Stationary states of atoms and molecules
|
|
|
- Gladys Henry
- 5 years ago
- Views:
Transcription
1 Statoary states of atos ad olecules
2 I followg wees the geeral aspects of the eergy level structure of atos ad olecules that are essetal for the terpretato ad the aalyss of spectral postos the rotatoal vbratoal ad electroc spectra of olecules wll be revewed. Spectroscopc easureets provde foratos o the saple uder study ecoded the for of le postos le testes ad le shapes. The le postos ca be used to extract forato o the eergy level structure of atos ad olecules. Le testes ad shapes provde characterstcs of the stregth of teracto as well as dyacal forato o tra- or exteral teractos of olecules.
3 Geeral coets o soluto of Schrödger equato te depedat Schödger equato separablty of the Schrödger equato separato of the ceter of ass ear separablty sutable coordates systes approxato techques
4 Descrpto of atoc or olecular states z x y z x N y N z N y For a syste of N partcles wth coordates qx y z wth...n the te depedat Schrödger equato s x x y z... x N yn zn x y z... x N N N y z -are the egefuctos of -ther eerges - represets a label a quatu uber or a set of quatu ubers for the state I x...z N I dx...dz N s the probablty that state partcle s located betwee x y z ad x dx y dy z dz partcle betwee x y z ad x dx y dy z 3 dz 3...
5 ... x z y x z y x q x p z y x p p p p h h... q p z y x z y x V p V T N N N N T ad V are operators of etc ad potetal eergy Soluto of the Schrödger equato for ay partcles proble s coplex ad geerally posble to obta explctly. Oe has to carefully set altoa of the syste: -separato of the ceter of ass oto -represetato the ost approprate coordate syste e.g. syetry of the force feld -separablty of the altoa o a su of operators that ca act o dstct sets of varables -cosder separato o doat ad perturbg altoa copoets ad use of aproxato ethods e.g. perturbato ad varatoal ethods
6 Atos datoc ad polyatoc olecules Atos: ucleus e - hydroge hydrogec atos or os ucleus N e - Molecules: ucle electros N ucle electros Coplexes ad clusters: coplex force feld Very large systes - atos: bul propertes---sold state physcs
7 erarchy of otos ad eerges atos ad olecules Atos ad olecules: oble ucleus ad fast ovg electros The dfferet types of oto olecule electroc vbratoal rotatoal taes place o dfferet te scales ad are assocated wth dfferet cotrbutos to the total eergy. Ths herarchy of te scales ples the approxate separablty of the correspodg otos that les behd the so-called Bor-Oppeheer approxato
8 Syetry A olecule possesses structural syetry ad t ca be descrbed ters of rotato axes ad reflecto plaes Use of the group theory ad cocept of syetry helps to uderstad olecules ad ther spectra.
9 Separablty- exaples
10 Separato of the ceter of ass oto I atos ad olecules free space the oto of the ceter of ass s exactly separable fro the teral oto because the potetal Vq oly depeds o the dstace r j betwee the ucle ad electros: Q c P c qt pt Coordates ad oetu operators of the ceter of ass oto ad these operators the ceter of ass coordates c The overal traslatoal oto of the ato/olecule ca be treated as that of free partcle of as M a free space or f the exteral potetals are preset accordg to the potetal eergy fucto. I spectroscopy oe studes the trastos betwee the eergy levels assocated wth the teral oto of atos ad olecules ad cocetrates o a proble of reduced desoalty 3N-3 It dffers fro the altoa c that the etc eergy ter cotas the reduced ass μ stead of for stace the free-electro ass e.
11 Separablty of altoa e.g. depedat coordates
12
13 Near separablty
14 Perturbato theory: revew It s cocer wth fdg the chages the dscrete eergy levels ad egefuctos of a syte whe a sall dsturbace s apped Sall suggests that oe ca expad the perturbed egefuctos ad egevalue as power seres. Ths s ost coetly accoplshed ters of a paraeter l such that the zero frst etc powers of l correspod to the zero frst...orders of perturbato calculatos λ λ λ... λ λ...
15 λ λ λ λ λ λ λ By equatg the coeffcets of equal powers λ o both sdes to obta seres of equatos represetg hgher orders of perturbato s ay of uperturbed egefuctos ad s ay of uperturbed egevalues *
16 Frst order perturbato s because a a a The wave fucto s calculated by expadg t ters of the : Substtuto t to the secod equato * gves: a The forer equato gves as the expectato value of for uperturbed state. > s s s s The calculatos of to a gve order requres owledge of oly to the ext lower order.
17 Secod-order perturbato I I a a a
18 ergy ad wave fuctos to the secod order I I ] [
19 Geeral coets:. Ay of the fuctos s ca have a arbtrary ultple of added to t wthout affectg the value of the left sde ad hece wthout otherwse affectg the deterato of s ters of lower-order fuctos. s s> * s dτ. Ier product of fo ad the left sde of each of solutos s zero ad oe ca develop followg equato: s s s s >
Non-degenerate Perturbation Theory
No-degeerate Perturbato Theory Proble : H E ca't solve exactly. But wth H H H' H" L H E Uperturbed egevalue proble. Ca solve exactly. E Therefore, kow ad. H ' H" called perturbatos Copyrght Mchael D. Fayer,
Coherent Potential Approximation
Coheret Potetal Approxato Noveber 29, 2009 Gree-fucto atrces the TB forals I the tght bdg TB pcture the atrx of a Haltoa H s the for H = { H j}, where H j = δ j ε + γ j. 2 Sgle ad double uderles deote
MOLECULAR VIBRATIONS
MOLECULAR VIBRATIONS Here we wsh to vestgate molecular vbratos ad draw a smlarty betwee the theory of molecular vbratos ad Hückel theory. 1. Smple Harmoc Oscllator Recall that the eergy of a oe-dmesoal
( t) ( t) ( t) ρ ψ ψ. (9.1)
Adre Toaoff, MT Departet of Cestry, 3/19/29 p. 9-1 9. THE DENSTY MATRX Te desty atrx or desty operator s a alterate represetato of te state of a quatu syste for wc we ave prevously used te wavefucto. Altoug
PRACTICAL CONSIDERATIONS IN HUMAN-INDUCED VIBRATION
PRACTICAL CONSIDERATIONS IN HUMAN-INDUCED VIBRATION Bars Erkus, 4 March 007 Itroducto Ths docuet provdes a revew of fudaetal cocepts structural dyacs ad soe applcatos hua-duced vbrato aalyss ad tgato of
DYNAMICS. Systems of Particles VECTOR MECHANICS FOR ENGINEERS: Seventh Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Ferdad P. eer E. Russell Johsto, Jr. Systes of Partcles Lecture Notes: J. Walt Oler Texas Tech Uersty 003 The Mcraw-Hll Copaes, Ic. ll rghts resered.
Solutions to problem set ); (, ) (
Solutos to proble set.. L = ( yp p ); L = ( p p ); y y L, L = yp p, p p = yp p, + p [, p ] y y y = yp + p = L y Here we use for eaple that yp, p = yp p p yp = yp, p = yp : factors that coute ca be treated
Simple Linear Regression
Statstcal Methods I (EST 75) Page 139 Smple Lear Regresso Smple regresso applcatos are used to ft a model descrbg a lear relatoshp betwee two varables. The aspects of least squares regresso ad correlato
Chapter 2 - Free Vibration of Multi-Degree-of-Freedom Systems - II
CEE49b Chapter - Free Vbrato of Mult-Degree-of-Freedom Systems - II We ca obta a approxmate soluto to the fudametal atural frequecy through a approxmate formula developed usg eergy prcples by Lord Raylegh
Lecture 07: Poles and Zeros
Lecture 07: Poles ad Zeros Defto of poles ad zeros The trasfer fucto provdes a bass for determg mportat system respose characterstcs wthout solvg the complete dfferetal equato. As defed, the trasfer fucto
Parallelized methods for solving polynomial equations
IOSR Joural of Matheatcs (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X. Volue 2, Issue 4 Ver. II (Jul. - Aug.206), PP 75-79 www.osrourals.org Paralleled ethods for solvg polyoal equatos Rela Kapçu, Fatr
Summary of the lecture in Biostatistics
Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the
A New Method for Solving Fuzzy Linear. Programming by Solving Linear Programming
ppled Matheatcal Sceces Vol 008 o 50 7-80 New Method for Solvg Fuzzy Lear Prograg by Solvg Lear Prograg S H Nasser a Departet of Matheatcs Faculty of Basc Sceces Mazadara Uversty Babolsar Ira b The Research
ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K
ROOT-LOCUS ANALYSIS Coder a geeral feedback cotrol yte wth a varable ga. R( Y( G( + H( Root-Locu a plot of the loc of the pole of the cloed-loop trafer fucto whe oe of the yte paraeter ( vared. Root locu
The theoretical background of
he theoretcal backgroud of -echologes he theoretcal backgroud of FactSage he followg sldes gve a abrdged overvew of the ajor uderlyg prcples of the calculatoal odules of FactSage. -echologes he bbs Eergy
Absorption in Solar Atmosphere
Absorpto Solar Atmosphere A black body spectrum emtted from solar surface causes exctato processes o atoms the solar atmosphere. Ths tur causes absorpto of characterstc wavelegths correspodg to those atoms
,...R) where r = H (1.4) + Tn + Vof. etic energy terms are: here. ZA ZB Vee = & Vnn = (1.6) (1.4) H = Te + Tn + Ven + Vee + Vnn. i A r i.
where r H r, r (r,,...r), r, RE R (r, RR),.., R represet theelectros. electro (.3) ad uclear coor,all,.ucle ates of ad all Itutvely, ollowgdates, SE: respectvely, ad H (r, R) E (r, R), we feel t are very
Functions of Random Variables
Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,
Standard Deviation for PDG Mass Data
4 Dec 06 Stadard Devato for PDG Mass Data M. J. Gerusa Retred, 47 Clfde Road, Worghall, HP8 9JR, UK. gerusa@aol.co, phoe: +(44) 844 339754 Abstract Ths paper aalyses the data for the asses of eleetary
CHAPTER VI Statistical Analysis of Experimental Data
Chapter VI Statstcal Aalyss of Expermetal Data CHAPTER VI Statstcal Aalyss of Expermetal Data Measuremets do ot lead to a uque value. Ths s a result of the multtude of errors (maly radom errors) that ca
Introduction. Free Electron Fermi Gas. Energy Levels in One Dimension
ree Electro er Gas Eergy Levels Oe Deso Effect of eperature o the er-drac Dstrbuto ree Electro Gas hree Desos Heat Capacty of the Electro Gas Electrcal Coductvty ad Oh s Law Moto Magetc elds heral Coductvty
Lecture IV : The Hartree-Fock method
Lecture IV : The Hartree-Fock method I. THE HARTREE METHOD We have see the prevous lecture that the may-body Hamltoa for a electroc system may be wrtte atomc uts as Ĥ = N e N e N I Z I r R I + N e N e
III-16 G. Brief Review of Grand Orthogonality Theorem and impact on Representations (Γ i ) l i = h n = number of irreducible representations.
III- G. Bref evew of Grad Orthogoalty Theorem ad mpact o epresetatos ( ) GOT: h [ () m ] [ () m ] δδ δmm ll GOT puts great restrcto o form of rreducble represetato also o umber: l h umber of rreducble
2/20/2013. Topics. Power Flow Part 1 Text: Power Transmission. Power Transmission. Power Transmission. Power Transmission
/0/0 Topcs Power Flow Part Text: 0-0. Power Trassso Revsted Power Flow Equatos Power Flow Proble Stateet ECEGR 45 Power Systes Power Trassso Power Trassso Recall that for a short trassso le, the power
best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best
Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg
C-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory
ROAD MAP... AE301 Aerodyamcs I UNIT C: 2-D Arfols C-1: Aerodyamcs of Arfols 1 C-2: Aerodyamcs of Arfols 2 C-3: Pael Methods C-4: Th Arfol Theory AE301 Aerodyamcs I Ut C-3: Lst of Subects Problem Solutos?
Outline. Point Pattern Analysis Part I. Revisit IRP/CSR
Pot Patter Aalyss Part I Outle Revst IRP/CSR, frst- ad secod order effects What s pot patter aalyss (PPA)? Desty-based pot patter measures Dstace-based pot patter measures Revst IRP/CSR Equal probablty:
KURODA S METHOD FOR CONSTRUCTING CONSISTENT INPUT-OUTPUT DATA SETS. Peter J. Wilcoxen. Impact Research Centre, University of Melbourne.
KURODA S METHOD FOR CONSTRUCTING CONSISTENT INPUT-OUTPUT DATA SETS by Peter J. Wlcoxe Ipact Research Cetre, Uversty of Melboure Aprl 1989 Ths paper descrbes a ethod that ca be used to resolve cossteces
1 Lyapunov Stability Theory
Lyapuov Stablty heory I ths secto we cosder proofs of stablty of equlbra of autoomous systems. hs s stadard theory for olear systems, ad oe of the most mportat tools the aalyss of olear systems. It may
Long blade vibration model for turbine-generator shafts torsional vibration analysis
Avalable ole www.ocpr.co Joural of Checal ad Pharaceutcal Research, 05, 7(3):39-333 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Log blade vbrato odel for turbe-geerator shafts torsoal vbrato aalyss
Some Different Perspectives on Linear Least Squares
Soe Dfferet Perspectves o Lear Least Squares A stadard proble statstcs s to easure a respose or depedet varable, y, at fed values of oe or ore depedet varables. Soetes there ests a deterstc odel y f (,,
A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions
Appled Matheatcs, 1, 4, 8-88 http://d.do.org/1.4/a.1.448 Publshed Ole Aprl 1 (http://www.scrp.org/joural/a) A Covetoal Approach for the Soluto of the Ffth Order Boudary Value Probles Usg Sth Degree Sple
Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:
Chapter 3 3- Busess Statstcs: A Frst Course Ffth Edto Chapter 2 Correlato ad Smple Lear Regresso Busess Statstcs: A Frst Course, 5e 29 Pretce-Hall, Ic. Chap 2- Learg Objectves I ths chapter, you lear:
Polyphase Filters. Section 12.4 Porat
Polyphase Flters Secto.4 Porat .4 Polyphase Flters Polyphase s a way of dog saplg-rate coverso that leads to very effcet pleetatos. But ore tha that, t leads to very geeral vewpots that are useful buldg
D. L. Bricker, 2002 Dept of Mechanical & Industrial Engineering The University of Iowa. CPL/XD 12/10/2003 page 1
D. L. Brcker, 2002 Dept of Mechacal & Idustral Egeerg The Uversty of Iowa CPL/XD 2/0/2003 page Capactated Plat Locato Proble: Mze FY + C X subject to = = j= where Y = j= X D, j =, j X SY, =,... X 0, =,
Analysis of System Performance IN2072 Chapter 5 Analysis of Non Markov Systems
Char for Network Archtectures ad Servces Prof. Carle Departmet of Computer Scece U Müche Aalyss of System Performace IN2072 Chapter 5 Aalyss of No Markov Systems Dr. Alexader Kle Prof. Dr.-Ig. Georg Carle
EVALUATION OF FUNCTIONAL INTEGRALS BY MEANS OF A SERIES AND THE METHOD OF BOREL TRANSFORM
EVALUATION OF FUNCTIONAL INTEGRALS BY MEANS OF A SERIES AND THE METHOD OF BOREL TRANSFORM Jose Javer Garca Moreta Ph. D research studet at the UPV/EHU (Uversty of Basque coutry) Departmet of Theoretcal
Assignment 5/MATH 247/Winter Due: Friday, February 19 in class (!) (answers will be posted right after class)
Assgmet 5/MATH 7/Wter 00 Due: Frday, February 9 class (!) (aswers wll be posted rght after class) As usual, there are peces of text, before the questos [], [], themselves. Recall: For the quadratc form
Lecture 9: Tolerant Testing
Lecture 9: Tolerat Testg Dael Kae Scrbe: Sakeerth Rao Aprl 4, 07 Abstract I ths lecture we prove a quas lear lower boud o the umber of samples eeded to do tolerat testg for L dstace. Tolerat Testg We have
Born-Oppenheimer Approximation. Kaito Takahashi
o-oppehee ppoato Kato Takahah toc Ut Fo quatu yte uch a ecto ad olecule t eae to ue ut that ft the=tomc UNT Ue a of ecto (ot kg) Ue chage of ecto (ot coulob) Ue hba fo agula oetu (ot kg - ) Ue 4pe 0 fo
Ideal multigrades with trigonometric coefficients
Ideal multgrades wth trgoometrc coeffcets Zarathustra Brady December 13, 010 1 The problem A (, k) multgrade s defed as a par of dstct sets of tegers such that (a 1,..., a ; b 1,..., b ) a j = =1 for all
L5 Polynomial / Spline Curves
L5 Polyomal / Sple Curves Cotets Coc sectos Polyomal Curves Hermte Curves Bezer Curves B-Sples No-Uform Ratoal B-Sples (NURBS) Mapulato ad Represetato of Curves Types of Curve Equatos Implct: Descrbe a
Derivation of 3-Point Block Method Formula for Solving First Order Stiff Ordinary Differential Equations
Dervato of -Pot Block Method Formula for Solvg Frst Order Stff Ordary Dfferetal Equatos Kharul Hamd Kharul Auar, Kharl Iskadar Othma, Zara Bb Ibrahm Abstract Dervato of pot block method formula wth costat
Rademacher Complexity. Examples
Algorthmc Foudatos of Learg Lecture 3 Rademacher Complexty. Examples Lecturer: Patrck Rebesch Verso: October 16th 018 3.1 Itroducto I the last lecture we troduced the oto of Rademacher complexty ad showed
d dt d d dt dt Also recall that by Taylor series, / 2 (enables use of sin instead of cos-see p.27 of A&F) dsin
Learzato of the Swg Equato We wll cover sectos.5.-.6 ad begg of Secto 3.3 these otes. 1. Sgle mache-fte bus case Cosder a sgle mache coected to a fte bus, as show Fg. 1 below. E y1 V=1./_ Fg. 1 The admttace
A tighter lower bound on the circuit size of the hardest Boolean functions
Electroc Colloquum o Computatoal Complexty, Report No. 86 2011) A tghter lower boud o the crcut sze of the hardest Boolea fuctos Masak Yamamoto Abstract I [IPL2005], Fradse ad Mlterse mproved bouds o the
7.0 Equality Contraints: Lagrange Multipliers
Systes Optzato 7.0 Equalty Cotrats: Lagrage Multplers Cosder the zato of a o-lear fucto subject to equalty costrats: g f() R ( ) 0 ( ) (7.) where the g ( ) are possbly also olear fuctos, ad < otherwse
Some results and conjectures about recurrence relations for certain sequences of binomial sums.
Soe results ad coectures about recurrece relatos for certa sequeces of boal sus Joha Cgler Faultät für Matheat Uverstät We A-9 We Nordbergstraße 5 Joha Cgler@uveacat Abstract I a prevous paper [] I have
Lecture 8 IEEE DCF Performance
Lecture 8 IEEE82. DCF Perforace IEEE82. DCF Basc Access Mechas A stato wth a ew packet to trast otors the chael actvty. If the chael s dle for a perod of te equal to a dstrbuted terfrae space (DIFS), the
Numerical Analysis Formulae Booklet
Numercal Aalyss Formulae Booklet. Iteratve Scemes for Systems of Lear Algebrac Equatos:.... Taylor Seres... 3. Fte Dfferece Approxmatos... 3 4. Egevalues ad Egevectors of Matrces.... 3 5. Vector ad Matrx
The E vs k diagrams are in general a function of the k -space direction in a crystal
vs dagram p m m he parameter s called the crystal mometum ad s a parameter that results from applyg Schrödger wave equato to a sgle-crystal lattce. lectros travelg dfferet drectos ecouter dfferet potetal
MULTIDIMENSIONAL HETEROGENEOUS VARIABLE PREDICTION BASED ON EXPERTS STATEMENTS. Gennadiy Lbov, Maxim Gerasimov
Iteratoal Boo Seres "Iformato Scece ad Computg" 97 MULTIIMNSIONAL HTROGNOUS VARIABL PRICTION BAS ON PRTS STATMNTS Geady Lbov Maxm Gerasmov Abstract: I the wors [ ] we proposed a approach of formg a cosesus
A Model Reduction Technique for linear Model Predictive Control for Non-linear Large Scale Distributed Systems
A Model Reducto Techque for lear Model Predctve Cotrol for No-lear Large Scale Dstrbuted Systes Weguo Xe ad Costatos Theodoropoulos School of Checal Egeerg ad Aalytcal Scece Uversty of Machester, Machester
Estimation of Stress- Strength Reliability model using finite mixture of exponential distributions
Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur
ECE 595, Section 10 Numerical Simulations Lecture 19: FEM for Electronic Transport. Prof. Peter Bermel February 22, 2013
ECE 595, Secto 0 Numercal Smulatos Lecture 9: FEM for Electroc Trasport Prof. Peter Bermel February, 03 Outle Recap from Wedesday Physcs-based devce modelg Electroc trasport theory FEM electroc trasport
ENGI 4421 Propagation of Error Page 8-01
ENGI 441 Propagato of Error Page 8-01 Propagato of Error [Navd Chapter 3; ot Devore] Ay realstc measuremet procedure cotas error. Ay calculatos based o that measuremet wll therefore also cota a error.
Darwin and mass-velocity relativistic corrections in non-born-oppenheimer variational calculations
THE JOURNAL OF CHEMICAL PHYSICS 5, 084303 006 Darw ad mass-velocty relatvstc correctos o-bor-oppehemer varatoal calculatos Darusz Kedzera Departmet of Chemstry, Ncholas Copercus Uversty, ul. Gagara 7,
Chapter 9 Jordan Block Matrices
Chapter 9 Jorda Block atrces I ths chapter we wll solve the followg problem. Gve a lear operator T fd a bass R of F such that the matrx R (T) s as smple as possble. f course smple s a matter of taste.
DIFFERENTIAL GEOMETRIC APPROACH TO HAMILTONIAN MECHANICS
DIFFERENTIAL GEOMETRIC APPROACH TO HAMILTONIAN MECHANICS Course Project: Classcal Mechacs (PHY 40) Suja Dabholkar (Y430) Sul Yeshwath (Y444). Itroducto Hamltoa mechacs s geometry phase space. It deals
Special Instructions / Useful Data
JAM 6 Set of all real umbers P A..d. B, p Posso Specal Istructos / Useful Data x,, :,,, x x Probablty of a evet A Idepedetly ad detcally dstrbuted Bomal dstrbuto wth parameters ad p Posso dstrbuto wth
Ordinary Least Squares Regression. Simple Regression. Algebra and Assumptions.
Ordary Least Squares egresso. Smple egresso. Algebra ad Assumptos. I ths part of the course we are gog to study a techque for aalysg the lear relatoshp betwee two varables Y ad X. We have pars of observatos
Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities
Chemstry 163B Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?
Chapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements
Aoucemets No-Parametrc Desty Estmato Techques HW assged Most of ths lecture was o the blacboard. These sldes cover the same materal as preseted DHS Bometrcs CSE 90-a Lecture 7 CSE90a Fall 06 CSE90a Fall
Lecture 3 Probability review (cont d)
STATS 00: Itroducto to Statstcal Iferece Autum 06 Lecture 3 Probablty revew (cot d) 3. Jot dstrbutos If radom varables X,..., X k are depedet, the ther dstrbuto may be specfed by specfyg the dvdual dstrbuto
The Mathematics of Portfolio Theory
The Matheatcs of Portfolo Theory The rates of retur of stocks, ad are as follows Market odtos state / scearo) earsh Neutral ullsh Probablty 0. 0.5 0.3 % 5% 9% -3% 3% % 5% % -% Notato: R The retur of stock
Chapter 4 Multiple Random Variables
Revew for the prevous lecture: Theorems ad Examples: How to obta the pmf (pdf) of U = g (, Y) ad V = g (, Y) Chapter 4 Multple Radom Varables Chapter 44 Herarchcal Models ad Mxture Dstrbutos Examples:
4 Inner Product Spaces
11.MH1 LINEAR ALGEBRA Summary Notes 4 Ier Product Spaces Ier product s the abstracto to geeral vector spaces of the famlar dea of the scalar product of two vectors or 3. I what follows, keep these key
{ }{ ( )} (, ) = ( ) ( ) ( ) Chapter 14 Exercises in Sampling Theory. Exercise 1 (Simple random sampling): Solution:
Chapter 4 Exercses Samplg Theory Exercse (Smple radom samplg: Let there be two correlated radom varables X ad A sample of sze s draw from a populato by smple radom samplg wthout replacemet The observed
Department of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Ideal Gas Mixtures. Lecture 31
Departet of echacal Egeerg E 322 echacal Egeerg Therodyacs Ideal Gas xtures Lecture 31 xtures Egeerg Applcatos atural gas ethae, ethae, propae, butae, troge, hydroge, carbo doxde, ad others Refrgerats
CONTENTS. 7. Variational Optimization of the Gaussian Nonlinear Parameters in Atomic and Molecular BO
pubs.acs.org/cr Bor Oppehemer ad No-Bor Oppehemer, Atomc ad Molecular Calculatos wth Explctly Correlated Gaussas Ths paper s part of the 0 Quatum Chemstry thematc ssue. Sergy Bub,*, Mchele Pavaello,*,
Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities
Chemstry 163 Itroducto to Multcompoet Systems ad Partal Molar Quattes 1 the problem of partal mmolar quattes mx: 10 moles ethaol C H 5 OH (580 ml) wth 1 mole water H O (18 ml) get (580+18)=598 ml of soluto?
( q Modal Analysis. Eigenvectors = Mode Shapes? Eigenproblem (cont) = x x 2 u 2. u 1. x 1 (4.55) vector and M and K are matrices.
4.3 - Modal Aalyss Physcal coordates are ot always the easest to work Egevectors provde a coveet trasformato to modal coordates Modal coordates are lear combato of physcal coordates Say we have physcal
Overview of the weighting constants and the points where we evaluate the function for The Gaussian quadrature Project two
Overvew of the weghtg costats ad the pots where we evaluate the fucto for The Gaussa quadrature Project two By Ashraf Marzouk ChE 505 Fall 005 Departmet of Mechacal Egeerg Uversty of Teessee Koxvlle, TN
Physics 114 Exam 2 Fall Name:
Physcs 114 Exam Fall 015 Name: For gradg purposes (do ot wrte here): Questo 1. 1... 3. 3. Problem Aswer each of the followg questos. Pots for each questo are dcated red. Uless otherwse dcated, the amout
Lecture 2 - What are component and system reliability and how it can be improved?
Lecture 2 - What are compoet ad system relablty ad how t ca be mproved? Relablty s a measure of the qualty of the product over the log ru. The cocept of relablty s a exteded tme perod over whch the expected
Queueing Networks. γ 3
Queueg Networks Systes odeled by queueg etworks ca roughly be grouped to four categores. Ope etworks Custoers arrve fro outsde the syste are served ad the depart. Exaple: acket swtched data etwork. γ µ
Investigation of Partially Conditional RP Model with Response Error. Ed Stanek
Partally Codtoal Radom Permutato Model 7- vestgato of Partally Codtoal RP Model wth Respose Error TRODUCTO Ed Staek We explore the predctor that wll result a smple radom sample wth respose error whe a
3D Reconstruction from Image Pairs. Reconstruction from Multiple Views. Computing Scene Point from Two Matching Image Points
D Recostructo fro Iage ars Recostructo fro ultple Ves Dael Deetho Fd terest pots atch terest pots Copute fudaetal atr F Copute caera atrces ad fro F For each atchg age pots ad copute pot scee Coputg Scee
We have already referred to a certain reaction, which takes place at high temperature after rich combustion.
ME 41 Day 13 Topcs Chemcal Equlbrum - Theory Chemcal Equlbrum Example #1 Equlbrum Costats Chemcal Equlbrum Example #2 Chemcal Equlbrum of Hot Bured Gas 1. Chemcal Equlbrum We have already referred to a
CS286.2 Lecture 4: Dinur s Proof of the PCP Theorem
CS86. Lecture 4: Dur s Proof of the PCP Theorem Scrbe: Thom Bohdaowcz Prevously, we have prove a weak verso of the PCP theorem: NP PCP 1,1/ (r = poly, q = O(1)). Wth ths result we have the desred costat
The Geometric Least Squares Fitting Of Ellipses
IOSR Joural of Matheatcs (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volue 4, Issue 3 Ver.I (May - Jue 8), PP -8 www.osrourals.org Abdellatf Bettayeb Departet of Geeral Studes, Jubal Idustral College, Jubal
hp calculators HP 30S Statistics Averages and Standard Deviations Average and Standard Deviation Practice Finding Averages and Standard Deviations
HP 30S Statstcs Averages ad Stadard Devatos Average ad Stadard Devato Practce Fdg Averages ad Stadard Devatos HP 30S Statstcs Averages ad Stadard Devatos Average ad stadard devato The HP 30S provdes several
Lecture 8: Linear Regression
Lecture 8: Lear egresso May 4, GENOME 56, Sprg Goals Develop basc cocepts of lear regresso from a probablstc framework Estmatg parameters ad hypothess testg wth lear models Lear regresso Su I Lee, CSE
arxiv:cond-mat/ v2 11 Dec 2000
arxv:cod-mat/0006 v Dec 000 THE NTURE OF THE LON TIME DECY T SECOND ORDER TRNSITION POINT Moshe Schwartz School of Physcs ad stroomy Tel vv Uversty Tel vv, Ramat vv, Israel d S. F. Edwards Cavedsh Laboratory
Analysis of Variance with Weibull Data
Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad
Chapter 3 Sampling For Proportions and Percentages
Chapter 3 Samplg For Proportos ad Percetages I may stuatos, the characterstc uder study o whch the observatos are collected are qualtatve ature For example, the resposes of customers may marketg surveys
Module 7: Probability and Statistics
Lecture 4: Goodess of ft tests. Itroducto Module 7: Probablty ad Statstcs I the prevous two lectures, the cocepts, steps ad applcatos of Hypotheses testg were dscussed. Hypotheses testg may be used to
A study of Fermi hole and partial Fermi hole for Li- and C-Atoms in different states 1s 2p, 1s 3p, 1s 3d and 2s 2p
Iraq Joural of Physcs, 05 Vol.3, No.7, PP. 5-6 A study of Fer hole ad partal Fer hole for L- ad C-Atos dfferet states s p, s 3p, s 3d ad s p Al. A. Alzubad, Khall H. AL-Bayat, Naeeah Ch. M. Physcs Departet,
( ) ( ) ( ( )) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) + ( ) ( ) = ( ( )) ( ) + ( ( )) ( ) Review. Second Derivatives for f : y R. Let A be an m n matrix.
Revew + v, + y = v, + v, + y, + y, Cato! v, + y, + v, + y geeral Let A be a atr Let f,g : Ω R ( ) ( ) R y R Ω R h( ) f ( ) g ( ) ( ) ( ) ( ( )) ( ) dh = f dg + g df A, y y A Ay = = r= c= =, : Ω R he Proof
Introduction to local (nonparametric) density estimation. methods
Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest
Reflection and transmission of light at a curved interface: coherent state approach. N.I. Petrov
Reflecto ad trasmsso of lght at a curved terface: coheret state approach N.I. Petrov Lea Street, 9-39, Istra, Moscow Rego 435, Russa Phase-space procedure based o coheret state represetato s proposed for
Cubic Nonpolynomial Spline Approach to the Solution of a Second Order Two-Point Boundary Value Problem
Joural of Amerca Scece ;6( Cubc Nopolyomal Sple Approach to the Soluto of a Secod Order Two-Pot Boudary Value Problem W.K. Zahra, F.A. Abd El-Salam, A.A. El-Sabbagh ad Z.A. ZAk * Departmet of Egeerg athematcs
Evolution Operators and Boundary Conditions for Propagation and Reflection Methods
voluto Operators ad for Propagato ad Reflecto Methods Davd Yevck Departmet of Physcs Uversty of Waterloo Physcs 5/3/9 Collaborators Frak Schmdt ZIB Tlma Frese ZIB Uversty of Waterloo] atem l-refae Nortel
DATA DOMAIN DATA DOMAIN
3//6 Coprght otce: Most ages these sldes are Gozalez ad oods Pretce-Hall Note: ages are [spatall] ostatoar sgals. e eed tools to aalze the locall at dfferet resolutos e ca do ths the data doa or sutable
Log1 Contest Round 2 Theta Complex Numbers. 4 points each. 5 points each
01 Log1 Cotest Roud Theta Complex Numbers 1 Wrte a b Wrte a b form: 1 5 form: 1 5 4 pots each Wrte a b form: 65 4 4 Evaluate: 65 5 Determe f the followg statemet s always, sometmes, or ever true (you may
Logistic regression (continued)
STAT562 page 138 Logstc regresso (cotued) Suppose we ow cosder more complex models to descrbe the relatoshp betwee a categorcal respose varable (Y) that takes o two (2) possble outcomes ad a set of p explaatory
Analytical Study of Fractal Dimension Types in the Context of SPC Technical Paper. Noa Ruschin Rimini, Irad Ben-Gal and Oded Maimon
Aalytcal Study of Fractal Deso Types the Cotext of SPC Techcal Paper oa Rusch R, Irad Be-Gal ad Oded Mao Departet of Idustral Egeerg, Tel-Avv Uversty, Tel-Avv, Israel Ths paper provdes a aalytcal study
A New Measure of Probabilistic Entropy. and its Properties
Appled Mathematcal Sceces, Vol. 4, 200, o. 28, 387-394 A New Measure of Probablstc Etropy ad ts Propertes Rajeesh Kumar Departmet of Mathematcs Kurukshetra Uversty Kurukshetra, Ida rajeesh_kuk@redffmal.com
F. Inequalities. HKAL Pure Mathematics. 進佳數學團隊 Dr. Herbert Lam 林康榮博士. [Solution] Example Basic properties
![F. Inequalities. HKAL Pure Mathematics. 進佳數學團隊 Dr. Herbert Lam 林康榮博士. [Solution] Example Basic properties](/thumbs/82/86768390.jpg "F. Inequalities. HKAL Pure Mathematics. 進佳數學團隊 Dr. Herbert Lam 林康榮博士. [Solution] Example Basic properties")
進佳數學團隊 Dr. Herbert Lam 林康榮博士 HKAL Pure Mathematcs F. Ieualtes. Basc propertes Theorem Let a, b, c be real umbers. () If a b ad b c, the a c. () If a b ad c 0, the ac bc, but f a b ad c 0, the ac bc. Theorem
Shiva and Kali diagrams for composite quantum particle many-body effects
1 arxv:0902.4588v1 [cod-at.es-hall] 26 Feb 2009 Shva ad Kal dagras for coposte quatu partcle ay-body effects M. Cobescot ad O. Betbeder-Matbet Isttut des NaoSceces de Pars, Uversté Perre et Mare Cure,