Size: px
Start display at page:

Download ""

Transcription

1

2

3

4

5

6

7 > >

8

9

10

11

12

13

14

15 π [] [] [] [π] [π] [π]

16 π π π π π π

17 π π π π

18

19 π π π π

20

21

22 [] [] [] [π] [π] [π] [π] π π π π π π π

23 π π π π π

24 π π π

25 π π π π π π

26 π π π π π π π π π

27

28 P L SG π π π π π π π π

29

30

31

32

33

34 λ

35

36

37

38

39

40

41

Transmission Line Input Impedance

Transmission Line Input Impedance 1/26/25 Transmission e Input Impedance.doc 1/9 Transmission e Input Impedance Consider a lossless le, length, termated with a load. I(z) I + V (z) -, β + V - z z et s determe the put impedance of this

More information

Solutions to Linear Algebra Practice Problems

Solutions to Linear Algebra Practice Problems Solutions to Linear Algebra Practice Problems. Find all solutions to the following systems of linear equations. (a) x x + x 5 x x x + x + x 5 (b) x + x + x x + x + x x + x + 8x Answer: (a) We create the

More information

Jointly Distributed Random Variables

Jointly Distributed Random Variables Jointly Distributed Random Variables COMP 245 STATISTICS Dr N A Heard Contents 1 Jointly Distributed Random Variables 1 1.1 Definition......................................... 1 1.2 Joint cdfs..........................................

More information

Lecture 12: Fraunhofer diffraction by a single slit

Lecture 12: Fraunhofer diffraction by a single slit Lecture 12: Fraunhofer diffraction y a single slit Lecture aims to explain: 1. Diffraction prolem asics (reminder) 2. Calculation of the diffraction integral for a long slit 3. Diffraction pattern produced

More information

Surface Area of Prisms

Surface Area of Prisms Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism

More information

Poisson and Normal Distributions

Poisson and Normal Distributions Poisson and Normal Distributions Lectures 7 Spring 2002 Poisson Distribution The Poisson distribution can be derived as a limiting form of the binomial distribution in which n is increased without limit

More information

CPI Inflation Targeting and the UIP Puzzle: An Appraisal of Instrument and Target Rules

CPI Inflation Targeting and the UIP Puzzle: An Appraisal of Instrument and Target Rules CPI Inflation Targeting and the UIP Puzzle: An Appraisal of Instrument and Target Rules By Alfred V Guender Department of Economics University of Canterbury I. Specification of Monetary Policy What Should

More information

What is the essence of waviness? The Wave Model. Waves: examples. Particles. Wave. 1. Ripples on a pond. Think of a leaf, or a cork on the water

What is the essence of waviness? The Wave Model. Waves: examples. Particles. Wave. 1. Ripples on a pond. Think of a leaf, or a cork on the water Chapter 20: Traveling Waves 20.1 The wave model 20.2 One-dimensional waves 20.3 Sinusoidal waves 20.4 Waves in 2- & 3-dimensions 20.5 Sound and Light Waves 20.6 Power and Intensity 20.7 Doppler Effect

More information

Gaussian Classifiers CS498

Gaussian Classifiers CS498 Gaussian Classifiers CS498 Today s lecture The Gaussian Gaussian classifiers A slightly more sophisticated classifier Nearest Neighbors We can classify with nearest neighbors x m 1 m 2 Decision boundary

More information

speed of light Planck constant Boltzmann constant electron mass proton mass neutron mass

speed of light Planck constant Boltzmann constant electron mass proton mass neutron mass Constants c =.998 8 s h = 6.66 34 J s ħ =.55 34 J s k =.38 3 J K hc/k =.4388 c K e =.6 9 C N A = 6. 3 ol speed of light Planck constant Boltzann constant eleentary charge Avogadro constant u =.6654 7 kg

More information

Low Dimensional Representations of the Loop Braid Group LB 3

Low Dimensional Representations of the Loop Braid Group LB 3 Low Dimensional Representations of the Loop Braid Group LB 3 Liang Chang Texas A&M University UT Dallas, June 1, 2015 Supported by AMS MRC Program Joint work with Paul Bruillard, Cesar Galindo, Seung-Moon

More information

22. Amplitude-Shift Keying (ASK) Modulation

22. Amplitude-Shift Keying (ASK) Modulation . mplitude-shift Keying (SK) Modulation Introduction he transmission of digital signals is increasing at a rapid rate. Low-frequency analogue signals are often converted to digital format (PM) before transmission.

More information

VIII. Magnetic Fields - Worked Examples

VIII. Magnetic Fields - Worked Examples MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.0 Spring 003 VIII. Magnetic Fields - Worked Examples Example : Rolling rod A rod with a mass m and a radius R is mounted on two parallel rails

More information

Commonly Used Probability Distributions

Commonly Used Probability Distributions Chapter Four 4.1 Introduction As we have seen in Charter 3, a probability density function (pdf) or a cumulative distribution function (cdf) can completely describe a random variable. Because of the physical

More information

Introduction to Sturm-Liouville Theory

Introduction to Sturm-Liouville Theory Introduction to Ryan C. Trinity University Partial Differential Equations April 10, 2012 Inner products with weight functions Suppose that w(x) is a nonnegative function on [a,b]. If f (x) and g(x) are

More information

Safety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Safety and Reliability Analysis Models: Overview

Safety and Reliability of Embedded Systems. (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Safety and Reliability Analysis Models: Overview 1 (Sicherheit und Zuverlässigkeit eingebetteter Systeme) Safety and Reliability Analysis Models: Overview Prof. Dr. Liggesmeyer, 1 Content Classification Hazard and Operability Study (HAZOP) Preliminary

More information

Efficient quantum algorithms for the principal ideal problem and class group problem in arbitrary-degree number fields

Efficient quantum algorithms for the principal ideal problem and class group problem in arbitrary-degree number fields Efficient quantum algorithms for the principal ideal problem and class group problem in arbitrary-degree number fields Fang Song Institute for Quantum Computing University of Waterloo Joint work with Jean-François

More information

) 1/2 ( J / K 298K. CHEM 4641 Physical Chemistry I Chapter 16 (long-book chapter 33) Recommended Problems

) 1/2 ( J / K 298K. CHEM 4641 Physical Chemistry I Chapter 16 (long-book chapter 33) Recommended Problems CHEM 4641 hysical Cheistry I Chapter 16 (long-book chapter 33) Recoended robles Chapter 16 (33) roble 1 Maxwell speed distribution in two diensions The velocity distribution is siply the Maxwell-Boltzann

More information

Statistics - Written Examination MEC Students - BOVISA

Statistics - Written Examination MEC Students - BOVISA Statistics - Written Examination MEC Students - BOVISA Prof.ssa A. Guglielmi 26.0.2 All rights reserved. Legal action will be taken against infringement. Reproduction is prohibited without prior consent.

More information

11 TRANSFORMING DENSITY FUNCTIONS

11 TRANSFORMING DENSITY FUNCTIONS 11 TRANSFORMING DENSITY FUNCTIONS It can be expedient to use a transformation function to transform one probability density function into another. As an introduction to this topic, it is helpful to recapitulate

More information

Chapter 11. Waves & Sound

Chapter 11. Waves & Sound Chapter 11 Waves & Sound 11.2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position.

More information

The SIS Epidemic Model with Markovian Switching

The SIS Epidemic Model with Markovian Switching The SIS Epidemic with Markovian Switching Department of Mathematics and Statistics University of Strathclyde Glasgow, G1 1XH (Joint work with A. Gray, D. Greenhalgh and J. Pan) Outline Motivation 1 Motivation

More information

G(θ) = max{g 1 (θ), G 2 (θ)}

G(θ) = max{g 1 (θ), G 2 (θ)} Rec. ITU-R F.1336 1 RECOMMENDATION ITU-R F.1336* Rec. ITU-R F.1336 REFERENCE RADIATION PATTERNS OF OMNIDIRECTIONAL AND OTHER ANTENNAS IN POINT-TO-MULTIPOINT SYSTEMS FOR USE IN SHARING STUDIES (Question

More information

Chapter 7: Superposition

Chapter 7: Superposition Chapter 7: Superposition Introduction The wave equation is linear, that is if ψ 1 (x, t) ψ 2 (x, t) satisfy the wave equation, then so does ψ(x, t) = ψ 1 (x, t) + ψ 2 (x, t). This suggests the Principle

More information

Linear and nonlinear resonance in viscous film flow over topography

Linear and nonlinear resonance in viscous film flow over topography Linear and nonlinear resonance in viscous film flow over topography N. Aksel 1, V. Bontozoglou 2, H. Uecker 3, A. Wierschem 4, C. Heining 1 1 University of Bayreuth, Department of Applied Mechanics and

More information

Methods - Solutions to Sheet B

Methods - Solutions to Sheet B Methods - Solutions to Sheet B 1. Equation is u t + u = 0 with, t > 0 and u(0, t) = sin t and u(, 0) = sin. First parametrise PDE: ds = 1...(1); d ds = 1...(2); du ds = ds u t + d ds u = 0...(3) Net, parametrise

More information

Lecture 6. Capacitance

Lecture 6. Capacitance Lectue 6 Capacitance In this lectue u will lean: Capacitance Capacitance f Sme Simple Stuctues Sme Simple Slutins f Laplace s Equatin Capacitance Cnsie tw metallic bjects cnnecte b a vltage suce ttal chage

More information

Curvature of double-membrane organelles generated by changes in membrane size and composition

Curvature of double-membrane organelles generated by changes in membrane size and composition Curvature of double-membrane organelles generated by changes in membrane size and composition Roland L. Knorr, Rumiana Dimova*, Reinhard Lipowsky Max Planck Institute of Colloids and Interfaces, Science

More information

X-Ray Diffraction. wavelength Electric field of light

X-Ray Diffraction. wavelength Electric field of light Light is composed of electromagnetic radiation with an electric component that modulates versus time perpendicular to the direction it is travelling (the magnetic component is also perpendicular to the

More information

Bayesian modeling of inseparable space-time variation in disease risk

Bayesian modeling of inseparable space-time variation in disease risk Bayesian modeling of inseparable space-time variation in disease risk Leonhard Knorr-Held Laina Mercer Department of Statistics UW May 23, 2013 Motivation Area and time-specific disease rates Area and

More information

Lorentzian Quantum Einstein Gravity

Lorentzian Quantum Einstein Gravity Lorentzian Quantum Einstein Gravity Stefan Rechenberger Uni Mainz 12.09.2011 Phys.Rev.Lett. 106 (2011) 251302 with Elisa Manrique and Frank Saueressig Stefan Rechenberger (Uni Mainz) Lorentzian Quantum

More information

THIS BOOK IS DESIGNED TO ENABLE FARM LIVESTOCK KEEPERS TO MEET THEIR LEGAL OBLIGATIONS

THIS BOOK IS DESIGNED TO ENABLE FARM LIVESTOCK KEEPERS TO MEET THEIR LEGAL OBLIGATIONS KEEPER/HOLDING - ADDRESS: TEL NO: HOLDING NO: HERD NO: THIS BOOK IS DESIGNED TO ENABLE FARM LIVESTOCK KEEPERS TO MEET THEIR LEGAL OBLIGATIONS These records may alternatively be kept on computer (and the

More information

Missing Data Approach to Handle Delayed Outcomes in Early

Missing Data Approach to Handle Delayed Outcomes in Early Missing Data Approach to Handle Delayed Outcomes in Early Phase Clinical Trials Department of Biostatistics The University of Texas, MD Anderson Cancer Center Outline Introduction Method Conclusion Background

More information

PETER G. CASAZZA AND GITTA KUTYNIOK

PETER G. CASAZZA AND GITTA KUTYNIOK A GENERALIZATION OF GRAM SCHMIDT ORTHOGONALIZATION GENERATING ALL PARSEVAL FRAMES PETER G. CASAZZA AND GITTA KUTYNIOK Abstract. Given an arbitrary finite sequence of vectors in a finite dimensional Hilbert

More information

Ellipsometry Data Analysis: a Tutorial

Ellipsometry Data Analysis: a Tutorial llipsometry Data Analysis: a Tutorial G.. Jellison, Jr. Solid State Division Oak Ridge National Laboratory WIS University of Michigan May 8-9, Motivation The Opportunity: Spectroscopic llipsometry (S is

More information

Equations and Example Benchmark Calculations for Emergency Scenario Required Relief Loads

Equations and Example Benchmark Calculations for Emergency Scenario Required Relief Loads WHITE PAPER Equations and Example Benchmark Calculations for Emergency Scenario Required Relief Loads V8.8: Control Valve Failure, Heat Exchanger Tube Rupture, Hydraulic Expansion and Fire Craig Powers,

More information

4.1: Angles and Radian Measure

4.1: Angles and Radian Measure 4.1: Angles and Radian Measure An angle is formed by two rays that have a common endpoint. One ray is called the initial side and the other is called the terminal side. The endpoint that they share is

More information

Paired Comparison Preference Models. The prefmod Package: Part I. Some Examples. Regina Dittrich & Reinhold Hatzinger. Paired Comparison Models

Paired Comparison Preference Models. The prefmod Package: Part I. Some Examples. Regina Dittrich & Reinhold Hatzinger. Paired Comparison Models 6.11.2010 1 Paired Comparison Models Paired Comparison Preference Models The prefmod Package: Part I Some Examples Regina Dittrich & Reinhold Hatzinger Department of Statistics and Mathematics, WU Vienna

More information

Discussion of Interbank Lending, Credit-Risk Premia, and Collateral

Discussion of Interbank Lending, Credit-Risk Premia, and Collateral Discussion of Interbank Lending, Credit-Risk Premia, and Collateral Ernst-Ludwig von Thadden University of Mannheim The paper by Heider and Hoerova (2009) is ambitious. It studies the interaction between

More information

Collateral Requirements and Asset Prices

Collateral Requirements and Asset Prices Collateral Requirements and Asset Prices J. Brumm, M. Grill, F. Kubler and K. Schmedders June 0th, 20 Motivation Two old ideas: Borrowing on collateral might enhance volatility of prices (e.g. Geanakoplos

More information

Examination 110 Probability and Statistics Examination

Examination 110 Probability and Statistics Examination Examination 0 Probability and Statistics Examination Sample Examination Questions The Probability and Statistics Examination consists of 5 multiple-choice test questions. The test is a three-hour examination

More information

Linear Speed and Angular Speed

Linear Speed and Angular Speed Preliminaries and Objectives Preliminaries: Circumference of a circle Conversion factors (dimensional analysis) Objectives: Given the central angle and radius (or diameter) of a circle, find the arc length

More information

The Center for Applied Probability Columbia University: Nov. 9, th Annual CAP Workshop on Derivative Securities and Risk Management

The Center for Applied Probability Columbia University: Nov. 9, th Annual CAP Workshop on Derivative Securities and Risk Management The Center for Applied Probability Columbia University: Nov. 9 00 8 th Annual CAP Workshop on Derivative Securities and Risk Management A Simple Option Formula for General Jump-Diffusion and other Exponential

More information

Gauss s law relates to total electric flux through a closed surface to the total enclosed charge.

Gauss s law relates to total electric flux through a closed surface to the total enclosed charge. Chapte : Gauss s Law Gauss s Law is an altenative fomulation of the elation between an electic field and the souces of that field in tems of electic flu. lectic Flu Φ though an aea ~ Numbe of Field Lines

More information

Normal distribution Approximating binomial distribution by normal 2.10 Central Limit Theorem

Normal distribution Approximating binomial distribution by normal 2.10 Central Limit Theorem 1.1.2 Normal distribution 1.1.3 Approimating binomial distribution by normal 2.1 Central Limit Theorem Prof. Tesler Math 283 October 22, 214 Prof. Tesler 1.1.2-3, 2.1 Normal distribution Math 283 / October

More information

AP CALCULUS AB 2008 SCORING GUIDELINES

AP CALCULUS AB 2008 SCORING GUIDELINES AP CALCULUS AB 2008 SCORING GUIDELINES Question 3 Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per

More information

Chapter 2 Effect Of A Lens

Chapter 2 Effect Of A Lens EE90F Chapter Eect O A Lens [Reading assignment: Goodman, Fourier Optics Ch. 5; 5.4 is optional ( xy, ) o 3 We consider the model o a thin lens, where we introduce a phase delay at (x, y) due to the lens

More information

Characterisation and prediction of stability of amorphous materials during pharmaceutical development: Pair-wise Distribution Function

Characterisation and prediction of stability of amorphous materials during pharmaceutical development: Pair-wise Distribution Function Characterisation and prediction of stability of amorphous materials during pharmaceutical development: Pair-wise Distribution Function Helen Blade, Steve Cosgrove, Jonathon Booth, Anne Kavanagh PAR&D,

More information

Relations and Functions

Relations and Functions Section 5. Relations and Functions 5.1. Cartesian Product 5.1.1. Definition: Ordered Pair Let A and B be sets and let a A and b B. An ordered pair ( a, b) is a pair of elements with the property that:

More information

Lecture 10: Other Continuous Distributions and Probability Plots

Lecture 10: Other Continuous Distributions and Probability Plots Lecture 10: Other Continuous Distributions and Probability Plots Devore: Section 4.4-4.6 Page 1 Gamma Distribution Gamma function is a natural extension of the factorial For any α > 0, Γ(α) = 0 x α 1 e

More information

Intersections of Polar Curves

Intersections of Polar Curves Intersections of Polar Curves The purpose of this supplement is to find a method for determining where graphs of polar equations intersect each other. Let s start with a fairly straightforward example.

More information

Stochastic Quantization of Topological Field Theory: Generalized Langevin Equation with Memory Kernel

Stochastic Quantization of Topological Field Theory: Generalized Langevin Equation with Memory Kernel : Generalized Langevin Equation with Memory Kernel Centro Brasileiro de Pesquisas Físicas -CBPF, Rua Dr. Xavier Sigaud 15, Rio de Janeiro, RJ, 9-18, Brazil E-mail: gsm@cbpf.br Nami F. Svaiter Centro Brasileiro

More information

UV/Vis (Ultraviolet and Visible) Spectroscopy

UV/Vis (Ultraviolet and Visible) Spectroscopy UV/Vis (Ultraviolet and Visible) Spectroscopy Agilent 8453 Diode Array UV-Vis Spectrophotometer Varian Cary 5000 UV-Vis-NIR Spectrophotometer To Do s Read Chapters 13 & 14. Complete the end-of-chapter

More information

Introduction to Computational Manifolds and Applications

Introduction to Computational Manifolds and Applications IMPA - Instituto de Matemática Pura e Aplicada, Rio de Janeiro, RJ, Brazil Introduction to Computational Manifolds and Applications Part 1 - Constructions Prof. Marcelo Ferreira Siqueira mfsiqueira@dimap.ufrn.br

More information

2010 HSC General Mathematics Sample Answers

2010 HSC General Mathematics Sample Answers 2010 HSC General Mathematics Sample Answers This document contains sample answers, or, in the case of some questions, answers could include. These are developed by the examination committee for two purposes.

More information

CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS

More information

Density Evolution. Telecommunications Laboratory. Alex Balatsoukas-Stimming. Technical University of Crete. October 21, 2009

Density Evolution. Telecommunications Laboratory. Alex Balatsoukas-Stimming. Technical University of Crete. October 21, 2009 Density Evolution Telecommunications Laboratory Alex Balatsoukas-Stimming Technical University of Crete October 21, 2009 Telecommunications Laboratory (TUC) Density Evolution October 21, 2009 1 / 27 Outline

More information

General Physics (PHY 2130)

General Physics (PHY 2130) General Physics (PHY 2130) Lecture 28 Waves standing waves Sound definitions standing sound waves and instruments Doppler s effect http://www.physics.wayne.edu/~apetrov/phy2130/ Lightning Review Last lecture:

More information

Perimeter, Circumference, Area and Ratio Long-Term Memory Review

Perimeter, Circumference, Area and Ratio Long-Term Memory Review Review 1 1. Which procedure is used to find the perimeter of any polygon? A) Add all the lengths B) Multiply length times width ( l w ) C) Add only one length and one width D) Multiply all of the lengths

More information

Internet Traffic Performance in High Speed Trains 1

Internet Traffic Performance in High Speed Trains 1 Internet Traffic Performance in High Speed Trains 1 Dmitry Sivchenko a, Bangnan Xu a, Gerd Zimmermann a, Sven Hischke b a T-Systems, Technologiezentrum, Am Kavalleriesand 3, D-64295 Darmstadt, Germany

More information

Passive Optical Resonators

Passive Optical Resonators Passive Optical Resonators Optical Cavities and Feedback Back mirror I 0 I 1 Laser medium with gain, G Output mirror I 3 R = 100% R < 100% I 2 Cavities are essential components of the lasers. They provide

More information

Pre-Calculus II. where 1 is the radius of the circle and t is the radian measure of the central angle.

Pre-Calculus II. where 1 is the radius of the circle and t is the radian measure of the central angle. Pre-Calculus II 4.2 Trigonometric Functions: The Unit Circle The unit circle is a circle of radius 1, with its center at the origin of a rectangular coordinate system. The equation of this unit circle

More information

it s refraction, it s diffraction, it s a kinoform lens - new concepts in focusing x-rays detlef smilgies chess

it s refraction, it s diffraction, it s a kinoform lens - new concepts in focusing x-rays detlef smilgies chess it s refraction, it s diffraction, it s a kinoform lens - new concepts in focusing x-rays detlef smilgies chess what is a lens? incoherent source > geometric optics > refraction Snell s law > lensmaker

More information

Number Systems I. CIS008-2 Logic and Foundations of Mathematics. David Goodwin. 11:00, Tuesday 18 th October

Number Systems I. CIS008-2 Logic and Foundations of Mathematics. David Goodwin. 11:00, Tuesday 18 th October Number Systems I CIS008-2 Logic and Foundations of Mathematics David Goodwin david.goodwin@perisic.com 11:00, Tuesday 18 th October 2011 Outline 1 Number systems Numbers Natural numbers Integers Rational

More information

CS540 Machine learning Lecture 14 Mixtures, EM, Non-parametric models

CS540 Machine learning Lecture 14 Mixtures, EM, Non-parametric models CS540 Machine learning Lecture 14 Mixtures, EM, Non-parametric models Outline Mixture models EM for mixture models K means clustering Conditional mixtures Kernel density estimation Kernel regression GMM

More information

Lab M1: The Simple Pendulum

Lab M1: The Simple Pendulum Lab M1: The Simple Pendulum Introduction. The simple pendulum is a favorite introductory exercise because Galileo's experiments on pendulums in the early 1600s are usually regarded as the beginning of

More information

THREE DIMENSIONAL GEOMETRY

THREE DIMENSIONAL GEOMETRY Chapter 11 THREE DIMENSIONAL GEOMETRY 111 Overview 1111 Direction cosines of a line are the cosines of the angles made by the line with positive directions of the co-ordinate axes 111 If l, m, n are the

More information

Systematic risk of of mortality on on an an annuity plan

Systematic risk of of mortality on on an an annuity plan www.winter-associes.fr Systematic risk of of mortality on on an an annuity plan Version Version 1.0 1.0 Frédéric PLANCHET / Marc JUILLARD / Laurent FAUCILLON ISFA WINTER & Associés July 2006 Page 1 Motivations

More information

Math 2250 Exam #1 Practice Problem Solutions. g(x) = x., h(x) =

Math 2250 Exam #1 Practice Problem Solutions. g(x) = x., h(x) = Math 50 Eam # Practice Problem Solutions. Find the vertical asymptotes (if any) of the functions g() = + 4, h() = 4. Answer: The only number not in the domain of g is = 0, so the only place where g could

More information

arxiv: v1 [hep-th] 3 Dec 2012

arxiv: v1 [hep-th] 3 Dec 2012 Thermal soliton correlation functions in theories with a Z(N) symmetry Leonardo Mondaini Grupo de Física Teórica e Experimental, Departamento de Ciências Naturais, arxiv:1212.0438v1 [hep-th] 3 Dec 2012

More information

Theta Functions. Lukas Lewark. Seminar on Modular Forms, 31. Januar 2007

Theta Functions. Lukas Lewark. Seminar on Modular Forms, 31. Januar 2007 Theta Functions Lukas Lewark Seminar on Modular Forms, 31. Januar 007 Abstract Theta functions are introduced, associated to lattices or quadratic forms. Their transformation property is proven and the

More information

The determinant of a skew-symmetric matrix is a square. This can be seen in small cases by direct calculation: 0 a. 12 a. a 13 a 24 a 14 a 23 a 14

The determinant of a skew-symmetric matrix is a square. This can be seen in small cases by direct calculation: 0 a. 12 a. a 13 a 24 a 14 a 23 a 14 4 Symplectic groups In this and the next two sections, we begin the study of the groups preserving reflexive sesquilinear forms or quadratic forms. We begin with the symplectic groups, associated with

More information

Examination paper for Solutions to Matematikk 4M and 4N

Examination paper for Solutions to Matematikk 4M and 4N Department of Mathematical Sciences Examination paper for Solutions to Matematikk 4M and 4N Academic contact during examination: Trygve K. Karper Phone: 99 63 9 5 Examination date:. mai 04 Examination

More information

Sufficient Statistics and Exponential Family. 1 Statistics and Sufficient Statistics. Math 541: Statistical Theory II. Lecturer: Songfeng Zheng

Sufficient Statistics and Exponential Family. 1 Statistics and Sufficient Statistics. Math 541: Statistical Theory II. Lecturer: Songfeng Zheng Math 541: Statistical Theory II Lecturer: Songfeng Zheng Sufficient Statistics and Exponential Family 1 Statistics and Sufficient Statistics Suppose we have a random sample X 1,, X n taken from a distribution

More information

Collapsing 3-manifolds

Collapsing 3-manifolds Collapsing 3-manifolds L. Bessières, G. Besson, M. Boileau, S. Maillot, J. Porti 4th William Rowan Hamilton Geometry and Topology Workshop HMI, TCD August 29, 2008 Collapsing 3-manifolds p.1/15 Main Theorem

More information

6.1: Angle Measure in degrees

6.1: Angle Measure in degrees 6.1: Angle Measure in degrees How to measure angles Numbers on protractor = angle measure in degrees 1 full rotation = 360 degrees = 360 half rotation = quarter rotation = 1/8 rotation = 1 = Right angle

More information

QVALUE: The Manual Version 1.0

QVALUE: The Manual Version 1.0 QVALUE: The Manual Version 1.0 Alan Dabney and John D. Storey Department of Biostatistics University of Washington Email: jstorey@u.washington.edu March 2003; Updated June 2003; Updated January 2004 Table

More information

Fading multipath radio channels

Fading multipath radio channels Fading multipath radio channels Narrowband channel modelling Wideband channel modelling Wideband WSSUS channel (functions, variables & distributions) Low-pass equivalent (LPE) signal ( ) = Re ( ) s t RF

More information

Lecture 11: Graphical Models for Inference

Lecture 11: Graphical Models for Inference Lecture 11: Graphical Models for Inference So far we have seen two graphical models that are used for inference - the Bayesian network and the Join tree. These two both represent the same joint probability

More information

Wheels Diameter / Distance Traveled

Wheels Diameter / Distance Traveled Mechanics Teacher Note to the teacher On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions and distance. Students will use formulas relating

More information

0.1 Dielectric Slab Waveguide

0.1 Dielectric Slab Waveguide 0.1 Dielectric Slab Waveguide At high frequencies (especially optical frequencies) the loss associated with the induced current in the metal walls is too high. A transmission line filled with dielectric

More information

Traces of high powers of the Frobenius class in the hyperelliptic ensemble

Traces of high powers of the Frobenius class in the hyperelliptic ensemble ACTA ARITHMETICA 143.1 (2010) Traces of high powers of the Frobenius class in the hyperelliptic ensemble by Zeév Rudnick (Tel Aviv and Princeton, NJ) 1. Introduction. Fix a finite field F q of odd cardinality,

More information

Week #15 - Word Problems & Differential Equations Section 8.1

Week #15 - Word Problems & Differential Equations Section 8.1 Week #15 - Word Problems & Differential Equations Section 8.1 From Calculus, Single Variable by Hughes-Hallett, Gleason, McCallum et. al. Copyright 25 by John Wiley & Sons, Inc. This material is used by

More information

AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity

AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity 7.1 Electromagnetic Radiation A. Types of EM Radiation (wavelengths in meters) 10-1 10-10 10-8 4 to 7x10-7 10-4 10-1 10 10 4 gamma

More information

CRN TECNOPART, S.A. SERIE HD 2021T TRANSMITTERS FOR ILLUMINANCE AND IRRADIANCE MEASUREMENTS.

CRN TECNOPART, S.A. SERIE HD 2021T TRANSMITTERS FOR ILLUMINANCE AND IRRADIANCE MEASUREMENTS. Kkkk CRN TECNOPART, S.A. Sant Roc 30 08340 VILASSAR DE MAR (Barcelona) Tel 902 404 748-937 591 484 Fax 937 591 547 e-mail:crn@crntp.com http:// www.crntecnopart.com DO-070.63E HD 2021T TRANSMITTERS FOR

More information

1 Online Educational Portal

1 Online Educational Portal VERY SHORT ANSWER TYPE QUESTIONS 1. Tick the correct answer in the following and justify your choice : 1. Mark the correct answer in the following. If the perimeter and area of a circle are numerically

More information

KINETIC THEORY OF GASES. Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure.

KINETIC THEORY OF GASES. Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure. KINETIC THEORY OF GASES Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure. Charle s Law: At constant pressure volume of a given mass of gas is directly

More information

Fundamentals of Geometry

Fundamentals of Geometry 10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount

More information

EconS 301 Review Session #8 Chapter 11: Monopoly and Monopsony

EconS 301 Review Session #8 Chapter 11: Monopoly and Monopsony EconS 301 Review Session #8 Chapter 11: Monopoly and Monopsony 1. Which of the following describes a correct relation between price elasticity of demand and a monopolist s marginal revenue when inverse

More information

Electromagnetic acceleration of permanent magnets

Electromagnetic acceleration of permanent magnets Electromagnetic acceleration of permanent magnets S. N. Dolya Joint Institute for Nuclear Research, Joliot - Curie 6, Dubna, Russia, 141980 Abstract We consider the acceleration of the permanent magnets,

More information

TUNABLE TRAFFIC CONTROL FOR MULTIHOP CSMA NETWORKS. Zhefu Shi, Cory Beard, Ken Mitchell University of Missouri-Kansas City

TUNABLE TRAFFIC CONTROL FOR MULTIHOP CSMA NETWORKS. Zhefu Shi, Cory Beard, Ken Mitchell University of Missouri-Kansas City TUNABLE TRAFFIC CONTROL FOR MULTIHOP CSMA NETWORKS Zhefu Shi, Cory Beard, Ken Mitchell University of Missouri-Kansas City ABSTRACT A new analytical model for multihop CSMA networks is presented, using

More information

Physics 403: Relativity Takehome Final Examination Due 07 May 2007

Physics 403: Relativity Takehome Final Examination Due 07 May 2007 Physics 403: Relativity Takehome Final Examination Due 07 May 2007 1. Suppose that a beam of protons (rest mass m = 938 MeV/c 2 of total energy E = 300 GeV strikes a proton target at rest. Determine the

More information

Math 2015 Lesson 21. We discuss the mean and the median, two important statistics about a distribution. p(x)dx = 0.5

Math 2015 Lesson 21. We discuss the mean and the median, two important statistics about a distribution. p(x)dx = 0.5 ean and edian We discuss the mean and the median, two important statistics about a distribution. The edian The median is the halfway point of a distribution. It is the point where half the population has

More information

Measuring the tracking error of exchange traded funds: an unobserved components approach

Measuring the tracking error of exchange traded funds: an unobserved components approach Measuring the tracking error of exchange traded funds: an unobserved components approach Giuliano De Rossi Quantitative analyst +44 20 7568 3072 UBS Investment Research June 2012 Analyst Certification

More information

Chapter : Part A:

Chapter : Part A: Objective Part A: Use the formula for circumference to solve real-world problems Circumference FORMULA: 1) A circular mat has a diameter of 53 centimeters. Lily wants to sew a decorative braid around the

More information

300 kv. Arendal. Pole 1 SVC 200 MVA FT1. Filter BP1. Feda. Pole 2 BP MVA, SC 132 kv 17 kv Krossen Steinsf. HP1. Electrode HP2.

300 kv. Arendal. Pole 1 SVC 200 MVA FT1. Filter BP1. Feda. Pole 2 BP MVA, SC 132 kv 17 kv Krossen Steinsf. HP1. Electrode HP2. Arendal Feda T1 SVC 200 MVA FT1 140 MVA, SC 132 kv 17 kv Krossen Steinsf. 300 kv KB1 KB2 KB3 Filter BP1 BP2 HP1 HP2 Pole 1 Pole 2 Electrode Pole 3 T Z=R+jX C L jx f 2 f f 1 R 160 Mvar 300 kv 150 kv 2940

More information

AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)

AREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square

More information

Bonus-Malus System in Iran: An Empirical Evaluation

Bonus-Malus System in Iran: An Empirical Evaluation Journal of Data Science 11(2013), 29-41 Bonus-Malus System in Iran: An Empirical Evaluation Rahim Mahmoudvand 1, Alireza Edalati 2 and Farhad Shokoohi 1 1 Shahid Beheshti University and 2 Institut für

More information

Measurement and Geometry: Perimeter and Circumference of Geometric Figures

Measurement and Geometry: Perimeter and Circumference of Geometric Figures OpenStax-CNX module: m35022 1 Measurement and Geometry: Perimeter and Circumference of Geometric Figures Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the Creative

More information

Common probability distributionsi Math 217/218 Probability and Statistics Prof. D. Joyce, 2016

Common probability distributionsi Math 217/218 Probability and Statistics Prof. D. Joyce, 2016 Introduction. ommon probability distributionsi Math 7/8 Probability and Statistics Prof. D. Joyce, 06 I summarize here some of the more common distributions used in probability and statistics. Some are

More information