Appenix ore on gneiclly C Couple Coils Iel Trnsformers C. Equivlen Circuis for gneiclly Couple Coils A imes, i is convenien o moel mgneiclly couple coils wih n equivlen circui h oes no involve mgneic coupling.
More informationTax Audit and Vertical Externalities
T Audi nd Vericl Eernliies Hidey Ko Misuyoshi Yngihr Ngoy Keizi Universiy Ngoy Universiy 1. Inroducion The vericl fiscl eernliies rise when he differen levels of governmens, such s he federl nd se governmens,
More information14. The fundamental theorem of the calculus
4. The funmenl heorem of he clculus V 20 00 80 60 40 20 0 0 0.2 0.4 0.6 0.8 v 400 200 0 0 0.2 0.5 0.8 200 400 Figure : () Venriculr volume for subjecs wih cpciies C = 24 ml, C = 20 ml, C = 2 ml n (b) he
More informationPARABOLA. moves such that PM. = e (constant > 0) (eccentricity) then locus of P is called a conic. or conic section.
wwwskshieducioncom PARABOLA Le S be given fixed poin (focus) nd le l be given fixed line (Direcrix) Le SP nd PM be he disnce of vrible poin P o he focus nd direcrix respecively nd P SP moves such h PM
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 NebrskLincoln Lincoln,NE 685880323 lerbe@@mh.unl.edu
More informationMotion in One Dimension 2
The curren bsolue lnd speed record holder is he Briish designed ThrusSSC, win urbofnpowered cr which chieved 763 miles per hour (1,8 km/h) for he mile (1.6 km), breking he sound brrier. The cr ws driven
More informationResearch Article New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals
Hindwi Pulishing orporion Inernionl Journl of Anlysis, Aricle ID 35394, 8 pges hp://d.doi.org/0.55/04/35394 Reserch Aricle New Generl Inegrl Inequliies for Lipschizin Funcions vi Hdmrd Frcionl Inegrls
More informationIntroduction to LoggerPro
Inroducion o LoggerPro Sr/Sop collecion Define zero Se d collecion prmeers Auoscle D Browser Open file Sensor seup window To sr d collecion, click he green Collec buon on he ool br. There is dely of second
More informationCHAPTER 11 PARAMETRIC EQUATIONS AND POLAR COORDINATES
CHAPTER PARAMETRIC EQUATIONS AND POLAR COORDINATES. PARAMETRIZATIONS OF PLANE CURVES., 9, _ _ Ê.,, Ê or, Ÿ. 5, 7, _ _.,, Ÿ Ÿ Ê Ê 5 Ê ( 5) Ê ˆ Ê 6 Ê ( 5) 7 Ê Ê, Ÿ Ÿ $ 5. cos, sin, Ÿ Ÿ 6. cos ( ), sin (
More informationElements of Computer Graphics
CS580: Compuer Graphics Min H. Kim KAIST School of Compuing Elemens of Compuer Graphics Geomery Maerial model Ligh Rendering Virual phoography 2 Foundaions of Compuer Graphics A PINHOLE CAMERA IN 3D 3
More informationNeural assembly binding in linguistic representation
Neurl ssembly binding in linguisic represenion Frnk vn der Velde & Mrc de Kmps Cogniive Psychology Uni, Universiy of Leiden, Wssenrseweg 52, 2333 AK Leiden, The Neherlnds, vdvelde@fsw.leidenuniv.nl Absrc.
More information() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration
Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you
More information