Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d

Size: px
Start display at page:

Download "Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d"

Transcription

1 Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c, Jinkun Peng1, d 1 tionl Engineering Lbortory for Electric Vehicles, Beijing Institute of Technology, Beijing 81, Chin hdpndeng@163.com, sunfch@bit.edu.cn, hwhebit@bit.edu.cn, d pengjinkun87719@163.com b c Keywords: Driving cycle; Mrkov processes; Grdient; Hybrid Bus Abstrct. By using the relevnt theory of Mrkov chin, the ctul driving dt re compressed nd reconstructed, nd then the city rod driving cycle is constructed bsed on chrcteristic prmeters such s velocity, ccelertion nd grdient. In the process of constructing the driving cycle, corresponding stte division principle nd the evlution criteri of chrcteristic prmeters re designed ginst hybrid bus. The comprison results show tht the driving cycle constructed using Mrkov processes cn reflect the rel driving chrcteristics on city rods. Introduction Driving cycle is velocity-time trce tht describes driving chrcteristics of specific vehicle in specific environment. Driving cycle hs been n importnt prmeter to estimte rel-world vehicle emissions nd fuel consumption which re evlution criterions of power chin design. [1,2] When vehicle is in motion, the driver chnges the output power of vehicle s power chin nd finlly chnges vehicle velocity. The vehicle stte in the next second is only relted with current rod condition. Then we could sy tht this rndom vrible follows Mrkov process. [3] Compred with trditionl construction method, the Mrkov driving cycle method better reflects the nture of velocity chnge. Rndom selection in trditionl method is substituted by selection bsed on Mrkov trnsition mtrix, nd the ccurcy of construction is improved. [4] 2 The originl driving dt collection The required prmeters of the originl driving dt collection re velocity, ccelertion nd grdient. This pper dopts the OXTS Inertil+ to mesure velocity, ccelertion nd grdient of vehicle. These prmeters re combined mesured by Stellite-bsed Globl Positioning System (GPS) nd Inertil vigtion System. OXTS Inertil+ mesurement ccurcy is shown in tble 1. Tble 1Mesurement ccurcy of the experimentl equipment Position Accurcy Velocity Accurcy Roll/Pitch 2cm 1σ.5 km/hrms.3 1σ Bis mm/s² 1σ Accelertion Linerity Scle Fctor.1%.1% 1σ Rnge m/s² 3 Dt Preprocessing The dt preprocessing is consists of four steps: division, stte cluster division, estimtion of the trnsition mtrix nd nlysis of chrcteristic prmeters. 3.1 Frgment Division The s, which re the minimum unit of the driving cycle construction, re divided from the originl driving dt ccording to specific rules. These s will be used to nlyze the chnge regultion of velocity The selection of velocity threshold The object of this study is hybrid electric bus. The pure electric mode is often pplied when the vehicle velocity is low. So if the vehicle velocity is lower thn the selected velocity threshold, this 15. The uthors - Published by Atlntis Press 1159

2 smpling point should be divided into the which we clled stop. Anlyze ll of smpling points, whose velocity is below 4Km/h, nd the sttisticl dt is shown in tble 2 Tble 2 Probbility distribution of smpling points in low velocity velocity rnge(km/h) ~.4.4~.7.7~1 1~ ~2 2~ ~3 3~ ~4 Probbility distribution.1% 17.32% 9.36% 7.85% 4.7% 3.36% 2.8% 2.42% 2.% It is obvious from tble 2 tht the smpling points whose velocity is less thn.7km/h ccount for 67.32% of ll the smpling points. After comprehensive considered,.7km/h is selected s the velocity threshold of stop The selection of ccelertion threshold The ccelertion threshold selection is s sme s the velocity threshold. When vehicle trvels t uniform velocity, the vehicle s ccelertion fluctuted in smll rnge. Tble 3 Probbility distribution of smpling points in stop s bsolute ccelertion ~.5.5~.1.1~.15.15~.2.2~.25.25~.3.3~.35 >.35 Probbility distribution 82.9% 9.92% 2.59% 1.23%.75%.6%.49% 2.33% As we cn see from tble 3, bout 94.6% of ccelerometer redings of the smpling points re between nd.15 when the vehicle is sttionry. And it is cceptble tht the ccelertion threshold should be set to Bsis of division The bsis of division is shown in Fig. 1. The originl test dt Velocity.7km/h Y Acclertion.15m/s 2 Y Acclertion -.15m/s 2 Stop Accelertion Decelertion Y Uniform Figure 1 Bsis of Frgment Division 3.2 Stte cluster division Clcultion for the rode power nd the nominl velocity To completely descript the driving condition, the rod power is introduced s n importnt bsis of stte cluster division. Rod power, clculted in Eq. 1, cptures the combined effects of rolling resistnce, erodynmic resistnce, ccelertion resistnce nd grdient resistnce. 3 1 Gfu (.15) ( Giu CDAu P = + + ),.15 ηt (1) 3 1 Gfu (.15) ( Giu CDAu d mu du P = ), > >.15 ηt dt Rod power is not direct prmeter to divide the originl dt, nd we need velocity prmeter to be the division criterion. ominl velocity, clculted in Eq. 2, is good choice. where u is the vehicle nominl velocity. 116

3 3 1 Gfu C (.15) ( D Au P = + ) = P (.15),.15 ηt C Au P(.15) = + + = P (.15) > > > ηt dt 3 1 Gfu ( D dmu du ), Stte cluster division According to the vehicle nominl velocity discussed bove, the verge nominl velocity of ech cn be clculted. According to the verge velocity, ll the s re lbeled by 7 stte clusters: (-,5],[5,15],[15,25],[25,35],[35,45],[45,55],[55, ]. The stte clusters re collections of s with similr verge velocity chrcteristics. 3.3 Estimtion of the trnsition mtrix Vehicle s driving condition trnsltes from one stte to nother long with the time. The trnsition mtrix is estimted by counting the trnsltion of stte in the originl dt. The expression of elements in the trnsition mtrix is shown in Eq. 3. (2) T = p ij ij = ij j (3) where ij is the number of individuls in stte i t time t-1 nd j t time t. The clcultion results T, 7 7 mtrix, is shown below: 3.4 Clcultion for PM PM (Performnce Mesure) chrcterize the difference between the originl dt nd lterntive driving cycles tht hve been constructed. We define the finl representtive cycle to be the one tht hs the lowest vlue of PM. The clcultion for PM is consists of three steps: (1) We obtin n 16 mtrix, denoted by M, by counting chrcteristic prmeters of every lterntive driving cycle. And then denote M s the chrcteristic prmeters mtrix of the originl dt. The prmeters, shown in tble 4, typiclly describe the chrcteristics of the verge driving behvior in term of velocity, ccelertion nd rod power, etc. [5] Tble 4 Chrcteristic prmeters of the originl dt Chrcteristic Prmeters sttistic Chrcteristic Prmeters sttistic 1 Proportion of stop time 24.9% 9 Mximum ccelertion Proportion of uniform velocity 19.91% Accelertion stndrd devition Proportion of ccelertion.31% 11 Minimum grdient -4.59% 4 Proportion of decelertion 25.69% 12 Mximum grdient 5.61% 5 Velocity stndrd devition Averge grdient.54% 6 Mximum velocity Minimum rod power Averge velocity Mximum rod power Minimum ccelertion Averge rod power (2) ote tht in tble 4, the rnges of chrcteristic prmeters re totlly different. Without normliztion, the PM vlue would be dominted by one or two chrcteristic prmeter tht hs lrge vlue rnge. The expression is shown in Eq

4 T pm = M ( ) ( 1,1, 1 16 ) ( 1 ) M n n ( 1 16 ) pm( ki, ) pmi min PM (, ) =, k 1, n i 1,16 ki pmimx pmimin ( ), ( ) (3) The finl PM of the kth lterntive driving cycle is obtined by integrting elements of row k in mtrix PM. 4 Driving Cycle Construction In this study, the entire driving cycle is divided into three prts: strting prt, middle prt nd ending prt. According to the theory of Mrkov chin, the probbility of the current stte s t depends only on the previous stte s t-1. In the strting prt nd the ending prt, however, the movement trend of vehicle hs been determined, nd the method bsed on Mrkov theory is not pplicble. Figure 2 The selected strting prt 4.1 Selection of strting prt The selection of strting prt is divided into 2 steps. First, ccording to specific rules, select ll lterntive strting prt from the originl dt. The durtion of ech lterntive strting prt lst 6s-1s. Second, clculte the PM vlue of ech prt, nd the prt hving the lowest PM vlue will be chosen s the finl strting prt. According to the relted literture t home nd brod, the durtion of strting prt is set to 75s. The selection rules re shown below: (1) Set the checkpoint is t time t. All velocities of smpling points in the rnge of (t-5,t) re less thn velocity threshold (.7 Km/h). (2) All velocities of smpling points in the rnge of (t,t+) re more thn velocity threshold (.7 Km/h). (3) When two criteri bove re met, record this checkpoint nd select ll smpling points in the rnge of (t-5,t+69) s the lterntive strting prt. Figure 3 The selected middle prt (4) 6 8 1, 1162

5 4.2 Construction of middle prt The construction of middle prt is typicl process solved by Monte Crlo method. Once is selected, its stte s well s terminl velocity re identified. A rndom number is generted to determinte the next s stte bsed on the probbility of the corresponding row in the trnsition mtrix. Before clculting the PM vlue, the lterntive middle prt should be combined with the selected strting prt. The one who hs the lowest PM vlue will be chosen s the finl middle prt. Figure 4 The selected ending prt 4.3 Selection of ending prt The ending prt selection method is s sme s the strting prt s. The selection rules re shown below: (1) Set the checkpoint is t time t. All velocities of smpling points in the rnge of (t-, t) re more thn velocity threshold (.7 Km/h). (2) All velocities of smpling points in the rnge of (t, t+5) re less thn velocity threshold. (3) When two criteri bove re met, record this checkpoint nd select ll smpling points in the rnge of (t-114, t+5). (4) Check ll smpling points in the rnge of (t-114, t+5). If there is such point tht the velocity of this point is very close to the terminl velocity of middle prt, record this point, note it by t, nd select ll smpling points in the rnge of (t, t+5) s the lterntive ending prt. Finlly, clculte the PM vlue of ech lterntive ending prt, nd choose the cycle tht hs the lowest PM vlue to be the finl ending prt. Figure 5 The finl driving cycle for hybrid bus 4.4 Construction of driving cycle Construct the finl driving cycle by combining the strting prt, the middle prt nd the ending prt selected bove to be complete velocity-time curve. 5 Conclusions , 1, 1 The mthemticl sttistics theories relted with Mrkov chin re used to construct driving cycle of city rod for hybrid bus. And new method to divide vehicle stte clusters is proposed during the construction process. 2 A specil method for PM clcultion, which elimintes differences cused by non-uniform unit between different chrcteristic prmeters, gurntees the resonbility of prt selection. 1163

6 Acknowledgments This work ws supported by the tionl High Technology Reserch nd Development Progrm of Chin (13BAG5B) in prt, the Progrm for ew Century Excellent Tlents in University (CET ) nd Beijing Institute of Technology Post Grdute Students Innovtion Foundtion in prt. The uthor would lso like to thnk the reviewers for their corrections nd helpful suggestions. References [1] Jing Pin, Shi Qin. A Reserch on the Construction of City Rod Driving Cycle Bsed on Wvelet Anlysis[J]. Automotive Engineering, 11(V1.33) o.1 (in Chinese) [2] Jie Lin. Mrkov Process Approch to Driving cycle Development. [D]. University of Cliforni 2. [3] He Xioqun.Multivrite Sttisticl Anlysis[M]. Beijing: Chin Renmin University Press, 4. [4] Yingyu Yng. Reserch of the City Bus Driving Cycle Bsed on Chrcteristics of Urbniztion Development in Chin [D].Beijing Institute of Technology 11.(in Chinese) [5]Jing Pin, Shi Qin. Driving Cycle Construction Methodology of City Rod Bsed on Mrkov Process[J].Trnsctions of the Chinese Society for Agriculturl Mchinery. 9, (11): 26~. (in Chinese) 1164

Predict Global Earth Temperature using Linier Regression

Predict Global Earth Temperature using Linier Regression Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Monte Carlo method in solving numerical integration and differential equation

Monte Carlo method in solving numerical integration and differential equation Monte Crlo method in solving numericl integrtion nd differentil eqution Ye Jin Chemistry Deprtment Duke University yj66@duke.edu Abstrct: Monte Crlo method is commonly used in rel physics problem. The

More information

New Expansion and Infinite Series

New Expansion and Infinite Series Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University

More information

Non-Linear & Logistic Regression

Non-Linear & Logistic Regression Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find

More information

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es

More information

Research on the Quality Competence in Manufacturing Industry

Research on the Quality Competence in Manufacturing Industry Reserch on the Qulity Competence in Mnufcturing Industry Xioping M, Zhijun Hn Economics nd Mngement School Nnjing University of Science nd Technology Nnjing 210094, Chin Tel: 86-25-8431-5400 E-mil: hnzhij4531@sin.com

More information

A New Statistic Feature of the Short-Time Amplitude Spectrum Values for Human s Unvoiced Pronunciation

A New Statistic Feature of the Short-Time Amplitude Spectrum Values for Human s Unvoiced Pronunciation Xiodong Zhung A ew Sttistic Feture of the Short-Time Amplitude Spectrum Vlues for Humn s Unvoiced Pronuncition IAODOG ZHUAG 1 1. Qingdo University, Electronics & Informtion College, Qingdo, 6671 CHIA Abstrct:

More information

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More information

Research on Modeling and Compensating Method of Random Drift of MEMS Gyroscope

Research on Modeling and Compensating Method of Random Drift of MEMS Gyroscope 01 4th Interntionl Conference on Signl Processing Systems (ICSPS 01) IPCSIT vol. 58 (01) (01) IACSIT Press, Singpore DOI: 10.7763/IPCSIT.01.V58.9 Reserch on Modeling nd Compensting Method of Rndom Drift

More information

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by. NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with

More information

Student Activity 3: Single Factor ANOVA

Student Activity 3: Single Factor ANOVA MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

Hybrid Group Acceptance Sampling Plan Based on Size Biased Lomax Model

Hybrid Group Acceptance Sampling Plan Based on Size Biased Lomax Model Mthemtics nd Sttistics 2(3): 137-141, 2014 DOI: 10.13189/ms.2014.020305 http://www.hrpub.org Hybrid Group Acceptnce Smpling Pln Bsed on Size Bised Lomx Model R. Subb Ro 1,*, A. Ng Durgmmb 2, R.R.L. Kntm

More information

Estimation of Binomial Distribution in the Light of Future Data

Estimation of Binomial Distribution in the Light of Future Data British Journl of Mthemtics & Computer Science 102: 1-7, 2015, Article no.bjmcs.19191 ISSN: 2231-0851 SCIENCEDOMAIN interntionl www.sciencedomin.org Estimtion of Binomil Distribution in the Light of Future

More information

13: Diffusion in 2 Energy Groups

13: Diffusion in 2 Energy Groups 3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups

More information

Multivariate problems and matrix algebra

Multivariate problems and matrix algebra University of Ferrr Stefno Bonnini Multivrite problems nd mtrix lgebr Multivrite problems Multivrite sttisticl nlysis dels with dt contining observtions on two or more chrcteristics (vribles) ech mesured

More information

Construction and Selection of Single Sampling Quick Switching Variables System for given Control Limits Involving Minimum Sum of Risks

Construction and Selection of Single Sampling Quick Switching Variables System for given Control Limits Involving Minimum Sum of Risks Construction nd Selection of Single Smpling Quick Switching Vribles System for given Control Limits Involving Minimum Sum of Risks Dr. D. SENHILKUMAR *1 R. GANESAN B. ESHA RAFFIE 1 Associte Professor,

More information

Songklanakarin Journal of Science and Technology SJST R1 Thongchan. A Modified Hyperbolic Secant Distribution

Songklanakarin Journal of Science and Technology SJST R1 Thongchan. A Modified Hyperbolic Secant Distribution A Modified Hyperbolic Secnt Distribution Journl: Songklnkrin Journl of Science nd Technology Mnuscript ID SJST-0-0.R Mnuscript Type: Originl Article Dte Submitted by the Author: 0-Mr-0 Complete List of

More information

Data Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading

Data Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3d-Vritionl Method

More information

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus Unit #9 : Definite Integrl Properties; Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl

More information

Credibility Hypothesis Testing of Fuzzy Triangular Distributions

Credibility Hypothesis Testing of Fuzzy Triangular Distributions 666663 Journl of Uncertin Systems Vol.9, No., pp.6-74, 5 Online t: www.jus.org.uk Credibility Hypothesis Testing of Fuzzy Tringulr Distributions S. Smpth, B. Rmy Received April 3; Revised 4 April 4 Abstrct

More information

CBE 291b - Computation And Optimization For Engineers

CBE 291b - Computation And Optimization For Engineers The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn

More information

CS667 Lecture 6: Monte Carlo Integration 02/10/05

CS667 Lecture 6: Monte Carlo Integration 02/10/05 CS667 Lecture 6: Monte Crlo Integrtion 02/10/05 Venkt Krishnrj Lecturer: Steve Mrschner 1 Ide The min ide of Monte Crlo Integrtion is tht we cn estimte the vlue of n integrl by looking t lrge number of

More information

Probabilistic Investigation of Sensitivities of Advanced Test- Analysis Model Correlation Methods

Probabilistic Investigation of Sensitivities of Advanced Test- Analysis Model Correlation Methods Probbilistic Investigtion of Sensitivities of Advnced Test- Anlysis Model Correltion Methods Liz Bergmn, Mtthew S. Allen, nd Dniel C. Kmmer Dept. of Engineering Physics University of Wisconsin-Mdison Rndll

More information

EFEFCTS OF GROUND MOTION UNCERTAINTY ON PREDICTING THE RESPONSE OF AN EXISTING RC FRAME STRUCTURE

EFEFCTS OF GROUND MOTION UNCERTAINTY ON PREDICTING THE RESPONSE OF AN EXISTING RC FRAME STRUCTURE 13 th World Conference on Erthquke Engineering Vncouver, B.C., Cnd August 1-6, 2004 Pper No. 2007 EFEFCTS OF GROUND MOTION UNCERTAINTY ON PREDICTING THE RESPONSE OF AN EXISTING RC FRAME STRUCTURE Ftemeh

More information

Lecture 3 Gaussian Probability Distribution

Lecture 3 Gaussian Probability Distribution Introduction Lecture 3 Gussin Probbility Distribution Gussin probbility distribution is perhps the most used distribution in ll of science. lso clled bell shped curve or norml distribution Unlike the binomil

More information

QUADRATURE is an old-fashioned word that refers to

QUADRATURE is an old-fashioned word that refers to World Acdemy of Science Engineering nd Technology Interntionl Journl of Mthemticl nd Computtionl Sciences Vol:5 No:7 011 A New Qudrture Rule Derived from Spline Interpoltion with Error Anlysis Hdi Tghvfrd

More information

A Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System

A Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 16-0, Orlndo FL. (Minor errors in published version corrected.) A Signl-Level Fusion Model for Imge-Bsed

More information

CHM Physical Chemistry I Chapter 1 - Supplementary Material

CHM Physical Chemistry I Chapter 1 - Supplementary Material CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion

More information

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses

More information

Continuous Random Variables

Continuous Random Variables STAT/MATH 395 A - PROBABILITY II UW Winter Qurter 217 Néhémy Lim Continuous Rndom Vribles Nottion. The indictor function of set S is rel-vlued function defined by : { 1 if x S 1 S (x) if x S Suppose tht

More information

DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE

DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING MOMENT INTERACTION AT MICROSCALE Determintion RevAdvMterSci of mechnicl 0(009) -7 properties of nnostructures with complex crystl lttice using DETERMINATION OF MECHANICAL PROPERTIES OF NANOSTRUCTURES WITH COMPLEX CRYSTAL LATTICE USING

More information

Math& 152 Section Integration by Parts

Math& 152 Section Integration by Parts Mth& 5 Section 7. - Integrtion by Prts Integrtion by prts is rule tht trnsforms the integrl of the product of two functions into other (idelly simpler) integrls. Recll from Clculus I tht given two differentible

More information

Quantum Physics II (8.05) Fall 2013 Assignment 2

Quantum Physics II (8.05) Fall 2013 Assignment 2 Quntum Physics II (8.05) Fll 2013 Assignment 2 Msschusetts Institute of Technology Physics Deprtment Due Fridy September 20, 2013 September 13, 2013 3:00 pm Suggested Reding Continued from lst week: 1.

More information

Session 13

Session 13 780.20 Session 3 (lst revised: Februry 25, 202) 3 3. 780.20 Session 3. Follow-ups to Session 2 Histogrms of Uniform Rndom Number Distributions. Here is typicl figure you might get when histogrmming uniform

More information

ELE B7 Power Systems Engineering. Power System Components Modeling

ELE B7 Power Systems Engineering. Power System Components Modeling Power Systems Engineering Power System Components Modeling Section III : Trnsformer Model Power Trnsformers- CONSTRUCTION Primry windings, connected to the lternting voltge source; Secondry windings, connected

More information

Probability-Based Seismic Assessments: Implementing Wide-Range Nonlinear Dynamic Analysis Methods

Probability-Based Seismic Assessments: Implementing Wide-Range Nonlinear Dynamic Analysis Methods Probbility-Bsed Seismic Assessments: Implementing Nonliner Dynmic Anlysis Methods Ftim Jlyer Postdoctorl Scholr University of Rome L Spienz Cliforni Institute of Technology (CIT) Outline A brief Introduction

More information

Shear and torsion interaction of hollow core slabs

Shear and torsion interaction of hollow core slabs Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction

More information

Distance And Velocity

Distance And Velocity Unit #8 - The Integrl Some problems nd solutions selected or dpted from Hughes-Hllett Clculus. Distnce And Velocity. The grph below shows the velocity, v, of n object (in meters/sec). Estimte the totl

More information

Numerical integration

Numerical integration 2 Numericl integrtion This is pge i Printer: Opque this 2. Introduction Numericl integrtion is problem tht is prt of mny problems in the economics nd econometrics literture. The orgniztion of this chpter

More information

Problem Set 3 Solutions

Problem Set 3 Solutions Chemistry 36 Dr Jen M Stndrd Problem Set 3 Solutions 1 Verify for the prticle in one-dimensionl box by explicit integrtion tht the wvefunction ψ ( x) π x is normlized To verify tht ψ ( x) is normlized,

More information

Lecture INF4350 October 12008

Lecture INF4350 October 12008 Biosttistics ti ti Lecture INF4350 October 12008 Anj Bråthen Kristoffersen Biomedicl Reserch Group Deprtment of informtics, UiO Gol Presenttion of dt descriptive tbles nd grphs Sensitivity, specificity,

More information

7.2 The Definite Integral

7.2 The Definite Integral 7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where

More information

Recitation 3: More Applications of the Derivative

Recitation 3: More Applications of the Derivative Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech

More information

KINEMATICS OF RIGID BODIES

KINEMATICS OF RIGID BODIES KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description

More information

2008 Mathematical Methods (CAS) GA 3: Examination 2

2008 Mathematical Methods (CAS) GA 3: Examination 2 Mthemticl Methods (CAS) GA : Exmintion GENERAL COMMENTS There were 406 students who st the Mthemticl Methods (CAS) exmintion in. Mrks rnged from to 79 out of possible score of 80. Student responses showed

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Statistical Physics I Spring Term Solutions to Problem Set #1

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Statistical Physics I Spring Term Solutions to Problem Set #1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Deprtment 8.044 Sttisticl Physics I Spring Term 03 Problem : Doping Semiconductor Solutions to Problem Set # ) Mentlly integrte the function p(x) given in

More information

Studies on Nuclear Fuel Rod Thermal Performance

Studies on Nuclear Fuel Rod Thermal Performance Avilble online t www.sciencedirect.com Energy Procedi 1 (1) 1 17 Studies on Nucler Fuel od herml Performnce Eskndri, M.1; Bvndi, A ; Mihndoost, A3* 1 Deprtment of Physics, Islmic Azd University, Shirz

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

38.2. The Uniform Distribution. Introduction. Prerequisites. Learning Outcomes

38.2. The Uniform Distribution. Introduction. Prerequisites. Learning Outcomes The Uniform Distribution 8. Introduction This Section introduces the simplest type of continuous probbility distribution which fetures continuous rndom vrible X with probbility density function f(x) which

More information

Review of Calculus, cont d

Review of Calculus, cont d Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some

More information

Section 14.3 Arc Length and Curvature

Section 14.3 Arc Length and Curvature Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in

More information

Multiscale Fourier Descriptor for Shape Classification

Multiscale Fourier Descriptor for Shape Classification Multiscle Fourier Descriptor for Shpe Clssifiction Iivri Kunttu, een epistö, Juhni Ruhm 2, nd Ari Vis Tmpere University of Technology Institute of Signl Processing P. O. Box 553, FI-330 Tmpere, Finlnd

More information

The steps of the hypothesis test

The steps of the hypothesis test ttisticl Methods I (EXT 7005) Pge 78 Mosquito species Time of dy A B C Mid morning 0.0088 5.4900 5.5000 Mid Afternoon.3400 0.0300 0.8700 Dusk 0.600 5.400 3.000 The Chi squre test sttistic is the sum of

More information

5 Probability densities

5 Probability densities 5 Probbility densities 5. Continuous rndom vribles 5. The norml distribution 5.3 The norml pproimtion to the binomil distribution 5.5 The uniorm distribution 5. Joint distribution discrete nd continuous

More information

A New Grey-rough Set Model Based on Interval-Valued Grey Sets

A New Grey-rough Set Model Based on Interval-Valued Grey Sets Proceedings of the 009 IEEE Interntionl Conference on Systems Mn nd Cybernetics Sn ntonio TX US - October 009 New Grey-rough Set Model sed on Intervl-Vlued Grey Sets Wu Shunxing Deprtment of utomtion Ximen

More information

Decision Science Letters

Decision Science Letters Decision Science Letters 8 (09) 37 3 Contents lists vilble t GrowingScience Decision Science Letters homepge: www.growingscience.com/dsl The negtive binomil-weighted Lindley distribution Sunthree Denthet

More information

SOLUTION OF QUADRATIC NONLINEAR PROBLEMS WITH MULTIPLE SCALES LINDSTEDT-POINCARE METHOD. Mehmet Pakdemirli and Gözde Sarı

SOLUTION OF QUADRATIC NONLINEAR PROBLEMS WITH MULTIPLE SCALES LINDSTEDT-POINCARE METHOD. Mehmet Pakdemirli and Gözde Sarı Mthemticl nd Computtionl Applictions, Vol., No., pp. 37-5, 5 http://dx.doi.org/.99/mc-5- SOLUTION OF QUADRATIC NONLINEAR PROBLEMS WITH MULTIPLE SCALES LINDSTEDT-POINCARE METHOD Mehmet Pkdemirli nd Gözde

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information

Transverse spin asymmetries at low momentum transfer at STAR

Transverse spin asymmetries at low momentum transfer at STAR Trnsverse spin symmetries t low momentum trnsfer t STAR Dmitry Svirid (ITEP) for the STAR Collbortion EDS Blois 2011 14th Workshop on Elstic nd Diffrctive Scttering, Qui Nhon, Vietnm, December 15-21, 2011

More information

APPROXIMATE INTEGRATION

APPROXIMATE INTEGRATION APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be

More information

Department of Chemical Engineering ChE-101: Approaches to Chemical Engineering Problem Solving MATLAB Tutorial VII

Department of Chemical Engineering ChE-101: Approaches to Chemical Engineering Problem Solving MATLAB Tutorial VII Tutoril VII: Liner Regression Lst updted 5/8/06 b G.G. Botte Deprtment of Chemicl Engineering ChE-0: Approches to Chemicl Engineering Problem Solving MATLAB Tutoril VII Liner Regression Using Lest Squre

More information

Chapter 5 : Continuous Random Variables

Chapter 5 : Continuous Random Variables STAT/MATH 395 A - PROBABILITY II UW Winter Qurter 216 Néhémy Lim Chpter 5 : Continuous Rndom Vribles Nottions. N {, 1, 2,...}, set of nturl numbers (i.e. ll nonnegtive integers); N {1, 2,...}, set of ll

More information

APPROPRIATE ATTENUATION MODEL FOR CHIANG MAI, THAILAND FROM FIELD MEASUREMENT TO MODEL EQUATION

APPROPRIATE ATTENUATION MODEL FOR CHIANG MAI, THAILAND FROM FIELD MEASUREMENT TO MODEL EQUATION Geotec., Const. Mt. & Env., DOI: https://doi.org/0.2660/20.47.gte95 ISSN: 26-292 (Print), 26-2990 (Online), Jpn APPROPRIATE ATTENUATION MODEL OR CHIANG MAI, THAILAND ROM IELD MEASUREMENT TO MODEL EQUATION

More information

Lecture 21: Order statistics

Lecture 21: Order statistics Lecture : Order sttistics Suppose we hve N mesurements of sclr, x i =, N Tke ll mesurements nd sort them into scending order x x x 3 x N Define the mesured running integrl S N (x) = 0 for x < x = i/n for

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct

More information

ECO 317 Economics of Uncertainty Fall Term 2007 Notes for lectures 4. Stochastic Dominance

ECO 317 Economics of Uncertainty Fall Term 2007 Notes for lectures 4. Stochastic Dominance Generl structure ECO 37 Economics of Uncertinty Fll Term 007 Notes for lectures 4. Stochstic Dominnce Here we suppose tht the consequences re welth mounts denoted by W, which cn tke on ny vlue between

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

Scientific notation is a way of expressing really big numbers or really small numbers.

Scientific notation is a way of expressing really big numbers or really small numbers. Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific

More information

Physics 202H - Introductory Quantum Physics I Homework #08 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/11/15

Physics 202H - Introductory Quantum Physics I Homework #08 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/11/15 Physics H - Introductory Quntum Physics I Homework #8 - Solutions Fll 4 Due 5:1 PM, Mondy 4/11/15 [55 points totl] Journl questions. Briefly shre your thoughts on the following questions: Of the mteril

More information

Method of stationary phase

Method of stationary phase Physics 4 Spring 16 Method of sttionry phse Lecture notes by M. G. Rozmn Lst modified: April 13, 16 There is n immedite generliztion of the Lplce integrls f t)e φt) dt 1) which we obtin by llowing the

More information

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of

More information

Modified method of a determination in the 1/E 1+a epithermal neutron spectrum of reactor

Modified method of a determination in the 1/E 1+a epithermal neutron spectrum of reactor J Rdionl Nucl Chem (2010) 285:331 336 DOI 10.1007/s10967-010-0549-x Modified method of determintion in the 1/E 1+ epitherml neutron spectrum of rector Trn Vn Hung Received: 19 Februry 2010 / Published

More information

CMDA 4604: Intermediate Topics in Mathematical Modeling Lecture 19: Interpolation and Quadrature

CMDA 4604: Intermediate Topics in Mathematical Modeling Lecture 19: Interpolation and Quadrature CMDA 4604: Intermedite Topics in Mthemticl Modeling Lecture 19: Interpoltion nd Qudrture In this lecture we mke brief diversion into the res of interpoltion nd qudrture. Given function f C[, b], we sy

More information

CHAPTER 4a. ROOTS OF EQUATIONS

CHAPTER 4a. ROOTS OF EQUATIONS CHAPTER 4. ROOTS OF EQUATIONS A. J. Clrk School o Engineering Deprtment o Civil nd Environmentl Engineering by Dr. Ibrhim A. Asskk Spring 00 ENCE 03 - Computtion Methods in Civil Engineering II Deprtment

More information

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah 1. Born-Oppenheimer pprox.- energy surfces 2. Men-field (Hrtree-Fock) theory- orbitls 3. Pros nd cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usully does HF-how? 6. Bsis sets nd nottions 7. MPn,

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 2013 Outline 1 Riemnn Sums 2 Riemnn Integrls 3 Properties

More information

The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O

The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O IAPWS R-7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem

More information

Chapters 4 & 5 Integrals & Applications

Chapters 4 & 5 Integrals & Applications Contents Chpters 4 & 5 Integrls & Applictions Motivtion to Chpters 4 & 5 2 Chpter 4 3 Ares nd Distnces 3. VIDEO - Ares Under Functions............................................ 3.2 VIDEO - Applictions

More information

Wind-induced vibration: a serviceability study

Wind-induced vibration: a serviceability study Proceedings of the 9th Interntionl Conference on Structurl Dynmics, EURODYN 214 Porto, Portugl, 3 June - 2 July 214 A. Cunh, E. Cetno, P. Ribeiro, G. Müller (eds.) ISSN: 2311-92; ISBN: 978-972-752-165-4

More information

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of

More information

n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1

n f(x i ) x. i=1 In section 4.2, we defined the definite integral of f from x = a to x = b as n f(x i ) x; f(x) dx = lim i=1 The Fundmentl Theorem of Clculus As we continue to study the re problem, let s think bck to wht we know bout computing res of regions enclosed by curves. If we wnt to find the re of the region below the

More information

INVESTIGATION OF MATHEMATICAL MODEL OF COMMUNICATION NETWORK WITH UNSTEADY FLOW OF REQUESTS

INVESTIGATION OF MATHEMATICAL MODEL OF COMMUNICATION NETWORK WITH UNSTEADY FLOW OF REQUESTS Trnsport nd Telecommuniction Vol No 4 9 Trnsport nd Telecommuniction 9 Volume No 4 8 34 Trnsport nd Telecommuniction Institute Lomonosov Rig LV-9 Ltvi INVESTIGATION OF MATHEMATICAL MODEL OF COMMUNICATION

More information

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from

More information

Matrix Solution to Linear Equations and Markov Chains

Matrix Solution to Linear Equations and Markov Chains Trding Systems nd Methods, Fifth Edition By Perry J. Kufmn Copyright 2005, 2013 by Perry J. Kufmn APPENDIX 2 Mtrix Solution to Liner Equtions nd Mrkov Chins DIRECT SOLUTION AND CONVERGENCE METHOD Before

More information

2D1431 Machine Learning Lab 3: Reinforcement Learning

2D1431 Machine Learning Lab 3: Reinforcement Learning 2D1431 Mchine Lerning Lb 3: Reinforcement Lerning Frnk Hoffmnn modified by Örjn Ekeberg December 7, 2004 1 Introduction In this lb you will lern bout dynmic progrmming nd reinforcement lerning. It is ssumed

More information

A general framework for estimating similarity of datasets and decision trees: exploring semantic similarity of decision trees

A general framework for estimating similarity of datasets and decision trees: exploring semantic similarity of decision trees A generl frmework for estimting similrity of dtsets nd decision trees: exploring semntic similrity of decision trees Irene Ntoutsi Alexndros Klousis Ynnis Theodoridis Abstrct Decision trees re mong the

More information

Expected Value of Function of Uncertain Variables

Expected Value of Function of Uncertain Variables Journl of Uncertin Systems Vol.4, No.3, pp.8-86, 2 Online t: www.jus.org.uk Expected Vlue of Function of Uncertin Vribles Yuhn Liu, Minghu H College of Mthemtics nd Computer Sciences, Hebei University,

More information

Electron Correlation Methods

Electron Correlation Methods Electron Correltion Methods HF method: electron-electron interction is replced by n verge interction E HF c E 0 E HF E 0 exct ground stte energy E HF HF energy for given bsis set HF Ec 0 - represents mesure

More information

Research Article Moment Inequalities and Complete Moment Convergence

Research Article Moment Inequalities and Complete Moment Convergence Hindwi Publishing Corportion Journl of Inequlities nd Applictions Volume 2009, Article ID 271265, 14 pges doi:10.1155/2009/271265 Reserch Article Moment Inequlities nd Complete Moment Convergence Soo Hk

More information

Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models

Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models eserch Journl of ecent Sciences ISSN 77-5 es.j.ecent Sci. Estimtion of Globl Solr dition t Onitsh with egression Anlysis nd Artificil Neurl Network Models Abstrct Agbo G.A., Ibeh G.F. *nd Ekpe J.E. Fculty

More information

Math 135, Spring 2012: HW 7

Math 135, Spring 2012: HW 7 Mth 3, Spring : HW 7 Problem (p. 34 #). SOLUTION. Let N the number of risins per cookie. If N is Poisson rndom vrible with prmeter λ, then nd for this to be t lest.99, we need P (N ) P (N ) ep( λ) λ ln(.)

More information

INSTRUMENTS USED FOR MEASURINNG THE MAGNETIC PROPERTIES OF ONE KILOGRAM MASS STANDARD IN CENTER FOR MEASUREMENT STANDARDS (CMS)

INSTRUMENTS USED FOR MEASURINNG THE MAGNETIC PROPERTIES OF ONE KILOGRAM MASS STANDARD IN CENTER FOR MEASUREMENT STANDARDS (CMS) INSTRUMENTS USED OR MEASURINNG THE MAGNETIC PROPERTIES O ONE KILOGRAM MASS STANDARD IN CENTER OR MEASUREMENT STANDARDS (CMS) Sheu-shi Pn, H. C. Lu nd C. S. Chng Center for Mesurement Stndrds, Industril

More information

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17 CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking

More information

1 Probability Density Functions

1 Probability Density Functions Lis Yn CS 9 Continuous Distributions Lecture Notes #9 July 6, 28 Bsed on chpter by Chris Piech So fr, ll rndom vribles we hve seen hve been discrete. In ll the cses we hve seen in CS 9, this ment tht our

More information

A Study of thethermal C-C and C-H Bond Cleavage in the Aromatic Molecules: Acenaphthene and Acenaphthylene

A Study of thethermal C-C and C-H Bond Cleavage in the Aromatic Molecules: Acenaphthene and Acenaphthylene JJC Jordn Journl of Chemistry Vol. 7 No.4, 2012, pp. 329-337 A Study of thetherml C-C nd C-H Bond Clevge in the Aromtic Molecules: Acenphthene nd Acenphthylene Muthn Shnshl nd Hssn H. Abdullh Deprtment

More information

University of Texas MD Anderson Cancer Center Department of Biostatistics. Inequality Calculator, Version 3.0 November 25, 2013 User s Guide

University of Texas MD Anderson Cancer Center Department of Biostatistics. Inequality Calculator, Version 3.0 November 25, 2013 User s Guide University of Texs MD Anderson Cncer Center Deprtment of Biosttistics Inequlity Clcultor, Version 3.0 November 5, 013 User s Guide 0. Overview The purpose of the softwre is to clculte the probbility tht

More information

Analysis for Transverse Sensitivity of the Microaccelerometer

Analysis for Transverse Sensitivity of the Microaccelerometer Engineering, 009, 1, 196-00 doi:10.436/eng.009.1303 Published Online November 009 (http://www.scirp.org/journl/eng). Anlsis for Trnsverse ensitivit of the Microccelerometer Abstrct Yu LIU 1,,3, Guocho

More information