NATIONAL RADIO ASTRONOMY OBSERVATORY SOCORRO, NEW MEXICO. VLA Test Memorandum No. 117 POINTING RUN - FEBRUARY 15-16, E. Fomalont.

Size: px
Start display at page:

Download "NATIONAL RADIO ASTRONOMY OBSERVATORY SOCORRO, NEW MEXICO. VLA Test Memorandum No. 117 POINTING RUN - FEBRUARY 15-16, E. Fomalont."

Transcription

1 NATIONAL RADIO ASTRONOMY OBSERVATORY SOCORRO, NEW MEXICO VLA Test Memorndum No. 117 POINTING RUN - FEBRUARY 15-16, 1977 E. Fomlont Februry 1977 Two twelve-hour periods of identicl pointing runs were mde on Februry to check the consistency of the telescope pointing. Three sources, 3C84, 3C120 nd 3C273 were observed in pointing mode t C nd K-Bnds. 1. Dy to Dy Pointing Consistency Pointing observtions were mde for 3 sources t C nd K-Bnd for telescope #2. The sources nd frequencies were interleved. A comprison of the two dys re shown in Figure 1. The difference in pointing between the two dys ppers to be function of time with excursions of -18" over severl hours. This behvior is independent of the source (i.e., position in the sky) nd frequency. The sctter bout smooth curve is ^±4". Pointing observtions of two dys for telescope #6 t C-Bnd only re shown in Figure 2. In this plot we hve shown the individul source observtions. The sctter is lrger here thn for telescope #2; however, there is systemtic difference of -12" in zimuth between the two dys. No significnt source dependence is suggested. 2. Frequency Dependence of the Pointing The pointing offset between C nd K-Bnds were mesured for telescope #2 nd #1. It is expected the offsets should be constnt. Results re given in Figure 3. For telescope #2 the pointing offsets re resonbly constnt over the two dys with sctter of -8", For telescope #1, however, the C to K elevtion offsets systemticlly chnges by ~40" over ten hours. The chnge does not pper to be significntly source dependent but is temporl in nture. The difference is minly cused by C-Bnd chnge in the elevtion pointing. Unfortuntely, telescope #1 operted on only one dy. The zimuth behvior is quite good on telescope #1.

2 3, Bem Offsets Between Right nd Left Circulr Polrizing The bem offsets were clibrted for severl ntenns nd frequencies nd re given below. (R-L) POINTING POSITIONS (ARC-MIN) C-BAND K-BAND Elev. Azim. Elev. Azim. Tel #1 #2. #6 #1 #2 #6 #1 #2 #1 #2 Offset ±0.02 ±0.02 ±0.04 ±0.02 ±0.01 ±0.01 ±0.01 ±0.01 ±0.01 ±0.01 As expected, the offsets re nonvrible nd scle roughly with wvelength. 4. Tenttive Conclusions With this limited dt it is cler tht the ntenn pointing behves in vriety of wys. ) In telescope #2 nd #6 there re temporl vritions of zimuth nd elevtion of ~18" on time scle of severl hours to dy. Lrger vritions over longer durtion re possible. These vritions seem to be independent of frequency for telescope #2. b) The elevtion offset in pointing between two frequencies vried by ~40" over 10 hours for telescope #1. This offset chnge ws temporl in nture nd seems to be unrelted to detiled subreflector motion or position in sky. However, such n effect plys hvoc with the determintion of collimtion differences between frequencies. The collimtion differences between C nd K for telescope #2 nd zimuth #1 ws well behved, i.e., constnt.with sctter of ±10". c) The Right-Left point difference is very stble nd 2

3 virtully identicl for ech telescope. It does not scle precisely with observing wvelength. These results suggest tht most of the pointing problem is temporl in nture nd my be relted to heting effects on dish nd subreflector, encoder drifts Detiled subreflector motion errors do not pper to be importnt. 5. Hlf-Power Bem-widths The bem-width t K-Bnd is nomlous for ntenn #1. The following tble shows the derived hlf-power width. HALF-POWER BEAM-WIDTHS (ARC-MIN) Telescope Freq. Elev. Width Azim. Width 1 C K C K C K-Bnd Elevtion Dependence Bseline 2-4 shows well-defined gin - elevtion i dependence. Observtions of two dys were combined with, 1 three sources ech scled inversely by their flux density rtio. This plot is shown in Figure 4. The sctter bout men line is ~5%. The dependence shows mrked decrese for elevtions less thn 25%, pek sensitivity t elevtion nd moderte drop towrds zenith. t low elevtion is bout equl to q»10% tmospheric ttenution (1+q sec z)/(l+q). The drop off Bseline 2-1 shows much poorer gin - elevtion dependence. This is nticipted by the strnge K-Bnd bem shpe for telescope 1 discussed in Section 5, is n zimuth dependence of the "gin There elevtion" behvior. Correction for system temperture chnges hve not been in ve s t i gt ed. 3

4 ret. mut blo/ (<*y d ^ * K-M'/b 0,1 1- f* S? H cj Oj o ~ i -OA \! t 4~ f + 4- i» + -OA! -03 HfP/m//? T jr i 7 t 1 /o // /z ) ^ / 6.6 OJ 4- * b -f- + -b- L7T ^<3 '

5 T L * L L sj (d*y I- JyZ) p }ciid 3c sq * 3c^y3 d.d I- P + r L$>> <f (> 7 % /c ^ TeL m i j? f, f f f f L^T & b 1 i i //

6 » r ^ Ju -. -b J, * ox \ L t* I SL fd'ssr/s/c CC~ of \ of o. 3 I trc it A. eu rowrinc * -o. 1 o.3> T C # I $irc*$el CC-K) Z- o.d 3? lo // IT-

7 \oo A. o3c(z 0 2 \0% w o A 0 D 0 TS'V 2 2rV?2> / 1 <10 2 / J?- 4 / K&/f*9> x. : ScALe "v - --'V -V two fyfocttt/c 3-t K&s*jp O O ^ A 4 d u 0 W 'v! 1 0 A 0 Q 10 io Jl ci 7o rt y *

8

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Entropy ISSN

Entropy ISSN Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

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

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we

More information

DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS

DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS V. N. Melnik *,H.O.Rucker, A. A. Konovlenko, V. V. Dorovskyy, E. P. Abrnin, nd A. Leccheux Abstrct We present n overview of the recent results in

More information

L35-Wed-23-Nov-2016-Sec-5-5-Properties-of-Logs-HW36-Moodle-Q29

L35-Wed-23-Nov-2016-Sec-5-5-Properties-of-Logs-HW36-Moodle-Q29 L35-Wed-3-Nov-016-Sec-5-5-Properties-of-Logs-HW36-Moodle-Q9 pge 49 L35-Wed-3-Nov-016-Sec-5-5-Properties-of-Logs-HW36-Moodle-Q9 We hve looked t severl chrcteristics of the log function. Now, we will look

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

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

f(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral

f(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral Improper Integrls Every time tht we hve evluted definite integrl such s f(x) dx, we hve mde two implicit ssumptions bout the integrl:. The intervl [, b] is finite, nd. f(x) is continuous on [, b]. If one

More information

N-2140 Sound Propagation

N-2140 Sound Propagation Pink noise, in contrst, is defined s hving the sme mplitude for ech octve bnd (or third-octve bnd), rther thn for ech frequency intervl. Its octve or third-octve bnd spectrum is truly stright, level line

More information

#6A&B Magnetic Field Mapping

#6A&B Magnetic Field Mapping #6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by

More information

Key comparison BIPM.RI(I)-K2 of the air-kerma standards of the PTB, Germany and the BIPM in low-energy x-rays

Key comparison BIPM.RI(I)-K2 of the air-kerma standards of the PTB, Germany and the BIPM in low-energy x-rays Key comprison BIPM.RI(I)-K2 of the ir-kerm stndrds of the PTB, Germny nd the BIPM in low-energy x-rys D.T. Burns 1, C Kessler 1 nd L Büermnn 2 1 Bureu Interntionl des Poids et Mesures, Pvillon de Breteuil,

More information

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite

Goals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite

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

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

Families of Solutions to Bernoulli ODEs

Families of Solutions to Bernoulli ODEs In the fmily of solutions to the differentil eqution y ry dx + = it is shown tht vrition of the initil condition y( 0 = cuses horizontl shift in the solution curve y = f ( x, rther thn the verticl shift

More information

Determination of the activation energy of silicone rubbers using different kinetic analysis methods

Determination of the activation energy of silicone rubbers using different kinetic analysis methods Determintion of the ctivtion energy of silicone rubbers using different kinetic nlysis methods OU Huibin SAHLI ohmed BAIEE Thierry nd GELIN Jen-Clude FETO-ST Institute / Applied echnics Deprtment, 2 rue

More information

WMAP satellite. 16 Feb Feb Feb 2012

WMAP satellite. 16 Feb Feb Feb 2012 16 Feb 2012 21 Feb 2012 23 Feb 2012 è Announcements è Problem 5 (Hrtle 18.3). Assume V * is nonreltivistic. The reltivistic cse requires more complicted functions. è Outline è WMAP stellite è Dipole nisotropy

More information

Applications of Bernoulli s theorem. Lecture - 7

Applications of Bernoulli s theorem. Lecture - 7 Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.

More information

Intro to Nuclear and Particle Physics (5110)

Intro to Nuclear and Particle Physics (5110) Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41

More information

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? PhysicsndMthsTutor.com 25 Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? 972//M/J/2 frequency speed (in vcuum) decreses

More information

Math Calculus with Analytic Geometry II

Math Calculus with Analytic Geometry II orem of definite Mth 5.0 with Anlytic Geometry II Jnury 4, 0 orem of definite If < b then b f (x) dx = ( under f bove x-xis) ( bove f under x-xis) Exmple 8 0 3 9 x dx = π 3 4 = 9π 4 orem of definite Problem

More information

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system Supplementry Mteril for Wve-pinning nd cell polrity from bistble rection-diffusion system Yoichiro Mori, Alendr Jilkine nd Leh Edelstein-Keshet Model Comprisons We concentrte here the three systems to

More information

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt

More information

Part I: Basic Concepts of Thermodynamics

Part I: Basic Concepts of Thermodynamics Prt I: Bsic Concepts o Thermodynmics Lecture 4: Kinetic Theory o Gses Kinetic Theory or rel gses 4-1 Kinetic Theory or rel gses Recll tht or rel gses: (i The volume occupied by the molecules under ordinry

More information

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION 19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, -7 SEPTEMBER 007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION PACS: 3.5.Uv Gudr, Tdeusz 1 ; Perkowski, Dniel ; Opielinski,

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

Introduction to Astrophysics

Introduction to Astrophysics PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT

More information

interatomic distance

interatomic distance Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule

More information

Synoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences?

Synoptic Meteorology I: Finite Differences September Partial Derivatives (or, Why Do We Care About Finite Differences? Synoptic Meteorology I: Finite Differences 16-18 September 2014 Prtil Derivtives (or, Why Do We Cre About Finite Differences?) With the exception of the idel gs lw, the equtions tht govern the evolution

More information

Kepler's Three LAWS. Universal Gravitation Chapter 12. Heliocentric Model. Geocentric Model. Other Models. Johannes Kepler

Kepler's Three LAWS. Universal Gravitation Chapter 12. Heliocentric Model. Geocentric Model. Other Models. Johannes Kepler Universl Grvittion Chpter 1 Johnnes Kepler Johnnes Kepler ws Germn mthemticin, stronomer nd strologer, nd key figure in the 17th century Scientific revolution. He is best known for his lws of plnetry motion,

More information

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40 Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since

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

+ x 2 dω 2 = c 2 dt 2 +a(t) [ 2 dr 2 + S 1 κx 2 /R0

+ x 2 dω 2 = c 2 dt 2 +a(t) [ 2 dr 2 + S 1 κx 2 /R0 Notes for Cosmology course, fll 2005 Cosmic Dynmics Prelude [ ds 2 = c 2 dt 2 +(t) 2 dx 2 ] + x 2 dω 2 = c 2 dt 2 +(t) [ 2 dr 2 + S 1 κx 2 /R0 2 κ (r) 2 dω 2] nd x = S κ (r) = r, R 0 sin(r/r 0 ), R 0 sinh(r/r

More information

Simulation of Eclipsing Binary Star Systems. Abstract

Simulation of Eclipsing Binary Star Systems. Abstract Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

MA 124 January 18, Derivatives are. Integrals are.

MA 124 January 18, Derivatives are. Integrals are. MA 124 Jnury 18, 2018 Prof PB s one-minute introduction to clculus Derivtives re. Integrls re. In Clculus 1, we lern limits, derivtives, some pplictions of derivtives, indefinite integrls, definite integrls,

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper. MEDICAL PHYSICS: Physics of Living Systems 2 2 HOURS

Data Provided: A formula sheet and table of physical constants is attached to this paper. MEDICAL PHYSICS: Physics of Living Systems 2 2 HOURS Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. Ancillry Mteril: None DEPARTMENT OF PHYSICS AND ASTRONOMY Spring Semester (2015/2016) MEDICAL PHYSICS: Physics of Living

More information

Introduction to Astrophysics

Introduction to Astrophysics PHY104 PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT

More information

Unit Six AP Calculus Unit 6 Review Definite Integrals. Name Period Date NON-CALCULATOR SECTION

Unit Six AP Calculus Unit 6 Review Definite Integrals. Name Period Date NON-CALCULATOR SECTION Unit Six AP Clculus Unit 6 Review Definite Integrls Nme Period Dte NON-CALCULATOR SECTION Voculry: Directions Define ech word nd give n exmple. 1. Definite Integrl. Men Vlue Theorem (for definite integrls)

More information

20 MATHEMATICS POLYNOMIALS

20 MATHEMATICS POLYNOMIALS 0 MATHEMATICS POLYNOMIALS.1 Introduction In Clss IX, you hve studied polynomils in one vrible nd their degrees. Recll tht if p(x) is polynomil in x, the highest power of x in p(x) is clled the degree of

More information

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block

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

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:

More information

The Thermodynamics of Aqueous Electrolyte Solutions

The Thermodynamics of Aqueous Electrolyte Solutions 18 The Thermodynmics of Aqueous Electrolyte Solutions As discussed in Chpter 10, when slt is dissolved in wter or in other pproprite solvent, the molecules dissocite into ions. In queous solutions, strong

More information

AN IMPROVED SMALL CLOSED DRIFT THRUSTER WITH BOTH CONDUCTING AND DIELECT RIC CHANNELS

AN IMPROVED SMALL CLOSED DRIFT THRUSTER WITH BOTH CONDUCTING AND DIELECT RIC CHANNELS AN IMPROVED SMALL CLOSED DRIFT THRUSTER WITH BOTH CONDUCTING AND DIELECT RIC CHANNELS A.I.Bugrov, A.D.Desitskov, H.R.Kufmn, V.K.Khrchevnikov, A.I.Morozov c, V.V.Zhurin d Moscow Institute of Rdioelectronics,

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

Section 5.5 from Basic Mathematics Review by Oka Kurniawan was developed by OpenStax College, licensed by Rice University, and is available on the

Section 5.5 from Basic Mathematics Review by Oka Kurniawan was developed by OpenStax College, licensed by Rice University, and is available on the Section 5.5 from Bsic Mthemtics Review by Ok Kurniwn ws developed by OpenStx College, licensed by Rice University, nd vilble on the Connexions website. It used under Cretive Commons Attribution 3.0 Unported

More information

This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2

This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2 1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion

More information

An approximation to the arithmetic-geometric mean. G.J.O. Jameson, Math. Gazette 98 (2014), 85 95

An approximation to the arithmetic-geometric mean. G.J.O. Jameson, Math. Gazette 98 (2014), 85 95 An pproximtion to the rithmetic-geometric men G.J.O. Jmeson, Mth. Gzette 98 (4), 85 95 Given positive numbers > b, consider the itertion given by =, b = b nd n+ = ( n + b n ), b n+ = ( n b n ) /. At ech

More information

Experiments with a Single Factor: The Analysis of Variance (ANOVA) Dr. Mohammad Abuhaiba 1

Experiments with a Single Factor: The Analysis of Variance (ANOVA) Dr. Mohammad Abuhaiba 1 Experiments with Single Fctor: The Anlsis of Vrince (ANOVA) Dr. Mohmmd Abuhib 1 Wht If There Are More Thn Two Fctor Levels? The t-test does not directl ppl There re lots of prcticl situtions where there

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

Improper Integrals. Type I Improper Integrals How do we evaluate an integral such as

Improper Integrals. Type I Improper Integrals How do we evaluate an integral such as Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph

More information

Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION

Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly.

More information

Hints for Exercise 1 on: Current and Resistance

Hints for Exercise 1 on: Current and Resistance Hints for Exercise 1 on: Current nd Resistnce Review the concepts of: electric current, conventionl current flow direction, current density, crrier drift velocity, crrier numer density, Ohm s lw, electric

More information

ESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability

ESCI 343 Atmospheric Dynamics II Lesson 14 Inertial/slantwise Instability ESCI 343 Atmospheric Dynmics II Lesson 14 Inertil/slntwise Instbility Reference: An Introduction to Dynmic Meteorology (3 rd edition), J.R. Holton Atmosphere-Ocen Dynmics, A.E. Gill Mesoscle Meteorology

More information

Pressure Wave Analysis of a Cylindrical Drum

Pressure Wave Analysis of a Cylindrical Drum Pressure Wve Anlysis of Cylindricl Drum Chris Clrk, Brin Anderson, Brin Thoms, nd Josh Symonds Deprtment of Mthemtics The University of Rochester, Rochester, NY 4627 (Dted: December, 24 In this pper, hypotheticl

More information

Adaptive optics performance model for optical interferometry

Adaptive optics performance model for optical interferometry Adptive optics performnce model for opticl interferometry D. Mozurkewich, 1 S. R. Restino, 2 J. T. Armstrong, 2, * nd G. C. Gilbreth 2 1 Sebrook Engineering, 9310 Dubrry Avenue, Sebrook, Mrylnd 20706,

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

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T Version 001 HW#6 - lectromgnetic Induction rts (00224) 1 This print-out should hve 12 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. AP 1998

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

Mathcad Lecture #1 In-class Worksheet Mathcad Basics

Mathcad Lecture #1 In-class Worksheet Mathcad Basics Mthcd Lecture #1 In-clss Worksheet Mthcd Bsics At the end of this lecture, you will be ble to: Evlute mthemticl epression numericlly Assign vrible nd use them in subsequent clcultions Distinguish between

More information

dt. However, we might also be curious about dy

dt. However, we might also be curious about dy Section 0. The Clculus of Prmetric Curves Even though curve defined prmetricly my not be function, we cn still consider concepts such s rtes of chnge. However, the concepts will need specil tretment. For

More information

Fast Feedback Reactivity Effects

Fast Feedback Reactivity Effects SUPPLEMENT TO CHAPTER 12 OF REACTOR PHYSICS FUNDAMENTALS This supplement summrizes some key physics principles in the text nd expnds on the mthemticl tretment. You should be milir with the text mteril

More information

Estimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor

Estimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor Glyndŵr University Reserch Online Conference Presenttion Estimtion of the prticle concentrtion in hydrulic liquid by the in-line utomtic prticle counter bsed on the CMOS imge sensor Kornilin, D.V., Kudryvtsev,

More information

Introduction to Astrophysics

Introduction to Astrophysics PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT

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

Math 131. Numerical Integration Larson Section 4.6

Math 131. Numerical Integration Larson Section 4.6 Mth. Numericl Integrtion Lrson Section. This section looks t couple of methods for pproimting definite integrls numericlly. The gol is to get good pproimtion of the definite integrl in problems where n

More information

Rates of chemical reactions

Rates of chemical reactions Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn

More information

1 The Riemann Integral

1 The Riemann Integral The Riemnn Integrl. An exmple leding to the notion of integrl (res) We know how to find (i.e. define) the re of rectngle (bse height), tringle ( (sum of res of tringles). But how do we find/define n re

More information

Exponentials & Logarithms Unit 8

Exponentials & Logarithms Unit 8 U n i t 8 AdvF Dte: Nme: Eponentils & Logrithms Unit 8 Tenttive TEST dte Big ide/lerning Gols This unit begins with the review of eponent lws, solving eponentil equtions (by mtching bses method nd tril

More information

Today in Astronomy 142: general relativity and the Universe

Today in Astronomy 142: general relativity and the Universe Tody in Astronomy 14: generl reltivity nd the Universe The Robertson- Wlker metric nd its use. The Friedmnn eqution nd its solutions. The ges nd ftes of flt universes The cosmologicl constnt. Glxy cluster

More information

Section 6: Area, Volume, and Average Value

Section 6: Area, Volume, and Average Value Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find

More information

Math 42 Chapter 7 Practice Problems Set B

Math 42 Chapter 7 Practice Problems Set B Mth 42 Chpter 7 Prctice Problems Set B 1. Which of the following functions is solution of the differentil eqution dy dx = 4xy? () y = e 4x (c) y = e 2x2 (e) y = e 2x (g) y = 4e2x2 (b) y = 4x (d) y = 4x

More information

First Semester Review Calculus BC

First Semester Review Calculus BC First Semester Review lculus. Wht is the coordinte of the point of inflection on the grph of Multiple hoice: No lcultor y 3 3 5 4? 5 0 0 3 5 0. The grph of piecewise-liner function f, for 4, is shown below.

More information

(See Notes on Spontaneous Emission)

(See Notes on Spontaneous Emission) ECE 240 for Cvity from ECE 240 (See Notes on ) Quntum Rdition in ECE 240 Lsers - Fll 2017 Lecture 11 1 Free Spce ECE 240 for Cvity from Quntum Rdition in The electromgnetic mode density in free spce is

More information

On the Linear Stability of Compound Capillary Jets

On the Linear Stability of Compound Capillary Jets ILASS Americs, th Annul Conference on Liquid Atomiztion nd Spry Systems, Chicgo, IL, My 7 On the Liner Stbility of Compound Cpillry Jets Mksud (Mx) Ismilov, Stephen D Heister School of Aeronutics nd Astronutics,

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

7/19/2011. Models of Solution Chemistry- III Acids and Bases

7/19/2011. Models of Solution Chemistry- III Acids and Bases Models of Solution Chemistry- III Acids nd Bses Ionic Atmosphere Model : Revisiting Ionic Strength Ionic strength - mesure of totl concentrtion of ions in the solution Chpter 8 1 2 i μ ( ) 2 c i z c concentrtion

More information

Key comparison BIPM.RI(I)-K7 of the air-kerma standards of the ENEA-INMRI, Italy and the BIPM in mammography x-rays

Key comparison BIPM.RI(I)-K7 of the air-kerma standards of the ENEA-INMRI, Italy and the BIPM in mammography x-rays Key comprison BIPM.RI(I)-K7 of the ir-kerm stndrds of the ENEA-INMRI, Itly nd the BIPM in mmmogrphy x-rys C Kessler, D T Burns, P Roger, M P Toni*, M Pinto*, M Bovi*, G Cppdozzi*, C Silvestri* Bureu Interntionl

More information

Vertical uniformity of cells and nuclei in epithelial monolayers

Vertical uniformity of cells and nuclei in epithelial monolayers Supplementry informtion Verticl uniformity of cells nd nuclei in epithelil monolyers Srujn Neelm b, Peter Hyes, Qio Zhng, Richrd B. Dickinson nd Tnmy P. Lele, Figure S1. Histogrm plots compre the frequency

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

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

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

Review of basic calculus

Review of basic calculus Review of bsic clculus This brief review reclls some of the most importnt concepts, definitions, nd theorems from bsic clculus. It is not intended to tech bsic clculus from scrtch. If ny of the items below

More information

UNIT 3 Indices and Standard Form Activities

UNIT 3 Indices and Standard Form Activities UNIT 3 Indices nd Stndrd Form Activities Activities 3.1 Towers 3.2 Bode's Lw 3.3 Mesuring nd Stndrd Form 3.4 Stndrd Inde Form Notes nd Solutions (1 pge) ACTIVITY 3.1 Towers How mny cubes re needed to build

More information

Understanding the relationship between floral fragrance, ethylene production and vase life of cut rose flowers

Understanding the relationship between floral fragrance, ethylene production and vase life of cut rose flowers Ethylene, Frgrnce nd Vse Life of Cut Rose Flowers 9/27/216 Progress Report Understnding the reltionship between florl frgrnce, ethylene production nd vse life of cut rose flowers An Mri Bord Dvid Clrk

More information

The graphs of Rational Functions

The graphs of Rational Functions Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior

More information

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

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 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,

More information

Terminal Velocity and Raindrop Growth

Terminal Velocity and Raindrop Growth Terminl Velocity nd Rindrop Growth Terminl velocity for rindrop represents blnce in which weight mss times grvity is equl to drg force. F 3 π3 ρ L g in which is drop rdius, g is grvittionl ccelertion,

More information

MATH 144: Business Calculus Final Review

MATH 144: Business Calculus Final Review MATH 144: Business Clculus Finl Review 1 Skills 1. Clculte severl limits. 2. Find verticl nd horizontl symptotes for given rtionl function. 3. Clculte derivtive by definition. 4. Clculte severl derivtives

More information

Key comparison BIPM.RI(I)-K3 of the air-kerma standards of the PTB, Germany and the BIPM in medium-energy x-rays

Key comparison BIPM.RI(I)-K3 of the air-kerma standards of the PTB, Germany and the BIPM in medium-energy x-rays Key comprison BIPM.RI(I)-K3 of the ir-kerm stndrds of the PTB, Germny nd the BIPM in medium-energy x-rys D.T. Burns 1, C Kessler 1, L Büermnn 2 1 Bureu Interntionl des Poids et Mesures (BIPM), Pvillon

More information

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER /2019

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER /2019 ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS MATH00030 SEMESTER 208/209 DR. ANTHONY BROWN 7.. Introduction to Integrtion. 7. Integrl Clculus As ws the cse with the chpter on differentil

More information

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source

More information

F (x) dx = F (x)+c = u + C = du,

F (x) dx = F (x)+c = u + C = du, 35. The Substitution Rule An indefinite integrl of the derivtive F (x) is the function F (x) itself. Let u = F (x), where u is new vrible defined s differentible function of x. Consider the differentil

More information

CHEMISTRY 3.5 Paper 1. Describe the structure and reactions of organic compounds containing selected organic groups

CHEMISTRY 3.5 Paper 1. Describe the structure and reactions of organic compounds containing selected organic groups CHEMISTRY 3.5 Pper 1 Describe the structure nd rections of orgnic compounds contining selected orgnic groups Credits: Five INSTRUCTIONS Answer ALL questions NZQA/Person Eduction 2006 - 2 - You re dvised

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

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

UNIFORM CONVERGENCE. Contents 1. Uniform Convergence 1 2. Properties of uniform convergence 3

UNIFORM CONVERGENCE. Contents 1. Uniform Convergence 1 2. Properties of uniform convergence 3 UNIFORM CONVERGENCE Contents 1. Uniform Convergence 1 2. Properties of uniform convergence 3 Suppose f n : Ω R or f n : Ω C is sequence of rel or complex functions, nd f n f s n in some sense. Furthermore,

More information