DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION"

Transcription

1 DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION Mohammad Rashed Iqbal Fauque* #1, Mohammad Taiqul Islam* 2, Nobahiah Misan* #3 * Institute of Space Science (ANGKASA), # Dept. of Electical, Electonic and Systems Engineeing, Faculty of Engineeing and Built Envionment, Univesiti Kebangsaan Malaysia, UKM, Bangi, Selango, Malaysia ABSTRACT In this pape, the local specific absoption ate (SAR) induced in spheical, cubical, and ealistic human head models exposed to a mobile phone is investigated. The highest degee diffeent shapes but almost the same volume of thee human head models is consideed. Obtained local maximum SAR induced in these thee human head models fo homogeneous cases ae establish to have an aveage diffeences of about 9% at 1800 MHz espectively. A compaison analysis of SAR induced in the ealistic human head model fo homogeneous and inhomogeneous cases is also discussed. Fom the esults, it can be obseved that the local maximum SAR induced in the homogeneous human head model is lage than that induced in the inhomogeneous human head model. Index Tems cellula phone, the finite-diffeence timedomain (FDTD) method, head size, specific absoption ate (SAR). 1. INTRODUCTION With the apid and eve moe widespead use of mobile phones, public concen egading the possible health hazads has been gowing, which bings an inceased equiement on electomagnetic (EM) dosimety fo mobile phones. The basic paamete in the EM dosimety is defined in tems of the specific absoption ate (SAR), o the absobed powe in unit mass of tissue [1]. The SAR is geneally evaluated using eithe phantom measuement o compute simulation. The finite-diffeence time-domain (FDTD) method is cuently the most widely accepted means fo the SAR computations [2]. In Euope the basic limit of SAR set fo the geneal public is 2 W/kg aveaged ove a volume equivalent to 10 gm and a pefect of 6 min. [3]. The ANSI/IEEE standad [4] defines a sticte limit fo an uncontolled envionment of 1.6 W/kg aveaged ove a volume of 1 gm and a peiod of 30 min. To analyze the possible ange of vaiations of the induced field stengths in the vaious tissues equies an extensive effot, since the local field stengths stongly depend on a lage numbe of paametes, such as: opeational fequency and antenna input powe; position of the device with espect to the head; design of the device; the oute shape of the head; the distibution of the diffeent tissues within the head, and the electic popeties of these tissues. The electic paametes of a human body vay with levels of physical and metabolic activity, health, and age. The vaiations in all these popeties lead to a stetch in the analyzed absoption distibution. The cuently most often used system fo testing handheld cellula telecommunications equipment is the measuement setup using a homogeneous anatomically-shaped phantom filled with a liquid simulating bain tissue [4-8]. The ationale behind this appoach comes fom the enegy absoption mechanism in the close nea-field of antennas [9-11], which concludes that the most detemining paametes fo volumeaveaged values ae the time-aveaged antenna input powe, opeational fequency, design of the device, and its position with espect to the head, and to a much lesse extent, on the physical popeties of the head. In this pape the authos focus on the effects of the factos of head popeties, such as size, shape, and electical popeties of tissues in ode to calculate the SAR induced in human head models exposed to a cellula phone. To find the effects of head size o shape on electomagnetic absoption chaacteistics, the ealistic head model, spheical head model, and a cubical head model ae scaled and then SAR distibutions fo these models, when exposed to a cellula telephone model have been investigating using the FDTD method.

2 2. HEAD MODELING Accuate phantoms of homogeneous human heads can be geneated on the basis of magnetic esonance imaging (MRI). The tanslation of the thee-dimensional (3-D) data sets of elaxation times into the tissue distibution is a difficult task and geneally equies a peson tained eithe in medicine o biology, which is able to distinguish both tansitional and maginal egions. MRI poduced in diffeent laboatoies, by diffeent scientists and fom diffeent test subjects pedictably contains diffeing discetizations. In these studies diffeent shapes, diffeent dielectic constant, diffeent conductivity, and diffeent mass density of homogeneous phantoms in diffeent tissues based on MRI data sets of thee diffeent adults ae used, also simulated to inhomogeneous phantoms and thei esults compaed. Fig. 1 shows the oute shapes and two coss-sectional views of these head phantoms and Table I gives the data of discetization. The ea closest to the antenna needs special attention, duing nomal use of a hand-held telephone; the ea is pessed against the head and, theefoe, changes its shape. In ode to avoid effects caused by the diffeent ea modeling, which may mask the effects of the head itself, the oute ight ea of the head phantoms was emoved. The fist phantom in ealistic head model was taken with the highest esolution. Its voxel size is 1 mm in all thee Catesian dimensions. Realistic head model has the lagest volume. The bain egion was segmented vey caefully. Fo the entie head 13 tissue types wee simulated. Howeve, the lowe pat of the head was assigned to only one tissue type. The second head phantom is consideed as cubical, which has nealy the same voxel size. It was developed fo the taining of medical students and distinguishes among 120 tissue types. Fo the EM analysis this lage numbe needed to be educed to 13 diffeent tissues fo which electic paametes ae available [5]. The thid head phantom is consideed as spheical that has taken with a voxel size of about 12 mm 3. The discetization is elatively cude. In the oiginal MRI model the skin was not identified. In the compute model the skin was added as an oute laye with a thickness of one voxel. The bain egion of head phantom Spheical is homogeneous and assigned only one tissue type compaing the data of diffeent publications eveals a spead in the values given fo the electic paametes of diffeent types of tissue. Table-2 and Table-3 show the electic paametes we have chosen fo this study. The pemittivity and the conductivity of the tissues of phantoms wee taken fom the dielectic database [7]. Table 1 Thee diffeent head models fo simulations Realistic head model [11] Spheical head model [5] Fig. 1 Test view of thee MRI phantoms. a).realistic head model b) Spheical head model c) Cubical head model 3. PHONE MODELING Cubical head model [7] Head 4.44 dm dm dm 3 Volume Tissues Computational Space Voxel Size ( 1 mm ) 3 ( mm) 3 (1.875 mm) 2 3 mm a) b) c) The numeical phone model opeating at 1800 MHz consists of a conducting box, a plastic casing, and a helix antenna, as shown in Fig.2. The antenna was fed using the coaxial feeding method. The electic field components of the same amplitude, tangential to the top suface of the phone, wee applied at the souce point, as shown in Fig.2 (c). Fo both of the head models, the phone was located on the efeence plane, which is defined by auditoy canal openings of both eas and the cente of the mouth. Regading the diection of the phone, the touch position that is a nomal opeating position was used fo the anatomical models, and fo the simple models, phone was diected paallel to the sagittal plane of the head, as shown in Fig.2.

3 mass density ρ of the thee homogeneous phantom-muscle ε = 53.5, σ = 1.34 S/m, ρ = 1.04 g/cm 3 ) head models ( at 1800 MHz ae obtained fom the liteatue [3-7], espectively. The cellula phone and human-head models ae assumed to be of nonmagnetic mateial ( µ = 1.0). 4. RESULTS Fig. 2 Phone model (unit: mm). (a) Font view. (b) Top view. (c) Feeding pat in FDTD mesh The cellula-phone model is constucted with a quatewavelength helix antenna mounted on the top of a ectangula box with dimensions height h = 108 mm, width w = 46 mm, and thickness d = 23 mm, which is filled with equivalent mateial, as shown in Fig. 2. The mateial on the outside suface of the handset box is adopted by a dielectic mateial ( ε = 3.78, σ = S/m) at 1800 MHz, only. Accoding to a study in ef. [10-11], the dielectic mateial used fo the outside suface of a handset box has significant impact on the eduction of the SAR induced in a human head. The tansmitted powe of the cellula phone is assumed to be W at 1800 MHz, espectively. Following the equation in ef. [7-9], V = P 8 R, whee the excitation souce voltage V at the feeding point of the monopole antenna can easily be calculated. Hee R and P ae the esistance and tansmitted powe of the cellula phone in fee space, espectively. Using the method of moments (MoM) [4-5], the impedance of the monopole antenna in ai obtained is j14.85 Ω at 1800 MHz, only. The calculations of SAR distibution induced in the human head ae made with an initial sinusoidal time-vaying electic.field Ez = (V/δ) sin(ωt) located at the gap between the helix antenna and the uppe cente of the box case, as shown in Fig. 2, whee δ = 2.0 mm is the cell size used in the FDTD simulation. A metallic mateial with ε =1.0 and σ = S/m is employed to simulate the helix antenna. Thee homogeneous human-head models (Fig. 1) including spheical, cubical, and ealistic shapes, ae discetized into , , and cubic cells of 2.0 mm on each side in the FDTD simulations, espectively. The elative dielectic constant ε conductivity σ and The esults of maximum local SARs induced in thee homogeneous human-head models vesus the distance between the cellula phone and the human-head model ae shown in Fig. 3. Fom Fig. 3, it is clea that the spheical head model has the maximum value of the local maximum SAR, while the ealistic human head model has the minimum value of the local maximum SAR. The esults of the local maximum SAR induced in the cubical and spheical head models ae close and they ae between those obtained by the ealistic head models. The aveage diffeence of the local maximum SAR induced in these thee head models is appoximately within 9% at 1800 MHz, espectively. This obsevation emphasizes that the shape of the human head plays a mino ole in calculating the SAR induced in the human-head models. These yield that the conclusion made in ef [5-7] that the maximum local SAR is scacely affected by the shape of the human head exposed to a cellula phone. In the following study, the ealistic humanhead model is simulated six times as a homogeneous model with six electical popety sets, such as the bone tissues, the skin tissues, the blood tissues, the eye tissues, the muscle, and bain tissues, and one time as an inhomogeneous model with six tissues taken into account to calculate the SAR esults at 1800 MHz only. Local Maximum SAR [W/kg] MHz Dis tanc e be twe e n the pho ne mo de l and the mo de l (mm) C ub ic a l S p e ic a l R e a lis t ic Fig. 3 SAR induced in fou homogeneous phantom-muscle head models with elative dielectic constant ε = 53.5, conductivity σ = 1.34 S/m, and mass density ρ = 1.04 g/cm3 at 1800 MHz

4 The electical popeties wee taken of muscle [8] is ε = 53.5, σ = 1.34 S/m, ρ = 1.04 g/cm 3 at 1800 MHz. A compaison of the data found in diffeent publications eveals a spead in the values given fo the electical popeties of diffeent types of tissue [3-7]. The electical popeties of the inhomogeneous human-head model with six tissues at 1800 MHz is shown in Table 2. Table 2 Dielectic tissue popeties at 1800MHz Tissue Type Density, ρ (1000 Kgm 3 ) Conductivity, σ ) (S-m 1 Dielectic Constant Ai Bone Skin Blood Eye Bain Muscle Compaisons of maximum local SAR induced in the ealistic human-head model fo homogeneous and inhomogeneous case at 1800 MHz is shown in Fig 4. It is found that local maximum SAR induced in homogeneous models has lage values than those induced in inhomogeneous models. It should be noted that the electical popety of a human head significantly affects the esult of the SAR induced in homogeneous o inhomogeneous head models. Today, coect calculation o measuement of SAR distibution in a human head while using a cellula phone has become an impotant issue. Local Maximum SAR (W/kg) MHz Distance between the phone model and the head model (mm) Fig. 4 Compaisons of maximum local SAR induced in the eal human head model fo homogeneous and inhomogeneous cases at 1800 MHz ε m o de l (B o ne ) m o de l (S kin) m o de l(b lo o d) m o de l (Eye ) m o de l (M us c le ) m o de l (B a in) Inho m o g e ne o us m o de l 5. CONCLUSIONS In this pape, the esults pove that the spatial peak SAR is baely affected by the size, diffeent dielectic popeties, and the shape of the human head fo electomagnetic souces at a defined distance fom the human head. Compaed to othe factos, such as distance of the souce fom the head and design of the devices, the effects caused by the complex anatomy ae mino especially in the case of volumeaveaged values. The compaison of the esults obtained fom the inhomogeneous and homogeneous phantoms suggests that homogeneous phantoms ae highly suited to be used in compliance tests fo handheld cellula telecommunications equipment opeating in the 1800 MHz. The esults of ou study can also be used to investigate diffeences of biological effects between human species and ages. ACKNOWLEDGEMENT The authos would like to thank Institute of Space Science (ANGKASA), Univesiti Kebangsaan Malaysia (UKM) and the MOSTI Secetaiat, Ministy of Science, Technology and Innovation of Malaysia, e- Science fund: SF0612, fo sponsoing this wok. REFERENCES [1] Repot of Telecommunications Technology Council fo the ministy of Posts and Telecommunications, Delibeation no. 89, Radio-Radiation Potection Guidelines fo Human Exposue to Electomagnetic Fields, Tokyo, [2] K. S. Kunz and R. J. Luebbes, The finite diffeence time domain method fo electomagnetic, Boca Raton, FL, CRC, [3] IEEE C , IEEE standads fo safety levels with espect to human exposue to adio fequency electomagnetic fields, 3 khz to 300 GHz," Institute of Electical and Electonics Enginees, New Yok, NY, [4] M. T. Islam, M. R. I. Fauque, and N. Misan, Design analysis of feite sheet attachment fo SAR eduction in human head, Pogess In Electomagnetics Reseach, PIER 98, , [5] K. H. Hohne, M. Bomans, M. Reime, R. Schubet, U. Tiede, and W. Liesc, A volume-based anatomical atlas, IEEE Compute Gaphics Applicati., pp , 1992 [6] A. Hiata, K. Shiai, and O. Fujiwaa, On aveaging mass of SAR coelating with tempeatue elevation due to a dipole antenna Pogess In Electomagnetics Reseach, PIER 84, , [7] 0. P. Gandhi..I. Y. Chen, and D. Wu, Electomagnetic absoption in the human head fo mobile telephones at

5 835 MHz and 1900 MHz, Int. Symp Elecomag. Compat., Roma, 1994, pp [8] M. R. I. Fauque, M. T. Islam, and N. Misan, Evaluation of specific absoption ate (SAR) eduction fo PIFA antenna using metamateials, Fequenz Jounal, vol. 7/8, pp , [9] Kiminami, K., A. Hiata, Y. Hoii, and T. Shiozawa, A study on human body modeling fo the mobile teminal antenna design at 400 MHz band, J. of Electomagnetic Waves and Appl, Vol. 19, , [10] Ae-kyoung, and Jeong-ki Pack, Effect of head size fo cellula telephone exposue on EM absoption, IEICE Tans. Commun., vol. E85-B, no. 3, [11] G. Bielke and S. Meindl, Deidimensionale segmentiete MR-Bilddatenatze. Tech. Rep. N. 6564/33038, Deutsche Klinik fu Diagnostik e. V., Foschungsvetdg DBP Telekom, 1993.

Multiband Microstrip Patch Antenna for Microwave Applications

Multiband Microstrip Patch Antenna for Microwave Applications IOSR Jounal of Electonics and Communication Engineeing (IOSR-JECE) ISSN: 2278-2834, ISBN: 2278-8735. Volume 3, Issue 5 (Sep. - Oct. 2012), PP 43-48 Multiband Micostip Patch Antenna fo Micowave Applications

More information

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy

More information

EFFECT OF HUMAN HEAD SHAPES FOR MOBILE PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION

EFFECT OF HUMAN HEAD SHAPES FOR MOBILE PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije 40(2010)3, Ljubljana EFFECT OF HUMAN HEAD SHAPES FOR MOBILE PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION 1 Mohammad Rashed Iqbal Faruque, 2 Mohammad Tariqul

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

NUCLEAR MAGNETIC RESONANCE

NUCLEAR MAGNETIC RESONANCE 19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic

More information

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

Effects of Mobile Phone Radiation onto Human Head with Variation of Holding Cheek and Tilt Positions

Effects of Mobile Phone Radiation onto Human Head with Variation of Holding Cheek and Tilt Positions Effects of Mobile Phone Radiation onto Human Head with Variation of Holding Cheek and Tilt Positions M. R. Iqbal-Faruque* 1, N. Aisyah-Husni 2, Md. Ikbal-Hossain 1, M. Tariqul-Islam 2 and N. Misran 2 1

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

SELF-INDUCTANCE AND INDUCTORS

SELF-INDUCTANCE AND INDUCTORS MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................

More information

Specific Absorption Rate (SAR) in the head of Tablet user's

Specific Absorption Rate (SAR) in the head of Tablet user's 7th Latin American Workshop On Communications - 2015 Specific Absorption Rate (SAR) in the head of Tablet user's Juliana Borges Ferreira Post-graduation program in Electrical Engineering Federal University

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing? The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity

More information

Timing Synchronization in High Mobility OFDM Systems

Timing Synchronization in High Mobility OFDM Systems Timing Synchonization in High Mobility OFDM Systems Yasamin Mostofi Depatment of Electical Engineeing Stanfod Univesity Stanfod, CA 94305, USA Email: yasi@wieless.stanfod.edu Donald C. Cox Depatment of

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

Avoided emissions kgco 2eq /m 2 Reflecting surfaces 130

Avoided emissions kgco 2eq /m 2 Reflecting surfaces 130 ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9-075-585846; F: +9-075-5848470; E: fossi@unipg.it

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

More information

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

Mobile Phone Antenna with Reduced Radiation into Inner Ear

Mobile Phone Antenna with Reduced Radiation into Inner Ear Int. J. Communications, Netwok and System Sciences, 2014, 7, 474-484 Published Online Novembe 2014 in SciRes. http://www.scip.og/jounal/ijcns http://dx.doi.og/10.4236/ijcns.2014.711048 Mobile Phone Antenna

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system

Electricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system Miao-Sheng Chen a Chien-Liang Wang b,c, Sheng-Chuan Wang d,e a Taichung Banch Gaduate

More information

Carter-Penrose diagrams and black holes

Carter-Penrose diagrams and black holes Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example

More information

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation

Data Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation (213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute

More information

Research on Risk Assessment of the Transformer Based on Life Cycle Cost

Research on Risk Assessment of the Transformer Based on Life Cycle Cost ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem

More information

An Infrastructure Cost Evaluation of Single- and Multi-Access Networks with Heterogeneous Traffic Density

An Infrastructure Cost Evaluation of Single- and Multi-Access Networks with Heterogeneous Traffic Density An Infastuctue Cost Evaluation of Single- and Multi-Access Netwoks with Heteogeneous Taffic Density Andes Fuuskä and Magnus Almgen Wieless Access Netwoks Eicsson Reseach Kista, Sweden [andes.fuuska, magnus.almgen]@eicsson.com

More information

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE 1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of

More information

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

Specific Absorption Rate (SAR) Induced in Human Heads of Various Sizes When Using a Mobile Phone

Specific Absorption Rate (SAR) Induced in Human Heads of Various Sizes When Using a Mobile Phone , June 30 - July 2, 2010, London, U.K. Specific Absorption Rate (SAR) Induced in Human Heads of Various Sizes When Using a Mobile Phone Adel Z. El Dein Alaeddin Amr Abstract - This paper analyzes the specific

More information

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,

More information

SUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA

SUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology, 4(), 20, pp. 67-7 SUPPORT VECTOR MACHIE FOR BADWIDTH AALYSIS OF SLOTTED MICROSTRIP ATEA Venmathi A.R. & Vanitha L.

More information

Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud

Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The

More information

Problems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968)

Problems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968) Poblems of the nd ntenational Physics Olympiads (Budapest Hungay 968) Péte Vankó nstitute of Physics Budapest Univesity of Technical Engineeing Budapest Hungay Abstact Afte a shot intoduction the poblems

More information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in

More information

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This

More information

ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION

ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION Michael Dedeing, Wolfgang Stausbeg, IBS Filtan, Industiestasse 19 D-51597 Mosbach-Lichtenbeg, Gemany. Oleg Iliev(*), Zaha Lakdawala, Faunhofe Institut

More information

Software Engineering and Development

Software Engineering and Development I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining

More information

DYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES

DYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

The Impact of Radio Propagation Models on Ad Hoc Networks Performances

The Impact of Radio Propagation Models on Ad Hoc Networks Performances Jounal of Compute Science 8 (5): 752-760, 2012 ISSN 1549-3636 2012 Science Publications The Impact of Radio Popagation Models on Ad Hoc Netwoks Pefomances 1 Rhattoy, A. and 2 A. Zatni 1 Depatment of Compute,

More information

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation Cicuits and Systems, 013, 4, 117-1 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0

More information

Model Question Paper Mathematics Class XII

Model Question Paper Mathematics Class XII Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat

More information

Do Vibrations Make Sound?

Do Vibrations Make Sound? Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact

More information

Effect of Metallic Materials on SAR

Effect of Metallic Materials on SAR Contemporary Engineering Sciences, Vol. 5, 2012, no. 9, 407-411 Effect of Metallic Materials on SAR Asma Lak Department of Electrical Engineering, Genaveh branch Islamic Azad University, Genaveh, Iran

More information

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011 The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility

More information

Manual ultrasonic inspection of thin metal welds

Manual ultrasonic inspection of thin metal welds Manual ultasonic inspection of thin metal welds Capucine Capentie and John Rudlin TWI Cambidge CB1 6AL, UK Telephone 01223 899000 Fax 01223 890689 E-mail capucine.capentie@twi.co.uk Abstact BS EN ISO 17640

More information

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea Double Integals in Pola Coodinates In the lectue on double integals ove non-ectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example

More information

Excitation energies for molecules by Time-Dependent. based on Effective Exact Exchange Kohn-Sham potential

Excitation energies for molecules by Time-Dependent. based on Effective Exact Exchange Kohn-Sham potential Excitation enegies fo molecules by Time-Dependent Density-Functional Theoy based on Effective Exact Exchange Kohn-Sham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling

More information

Magnetic Bearing with Radial Magnetized Permanent Magnets

Magnetic Bearing with Radial Magnetized Permanent Magnets Wold Applied Sciences Jounal 23 (4): 495-499, 2013 ISSN 1818-4952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

Japan s trading losses reach JPY20 trillion

Japan s trading losses reach JPY20 trillion IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup

More information

Lesson 7 Gauss s Law and Electric Fields

Lesson 7 Gauss s Law and Electric Fields Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual

More information

A Capacitated Commodity Trading Model with Market Power

A Capacitated Commodity Trading Model with Market Power A Capacitated Commodity Tading Model with Maket Powe Victo Matínez-de-Albéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu

More information

Chapter 2 Modelling of Fluid Flow and Heat Transfer in Rotating-Disk Systems

Chapter 2 Modelling of Fluid Flow and Heat Transfer in Rotating-Disk Systems Chapte 2 Modelling of Fluid Flow and Heat Tansfe in Rotating-Disk Systems 2.1 Diffeential and Integal Equations 2.1.1 Diffeential Navie Stokes and Enegy Equations We will conside hee stationay axisymmetic

More information

Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri

Complex Envelope Vectorization for the solution of mid-high frequency acoustic problems. A. Sestieri Complex Envelope Vectoization fo the solution of mid-high fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza Pesentation layout - Low fequency

More information

An application of stochastic programming in solving capacity allocation and migration planning problem under uncertainty

An application of stochastic programming in solving capacity allocation and migration planning problem under uncertainty An application of stochastic pogamming in solving capacity allocation and migation planning poblem unde uncetainty Yin-Yann Chen * and Hsiao-Yao Fan Depatment of Industial Management, National Fomosa Univesity,

More information

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING U.P.B. Sci. Bull., Seies C, Vol. 77, Iss. 2, 2015 ISSN 2286-3540 HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING Roxana MARCU 1, Dan POPESCU 2, Iulian DANILĂ 3 A high numbe of infomation systems ae available

More information

STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION

STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research

30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research RAIRO Rech. Opé. (vol. 33, n 1, 1999, pp. 29-45) A GOOD APPROXIMATION OF THE INVENTORY LEVEL IN A(Q ) PERISHABLE INVENTORY SYSTEM (*) by Huan Neng CHIU ( 1 ) Communicated by Shunji OSAKI Abstact. This

More information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013 PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Cloud Service Reliability: Modeling and Analysis

Cloud Service Reliability: Modeling and Analysis Cloud Sevice eliability: Modeling and Analysis Yuan-Shun Dai * a c, Bo Yang b, Jack Dongaa a, Gewei Zhang c a Innovative Computing Laboatoy, Depatment of Electical Engineeing & Compute Science, Univesity

More information

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer

CRRC-1 Method #1: Standard Practice for Measuring Solar Reflectance of a Flat, Opaque, and Heterogeneous Surface Using a Portable Solar Reflectometer CRRC- Method #: Standad Pactice fo Measuing Sola Reflectance of a Flat, Opaque, and Heteogeneous Suface Using a Potable Sola Reflectomete Scope This standad pactice coves a technique fo estimating the

More information

Approximation Algorithms for Data Management in Networks

Approximation Algorithms for Data Management in Networks Appoximation Algoithms fo Data Management in Netwoks Chistof Kick Heinz Nixdof Institute and Depatment of Mathematics & Compute Science adebon Univesity Gemany kueke@upb.de Haald Räcke Heinz Nixdof Institute

More information

Thermal Effects of Mobile Phones

Thermal Effects of Mobile Phones Thermal Effects of Mobile Phones S. Kassimi 1, A. ELfadl, S. Bri 3, A. Nakheli 4, M. Habibi 5, M. Ben Ahmed 6 Systems and Telecommunications Engineering Decision Laboratory,Ibn Tofail University, Faculty

More information

Mean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice

Mean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice Jounal of Applied Finance & aning, vol. 3, no. 5, 03, 35-36 ISSN: 79-6580 pint vesion, 79-6599 online Scienpess Ltd, 03 Mean-Reveting-bit-ased Stoc Option valuation: Theoy and Pactice Hassan l Ibami Abstact

More information

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications JIS (Japanese Industial Standad) Scew Thead Specifications TECNICAL DATA Note: Although these specifications ae based on JIS they also apply to and DIN s. Some comments added by Mayland Metics Coutesy

More information

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods

A framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com

More information

Channel selection in e-commerce age: A strategic analysis of co-op advertising models

Channel selection in e-commerce age: A strategic analysis of co-op advertising models Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of

More information

CIRCUITS LABORATORY EXPERIMENT 7

CIRCUITS LABORATORY EXPERIMENT 7 CIRCUITS LABORATORY EXPERIMENT 7 Design of a Single Tansisto Amplifie 7. OBJECTIVES The objectives of this laboatoy ae to: (a) Gain expeience in the analysis and design of an elementay, single tansisto

More information

Geneviève Parmentier

Geneviève Parmentier Heidelbeg Joint Astonomical Colloquium, 19 Octobe 2010 Splinte Meeting@AG2010, Bonn, 15 Septembe 2010 Sta Clustes as Cucial Taces of Galaxy Evolution and Pobes into Sta Fomation Geneviève Pamentie Agelande-Institut

More information

CHAT Pre-Calculus Section 10.7. Polar Coordinates

CHAT Pre-Calculus Section 10.7. Polar Coordinates CHAT Pe-Calculus Pola Coodinates Familia: Repesenting gaphs of equations as collections of points (, ) on the ectangula coodinate sstem, whee and epesent the diected distances fom the coodinate aes to

More information

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the

More information

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions Name St.No. - Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100-minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,

More information

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

An Approach to Optimized Resource Allocation for Cloud Simulation Platform

An Approach to Optimized Resource Allocation for Cloud Simulation Platform An Appoach to Optimized Resouce Allocation fo Cloud Simulation Platfom Haitao Yuan 1, Jing Bi 2, Bo Hu Li 1,3, Xudong Chai 3 1 School of Automation Science and Electical Engineeing, Beihang Univesity,

More information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

More information

2. Orbital dynamics and tides

2. Orbital dynamics and tides 2. Obital dynamics and tides 2.1 The two-body poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body

More information

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors

Tracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg

More information

Theory and practise of the g-index

Theory and practise of the g-index Theoy and pactise of the g-index by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B-3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,

More information

THERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS

THERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS THERMAL OLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS E.K.G. Boateng, P.J. Schubel, N.A. Waio Polyme Composites Goup Division of Mateials, Mechanics and Stuctues Faculty of Engineeing

More information