OPTICA PURA Y APLICADA - Vol

Size: px
Start display at page:

Download "OPTICA PURA Y APLICADA - Vol"

Transcription

1 OPTICA PURA Y APLICADA - Vol CLASSIFIED LINES IN THE SPECTRUM OF Xe II G. BERTUCCELLI*, J. REYNA ALMANDOS, O. DI ROCCO* and M. GALLARDO * Universidad Nacional del Centro, 7000 Tandil, Rep. Argentina Centro de Investigaciones Opticas La Plata. Rep. Argentina ABSTRACT Te spectrum of xenón emitted by a non-conventional ligt source as been studied. A bout 123 lines are classied in te range A. RESUMEN Ha sido estudiado el espectro del xenón em itido por una fuente luminosa no convencional. Son clasicadas alrededor de 123 I fneas en el rango de A. 1. INTRODUCTION Reyna Almandos et al (1) recently reported results n te spectrum of singly onized xenón. About 40 lines were classied in te A range belonging to 6s-4f and 5d-4f transitions. An extended compilation oines of te xenón spectra by Gallardo and Reyna Almandos (2) sows tat tere are many unclassied lines distributed trougout te wole wavelengt range investigated. Te present work as made use of tis compilation and additional material for classifying 123 lines corresponding to 5d-6f, 6s-7p, 5d-7p, 6s-6p, 4f-5g, 8s-6p, 7s-4f, 6s-4f, 5d-4f, 5d-5f, 5d-6p, 6d-4f, 6d-5g, 6p-7s, 6p-8s, 6p-5g, 6p-6g, 6p-6d, 6p-5d, 7p-5g, 7p-8s, 7p-6d, 4f-6g and 4f-7g transitions. 2. EXPERIMENTAL METHODS All spectra were produced in puré xenón conned in a tube originally designed for pulsed láser operation. Te ligt source is similar to tat described by Reyna Almandos et al (1). Spectrograms were recorded using torium (3) as a reference spectrum, and te probable wavelengt error seldom exceeds 0.05 A, 0.03 A and 0.01 A for lines measured in te rst, second and tird diffraction orders respectively. Systematic sifts, resulting from te use of a non-conventional ligt source, were frequently found. A com paration between lines measured by Humpreys (4) and tose determined wit our source revealed sifts tat are different for different transitions, te máximum differences aobs- a H u m p re y s 6eing about cm 1 corresponding to 6p-6d and 6p-7s transitions. However, greater sifts can be observed in oter transitions, but not systematically. Full experimental details are given in (1), wic also assign 50 new lines to Xe II spectra. 3. RESULTS Not only te wavelengts listed in (2) but also a number oines corresponding to unpublised material (5,6) as been used for classifying te Xe II lines. Partof tis matrial (6) contains new lines and te revised ionic assignation of a group oines tat is reported as Xe II or Xe ll-lll in (2). All Xe II lines were classied in accordance wit data obtained in AEL (7) and modications proposed by Hansen and Person (8) are given in Table I. Te tird and fourt columns of te table give te wavenumber of te lines and sow te degree of agreement between observed and calculated valúes taking into account te sifts in our lines. 163

2 TABLE I Classied Xe II Lines in te Región A Comments o ines sapes: A = asymetric; B = blended; H = wide Symbols in colum n ve; a = unpublised material (5,6); b = revised assignation 164

3 165

4 166

5 O ( 3P i)5d[2] s^ - ( 3P2)7 p [1] ^ ( *D2)5 d[2 ]5^ - ( 3P2) 7p[2] 3^ 1A ( 3D2) 5d[ 2] 3P1) 4f[ ( 3P i)6p [1]! - ( 3D2)7s[2] 3^ a ( 3P 1 ) 6p[2]5^ -( 3P 1 )6d[2] ( 3P0)5d[2] 3^ - ( 1D2) 6p [2] ( 3Pa)6p[2] 3^ - ( 3P2) 8s[2] ( 3P i)6p [2]s -(3P2) 83[2]s/ ( 3P2) 7s[2] 5^ - ( 3D2)4f [2] 5/z 3B ( 3P2)5d[3] 5 -(*D 2) 6p [3] 1A ( 3P i ) 6p[ 1] 3^ - ( 3P2) 8s[2] 3^ ( 3P2) 5d[ 315^ -( 'Dz) 6p[ 1] 3^ b ( 3P2) 7s[2]5^ - ( 1D2)4 f[ 1] 3^ a ( 3P j ) 6s[ 1 ] i^-( 3D2) 6pC 1] 3^ a ( ^ j. ) 6p [3 ] 3P2) 5g[2]S/z ( 1D2)6p[3]5/2- ( 3Pz) 5g[4] 7^ a ( 3P2)4 f[4 ],^ - ( 3Pi) 5g[3]7/i a 0A ( 3P2) 4f [3 ]s^-( 3P1) 5g[4] 7^ 2B ( 3P0) 6p[ 1] i^-( 3P 1) 7s[ 1 ] 3^ ( 3P, ) 6.C 1 ] P i)6p[ 1] 5 í >24 ( 3P2) 7p[ 3] 5/ - ( 3P1) 5g[ 3] 5 ( ( 3PZ)7pC3 ]5, - ( 3P 1) 5gC3 ]s, * 1H ( 3D2) 6p[ 3] 7/2- ( 3P2) 5g[4]<>^ ('ü^ópc 3] 7^ - ( 3P2) 5g[4] 7^ 1H j ' 77 K M 4f[ 5] ( *P i ) 5BC5 3,^ 3.82 ( 3P2)4 f[5 ]9 ^ -(3Pi)5gC5]n^ 167

6 O ( 3P2) 4f[5 ] ^ - ( 3Pi) 5gC3] ^ a IB ( B '93 ( 3P2)6d[4]<^-( 1D2)4f[4],^ ( 3P2) *fc *3T^-(3Pi) 5gC5D9^ }'23 ( ( P2)4f[4]7^-( Pi)5g[ 3]?^ a /.08 /( sp2)4f[4]7a- ( 3Pi)3g[3]5^ ( 3PZ) 4f [ 2] 5^-( 3P2) 5g[4 ] 7^ 1A ( 3P2) 6d[ 4 ] 7, - ( ^ 2) 4f[4]7, 2B ( 3P2) 6d[ 3] 7, - ( % ) 4f[5]9, IB ( % ) 5d[ 3]5/- ( 3P2) 7p[ 3] i L f i ( 3P2)6d[4]7/- ( 1Dz)4f[3]S/ í i ( 3P2)4 f[5 ]9, - ( 3P2)7g[5]11, 0B ( 3P2)4fC5]11^ ( 3P0) 5g[4],^ ( 3P2) 6d[ 2]S/- ( 3D2) 4f[ 1] 3/ a ( 3P2)4f[ 4],. - ( 3Pz)6g[6], 1 a O ( 3P2) 7p[ 3] 3P1) 8s[ 1] 3 O ,90 ( ( ^ 2) 4f[5] 1 y-( P2)6g[5] 1 a.84 ) ( 3P 2 )«[5 ]n /- ( 3P2)6g[5],/í; ( 3P2)4f[ 5]9/- ( 3P2)6g[4], a ( 3P2)4f[5 ],.- ( 3P2)6g[5]1 j. a ( 3P2)7p[2]5, - ( 3D2) 6d[2]3/ f i O ( 3P1) 6p[0]j.- ( 3P2) 6p[1]j. O ( 3P2) 8s[2] 3^ - ( 1D2) 6p[2]5^ O ( 3P1) 6p[ 1] 3. - ( ) 5d[ 2] 3/ f i O ( 3P2) 6p [ l ] -(3P )6d[2], ( 3D2)6p[2]5, - ( 3P2)8 s[2 ]5, OA ( 3P2)7s[2]3, - ( S0)6p[1]1, O ( 3P,0) 6p[ 1] 3, - ( 3P2) 6d[ 1] j. /2 O ( 1D2) 6p [1 ],,-(3P2) 8s[2]3, a

7 ACKNOWLEDGEMENT Te autors wis to tank Dr. W. Persson, from Lund University, for is elpful suggestion wic made possible te present paper. REFERENCES 1. J.G. R E Y N A ALM ANDOS. M. G A LLA R D O and M. G A R A V A G L IA : Opt. Pur. ApL, 15, 1 (1982). 2. M. G ALLARDO and J.G. REYNA ALM ANDOS: "Xenón Lines in te Range from 2000 Ato 7000 A (Centro de Investigaciones Opticas 1981). 3. F.P.J. V A L E R O :;. Opt. Soc. Am., (1968). 4. C.J. HUMPHREYS: J. Res. Nat. Bur. Stand., 22, 19 (1939). 5. M. G ALLARDO, C.A. MASSONE, A.A. TA G LIA FE R R I, M. G A R A V A G LIA and W. PERSSON: Unpublis material (1973). 6. J.G. REYNA ALM ANDOS, G. BERTUCCELLI and M. G ALLARD O : Unpublised material (1980). 7. CH.E. MOORE: "A tom ic Energy Levels IM " (Nat. Bur. Stand. 1958). 8. J.C. HANSEN and W. PERSSON: Prívate communication (1980). 169

386 Brazilian Journal of Physics, vol. 30, no. 2, June, 2000 Atomic Transitions for the Doubly Ionized Argon Spectrum, Ar III 1 F. R. T. Luna, 2 F. Br

386 Brazilian Journal of Physics, vol. 30, no. 2, June, 2000 Atomic Transitions for the Doubly Ionized Argon Spectrum, Ar III 1 F. R. T. Luna, 2 F. Br 386 Brazilian Journal of Physics, vol. 30, no. 2, June, 2000 Atomic Transitions for the Doubly Ionized Argon Spectrum, Ar III 1 F. R. T. Luna, 2 F. Bredice, 3 G. H. Cavalcanti, and 1;4 A. G. Trigueiros,

More information

The Derivative as a Function

The Derivative as a Function Section 2.2 Te Derivative as a Function 200 Kiryl Tsiscanka Te Derivative as a Function DEFINITION: Te derivative of a function f at a number a, denoted by f (a), is if tis limit exists. f (a) f(a + )

More information

Lecture XVII. Abstract We introduce the concept of directional derivative of a scalar function and discuss its relation with the gradient operator.

Lecture XVII. Abstract We introduce the concept of directional derivative of a scalar function and discuss its relation with the gradient operator. Lecture XVII Abstract We introduce te concept of directional derivative of a scalar function and discuss its relation wit te gradient operator. Directional derivative and gradient Te directional derivative

More information

64 IX. The Exceptional Lie Algebras

64 IX. The Exceptional Lie Algebras 64 IX. Te Exceptional Lie Algebras IX. Te Exceptional Lie Algebras We ave displayed te four series of classical Lie algebras and teir Dynkin diagrams. How many more simple Lie algebras are tere? Surprisingly,

More information

Math 1241 Calculus Test 1

Math 1241 Calculus Test 1 February 4, 2004 Name Te first nine problems count 6 points eac and te final seven count as marked. Tere are 120 points available on tis test. Multiple coice section. Circle te correct coice(s). You do

More information

Preview from Notesale.co.uk Page 2 of 42

Preview from Notesale.co.uk Page 2 of 42 1 PHYSICAL CHEMISTRY Dalton (1805) Tomson (1896) - Positive and negative carges Ruterford (1909) - Te Nucleus Bor (1913) - Energy levels Atomic Model : Timeline CATHODE RAYS THE DISCOVERY OF ELECTRON Scrödinger

More information

Physics Teach Yourself Series Topic 15: Wavelike nature of matter (Unit 4)

Physics Teach Yourself Series Topic 15: Wavelike nature of matter (Unit 4) Pysics Teac Yourself Series Topic 15: Wavelie nature of atter (Unit 4) A: Level 14, 474 Flinders Street Melbourne VIC 3000 T: 1300 134 518 W: tss.co.au E: info@tss.co.au TSSM 2017 Page 1 of 8 Contents

More information

The Electromagnetic Spectrum. Today

The Electromagnetic Spectrum. Today Today Announcements: HW#7 is due after Spring Break on Wednesday Marc 1 t Exam # is on Tursday after Spring Break Te fourt extra credit project will be a super bonus points project. Tis extra credit can

More information

MTH-112 Quiz 1 Name: # :

MTH-112 Quiz 1 Name: # : MTH- Quiz Name: # : Please write our name in te provided space. Simplif our answers. Sow our work.. Determine weter te given relation is a function. Give te domain and range of te relation.. Does te equation

More information

Math 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006

Math 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006 Mat 102 TEST CHAPTERS 3 & 4 Solutions & Comments Fall 2006 f(x+) f(x) 10 1. For f(x) = x 2 + 2x 5, find ))))))))) and simplify completely. NOTE: **f(x+) is NOT f(x)+! f(x+) f(x) (x+) 2 + 2(x+) 5 ( x 2

More information

Canadian Journal of Physics. Extended Analysis of Xe VII and Xe VIII

Canadian Journal of Physics. Extended Analysis of Xe VII and Xe VIII Canadian Journal of Physics Extended Analysis of Xe VII and Xe VIII Journal: Canadian Journal of Physics Manuscript ID cjp-2016-0728.r1 Manuscript Type: Review Date Submitted by the Author: 05-Dec-2016

More information

The total error in numerical differentiation

The total error in numerical differentiation AMS 147 Computational Metods and Applications Lecture 08 Copyrigt by Hongyun Wang, UCSC Recap: Loss of accuracy due to numerical cancellation A B 3, 3 ~10 16 In calculating te difference between A and

More information

1 The concept of limits (p.217 p.229, p.242 p.249, p.255 p.256) 1.1 Limits Consider the function determined by the formula 3. x since at this point

1 The concept of limits (p.217 p.229, p.242 p.249, p.255 p.256) 1.1 Limits Consider the function determined by the formula 3. x since at this point MA00 Capter 6 Calculus and Basic Linear Algebra I Limits, Continuity and Differentiability Te concept of its (p.7 p.9, p.4 p.49, p.55 p.56). Limits Consider te function determined by te formula f Note

More information

Solution for the Homework 4

Solution for the Homework 4 Solution for te Homework 4 Problem 6.5: In tis section we computed te single-particle translational partition function, tr, by summing over all definite-energy wavefunctions. An alternative approac, owever,

More information

More on generalized inverses of partitioned matrices with Banachiewicz-Schur forms

More on generalized inverses of partitioned matrices with Banachiewicz-Schur forms More on generalized inverses of partitioned matrices wit anaciewicz-scur forms Yongge Tian a,, Yosio Takane b a Cina Economics and Management cademy, Central University of Finance and Economics, eijing,

More information

Chapter 4 Derivatives [ ] = ( ) ( )= + ( ) + + = ()= + ()+ Exercise 4.1. Review of Prerequisite Skills. 1. f. 6. d. 4. b. lim. x x. = lim = c.

Chapter 4 Derivatives [ ] = ( ) ( )= + ( ) + + = ()= + ()+ Exercise 4.1. Review of Prerequisite Skills. 1. f. 6. d. 4. b. lim. x x. = lim = c. Capter Derivatives Review of Prerequisite Skills. f. p p p 7 9 p p p Eercise.. i. ( a ) a ( b) a [ ] b a b ab b a. d. f. 9. c. + + ( ) ( + ) + ( + ) ( + ) ( + ) + + + + ( ) ( + ) + + ( ) ( ) ( + ) + 7

More information

On convexity of polynomial paths and generalized majorizations

On convexity of polynomial paths and generalized majorizations On convexity of polynomial pats and generalized majorizations Marija Dodig Centro de Estruturas Lineares e Combinatórias, CELC, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

More information

A Reconsideration of Matter Waves

A Reconsideration of Matter Waves A Reconsideration of Matter Waves by Roger Ellman Abstract Matter waves were discovered in te early 20t century from teir wavelengt, predicted by DeBroglie, Planck's constant divided by te particle's momentum,

More information

Higher Derivatives. Differentiable Functions

Higher Derivatives. Differentiable Functions Calculus 1 Lia Vas Higer Derivatives. Differentiable Functions Te second derivative. Te derivative itself can be considered as a function. Te instantaneous rate of cange of tis function is te second derivative.

More information

OSCILLATION OF SOLUTIONS TO NON-LINEAR DIFFERENCE EQUATIONS WITH SEVERAL ADVANCED ARGUMENTS. Sandra Pinelas and Julio G. Dix

OSCILLATION OF SOLUTIONS TO NON-LINEAR DIFFERENCE EQUATIONS WITH SEVERAL ADVANCED ARGUMENTS. Sandra Pinelas and Julio G. Dix Opuscula Mat. 37, no. 6 (2017), 887 898 ttp://dx.doi.org/10.7494/opmat.2017.37.6.887 Opuscula Matematica OSCILLATION OF SOLUTIONS TO NON-LINEAR DIFFERENCE EQUATIONS WITH SEVERAL ADVANCED ARGUMENTS Sandra

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

HOMEWORK HELP 2 FOR MATH 151

HOMEWORK HELP 2 FOR MATH 151 HOMEWORK HELP 2 FOR MATH 151 Here we go; te second round of omework elp. If tere are oters you would like to see, let me know! 2.4, 43 and 44 At wat points are te functions f(x) and g(x) = xf(x)continuous,

More information

1. Questions (a) through (e) refer to the graph of the function f given below. (A) 0 (B) 1 (C) 2 (D) 4 (E) does not exist

1. Questions (a) through (e) refer to the graph of the function f given below. (A) 0 (B) 1 (C) 2 (D) 4 (E) does not exist Mat 1120 Calculus Test 2. October 18, 2001 Your name Te multiple coice problems count 4 points eac. In te multiple coice section, circle te correct coice (or coices). You must sow your work on te oter

More information

The structure of the atoms

The structure of the atoms Te structure of te atoms Atomos = indivisible University of Pécs, Medical Scool, Dept. Biopysics All tat exists are atoms and empty space; everyting else is merely tougt to exist. Democritus, 415 B.C.

More information

A = h w (1) Error Analysis Physics 141

A = h w (1) Error Analysis Physics 141 Introduction In all brances of pysical science and engineering one deals constantly wit numbers wic results more or less directly from experimental observations. Experimental observations always ave inaccuracies.

More information

Differential Calculus: Differentiation (First Principles, Rules) and Sketching Graphs (Grade 12) *

Differential Calculus: Differentiation (First Principles, Rules) and Sketching Graphs (Grade 12) * OpenStax-CNX moule: m39313 1 Differential Calculus: Differentiation (First Principles, Rules) an Sketcing Graps (Grae 12) * Free Hig Scool Science Texts Project Tis work is prouce by OpenStax-CNX an license

More information

Reminder: Exam 3 Friday, July 6. The Compton Effect. General Physics (PHY 2140) Lecture questions. Show your work for credit.

Reminder: Exam 3 Friday, July 6. The Compton Effect. General Physics (PHY 2140) Lecture questions. Show your work for credit. General Pysics (PHY 2140) Lecture 15 Modern Pysics Cater 27 1. Quantum Pysics Te Comton Effect Potons and EM Waves Wave Proerties of Particles Wave Functions Te Uncertainty Princile Reminder: Exam 3 Friday,

More information

Introduction. Learning Objectives. On completion of this chapter you will be able to:

Introduction. Learning Objectives. On completion of this chapter you will be able to: Introduction Learning Objectives On completion of tis capter you will be able to: 1. Define Compton Effect. 2. Derive te sift in incident ligt wavelengt and Compton wavelengt. 3. Explain ow te Compton

More information

Tutorial 2 (Solution) 1. An electron is confined to a one-dimensional, infinitely deep potential energy well of width L = 100 pm.

Tutorial 2 (Solution) 1. An electron is confined to a one-dimensional, infinitely deep potential energy well of width L = 100 pm. Seester 007/008 SMS0 Modern Pysics Tutorial Tutorial (). An electron is confined to a one-diensional, infinitely deep potential energy well of widt L 00 p. a) Wat is te least energy te electron can ave?

More information

The Doppler Factor and Quantum Electrodynamics Basics in Laser-Driven Light Sailing

The Doppler Factor and Quantum Electrodynamics Basics in Laser-Driven Light Sailing International Letters of Cemistry, Pysics and Astronomy Online: 013-10-0 ISSN: 99-3843, Vol. 19, pp 10-14 doi:10.1805/www.scipress.com/ilcpa.19.10 013 SciPress Ltd., Switzerland Te Doppler Factor and Quantum

More information

Average Rate of Change

Average Rate of Change Te Derivative Tis can be tougt of as an attempt to draw a parallel (pysically and metaporically) between a line and a curve, applying te concept of slope to someting tat isn't actually straigt. Te slope

More information

Derivation Of The Schwarzschild Radius Without General Relativity

Derivation Of The Schwarzschild Radius Without General Relativity Derivation Of Te Scwarzscild Radius Witout General Relativity In tis paper I present an alternative metod of deriving te Scwarzscild radius of a black ole. Te metod uses tree of te Planck units formulas:

More information

Multi-scale process model description by generalized hierarchical CPN models. E. Németh, K. M. Hangos

Multi-scale process model description by generalized hierarchical CPN models. E. Németh, K. M. Hangos Multi-scale process model description by generalized ierarcical CPN models E. Német, K. M. Hangos Researc Report SCL-002/2004 Researc Report SCL-002/2004 1 Contents 1 Introduction 2 2 Coloured Petri nets

More information

. If lim. x 2 x 1. f(x+h) f(x)

. If lim. x 2 x 1. f(x+h) f(x) Review of Differential Calculus Wen te value of one variable y is uniquely determined by te value of anoter variable x, ten te relationsip between x and y is described by a function f tat assigns a value

More information

Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143

Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143 Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143 Approximately 7 questions/6 problems Approximately 50% material since last test, 50% everyting covered on Exams I-III About 50% of everyting closely

More information

On the computation of wavenumber integrals in phase-shift migration of common-offset sections

On the computation of wavenumber integrals in phase-shift migration of common-offset sections Computation of offset-wavenumber integrals On te computation of wavenumber integrals in pase-sift migration of common-offset sections Xiniang Li and Gary F. Margrave ABSTRACT Te evaluation of wavenumber

More information

1. Consider the trigonometric function f(t) whose graph is shown below. Write down a possible formula for f(t).

1. Consider the trigonometric function f(t) whose graph is shown below. Write down a possible formula for f(t). . Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd, periodic function tat as been sifted upwards, so we will use

More information

Material for Difference Quotient

Material for Difference Quotient Material for Difference Quotient Prepared by Stepanie Quintal, graduate student and Marvin Stick, professor Dept. of Matematical Sciences, UMass Lowell Summer 05 Preface Te following difference quotient

More information

Numerical Differentiation

Numerical Differentiation Numerical Differentiation Finite Difference Formulas for te first derivative (Using Taylor Expansion tecnique) (section 8.3.) Suppose tat f() = g() is a function of te variable, and tat as 0 te function

More information

Lecture 21. Numerical differentiation. f ( x+h) f ( x) h h

Lecture 21. Numerical differentiation. f ( x+h) f ( x) h h Lecture Numerical differentiation Introduction We can analytically calculate te derivative of any elementary function, so tere migt seem to be no motivation for calculating derivatives numerically. However

More information

2.8 The Derivative as a Function

2.8 The Derivative as a Function .8 Te Derivative as a Function Typically, we can find te derivative of a function f at many points of its domain: Definition. Suppose tat f is a function wic is differentiable at every point of an open

More information

Consider a function f we ll specify which assumptions we need to make about it in a minute. Let us reformulate the integral. 1 f(x) dx.

Consider a function f we ll specify which assumptions we need to make about it in a minute. Let us reformulate the integral. 1 f(x) dx. Capter 2 Integrals as sums and derivatives as differences We now switc to te simplest metods for integrating or differentiating a function from its function samples. A careful study of Taylor expansions

More information

Notes on wavefunctions II: momentum wavefunctions

Notes on wavefunctions II: momentum wavefunctions Notes on wavefunctions II: momentum wavefunctions and uncertainty Te state of a particle at any time is described by a wavefunction ψ(x). Tese wavefunction must cange wit time, since we know tat particles

More information

ON THE LOCATION AND CLASSIFICATION OF ALL PRIME NUMBERS

ON THE LOCATION AND CLASSIFICATION OF ALL PRIME NUMBERS ON THE LOCATION AND CLASSIFICATION OF ALL PRIME NUMBERS Leopoldo Garavaglia, Aranjuez, ESPAÑA, and Mario Garavaglia, Universidad Nacional de La Plata and Centro de Investigaciones Opticas, La Plata, ARGENTINA.

More information

2.3 Product and Quotient Rules

2.3 Product and Quotient Rules .3. PRODUCT AND QUOTIENT RULES 75.3 Product and Quotient Rules.3.1 Product rule Suppose tat f and g are two di erentiable functions. Ten ( g (x)) 0 = f 0 (x) g (x) + g 0 (x) See.3.5 on page 77 for a proof.

More information

Week #15 - Word Problems & Differential Equations Section 8.2

Week #15 - Word Problems & Differential Equations Section 8.2 Week #1 - Word Problems & Differential Equations Section 8. From Calculus, Single Variable by Huges-Hallett, Gleason, McCallum et. al. Copyrigt 00 by Jon Wiley & Sons, Inc. Tis material is used by permission

More information

Exponential and logarithmic functions (pp ) () Supplement October 14, / 1. a and b positive real numbers and x and y real numbers.

Exponential and logarithmic functions (pp ) () Supplement October 14, / 1. a and b positive real numbers and x and y real numbers. MA123, Supplement Exponential and logaritmic functions pp. 315-319) Capter s Goal: Review te properties of exponential and logaritmic functions. Learn ow to differentiate exponential and logaritmic functions.

More information

nucleus orbital electron wave 2/27/2008 Quantum ( F.Robilliard) 1

nucleus orbital electron wave 2/27/2008 Quantum ( F.Robilliard) 1 r nucleus orbital electron wave λ /7/008 Quantum ( F.Robilliard) 1 Wat is a Quantum? A quantum is a discrete amount of some quantity. For example, an atom is a mass quantum of a cemical element te mass

More information

S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP.

S U E K E AY S S H A R O N T IM B E R W IN D M A R T Z -PA U L L IN. Carlisle Franklin Springboro. Clearcreek TWP. Middletown. Turtlecreek TWP. F R A N K L IN M A D IS O N S U E R O B E R T LE IC H T Y A LY C E C H A M B E R L A IN T W IN C R E E K M A R T Z -PA U L L IN C O R A O W E N M E A D O W L A R K W R E N N LA N T IS R E D R O B IN F

More information

Learning based super-resolution land cover mapping

Learning based super-resolution land cover mapping earning based super-resolution land cover mapping Feng ing, Yiang Zang, Giles M. Foody IEEE Fellow, Xiaodong Xiuua Zang, Siming Fang, Wenbo Yun Du is work was supported in part by te National Basic Researc

More information

Calculus I Homework: The Derivative as a Function Page 1

Calculus I Homework: The Derivative as a Function Page 1 Calculus I Homework: Te Derivative as a Function Page 1 Example (2.9.16) Make a careful sketc of te grap of f(x) = sin x and below it sketc te grap of f (x). Try to guess te formula of f (x) from its grap.

More information

Part C : Quantum Physics

Part C : Quantum Physics Part C : Quantum Pysics 1 Particle-wave duality 1.1 Te Bor model for te atom We begin our discussion of quantum pysics by discussing an early idea for atomic structure, te Bor model. Wile tis relies on

More information

Math Module Preliminary Test Solutions

Math Module Preliminary Test Solutions SSEA Summer 207 Mat Module Preliminar Test Solutions. [3 points] Find all values of tat satisf =. Solution: = ( ) = ( ) = ( ) =. Tis means ( ) is positive. Tat is, 0, wic implies. 2. [6 points] Find all

More information

Poisson Equation in Sobolev Spaces

Poisson Equation in Sobolev Spaces Poisson Equation in Sobolev Spaces OcMountain Dayligt Time. 6, 011 Today we discuss te Poisson equation in Sobolev spaces. It s existence, uniqueness, and regularity. Weak Solution. u = f in, u = g on

More information

Quantum Numbers and Rules

Quantum Numbers and Rules OpenStax-CNX module: m42614 1 Quantum Numbers and Rules OpenStax College Tis work is produced by OpenStax-CNX and licensed under te Creative Commons Attribution License 3.0 Abstract Dene quantum number.

More information

Computational Method of Structural Reliability Based on Integration Algorithms

Computational Method of Structural Reliability Based on Integration Algorithms Sensors & ransducers, Vol. 54, Issue 7, July 03, pp. 5-59 Sensors & ransducers 03 by IFSA ttp://www.sensorsportal.com Computational Metod of Structural Based on Integration Algoritms * Cong Cen, Yi Wan

More information

Calculus I Practice Exam 1A

Calculus I Practice Exam 1A Calculus I Practice Exam A Calculus I Practice Exam A Tis practice exam empasizes conceptual connections and understanding to a greater degree tan te exams tat are usually administered in introductory

More information

Polynomials 3: Powers of x 0 + h

Polynomials 3: Powers of x 0 + h near small binomial Capter 17 Polynomials 3: Powers of + Wile it is easy to compute wit powers of a counting-numerator, it is a lot more difficult to compute wit powers of a decimal-numerator. EXAMPLE

More information

REVIEW LAB ANSWER KEY

REVIEW LAB ANSWER KEY REVIEW LAB ANSWER KEY. Witout using SN, find te derivative of eac of te following (you do not need to simplify your answers): a. f x 3x 3 5x x 6 f x 3 3x 5 x 0 b. g x 4 x x x notice te trick ere! x x g

More information

On the Concept of Returns to Scale: Revisited

On the Concept of Returns to Scale: Revisited 3 J. Asian Dev. Stud, Vol. 5, Issue, (Marc 206) ISSN 2304-375X On te Concept of Returns to Scale: Revisited Parvez Azim Abstract Tis paper sows w it is tat in Economics text books and literature we invariabl

More information

UNIT-1 MODERN PHYSICS

UNIT-1 MODERN PHYSICS UNIT- MODERN PHYSICS Introduction to blackbody radiation spectrum: A body wic absorbs all radiation tat is incident on it is called a perfect blackbody. Wen radiation allowed to fall on suc a body, it

More information

INTEGRATED CIRCUITS. For a complete data sheet, please also download:

INTEGRATED CIRCUITS. For a complete data sheet, please also download: NTEGRATED CRCUTS DATA SEET For a complete data seet, please also download: Te C 74C/CT/CU/CMOS Logic Family Specifications Te C 74C/CT/CU/CMOS Logic Package nformation Te C 74C/CT/CU/CMOS Logic Package

More information

( ) ( s ) Answers to Practice Test Questions 4 Electrons, Orbitals and Quantum Numbers. Student Number:

( ) ( s ) Answers to Practice Test Questions 4 Electrons, Orbitals and Quantum Numbers. Student Number: Anwer to Practice Tet Quetion 4 Electron, Orbital Quantu Nuber. Heienberg uncertaint principle tate tat te preciion of our knowledge about a particle poition it oentu are inverel related. If we ave ore

More information

Differentiation Techniques 1: Power, Constant Multiple, Sum and Difference Rules

Differentiation Techniques 1: Power, Constant Multiple, Sum and Difference Rules Differetiatio Teciques : Power, Costat Multiple, Sum ad Differece Rules 97 Differetiatio Teciques : Power, Costat Multiple, Sum ad Differece Rules Model : Fidig te Equatio of f '() from a Grap of f ()

More information

2.1 THE DEFINITION OF DERIVATIVE

2.1 THE DEFINITION OF DERIVATIVE 2.1 Te Derivative Contemporary Calculus 2.1 THE DEFINITION OF DERIVATIVE 1 Te grapical idea of a slope of a tangent line is very useful, but for some uses we need a more algebraic definition of te derivative

More information

INJECTIVE AND PROJECTIVE PROPERTIES OF REPRESENTATIONS OF QUIVERS WITH n EDGES. Sangwon Park

INJECTIVE AND PROJECTIVE PROPERTIES OF REPRESENTATIONS OF QUIVERS WITH n EDGES. Sangwon Park Korean J. Mat. 16 (2008), No. 3, pp. 323 334 INJECTIVE AND PROJECTIVE PROPERTIES OF REPRESENTATIONS OF QUIVERS WITH n EDGES Sanwon Park Abstract. We define injective and projective representations of quivers

More information

Math 1210 Midterm 1 January 31st, 2014

Math 1210 Midterm 1 January 31st, 2014 Mat 110 Midterm 1 January 1st, 01 Tis exam consists of sections, A and B. Section A is conceptual, wereas section B is more computational. Te value of every question is indicated at te beginning of it.

More information

model-independent determination of Higgs e+e- colliders

model-independent determination of Higgs e+e- colliders model-independent determination of Higgs (self-)couplings @ e+e- colliders Junping Tian (U of Tokyo) Te 20t Regular Meeting of te New Higgs Working Group, August 18-19, 2017 @ Osaka University outline

More information

First we will go over the following derivative rule. Theorem

First we will go over the following derivative rule. Theorem Tuesday, Feb 1 Tese slides will cover te following 1 d [cos(x)] = sin(x) iger-order derivatives 3 tangent line problems 4 basic differential equations First we will go over te following derivative rule

More information

Symmetry Labeling of Molecular Energies

Symmetry Labeling of Molecular Energies Capter 7. Symmetry Labeling of Molecular Energies Notes: Most of te material presented in tis capter is taken from Bunker and Jensen 1998, Cap. 6, and Bunker and Jensen 2005, Cap. 7. 7.1 Hamiltonian Symmetry

More information

Some Review Problems for First Midterm Mathematics 1300, Calculus 1

Some Review Problems for First Midterm Mathematics 1300, Calculus 1 Some Review Problems for First Midterm Matematics 00, Calculus. Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd,

More information

Notes on Planetary Motion

Notes on Planetary Motion (1) Te motion is planar Notes on Planetary Motion Use 3-dimensional coordinates wit te sun at te origin. Since F = ma and te gravitational pull is in towards te sun, te acceleration A is parallel to te

More information

A MONTE CARLO ANALYSIS OF THE EFFECTS OF COVARIANCE ON PROPAGATED UNCERTAINTIES

A MONTE CARLO ANALYSIS OF THE EFFECTS OF COVARIANCE ON PROPAGATED UNCERTAINTIES A MONTE CARLO ANALYSIS OF THE EFFECTS OF COVARIANCE ON PROPAGATED UNCERTAINTIES Ronald Ainswort Hart Scientific, American Fork UT, USA ABSTRACT Reports of calibration typically provide total combined uncertainties

More information

Analysis: The speed of the proton is much less than light speed, so we can use the

Analysis: The speed of the proton is much less than light speed, so we can use the Section 1.3: Wave Proerties of Classical Particles Tutorial 1 Practice, age 634 1. Given: 1.8! 10 "5 kg # m/s; 6.63! 10 "34 J #s Analysis: Use te de Broglie relation, λ. Solution:! 6.63 " 10#34 kg $ m

More information

Fractional Derivatives as Binomial Limits

Fractional Derivatives as Binomial Limits Fractional Derivatives as Binomial Limits Researc Question: Can te limit form of te iger-order derivative be extended to fractional orders? (atematics) Word Count: 669 words Contents - IRODUCIO... Error!

More information

Section 2.7 Derivatives and Rates of Change Part II Section 2.8 The Derivative as a Function. at the point a, to be. = at time t = a is

Section 2.7 Derivatives and Rates of Change Part II Section 2.8 The Derivative as a Function. at the point a, to be. = at time t = a is Mat 180 www.timetodare.com Section.7 Derivatives and Rates of Cange Part II Section.8 Te Derivative as a Function Derivatives ( ) In te previous section we defined te slope of te tangent to a curve wit

More information

LECTURE 14 NUMERICAL INTEGRATION. Find

LECTURE 14 NUMERICAL INTEGRATION. Find LECTURE 14 NUMERCAL NTEGRATON Find b a fxdx or b a vx ux fx ydy dx Often integration is required. However te form of fx may be suc tat analytical integration would be very difficult or impossible. Use

More information

QUESTIONS ) Of the following the graph which represents the variation of Energy (E) of the photon with the wavelength (λ) is E E 1) 2) 3) 4)

QUESTIONS ) Of the following the graph which represents the variation of Energy (E) of the photon with the wavelength (λ) is E E 1) 2) 3) 4) CET II PUC: PHYSICS: ATOMIC PHYSICS INTRODUCTION TO ATOMIC PHYSICS, PHOTOELECTRIC EFFECT DUAL NATURE OF MATTER, BOHR S ATOM MODEL SCATTERING OF LIGHT and LASERS QUESTIONS ) Wic of te following statements

More information

Lecture Notes Di erentiating Trigonometric Functions page 1

Lecture Notes Di erentiating Trigonometric Functions page 1 Lecture Notes Di erentiating Trigonometric Functions age (sin ) 7 sin () sin 8 cos 3 (tan ) sec tan + 9 tan + 4 (cot ) csc cot 0 cot + 5 sin (sec ) cos sec tan sec jj 6 (csc ) sin csc cot csc jj c Hiegkuti,

More information

Results as of 30 September 2018

Results as of 30 September 2018 rt Results as of 30 September 2018 F r e e t r a n s l a t ion f r o m t h e o r ig ina l in S p a n is h. I n t h e e v e n t o f d i s c r e p a n c y, t h e Sp a n i s h - la n g u a g e v e r s ion

More information

Order of Accuracy. ũ h u Ch p, (1)

Order of Accuracy. ũ h u Ch p, (1) Order of Accuracy 1 Terminology We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, wic can be for instance te grid size or time step in a numerical

More information

Quantum Mechanics and Atomic Theory

Quantum Mechanics and Atomic Theory A. Electromagnetic Radiation Quantum Mecanics and Atomic Teory 1. Ligt: consists of waves of oscillating electric field ( E ) and magnetic field ( B ) tat are perpendicular to eac oter and to te direction

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

AMPLITUDE FLUCTUATIONS IN CURVATURE SENSING: COMPARISON OF TWO SCHEMES

AMPLITUDE FLUCTUATIONS IN CURVATURE SENSING: COMPARISON OF TWO SCHEMES Revista Mexicana de Astronomía y Astrofísica, 46, 145 152 (2010) AMPLITUDE FLUCTUATIONS IN CURVATURE SENSING: COMPARISON OF TWO SCHEMES V. V. Voitsekhovich and V. G. Orlov Instituto de Astronomía, Universidad

More information

Optimal Control Applied to the Spread of Influenza A(H1N1)

Optimal Control Applied to the Spread of Influenza A(H1N1) Applied Matematical Sciences, Vol. 6, 2012, no. 82, 4057-4065 Optimal Control Applied to te Spread of Influenza AH11 M. El ia 1, O. Balatif 2, J. Bouyagroumni, E. Labriji, M. Racik Laboratoire d Analyse

More information

ELA

ELA Electronic Journal of Linear Algebra ISSN 181-81 A publication of te International Linear Algebra Society ttp://mat.tecnion.ac.il/iic/ela RANK AND INERTIA OF SUBMATRICES OF THE MOORE PENROSE INVERSE OF

More information

Physics 121, April 1, Equilibrium. Physics 121. April 1, Physics 121. April 1, Course Information. Discussion of Exam # 2

Physics 121, April 1, Equilibrium. Physics 121. April 1, Physics 121. April 1, Course Information. Discussion of Exam # 2 Pysics 121, April 1, 2008. Pysics 121. April 1, 2008. Course Information Discussion of Exam # 2 Topics to be discussed today: Requirements for Equilibrium Gravitational Equilibrium Sample problems Pysics

More information

APPENDIXES. Let the following constants be established for those using the active Mathcad

APPENDIXES. Let the following constants be established for those using the active Mathcad 3 APPENDIXES Let te following constants be establised for tose using te active Matcad form of tis book: m.. e 9.09389700 0 3 kg Electron rest mass. q.. o.6077330 0 9 coul Electron quantum carge. µ... o.5663706

More information

Physics 41 Homework Set 3 Chapter 17 Serway 7 th Edition

Physics 41 Homework Set 3 Chapter 17 Serway 7 th Edition Pyic 41 Homework Set 3 Capter 17 Serway 7 t Edition Q: 1, 4, 5, 6, 9, 1, 14, 15 Quetion *Q17.1 Anwer. Te typically iger denity would by itelf make te peed of ound lower in a olid compared to a ga. Q17.4

More information

Comment on Experimental observations of saltwater up-coning

Comment on Experimental observations of saltwater up-coning 1 Comment on Experimental observations of saltwater up-coning H. Zang 1,, D.A. Barry 2 and G.C. Hocking 3 1 Griffit Scool of Engineering, Griffit University, Gold Coast Campus, QLD 4222, Australia. Tel.:

More information

Derivatives of Exponentials

Derivatives of Exponentials mat 0 more on derivatives: day 0 Derivatives of Eponentials Recall tat DEFINITION... An eponential function as te form f () =a, were te base is a real number a > 0. Te domain of an eponential function

More information

This document is published in: Economics Letters (2001), 72(3), DOI: /S (01) Elsevier Science B.V.

This document is published in: Economics Letters (2001), 72(3), DOI: /S (01) Elsevier Science B.V. Tis document is publised in: Economics Letters (2001), 72(3), 303-307. DOI: 10.1016/S0165-1765(01)00445-1 2001 Elsevier Science B.V. Extending communication-proof equilibrium to infinit games José Luis

More information

Continuity and Differentiability Worksheet

Continuity and Differentiability Worksheet Continuity and Differentiability Workseet (Be sure tat you can also do te grapical eercises from te tet- Tese were not included below! Typical problems are like problems -3, p. 6; -3, p. 7; 33-34, p. 7;

More information

HOW TO DEAL WITH FFT SAMPLING INFLUENCES ON ADEV CALCULATIONS

HOW TO DEAL WITH FFT SAMPLING INFLUENCES ON ADEV CALCULATIONS HOW TO DEAL WITH FFT SAMPLING INFLUENCES ON ADEV CALCULATIONS Po-Ceng Cang National Standard Time & Frequency Lab., TL, Taiwan 1, Lane 551, Min-Tsu Road, Sec. 5, Yang-Mei, Taoyuan, Taiwan 36 Tel: 886 3

More information

ch (for some fixed positive number c) reaching c

ch (for some fixed positive number c) reaching c GSTF Journal of Matematics Statistics and Operations Researc (JMSOR) Vol. No. September 05 DOI 0.60/s4086-05-000-z Nonlinear Piecewise-defined Difference Equations wit Reciprocal and Cubic Terms Ramadan

More information

Differentiation. Area of study Unit 2 Calculus

Differentiation. Area of study Unit 2 Calculus Differentiation 8VCE VCEco Area of stud Unit Calculus coverage In tis ca 8A 8B 8C 8D 8E 8F capter Introduction to limits Limits of discontinuous, rational and brid functions Differentiation using first

More information

, meant to remind us of the definition of f (x) as the limit of difference quotients: = lim

, meant to remind us of the definition of f (x) as the limit of difference quotients: = lim Mat 132 Differentiation Formulas Stewart 2.3 So far, we ave seen ow various real-world problems rate of cange and geometric problems tangent lines lead to derivatives. In tis section, we will see ow to

More information

Preface. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.

Preface. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. Preface Here are my online notes for my course tat I teac ere at Lamar University. Despite te fact tat tese are my class notes, tey sould be accessible to anyone wanting to learn or needing a refreser

More information

The Verlet Algorithm for Molecular Dynamics Simulations

The Verlet Algorithm for Molecular Dynamics Simulations Cemistry 380.37 Fall 2015 Dr. Jean M. Standard November 9, 2015 Te Verlet Algoritm for Molecular Dynamics Simulations Equations of motion For a many-body system consisting of N particles, Newton's classical

More information

Math 312 Lecture Notes Modeling

Math 312 Lecture Notes Modeling Mat 3 Lecture Notes Modeling Warren Weckesser Department of Matematics Colgate University 5 7 January 006 Classifying Matematical Models An Example We consider te following scenario. During a storm, a

More information