International Journal of Mathematics Trends and Technology (IJMTT) Volume 53 Number 5 January 2018
|
|
- Jayson Arnold
- 5 years ago
- Views:
Transcription
1 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 Effecs of ime Depede acceleraio o he flow of Blood i rery wih periodic body acceleraio mi Gupa #1, Dr. GajedraSaraswa *, Dr. Ravedra Sigh $3 #1 Deparme of Mahemaics, Magalayaa Uiversiy, ligarh (UP), Idia *Deparme of Mahemaics, Magalayaa Uiversiy, ligarh (UP), Idia $3 K R Magalam Uiversiy, Soha,Palwal, (Haryaa), Idia bsrac- he aim of his paper is o develop a mahemaical model describig he effec of ime depede acceleraio wih periodic body acceleraio o he flow of blood i a arery. he flowig blood is reaed o be Newoia i characer ad he aalyical soluios are obaied for his blood flow problem. he soluio valid for he fas oscillaios ad a small exeral acceleraio, are obaied for he velociy, flux ad sress field. compuaioal aalysis for he fluid mechaics of blood flow is also performed for he assumed siuaio. he effec of periodic body acceleraio o he isaaeous flow rae, acceleraio ad shear sress are obaied ad observed ha i icreases if we icrease he magiude of periodic body acceleraio. Keywords:- Blood flow, areries, acceleraed moio, body acceleraio ad periodic exeral acceleraio. INRODUCION: he flow of blood hrough a arery i huma beig is a prese difficul o measure wihou major surgery. I is herefore ecessary o model blood problems hrough he arerial, eiher heoreically or experimeally. Whe developig a heoreical model, oe mus simplify he equaios of moio sufficiely o permi he calculaio of he required flow variables while a he same ime maiaiig he realism of he model. Various aalyical ad umerical approaches have bee made usig differe simplifyig assumpios. he effec of acceleraed blood flood flow i huma beig ca be very serious, which may cause a icrease i pulse rae loss of visio ad veous poolig of blood i exremiies.rzeiusee. al. [1] ad Verdouw e al. [] obaied a very good resul i his direcio ha idicaes ha blood pressure ad cardiac oupu are raised whe body acceleraio sychroous wih he hear bea is applied i a fooward direcio. Sud[3] made a aalysis of blood flow uder ime depede acceleraio ad obaied a resul which shows ha high blood velociies ad high shear rae capable of harmig he circulaio are produced uder he ifluece of such ime depede acceleraio. Sud e al. [4] agai worked o he flow hrough seosed arery subjec o periodic body acceleraio ad shows ha body acceleraio icreases he flow rae. he pulsaile flow of blood hrough rigid ube uder he ifluece of body acceleraio was sudied by Chaurai[6].Madal [7] observed he effec of body acceleraio o seady pulsaile flow of o Newoia fluid hrough a seosedarey. Sharma M. K. e. al.[11] sudied aboupulsaile blood flow hrough seosed arery wih axial raslaio. here is lo of ivesigaio, which was made for blood flow wih ime depede acceleraio, ad i is well kow ha he vibraio ampliudes of mechaical equipme e.g. a aeroplae, he effec of such vibraios o he huma sysem ca be quie closely approximaed by imposig a siusoidal velociy whose ampliude grows wih ime o he liear acceleraio of he body. hus a heoreical aalysis for predicig he ime depede acceleraio of blood flow is very impora subjec o ivesigaio for he desig of ai-gsuie ad cordie assis devices. herefore i his chaper a sudy which deals wih he problem of blood uder ime depede acceleraio uder periodic body acceleraio has bee made o fid a mahemaical model for compuaioal resul for he effec of hese facor o he blood flow velociy, flow rae ad shearig sress wih respec o radial disace. FORMION OF HE PROBLEM: o simplify he aalysis. We addiioally make he followig supposiios: 1. he flow is lamiar ad here is roaioal symmery of flow.. he frequece of body acceleraio is so small ha wave effec ca we egleced. 3. he variaio of velociy alog he ube legh is small compared wih he rae of chage of velociy wih respec o ime. 4. he arery is sufficiely alog ha he flows of blood alog ha he ed effecs ca be igored. 5. For simpliciy cosider f fb i.. e bwhere f & f b he frequecies i Hz be. ISSN: hp:// Page 49
2 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 GEOMERY OF BLOOD FLOW IN RERIES Cosider he flow of blood i he ube of radius R. he ube is iiially a ime. ime i suddely sars oscillaig alog is logiudial direcio wih velociy V cos a [3]Le a is he acceleraio i m / s, f is he agular frequecy i R/sec ad f is he frequecy i Hz. he imposed acceleraio herefore is a (cos si ). he V has ampliude a, which icreases liearly wih respec o ime. Now le us cosider he sysem.subjeced o periodic body acceleraiof()[4], is give by F( ) cos( ) Where b b b f is he circular frequecy i Hz. is he lead agle of F() wih respec o hear acio. he basic equaio goverig he flow of blood alog he logiudial direcio i he ube ca be wrie as (Bachlor, 1967) w w 1 w. ( ). (1). r r r While equaio(1)subjec o periodic body acceleraio may be wrie as: 1 w cos( ) ( w w ) r r r w 1 w w cos( ) i.e. r r r... () Where w is he axial velociy, is he desiy, is he viscosiy of he blood r is he radial disace. he presece of hepressuregradie i he Navier sokes equaio () was also used by womersley (1955) for aalyzig he oscillaory blood flow. he iiial ad boudary codiios of he problem are[3]: w( r, ) a For all r... (3) w( r, ) Fiie value as r for all... (4) V w( R, ) a cos w r=r, for >... (5) he imposed velociy[3] V is such ha: o 3 5, ad whev While, 3, whev MEHOD OF SOLUION: By applyig Laplace rasform ad followig Carslaw(1963) heory, ad omiig he calculaios, he soluio for he flow velociy ca be fially wrie as: ISSN: hp:// Page 41
3 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 k e j( y)si 3/ 1/ 3/ 3/ 1 1 a ( ) 1 j i y j i i j i y i w( y, ) wcos k si 4 e R y 3/ 3/ 3/ 1 j1 ( )( k ) j( i ) j( i y) j( i ) 3/ 1/ 1/ 1/ a iw j( i y) 1 i j1 i j1 i e R y 3/ 1/ 1/ j( i ) j( i y) j( i ) ka e k j (, y) k j1 ( ) k Where 1 (6) j ad j are Bessel fucios of zero ad firs order respecively, he kiemaic viscosiy ad k R r Dimesioless umber R ad y R he expressio for he rae Q ca be wrie as[7]: (7) 1/ R Q rw( r, ) dr are he zeroes of j i R Now usig equiio (6)i equaio (7) we ge he expressio for he flow rae: 1 / 1 / 1 / 3 / 3 / 1 / 3 / j ( i y) j i j i ( ) 1 / 1 a j i j 1 i j 1 i 1 i i iw i 1 i ir 1 / 1 / 1 / 3 / 3 / 3 / j ( i ) j ( i ) j ( i ) j ( i ) j ( i ) j ( i ) Q Ra e R R e k 4 e k k r r 1 e R ka R w cos k si j ( )( k ) r r k 1 r r. (8) he aalyical soluio for he velociy w(r, ) ad flow rae Q ()coais Bessel fucios wih complex argumes hece we shall obai explici soluios for small ad large values of various argumes of Bessel fucios. CSE: (a) IF. For small values of he dimesioless umber, he zero ad firs order Bessel fucios correspodig o he above argumes, up o wo erms ca be approximae as followig: x x j( x) 1, j1( x) 4 Where x is he approximaed argume. Subsiuig he velociy profile ca be wrie afer some simplificaios as: ISSN: hp:// Page 411
4 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 R a w y, a y 1 cos y 1si 4 4 k 4 e k 4 k j ka j y 1 1 k e j y si cos k si 1 j1 4 k (9) he expressio of he fluid acceleraio f ca be obaied from equaio (9) d i is as: a a f acos a si ( y 1) si ( y 1) cos k k e j y j k 3 4 ka j y j 4 k 1 1 k ke si cos k si cos k e k cos si si cos... (1) Usig equaio (9) ad (1) we also calculae he values of shear sress.he shear sress ca be defied as: dw df (11) CSE: (b) IF obaied by employig he asympoic expressio of he Bessel fucio. he Bessel fucio j (x) ad argume x ca be wrie as: he soluio valid for he large values of he dimesioless variable, ca be 1/ 1 j x coa x x of order Followig Mchachla (1955) ad usig he asympoic argumes ad order as required i he equaio (9) subsiuig he approximaios he velociy profile ca be wrie afer some simplificaios as: b1 b 1 b1 b1 w y, b cos cos si k 4 e k 4 1 k j1 ka j y k e j y si cos k si 1 j1 4 k ISSN: hp:// Page 41
5 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 f (13) (1) Where for simpliciy we cosider: a y1 1 1 b e ad b y 1 y he expressio of he fluid acceleraio f ca be obaied from equaio (11) ad ha is: b1 b cos si 1 b1 b si 1 b b cos 1 k a k k e j y j k j y j 4 k 1 1 k ke si cos k si cos k e k cos si si cos Usig equaio (11) ND (1) we also calculae he value of shear sress. he shear sress ca be defied as: dw df... (14) RESULS ND DISCUSSION: o evaluae he soluio we cosider ha he case of blood flow i small ad large areries ad for he case of blood flow we cosider ha =15kg m -3, =.4 kg m -1 s -1 ad he value of a is akig as 4.95 ms -1 while he frequecy f is 1. Hz. he equaio (9),(1) ad (11) represes soluio for he small arery whereas he equaio (1),(13) ad (14) represes soluio for he large arery. Here we cosider a =.g For he differe values of we plo he variaio of velociy w wih respec o radial disace a four pois i cycle by ake R=.1 m ad =14.1 ad for differe values of he chage of shear sress wih respec o radial disace. I is clear ha whe blood flood flow i a arery uder he ifluece of a ime depede acceleraio he here are some subsaial disurbaces. From he above calculaio we foud he i his chaper ha due o he periodic body acceleraio he flow velociy, flow acceleraio as well as shear sress icreases. From figure i is also clear ha here flucuaio become larger wih ime, as does he exeral acceleraio.... ISSN: hp:// Page 413
6 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 ISSN: hp:// Page 414
7 Ieraioal Joural of Mahemaics reds ad echology (IJM) Volume 53 Number 5 Jauary 18 REFERENCES: 1. rzeius,.c., Laird, J.D., (197); Body acceleraio sychroous wih he hear bea, Bibl. Cardiol., 9, Verdouw, P. D., Noordergraaf,., rzeius,.c. (1973); Relaive moveme bewee subjec ad suppor i body acceleraio appliedsychroous wih he hear bea Bibl. Cardiol., 31, Sud, V.K., Gierke, H.E., Kaleps, I. ad Oesreicher (1985); alysis of blood flow uder ime depede acceleraio, Med.&Biol.Eg.&Compu., vol. 3, pp Sud, V.K. ad Sekho, G.S. (1985); rerial flow uder periodic body acceleraio, Bullei of Mahemaical Biology, vol.47,pp Kapur,J.N. (1985); Mahemaical models i Biology ad medicie, Eas- wes press Pv Ld (idia) 6. Chaurai, P. ad Upadhya, V.S. (1981); wo- fluid model for blood flow hrough small diameer ubes wih o zerocouole sress boudary codiio a he ierface, Biorheology, vol.18,pp Madal, P.K., Chakravarhy, S. Madal,., ad mi, N. (7); Effec of body acceleraio o useady pulsaile flow of oewoia fluid hrough a seosed arery, pplied Mahemaics ad compuaio, Vol.189,pp orrisi M., racia R. ad Valei. (1996); group aalysis approach for a oliear differeial sysem arisig i diffusio pheomea, Joural of Mahemaical Physics, Vol. 37, pp Cheriha R. (1); New exac soluios of oe oliear equaio imahemaical biology ad heir properies, Ukraiia Mahemaical Joural, Spriger New York, Vol. 53, No. 1, pp Kumar D. ad Kumar S. (6); compuaioal model for he ieracio bewee cell desiy ad immue respose, cacieciaidica, Vol. XXXII M, No., PP Sharma M. K. e. al.(15); Pulsaile blood flow hrough seosed arery wih axial raslaio, I J. Biomah 8,1558(15)[1 pages] 1. Kumar S. ad Kumar S. (6); Numerical sudy of he axisymmeric blood flow i a cosriced rigid ube, Ieraioal review of pure ad applied mahemaics, vol. (),pp ISSN: hp:// Page 415
Problems and Solutions for Section 3.2 (3.15 through 3.25)
3-7 Problems ad Soluios for Secio 3 35 hrough 35 35 Calculae he respose of a overdamped sigle-degree-of-freedom sysem o a arbirary o-periodic exciaio Soluio: From Equaio 3: x = # F! h "! d! For a overdamped
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 informationFresnel Dragging Explained
Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field
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 informationApproximating Solutions for Ginzburg Landau Equation by HPM and ADM
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 193-9466 Vol. 5, No. Issue (December 1), pp. 575 584 (Previously, Vol. 5, Issue 1, pp. 167 1681) Applicaios ad Applied Mahemaics: A Ieraioal Joural
More informationSection 8 Convolution and Deconvolution
APPLICATIONS IN SIGNAL PROCESSING Secio 8 Covoluio ad Decovoluio This docume illusraes several echiques for carryig ou covoluio ad decovoluio i Mahcad. There are several operaors available for hese fucios:
More informationThe Solution of the One Species Lotka-Volterra Equation Using Variational Iteration Method ABSTRACT INTRODUCTION
Malaysia Joural of Mahemaical Scieces 2(2): 55-6 (28) The Soluio of he Oe Species Loka-Volerra Equaio Usig Variaioal Ieraio Mehod B. Baiha, M.S.M. Noorai, I. Hashim School of Mahemaical Scieces, Uiversii
More informationInverse Heat Conduction Problem in a Semi-Infinite Circular Plate and its Thermal Deflection by Quasi-Static Approach
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 93-9466 Vol. 5 Issue ue pp. 7 Previously Vol. 5 No. Applicaios ad Applied Mahemaics: A Ieraioal oural AAM Iverse Hea Coducio Problem i a Semi-Ifiie
More informationOptimization of Rotating Machines Vibrations Limits by the Spring - Mass System Analysis
Joural of aerials Sciece ad Egieerig B 5 (7-8 (5 - doi: 765/6-6/57-8 D DAVID PUBLISHING Opimizaio of Roaig achies Vibraios Limis by he Sprig - ass Sysem Aalysis BENDJAIA Belacem sila, Algéria Absrac: The
More informationHomotopy Analysis Method for Solving Fractional Sturm-Liouville Problems
Ausralia Joural of Basic ad Applied Scieces, 4(1): 518-57, 1 ISSN 1991-8178 Homoopy Aalysis Mehod for Solvig Fracioal Surm-Liouville Problems 1 A Neamay, R Darzi, A Dabbaghia 1 Deparme of Mahemaics, Uiversiy
More informationSolutions Manual 4.1. nonlinear. 4.2 The Fourier Series is: and the fundamental frequency is ω 2π
Soluios Maual. (a) (b) (c) (d) (e) (f) (g) liear oliear liear liear oliear oliear liear. The Fourier Series is: F () 5si( ) ad he fudameal frequecy is ω f ----- H z.3 Sice V rms V ad f 6Hz, he Fourier
More informationAvailable online at J. Math. Comput. Sci. 4 (2014), No. 4, ISSN:
Available olie a hp://sci.org J. Mah. Compu. Sci. 4 (2014), No. 4, 716-727 ISSN: 1927-5307 ON ITERATIVE TECHNIQUES FOR NUMERICAL SOLUTIONS OF LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS S.O. EDEKI *, A.A.
More informationElectrical Engineering Department Network Lab.
Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por
More informationSamuel Sindayigaya 1, Nyongesa L. Kennedy 2, Adu A.M. Wasike 3
Ieraioal Joural of Saisics ad Aalysis. ISSN 48-9959 Volume 6, Number (6, pp. -8 Research Idia Publicaios hp://www.ripublicaio.com The Populaio Mea ad is Variace i he Presece of Geocide for a Simple Birh-Deah-
More informationVibration 2-1 MENG331
Vibraio MENG33 Roos of Char. Eq. of DOF m,c,k sysem for λ o he splae λ, ζ ± ζ FIG..5 Dampig raios of commo maerials 3 4 T d T d / si cos B B e d d ζ ˆ ˆ d T N e B e B ζ ζ d T T w w e e e B e B ˆ ˆ ζ ζ
More informationClock Skew and Signal Representation
Clock Skew ad Sigal Represeaio Ch. 7 IBM Power 4 Chip 0/7/004 08 frequecy domai Program Iroducio ad moivaio Sequeial circuis, clock imig, Basic ools for frequecy domai aalysis Fourier series sigal represeaio
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 informationNumerical Solution of Parabolic Volterra Integro-Differential Equations via Backward-Euler Scheme
America Joural of Compuaioal ad Applied Maemaics, (6): 77-8 DOI:.59/.acam.6. Numerical Soluio of Parabolic Volerra Iegro-Differeial Equaios via Bacward-Euler Sceme Ali Filiz Deparme of Maemaics, Ada Mederes
More informationA Novel Approach for Solving Burger s Equation
Available a hp://pvamu.edu/aam Appl. Appl. Mah. ISSN: 93-9466 Vol. 9, Issue (December 4), pp. 54-55 Applicaios ad Applied Mahemaics: A Ieraioal Joural (AAM) A Novel Approach for Solvig Burger s Equaio
More informationLet s express the absorption of radiation by dipoles as a dipole correlation function.
MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles
More informationMean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
America Joural of Compuaioal Mahemaics, 04, 4, 80-88 Published Olie Sepember 04 i SciRes. hp://www.scirp.org/joural/ajcm hp://dx.doi.org/0.436/ajcm.04.4404 Mea Square Coverge Fiie Differece Scheme for
More informationResearch Article A Generalized Nonlinear Sum-Difference Inequality of Product Form
Joural of Applied Mahemaics Volume 03, Aricle ID 47585, 7 pages hp://dx.doi.org/0.55/03/47585 Research Aricle A Geeralized Noliear Sum-Differece Iequaliy of Produc Form YogZhou Qi ad Wu-Sheg Wag School
More informationCHAPTER 2 TORSIONAL VIBRATIONS
Dr Tiwari, Associae Professor, De. of Mechaical Egg., T Guwahai, (riwari@iig.ere.i) CHAPTE TOSONAL VBATONS Torsioal vibraios is redomia wheever here is large discs o relaively hi shafs (e.g. flywheel of
More informationIf boundary values are necessary, they are called mixed initial-boundary value problems. Again, the simplest prototypes of these IV problems are:
3. Iiial value problems: umerical soluio Fiie differeces - Trucaio errors, cosisecy, sabiliy ad covergece Crieria for compuaioal sabiliy Explici ad implici ime schemes Table of ime schemes Hyperbolic ad
More informationλiv Av = 0 or ( λi Av ) = 0. In order for a vector v to be an eigenvector, it must be in the kernel of λi
Liear lgebra Lecure #9 Noes This week s lecure focuses o wha migh be called he srucural aalysis of liear rasformaios Wha are he irisic properies of a liear rasformaio? re here ay fixed direcios? The discussio
More informationA Two-Level Quantum Analysis of ERP Data for Mock-Interrogation Trials. Michael Schillaci Jennifer Vendemia Robert Buzan Eric Green
A Two-Level Quaum Aalysis of ERP Daa for Mock-Ierrogaio Trials Michael Schillaci Jeifer Vedemia Rober Buza Eric Gree Oulie Experimeal Paradigm 4 Low Workload; Sigle Sessio; 39 8 High Workload; Muliple
More informationThe Hyperbolic Model with a Small Parameter for. Studying the Process of Impact of a Thermoelastic. Rod against a Heated Rigid Barrier
Applied Mahemaical Scieces, Vol., 6, o. 4, 37-5 HIKARI Ld, www.m-hikari.com hp://dx.doi.org/.988/ams.6.6457 The Hyperbolic Model wih a Small Parameer for Sudyig he Process of Impac of a Thermoelasic Rod
More informationTransverse Vibrations of Elastic Thin Beam Resting on Variable Elastic Foundations and Subjected to Traveling Distributed Forces.
Trasverse Vibraios of Elasic Thi Beam Resig o Variable Elasic Foudaios ad Subjeced o Travelig Disribued Forces. B. Omolofe ad S.N. Oguyebi * Deparme of Mahemaical Scieces, Federal Uiversiy of Techology,
More informationApplication of the Adomian Decomposition Method (ADM) and the SOME BLAISE ABBO (SBA) method to solving the diffusion-reaction equations
Advaces i Theoreical ad Alied Mahemaics ISSN 973-4554 Volume 9, Number (4),. 97-4 Research Idia Publicaios h://www.riublicaio.com Alicaio of he Adomia Decomosiio Mehod (ADM) ad he SOME BLAISE ABBO (SBA)
More informationSTK4080/9080 Survival and event history analysis
STK48/98 Survival ad eve hisory aalysis Marigales i discree ime Cosider a sochasic process The process M is a marigale if Lecure 3: Marigales ad oher sochasic processes i discree ime (recap) where (formally
More informationB. Maddah INDE 504 Simulation 09/02/17
B. Maddah INDE 54 Simulaio 9/2/7 Queueig Primer Wha is a queueig sysem? A queueig sysem cosiss of servers (resources) ha provide service o cusomers (eiies). A Cusomer requesig service will sar service
More informationMETHOD OF THE EQUIVALENT BOUNDARY CONDITIONS IN THE UNSTEADY PROBLEM FOR ELASTIC DIFFUSION LAYER
Maerials Physics ad Mechaics 3 (5) 36-4 Received: March 7 5 METHOD OF THE EQUIVAENT BOUNDARY CONDITIONS IN THE UNSTEADY PROBEM FOR EASTIC DIFFUSION AYER A.V. Zemsov * D.V. Tarlaovsiy Moscow Aviaio Isiue
More informationEffect of Heat Exchangers Connection on Effectiveness
Joural of Roboics ad Mechaical Egieerig Research Effec of Hea Exchagers oecio o Effeciveess Voio W Koiaho Maru J Lampie ad M El Haj Assad * Aalo Uiversiy School of Sciece ad echology P O Box 00 FIN-00076
More informationDynamics of Particle in a Box in Time Varying Potential Due to Chirped Laser Pulse
Joural of Moder Physics, 21, 1, 372-378 doi:1.4236/jmp.21.1653 Published Olie December 21 (hp://www.scirp.org/joural/jmp) Dyamics of Paricle i a Box i Time Varyig Poeial Due o Chirped Laser Pulse Absrac
More information3.8. Other Unipolar Junctions
3.8. Oher Uipolar ucios The meal-semicoducor jucio is he mos sudied uipolar jucio, be o he oly oe ha occurs i semicoducor devices. Two oher uipolar jucios are he - homojucio ad he - Heerojucio. The - homojucio
More informationPure Math 30: Explained!
ure Mah : Explaied! www.puremah.com 6 Logarihms Lesso ar Basic Expoeial Applicaios Expoeial Growh & Decay: Siuaios followig his ype of chage ca be modeled usig he formula: (b) A = Fuure Amou A o = iial
More information12 Getting Started With Fourier Analysis
Commuicaios Egieerig MSc - Prelimiary Readig Geig Sared Wih Fourier Aalysis Fourier aalysis is cocered wih he represeaio of sigals i erms of he sums of sie, cosie or complex oscillaio waveforms. We ll
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 informationThe Moment Approximation of the First Passage Time for the Birth Death Diffusion Process with Immigraton to a Moving Linear Barrier
America Joural of Applied Mahemaics ad Saisics, 015, Vol. 3, No. 5, 184-189 Available olie a hp://pubs.sciepub.com/ajams/3/5/ Sciece ad Educaio Publishig DOI:10.1691/ajams-3-5- The Mome Approximaio of
More informationDavid Randall. ( )e ikx. k = u x,t. u( x,t)e ikx dx L. x L /2. Recall that the proof of (1) and (2) involves use of the orthogonality condition.
! Revised April 21, 2010 1:27 P! 1 Fourier Series David Radall Assume ha u( x,) is real ad iegrable If he domai is periodic, wih period L, we ca express u( x,) exacly by a Fourier series expasio: ( ) =
More informationINTEGER INTERVAL VALUE OF NEWTON DIVIDED DIFFERENCE AND FORWARD AND BACKWARD INTERPOLATION FORMULA
Volume 8 No. 8, 45-54 ISSN: 34-3395 (o-lie versio) url: hp://www.ijpam.eu ijpam.eu INTEGER INTERVAL VALUE OF NEWTON DIVIDED DIFFERENCE AND FORWARD AND BACKWARD INTERPOLATION FORMULA A.Arul dass M.Dhaapal
More informationFourier transform. Continuous-time Fourier transform (CTFT) ω ω
Fourier rasform Coiuous-ime Fourier rasform (CTFT P. Deoe ( he Fourier rasform of he sigal x(. Deermie he followig values, wihou compuig (. a (0 b ( d c ( si d ( d d e iverse Fourier rasform for Re { (
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 informationDynamic h-index: the Hirsch index in function of time
Dyamic h-idex: he Hirsch idex i fucio of ime by L. Egghe Uiversiei Hassel (UHassel), Campus Diepebeek, Agoralaa, B-3590 Diepebeek, Belgium ad Uiversiei Awerpe (UA), Campus Drie Eike, Uiversieisplei, B-260
More informationParametric Iteration Method for Solving Linear Optimal Control Problems
Applied Mahemaics,, 3, 59-64 hp://dx.doi.org/.436/am..3955 Published Olie Sepember (hp://www.scirp.org/joural/am) Parameric Ieraio Mehod for Solvig Liear Opimal Corol Problems Abdolsaeed Alavi, Aghileh
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 informationA Generalized Cost Malmquist Index to the Productivities of Units with Negative Data in DEA
Proceedigs of he 202 Ieraioal Coferece o Idusrial Egieerig ad Operaios Maageme Isabul, urey, July 3 6, 202 A eeralized Cos Malmquis Ide o he Produciviies of Uis wih Negaive Daa i DEA Shabam Razavya Deparme
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 informationDissipative Relativistic Bohmian Mechanics
[arxiv 1711.0446] Dissipaive Relaivisic Bohmia Mechaics Roume Tsekov Deparme of Physical Chemisry, Uiversiy of Sofia, 1164 Sofia, Bulgaria I is show ha quaum eagleme is he oly force able o maiai he fourh
More informationInternational Journal of Multidisciplinary Approach and Studies. Channel Capacity Analysis For L-Mrc Receiver Over Η-µ Fading Channel
Chael Capaciy Aalysis For L-Mrc eceiver Over Η-µ Fadig Chael Samom Jayaada Sigh* Pallab Dua** *NEIST, Deparme of ECE, Iaagar, Aruachal Pradesh-799, Idia **Tezpur Uiversiy, Deparme of ECE, Tezpur, Assam,
More informationANALYSIS OF THE CHAOS DYNAMICS IN (X n,x n+1) PLANE
ANALYSIS OF THE CHAOS DYNAMICS IN (X,X ) PLANE Soegiao Soelisioo, The Houw Liog Badug Isiue of Techolog (ITB) Idoesia soegiao@sude.fi.ib.ac.id Absrac I he las decade, sudies of chaoic ssem are more ofe
More informationOn the Differential Fractional Transformation Method of MSEIR Epidemic Model
Ieraioal Joural of Compuer Applicaios (975 8887 Volume No., March 5 O he Differeial Fracioal Trasformaio Mehod of MSEIR Epidemic Model Haaa Abdelhamed Asfour Mahemaics Deparme, Faculy of Educio, Ai Shams
More informationSupplementary Information for Thermal Noises in an Aqueous Quadrupole Micro- and Nano-Trap
Supplemeary Iformaio for Thermal Noises i a Aqueous Quadrupole Micro- ad Nao-Trap Jae Hyu Park ad Predrag S. Krsić * Physics Divisio, Oak Ridge Naioal Laboraory, Oak Ridge, TN 3783 E-mail: krsicp@orl.gov
More informationSUMMATION OF INFINITE SERIES REVISITED
SUMMATION OF INFINITE SERIES REVISITED I several aricles over he las decade o his web page we have show how o sum cerai iiie series icludig he geomeric series. We wa here o eed his discussio o he geeral
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 21 Base Excitation Shock: Classical Pulse
SHOCK AND VIBRAION RESPONSE SPECRA COURSE Ui 1 Base Exciaio Shock: Classical Pulse By om Irvie Email: omirvie@aol.com Iroucio Cosier a srucure subjece o a base exciaio shock pulse. Base exciaio is also
More informationChemical Engineering 374
Chemical Egieerig 374 Fluid Mechaics NoNeoia Fluids Oulie 2 Types ad properies of o-neoia Fluids Pipe flos for o-neoia fluids Velociy profile / flo rae Pressure op Fricio facor Pump poer Rheological Parameers
More informationTime Dependent Queuing
Time Depede Queuig Mark S. Daski Deparme of IE/MS, Norhweser Uiversiy Evaso, IL 628 Sprig, 26 Oulie Will look a M/M/s sysem Numerically iegraio of Chapma- Kolmogorov equaios Iroducio o Time Depede Queue
More informationBE.430 Tutorial: Linear Operator Theory and Eigenfunction Expansion
BE.43 Tuorial: Liear Operaor Theory ad Eigefucio Expasio (adaped fro Douglas Lauffeburger) 9//4 Moivaig proble I class, we ecouered parial differeial equaios describig rasie syses wih cheical diffusio.
More informationPaper 3A3 The Equations of Fluid Flow and Their Numerical Solution Handout 1
Paper 3A3 The Equaios of Fluid Flow ad Their Numerical Soluio Hadou Iroducio A grea ma fluid flow problems are ow solved b use of Compuaioal Fluid Damics (CFD) packages. Oe of he major obsacles o he good
More informationOn stability of first order linear impulsive differential equations
Ieraioal Joural of aisics ad Applied Mahemaics 218; 3(3): 231-236 IN: 2456-1452 Mahs 218; 3(3): 231-236 218 as & Mahs www.mahsoural.com Received: 18-3-218 Acceped: 22-4-218 IM Esuabaa Deparme of Mahemaics,
More information11. Adaptive Control in the Presence of Bounded Disturbances Consider MIMO systems in the form,
Lecure 6. Adapive Corol i he Presece of Bouded Disurbaces Cosider MIMO sysems i he form, x Aref xbu x Bref ycmd (.) y Cref x operaig i he presece of a bouded ime-depede disurbace R. All he assumpios ad
More informationThe analysis of the method on the one variable function s limit Ke Wu
Ieraioal Coferece o Advaces i Mechaical Egieerig ad Idusrial Iformaics (AMEII 5) The aalysis of he mehod o he oe variable fucio s i Ke Wu Deparme of Mahemaics ad Saisics Zaozhuag Uiversiy Zaozhuag 776
More information(1) f ( Ω) Keywords: adjoint problem, a posteriori error estimation, global norm of error.
O a poseriori esimaio of umerical global error orms usig adjoi equaio A.K. Aleseev a ad I. M. Navo b a Deparme of Aerodyamics ad Hea Trasfer, RSC ENERGIA, Korolev, Moscow Regio, 4070, Russia Federaio b
More informationAn interesting result about subset sums. Nitu Kitchloo. Lior Pachter. November 27, Abstract
A ieresig resul abou subse sums Niu Kichloo Lior Pacher November 27, 1993 Absrac We cosider he problem of deermiig he umber of subses B f1; 2; : : :; g such ha P b2b b k mod, where k is a residue class
More informationHarmonic excitation (damped)
Harmoic eciaio damped k m cos EOM: m&& c& k cos c && ζ & f cos The respose soluio ca be separaed io par;. Homogeeous soluio h. Paricular soluio p h p & ζ & && ζ & f cos Homogeeous soluio Homogeeous soluio
More informationClock Skew and Signal Representation. Program. Timing Engineering
lock Skew ad Sigal epreseaio h. 7 IBM Power 4 hip Iroducio ad moivaio Sequeial circuis, clock imig, Basic ools for frequecy domai aalysis Fourier series sigal represeaio Periodic sigals ca be represeed
More informationK3 p K2 p Kp 0 p 2 p 3 p
Mah 80-00 Mo Ar 0 Chaer 9 Fourier Series ad alicaios o differeial equaios (ad arial differeial equaios) 9.-9. Fourier series defiiio ad covergece. The idea of Fourier series is relaed o he liear algebra
More informationKing Fahd University of Petroleum & Minerals Computer Engineering g Dept
Kig Fahd Uiversiy of Peroleum & Mierals Compuer Egieerig g Dep COE 4 Daa ad Compuer Commuicaios erm Dr. shraf S. Hasa Mahmoud Rm -4 Ex. 74 Email: ashraf@kfupm.edu.sa 9/8/ Dr. shraf S. Hasa Mahmoud Lecure
More information5.74 Introductory Quantum Mechanics II
MIT OpeCourseWare hp://ocw.mi.edu 5.74 Iroducory Quaum Mechaics II Sprig 009 For iformaio aou ciig hese maerials or our Terms of Use, visi: hp://ocw.mi.edu/erms. drei Tokmakoff, MIT Deparme of Chemisry,
More informationNEWTON METHOD FOR DETERMINING THE OPTIMAL REPLENISHMENT POLICY FOR EPQ MODEL WITH PRESENT VALUE
Yugoslav Joural of Operaios Research 8 (2008, Number, 53-6 DOI: 02298/YUJOR080053W NEWTON METHOD FOR DETERMINING THE OPTIMAL REPLENISHMENT POLICY FOR EPQ MODEL WITH PRESENT VALUE Jeff Kuo-Jug WU, Hsui-Li
More informationDETERMINATION OF PARTICULAR SOLUTIONS OF NONHOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS BY DISCRETE DECONVOLUTION
U.P.B. ci. Bull. eries A Vol. 69 No. 7 IN 3-77 DETERMINATION OF PARTIULAR OLUTION OF NONHOMOGENEOU LINEAR DIFFERENTIAL EQUATION BY DIRETE DEONVOLUTION M. I. ÎRNU e preziă o ouă meoă e eermiare a soluţiilor
More informationManipulations involving the signal amplitude (dependent variable).
Oulie Maipulaio of discree ime sigals: Maipulaios ivolvig he idepede variable : Shifed i ime Operaios. Foldig, reflecio or ime reversal. Time Scalig. Maipulaios ivolvig he sigal ampliude (depede variable).
More informationCLOSED FORM EVALUATION OF RESTRICTED SUMS CONTAINING SQUARES OF FIBONOMIAL COEFFICIENTS
PB Sci Bull, Series A, Vol 78, Iss 4, 2016 ISSN 1223-7027 CLOSED FORM EVALATION OF RESTRICTED SMS CONTAINING SQARES OF FIBONOMIAL COEFFICIENTS Emrah Kılıc 1, Helmu Prodiger 2 We give a sysemaic approach
More informationThe Change of the Distances between the Wave Fronts
Joural of Physical Mahemaics IN: 9-9 Research Aricle Aricle Joural of Physical Mahemaics Geadiy ad iali, J Phys Mah 7, 8: DOI: 47/9-97 OMI Ope Ieraioal Access Opical Fizeau Experime wih Movig Waer is Explaied
More informationTime-domain Aeroelastic Analysis of Bridge using a Truncated Fourier Series of the Aerodynamic Transfer Function
Time-domai Aeroelasic Aalysis of ridge usig a Trucaed Fourier Series of he Aerodyamic Trasfer Fucio Jiwook PA Graduae Sude Seoul aioal iversiy Seoul, orea jwpark7@su.ac.kr H Sug LEE Professor Seoul aioal
More informationFour equations describe the dynamic solution to RBC model. Consumption-leisure efficiency condition. Consumption-investment efficiency condition
LINEARIZING AND APPROXIMATING THE RBC MODEL SEPTEMBER 7, 200 For f( x, y, z ), mulivariable Taylor liear expasio aroud ( x, yz, ) f ( x, y, z) f( x, y, z) + f ( x, y, z)( x x) + f ( x, y, z)( y y) + f
More informationECE 350 Matlab-Based Project #3
ECE 350 Malab-Based Projec #3 Due Dae: Nov. 26, 2008 Read he aached Malab uorial ad read he help files abou fucio i, subs, sem, bar, sum, aa2. he wrie a sigle Malab M file o complee he followig ask for
More informationProcedia - Social and Behavioral Sciences 230 ( 2016 ) Joint Probability Distribution and the Minimum of a Set of Normalized Random Variables
Available olie a wwwsciecedireccom ScieceDirec Procedia - Social ad Behavioral Scieces 30 ( 016 ) 35 39 3 rd Ieraioal Coferece o New Challeges i Maageme ad Orgaizaio: Orgaizaio ad Leadership, May 016,
More informationCurrent Control of IPMSM to Avoid Voltage Saturation for Changing Frequency and Amplitude of Vibration Torque Reference
IEEE PEDS 17, Hoolulu, USA 1-15 December 17 Corol of IPMSM o Avoid Sauraio for Chagig Frequecy ad Ampliude of ibraio Referece Ryohei Masuura, Takeo Sugiyama, Takaharu Takeshia, Yugo Tadao, Shizuori Hamada,
More informationINVESTMENT PROJECT EFFICIENCY EVALUATION
368 Miljeko Crjac Domiika Crjac INVESTMENT PROJECT EFFICIENCY EVALUATION Miljeko Crjac Professor Faculy of Ecoomics Drsc Domiika Crjac Faculy of Elecrical Egieerig Osijek Summary Fiacial efficiecy of ivesme
More informationFuzzy Dynamic Equations on Time Scales under Generalized Delta Derivative via Contractive-like Mapping Principles
Idia Joural of Sciece ad echology Vol 9(5) DOI: 7485/ijs/6/v9i5/8533 July 6 ISSN (Pri) : 974-6846 ISSN (Olie) : 974-5645 Fuzzy Dyamic Euaios o ime Scales uder Geeralized Dela Derivaive via Coracive-lie
More informationA Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix
4h Ieraioal Coferece o Sesors, Mecharoics ad Auomaio (ICSMA 06) A Complex Neural Newor Algorihm for Compuig he Larges eal Par Eigevalue ad he correspodig Eigevecor of a eal Marix HANG AN, a, XUESONG LIANG,
More informationOn Numerical Solution of Boundary Integral Equations of the Plane Elasticity Theory by Singular Integral Approximation Methods
Proceedigs of he 5h WSEAS I Cof o Sysem Sciece ad Simulaio i Egieerig Teerife Caary Islads Spai December 6-8 6 88 O Numerical Soluio of Boudary Iegral Equaios of he Plae Elasiciy Theory by Sigular Iegral
More informationEconomics 8723 Macroeconomic Theory Problem Set 2 Professor Sanjay Chugh Spring 2017
Deparme of Ecoomics The Ohio Sae Uiversiy Ecoomics 8723 Macroecoomic Theory Problem Se 2 Professor Sajay Chugh Sprig 207 Labor Icome Taxes, Nash-Bargaied Wages, ad Proporioally-Bargaied Wages. I a ecoomy
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 informationth m m m m central moment : E[( X X) ] ( X X) ( x X) f ( x)
1 Trasform Techiques h m m m m mome : E[ ] x f ( x) dx h m m m m ceral mome : E[( ) ] ( ) ( x) f ( x) dx A coveie wa of fidig he momes of a radom variable is he mome geeraig fucio (MGF). Oher rasform echiques
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 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 informationECE 340 Lecture 19 : Steady State Carrier Injection Class Outline:
ECE 340 ecure 19 : Seady Sae Carrier Ijecio Class Oulie: iffusio ad Recombiaio Seady Sae Carrier Ijecio Thigs you should kow whe you leave Key Quesios Wha are he major mechaisms of recombiaio? How do we
More informationVARIOUS phenomena occurring in the applied sciences
roceedigs of he Ieraioal MuliCoferece of Egieers ad Compuer Scieiss 8 Vol I IMECS 8 March -6 8 Hog Kog Exac Soluios ad Numerical Compariso of Mehods for Solvig Fracioal-Order Differeial Sysems Nachapo
More informationOn Another Type of Transform Called Rangaig Transform
Ieraioal Joural of Parial Differeial Equaios ad Applicaios, 7, Vol 5, No, 4-48 Available olie a hp://pubssciepubcom/ijpdea/5//6 Sciece ad Educaio Publishig DOI:69/ijpdea-5--6 O Aoher Type of Trasform Called
More informationThree Point Bending Analysis of a Mobile Phone Using LS-DYNA Explicit Integration Method
9 h Ieraioal LS-DYNA Users Coerece Simulaio Techology (3) Three Poi Bedig Aalysis o a Mobile Phoe Usig LS-DYNA Explici Iegraio Mehod Feixia Pa, Jiase Zhu, Ai O. Helmie, Rami Vaaparas NOKIA Ic. Absrac I
More informationF D D D D F. smoothed value of the data including Y t the most recent data.
Module 2 Forecasig 1. Wha is forecasig? Forecasig is defied as esimaig he fuure value ha a parameer will ake. Mos scieific forecasig mehods forecas he fuure value usig pas daa. I Operaios Maageme forecasig
More informationBoundary-to-Displacement Asymptotic Gains for Wave Systems With Kelvin-Voigt Damping
Boudary-o-Displaceme Asympoic Gais for Wave Sysems Wih Kelvi-Voig Dampig Iasso Karafyllis *, Maria Kooriaki ** ad Miroslav Krsic *** * Dep. of Mahemaics, Naioal Techical Uiversiy of Ahes, Zografou Campus,
More informationCONTACT BETWEEN FLEXIBLE BODIES IN NONLINEAR ANALYSIS, USING LAGRANGE MULTIPLIERS
COAC BEWEE FLEXIBLE BODIES I OLIEAR AALYSIS, USIG LAGRAGE MULIPLIERS Dr. Phillipe Jeeur Philippe.jeeur@samcef.com Samech, Parc Scieifiue du Sar-ilma Rue des Chasseurs Ardeais, 8 B-403 Agleur-Liège, Belgium
More informationFRACTIONAL VARIATIONAL ITERATION METHOD FOR TIME-FRACTIONAL NON-LINEAR FUNCTIONAL PARTIAL DIFFERENTIAL EQUATION HAVING PROPORTIONAL DELAYS
S33 FRACTIONAL VARIATIONAL ITERATION METHOD FOR TIME-FRACTIONAL NON-LINEAR FUNCTIONAL PARTIAL DIFFERENTIAL EQUATION HAVING PROPORTIONAL DELAYS by Derya DOGAN DURGUN ad Ali KONURALP * Deparme of Mahemaics
More informationECE 340 Lecture 15 and 16: Diffusion of Carriers Class Outline:
ECE 340 Lecure 5 ad 6: iffusio of Carriers Class Oulie: iffusio rocesses iffusio ad rif of Carriers Thigs you should kow whe you leave Key Quesios Why do carriers diffuse? Wha haes whe we add a elecric
More informationAvailable online at ScienceDirect. Procedia Computer Science 103 (2017 ) 67 74
Available olie a www.sciecedirec.com ScieceDirec Procedia Compuer Sciece 03 (07 67 74 XIIh Ieraioal Symposium «Iellige Sysems» INELS 6 5-7 Ocober 06 Moscow Russia Real-ime aerodyamic parameer ideificaio
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 informationMODIFIED ADOMIAN DECOMPOSITION METHOD FOR SOLVING RICCATI DIFFERENTIAL EQUATIONS
Review of he Air Force Academy No 3 (3) 15 ODIFIED ADOIAN DECOPOSIION EHOD FOR SOLVING RICCAI DIFFERENIAL EQUAIONS 1. INRODUCION Adomia decomposiio mehod was foud by George Adomia ad has recely become
More information