Band structure calculations
|
|
|
- Margaret Dean
- 6 years ago
- Views:
Transcription
1 Bad structure cacuatos group semar 00-0 Georg Wrth Isttut für Laser Physk Jauary 00
2 Motvato attce ad stab. aser are outcouped from SM-PM-fber Mcheso terferometer braches overap uder 90 attce forms overappg rego pezo-drve mrrors aow to adust reatve phase dfferece θ pae waves vertca poarzato photodode cod atoms 50% pezomouted mrror Georg Wrth Isttut für Laser-Physk
3 Motvato dpoe poteta at has terferece term attce structure depeds o phase dfferece θ bad structure ad wavefuctos chage wth phase at y 0 cos k cos ky cos k cos ky cos θ sum of pae waves terferece term Georg Wrth Isttut für Laser-Physk 3
4 Oute How to cacuate a bad structure Boch Theorem ad Fourer epaso Schrödger euato matr form Oe- ad two-dmesoa bad structure Boch- ad Waer-fuctos Topc Iterferece chages depth of eghbour stes Effect o oe-dmesoa bad structure Modfed Boch ad Waer?-fuctos Epermeta sgature & Summary Georg Wrth Isttut für Laser-Physk 4
5 Georg Wrth Isttut für Laser-Physk 5 Boch theorem ad Fourer epaso ˆ E H Φ Φ wth Schrödger euato wth perodc poteta cos ˆ ˆ k m p H at / ep u Φ h Boch theorem ˆ u E u H B Schrödger euato for u-fuctos wth cos ˆ ˆ k m p H at B k ep Epress u-fuctos ad poteta as dscrete Fourer sums k c u ep ad ep / ˆ k c E k u m p rec h ketc eergy of H B becomes
6 Georg Wrth Isttut für Laser-Physk 6 Schrödger euato matr form Fourer coeffcets at at at at k k k ep ep cos ep k c u poteta eergy of H B becomes put t together ± ± at at k c k c u ep : 0 ep : 4 wrte Schrödger euato matr form 0 : ese : / : ˆ ˆ ep ep ˆ ˆ 4 at at rec B E k H c E c H k c E k c H u H h M M M L
7 -dm bad structure sove egevaue probem umercay Mathematca: Egevaues[] wth fte umber of Fourer coeffcets good appromato f hgher bads are ot popuated Hamto-operator s matr oy bads are take to accout! free partce harm. oscator k π / λ s NOT recproca attce vector Georg Wrth Isttut für Laser-Physk 7
8 -dm bad structure reca attce poteta at z 0 cos k cos kz cos k cos kz cos θ sum of pae waves terferece term for θ π/ phase dfferece Hamto separabe two or three dmesos wavefuctos ca be cacuated separatey ad supermposed eergy s sum of dfferet drectos Georg Wrth Isttut für Laser-Physk 8
9 Boch-fuctos for gve bad ad uas-mpuse use egevector c - c to cacuate u- fuctos ad Boch-wavefucto Φ ep / h c ep k Georg Wrth Isttut für Laser-Physk 9
10 Waer-fuctos Boch-fuctos are the atura bass the mode of uas-free partce but deocazed Waer-fuctos are ocazed o partcuar stes ad form a compete set of orthogoa bass states w N / BZ d ep / h Φ appromate Itegrato over Brou-zoe by dscrete sum makes Waer-fucto perodca rgg! Georg Wrth Isttut für Laser-Physk 0
11 Waer-fuctos dscrete sum Georg Wrth Isttut für Laser-Physk
12 Waer-fuctos Georg Wrth Isttut für Laser-Physk
13 Iterferece chages depth of eghbour stes at z 0 cos k cos kz cos k cos kz cos θ sum of pae waves terferece term Georg Wrth Isttut für Laser-Physk 3
14 Iterferece chages depth of eghbour stes ook at vertca cut at z0 sma devatos from θ π/ ead to sgfcat chages we depth Georg Wrth Isttut für Laser-Physk 4
15 Effect o -dm. bad structure -dm. attce poteta s at 0 at at [ cos k cos θ cos k ] [ 4 ep k 4 ep k cos θ ep k cos θ ep k 3 ] Fourer sums ow wth perodcty k stead of k 3 4 at cos θ at 0 at Schrödger euato s ow Hˆ Hˆ c E c / hk : E : cos θ at : 4 at ese : 0 rec 3 at Georg Wrth Isttut für Laser-Physk 5
16 Effect o -dm. bad structure Georg Wrth Isttut für Laser-Physk 6
17 Effect o -dm. bad structure f phase devates from θ π/ addtoa Bragg-refecto from superattce sets coupg betwee mpuse casses ħk/ ad -ħk/ eads to spttg eergy gap Georg Wrth Isttut für Laser-Physk 7
18 Effect o -dm. bad structure the Bose-Hubbard-mode the tueg matr eemet s gve by J ma m E E owest bad s dramatcay fatteed partces are ped to deep attce stes tueg s suppressed euay spaced eves ke harm. osc. Georg Wrth Isttut für Laser-Physk 8
19 Modfed Boch-fuctos cacuate Boch-fuctos wth ew k/ perodcty Φ ep / h c ep k Georg Wrth Isttut für Laser-Physk 9
20 Modfed Waer-fuctos cacuate waer-states by summato over smaer Brou-zoe w N / BZ d ep / h Φ Georg Wrth Isttut für Laser-Physk 0
21 Epermeta sgatures & Summary TOF-mages show mpuse-spectra of atoms the attce whe attce poteta s swtched of fasty sma devatos from 90 strogy popuate the 0 peaks comparabe to theoretca resuts Georg Wrth Isttut für Laser-Physk
Transforms that are commonly used are separable
Trasforms s Trasforms that are commoly used are separable Eamples: Two-dmesoal DFT DCT DST adamard We ca the use -D trasforms computg the D separable trasforms: Take -D trasform of the rows > rows ( )
Landé interval rule (assignment!) l examples
36 - Read CTD, pp. 56-78 AT TIME: O H = ar s ζ(,, ) s adé terva rue (assgmet!) ζ(,, ) ζ exampes ζ (oe ζfor each - term) (oe ζfor etre cofgurato) evauate matrx eemets ater determata bass ad may-e M or M
Econometric Methods. Review of Estimation
Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators
Computational learning and discovery
Computatoa earg ad dscover CSI 873 / MAH 689 Istructor: I. Grva Wedesda 7:2-1 pm Gve a set of trag data 1 1 )... ) { 1 1} fd a fucto that ca estmate { 1 1} gve ew ad mmze the frequec of the future error.
Face Recognition. Face Recognition. Why is Face Recognition. Automated Face Recognition Difficult? Why is it Difficult?
Face Recogto Face Recogto If I ook at your face I mmedatey recogze that I have see t before Yet there s o mache whch, wth that speed, ca take a pcture of a face ad say eve that t s a ma; ad much ess that
CS 2750 Machine Learning. Lecture 8. Linear regression. CS 2750 Machine Learning. Linear regression. is a linear combination of input components x
CS 75 Mache Learg Lecture 8 Lear regresso Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 75 Mache Learg Lear regresso Fucto f : X Y s a lear combato of put compoets f + + + K d d K k - parameters
1. A real number x is represented approximately by , and we are told that the relative error is 0.1 %. What is x? Note: There are two answers.
PROBLEMS A real umber s represeted appromately by 63, ad we are told that the relatve error s % What s? Note: There are two aswers Ht : Recall that % relatve error s What s the relatve error volved roudg
x y exp λ'. x exp λ 2. x exp 1.
egecosmcd Egevalue-egevector of the secod dervatve operator d /d hs leads to Fourer seres (se, cose, Legedre, Bessel, Chebyshev, etc hs s a eample of a systematc way of geeratg a set of mutually orthogoal
Lecture 12 APPROXIMATION OF FIRST ORDER DERIVATIVES
FDM: Appromato of Frst Order Dervatves Lecture APPROXIMATION OF FIRST ORDER DERIVATIVES. INTRODUCTION Covectve term coservato equatos volve frst order dervatves. The smplest possble approach for dscretzato
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
Arithmetic Mean Suppose there is only a finite number N of items in the system of interest. Then the population arithmetic mean is
Topc : Probablty Theory Module : Descrptve Statstcs Measures of Locato Descrptve statstcs are measures of locato ad shape that perta to probablty dstrbutos The prmary measures of locato are the arthmetc
Energy method in solving the problems of stability for a viscoelastic polymer rods
MATEC Web of Cofereces 19 51 (17) ICMTMTE 17 DOI: 1151/mateccof/171951 Eergy method sovg the probems of stabty for a vscoeastc poymer rods Serdar Yazyev 1 Mara Kozeskaya 1 Grgory Strekov 1 ad Stepa Ltvov
IFYMB002 Mathematics Business Appendix C Formula Booklet
Iteratoal Foudato Year (IFY IFYMB00 Mathematcs Busess Apped C Formula Booklet Related Documet: IFY Mathematcs Busess Syllabus 07/8 IFYMB00 Maths Busess Apped C Formula Booklet Cotets lease ote that the
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
Charge Exchange of Proton Sodium Atom Collision
Amerca Joura o Physcs ad Appcatos 7; 5(5: 73-79 http://wwwscecepubshroupcom/j/ajpa do: 648/jajpa7553 ISSN: 33-486 (Prt; ISSN: 33-438 (Oe Chare Echae o Proto Sodum Atom Coso Sabbah A Ekay, Departmet o Mathematcs,
EECE 301 Signals & Systems
EECE 01 Sgals & Systems Prof. Mark Fowler Note Set #9 Computg D-T Covoluto Readg Assgmet: Secto. of Kame ad Heck 1/ Course Flow Dagram The arrows here show coceptual flow betwee deas. Note the parallel
Bounds on the expected entropy and KL-divergence of sampled multinomial distributions. Brandon C. Roy
Bouds o the expected etropy ad KL-dvergece of sampled multomal dstrbutos Brado C. Roy bcroy@meda.mt.edu Orgal: May 18, 2011 Revsed: Jue 6, 2011 Abstract Iformato theoretc quattes calculated from a sampled
Fourth Order Four-Stage Diagonally Implicit Runge-Kutta Method for Linear Ordinary Differential Equations ABSTRACT INTRODUCTION
Malasa Joural of Mathematcal Sceces (): 95-05 (00) Fourth Order Four-Stage Dagoall Implct Ruge-Kutta Method for Lear Ordar Dfferetal Equatos Nur Izzat Che Jawas, Fudzah Ismal, Mohamed Sulema, 3 Azm Jaafar
Supervised Learning! B." Neural Network Learning! Typical Artificial Neuron! Feedforward Network! Typical Artificial Neuron! Equations!
Part 4B: Neura Networ earg 10/22/08 Superved earg B. Neura Networ earg Produce dered output for trag put Geeraze reaoaby appropratey to other put Good exampe: patter recogto Feedforward mutayer etwor 10/22/08
PART ONE. Solutions to Exercises
PART ONE Soutos to Exercses Chapter Revew of Probabty Soutos to Exercses 1. (a) Probabty dstrbuto fucto for Outcome (umber of heads) 0 1 probabty 0.5 0.50 0.5 Cumuatve probabty dstrbuto fucto for Outcome
Solutions for HW4. x k n+1. k! n(n + 1) (n + k 1) =.
Exercse 13 (a Proe Soutos for HW4 (1 + x 1 + x 2 1 + (1 + x 2 + x 2 2 + (1 + x + x 2 + by ducto o M(Sν x S x ν(x Souto: Frst ote that sce the mutsets o {x 1 } are determed by ν(x 1 the set of mutsets o
CS5620 Intro to Computer Graphics
CS56 Itro to Computer Graphcs Geometrc Modelg art II Geometrc Modelg II hyscal Sples Curve desg pre-computers Cubc Sples Stadard sple put set of pots { } =, No dervatves specfed as put Iterpolate by cubc
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
Principal Component Analysis (PCA)
BBM0 - Itroduc0o to ML Sprg 0 Prcpa Compoet Aayss PCA Mo0va0o PCA agorthms Appca0os PCA shortcomgs ere PCA oday Ayut Erdem Dept. of Computer Egeerg HaceDepe Uversty Sdes adopted from Barabás Póczos ar
QR Factorization and Singular Value Decomposition COS 323
QR Factorzato ad Sgular Value Decomposto COS 33 Why Yet Aother Method? How do we solve least-squares wthout currg codto-squarg effect of ormal equatos (A T A A T b) whe A s sgular, fat, or otherwse poorly-specfed?
Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.?
Ch 4. Statstcs 4.1 Quattatve aalyss requres : soud kowledge of chemstry : possblty of terfereces WHY do we eed to use STATISTICS Aal. Chem.? ucertaty ests. wll we accept ucertaty always? f ot, from how
STK4011 and STK9011 Autumn 2016
STK4 ad STK9 Autum 6 Pot estmato Covers (most of the followg materal from chapter 7: Secto 7.: pages 3-3 Secto 7..: pages 3-33 Secto 7..: pages 35-3 Secto 7..3: pages 34-35 Secto 7.3.: pages 33-33 Secto
Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Aalyss of Varace ad Desg of Exermets-I MODULE II LECTURE - GENERAL LINEAR HYPOTHESIS AND ANALYSIS OF VARIANCE Dr Shalabh Deartmet of Mathematcs ad Statstcs Ida Isttute of Techology Kaur Tukey s rocedure
Different Kinds of Boundary Elements for Solving the Problem of the Compressible Fluid Flow around Bodies-a Comparison Study
Proceedgs of the Word Cogress o Egeerg 8 Vo II WCE 8, Ju - 4, 8, Lodo, U.K. Dfferet Kds of Boudar Eemets for Sovg the Probem of the Compressbe Fud Fow aroud Bodes-a Comparso Stud Lumta Grecu, Gabrea Dema
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
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
Machine Learning. Topic 4: Measuring Distance
Mache Learg Topc 4: Measurg Dstace Bra Pardo Mache Learg: EECS 349 Fall 2009 Wh measure dstace? Clusterg requres dstace measures. Local methods requre a measure of localt Search eges requre a measure of
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
Ellipsometry Overview
llpsometry Overvew ~ R Δ p ρ = ta( Ψ) e = ~ Rs ñ(λ) = (λ) + k(λ) ε = ñ 2 p-plae s-plae p-plae plae of cdece s-plae llpsometry buldg-blocks Lght ad Polarzato Materals / Optcal Costats Iteracto of Lght wth
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
Finsler Geometry & Cosmological constants
Avaabe oe at www.peaaresearchbrary.com Peaa esearch Lbrary Advaces Apped Scece esearch, 0, (6):44-48 Fser Geometry & Cosmooca costats. K. Mshra ad Aruesh Padey ISSN: 0976-860 CODEN (USA): AASFC Departmet
Optimal Constants in the Rosenthal Inequality for Random Variables with Zero Odd Moments.
Optma Costats the Rosetha Iequaty for Radom Varabes wth Zero Odd Momets. The Harvard commuty has made ths artce opey avaabe. Pease share how ths access beefts you. Your story matters Ctato Ibragmov, Rustam
A Study of the Reproducibility of Measurements with HUR Leg Extension/Curl Research Line
HUR Techcal Report 000--9 verso.05 / Frak Borg (borgbros@ett.f) A Study of the Reproducblty of Measuremets wth HUR Leg Eteso/Curl Research Le A mportat property of measuremets s that the results should
Mean is only appropriate for interval or ratio scales, not ordinal or nominal.
Mea Same as ordary average Sum all the data values ad dvde by the sample sze. x = ( x + x +... + x Usg summato otato, we wrte ths as x = x = x = = ) x Mea s oly approprate for terval or rato scales, ot
PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation
PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad
Multiple Choice Test. Chapter Adequacy of Models for Regression
Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to
Supervised learning: Linear regression Logistic regression
CS 57 Itroducto to AI Lecture 4 Supervsed learg: Lear regresso Logstc regresso Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 57 Itro to AI Data: D { D D.. D D Supervsed learg d a set of eamples s
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
CS475 Parallel Programming
CS475 Parallel Programmg Deretato ad Itegrato Wm Bohm Colorado State Uversty Ecept as otherwse oted, the cotet o ths presetato s lcesed uder the Creatve Commos Attrbuto.5 lcese. Pheomea Physcs: heat, low,
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,
Parameter Estimation
arameter Estmato robabltes Notatoal Coveto Mass dscrete fucto: catal letters Desty cotuous fucto: small letters Vector vs. scalar Scalar: la Vector: bold D: small Hgher dmeso: catal Notes a cotuous state
Stationary states of atoms and molecules
Statoary states of atos ad olecules 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
Chem 442 Review for Exam 1. Hamiltonian operator in 1 dimension: ˆ d first term is kinetic energy, second term is potential energy
Chem 44 Review for Eam 1 Eergies are quatized Wave/partice duaity de Brogie waveegth: h p Eergy: E h mometum operator: pˆ positio operator: ˆ d i d potetia eergy operator: V ˆ( ) pˆ d kietic eergy operator
Test Paper-II. 1. If sin θ + cos θ = m and sec θ + cosec θ = n, then (a) 2n = m (n 2 1) (b) 2m = n (m 2 1) (c) 2n = m (m 2 1) (d) none of these
Test Paer-II. If s θ + cos θ = m ad sec θ + cosec θ =, the = m ( ) m = (m ) = m (m ). If a ABC, cos A = s B, the t s C a osceles tragle a eulateral tragle a rght agled tragle. If cos B = cos ( A+ C), the
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
Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades
STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos
Continuous Distributions
7//3 Cotuous Dstrbutos Radom Varables of the Cotuous Type Desty Curve Percet Desty fucto, f (x) A smooth curve that ft the dstrbuto 3 4 5 6 7 8 9 Test scores Desty Curve Percet Probablty Desty Fucto, f
Objectives of Multiple Regression
Obectves of Multple Regresso Establsh the lear equato that best predcts values of a depedet varable Y usg more tha oe eplaator varable from a large set of potetal predctors {,,... k }. Fd that subset of
Conservative Averaging and Finite Difference Methods for Transient Heat Conduction in 3D Fuse
Ramods Vums Adrs Buks Coservatve Averagg ad Fte Dfferece Metods for Traset Heat Coducto 3D Fuse RAIMONDS VIUMS ANDRIS BUIKIS Isttute of Matematcs ad Computer Scece Uversty of atva Raa uv 9 Rga V459 ATVIA
Bounds for block sparse tensors
A Bouds for bock sparse tesors Oe of the ma bouds to cotro s the spectra orm of the sparse perturbato tesor S The success of the power teratos ad the mprovemet accuracy of recovery over teratve steps of
Methods for solving the radiative transfer equation with multiple scattering. Part 3: Exact methods: Discrete-ordinate and Adding.
Lecture. Methos for sovg the raatve trasfer equato wth utpe scatterg. art 3: Exact ethos: screte-orate a Ag. Obectves:. screte-orate etho for the case of sotropc scatterg.. Geerazato of the screte-orate
Unsupervised Learning and Other Neural Networks
CSE 53 Soft Computg NOT PART OF THE FINAL Usupervsed Learg ad Other Neural Networs Itroducto Mture Destes ad Idetfablty ML Estmates Applcato to Normal Mtures Other Neural Networs Itroducto Prevously, all
means the first term, a2 means the term, etc. Infinite Sequences: follow the same pattern forever.
9.4 Sequeces ad Seres Pre Calculus 9.4 SEQUENCES AND SERIES Learg Targets:. Wrte the terms of a explctly defed sequece.. Wrte the terms of a recursvely defed sequece. 3. Determe whether a sequece s arthmetc,
Black or White Video. Lecture 3: Face Detection. Face Detection. Why is Face Detection Difficult? Automated Face Detection Why is it Difficult?
Back or Whte Veo ecture : Face Detecto Reag: Egeaces oe paper FP pgs 55-5 Haouts: Course Descrpto P Assge Face Detecto Face ocazato egmetato Face rackg Faca eatures ocazato Faca eatures trackg orphg wwwyoutubecom/watch?vzi9oyrwq
Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model
Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The
Fractional Order Finite Difference Scheme For Soil Moisture Diffusion Equation And Its Applications
IOS Joural of Mathematcs (IOS-JM e-iss: 78-578. Volume 5, Issue 4 (Ja. - Feb. 3, PP -8 www.osrourals.org Fractoal Order Fte Dfferece Scheme For Sol Mosture Dffuso quato Ad Its Applcatos S.M.Jogdad, K.C.Takale,
i 2 σ ) i = 1,2,...,n , and = 3.01 = 4.01
ECO 745, Homework 6 Le Cabrera. Assume that the followg data come from the lear model: ε ε ~ N, σ,,..., -6. -.5 7. 6.9 -. -. -.9. -..6.4.. -.6 -.7.7 Fd the mamum lkelhood estmates of,, ad σ ε s.6. 4. ε
Module 1 : The equation of continuity. Lecture 5: Conservation of Mass for each species. & Fick s Law
Module : The equato of cotuty Lecture 5: Coservato of Mass for each speces & Fck s Law NPTEL, IIT Kharagpur, Prof. Sakat Chakraborty, Departmet of Chemcal Egeerg 2 Basc Deftos I Mass Trasfer, we usually
Solving the Problem of the Compressible Fluid Flow around Obstacles by an Indirect Approach with Vortex Distribution and Linear Boundary Elements
Lumta Grecu Sov the Probem of the ompressbe Fud Fow aroud Obstaces b a Idrect Approach wth Vorte Dstrbuto ad Lear Boudar Eemets LUMINITA GREU Departmet of Apped Sceces, Navato ad Evromet Protecto Facut
A stopping criterion for Richardson s extrapolation scheme. under finite digit arithmetic.
A stoppg crtero for cardso s extrapoato sceme uder fte dgt artmetc MAKOO MUOFUSHI ad HIEKO NAGASAKA epartmet of Lbera Arts ad Sceces Poytecc Uversty 4-1-1 Hasmotoda,Sagamara,Kaagawa 229-1196 JAPAN Abstract:
12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model
1. Estmatg Model parameters Assumptos: ox ad y are related accordg to the smple lear regresso model (The lear regresso model s the model that says that x ad y are related a lear fasho, but the observed
Can we take the Mysticism Out of the Pearson Coefficient of Linear Correlation?
Ca we tae the Mstcsm Out of the Pearso Coeffcet of Lear Correlato? Itroducto As the ttle of ths tutoral dcates, our purpose s to egeder a clear uderstadg of the Pearso coeffcet of lear correlato studets
Layered structures: transfer matrix formalism
Layered tructure: trafer matrx formalm Iterface betwee LI meda Trafer matrx formalm Petr Kužel Practcally oly oe formula to be kow order to calculate ay tructure Applcato: Atreflectve coatg Delectrc mrror,
D. VQ WITH 1ST-ORDER LOSSLESS CODING
VARIABLE-RATE VQ (AKA VQ WITH ENTROPY CODING) Varable-Rate VQ = Quatzato + Lossless Varable-Legth Bary Codg A rage of optos -- from smple to complex A. Uform scalar quatzato wth varable-legth codg, oe
Linear Regression Linear Regression with Shrinkage. Some slides are due to Tommi Jaakkola, MIT AI Lab
Lear Regresso Lear Regresso th Shrkage Some sldes are due to Tomm Jaakkola, MIT AI Lab Itroducto The goal of regresso s to make quattatve real valued predctos o the bass of a vector of features or attrbutes.
1 Onto functions and bijections Applications to Counting
1 Oto fuctos ad bectos Applcatos to Coutg Now we move o to a ew topc. Defto 1.1 (Surecto. A fucto f : A B s sad to be surectve or oto f for each b B there s some a A so that f(a B. What are examples of
CS 1675 Introduction to Machine Learning Lecture 12 Support vector machines
CS 675 Itroducto to Mache Learg Lecture Support vector maches Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square Mdterm eam October 9, 7 I-class eam Closed book Stud materal: Lecture otes Correspodg chapters
NUMERICAL SIMULATION ON MELTING AND SOLIDIFICATION BASED ON LAGRANGIAN APPROACH
NUMERICAL SIMULATION ON MELTING AND SOLIDIFICATION BASED ON LAGRANGIAN APPROACH J-Bao Xog Hog-Ya Wag Xu Cheg Ya-Hua Yag Schoo of Nucear Scece ad Egeerg, Shagha Jao Tog Uversty 8 Dogchua Road Mhag Shagha
Signal,autocorrelation -0.6
Sgal,autocorrelato Phase ose p/.9.3.7. -.5 5 5 5 Tme Sgal,autocorrelato Phase ose p/.5..7.3 -. -.5 5 5 5 Tme Sgal,autocorrelato. Phase ose p/.9.3.7. -.5 5 5 5 Tme Sgal,autocorrelato. Phase ose p/.8..6.
PHYS Look over. examples 2, 3, 4, 6, 7, 8,9, 10 and 11. How To Make Physics Pay PHYS Look over. Examples: 1, 4, 5, 6, 7, 8, 9, 10,
PHYS Look over Chapter 9 Sectos - Eamples:, 4, 5, 6, 7, 8, 9, 0, PHYS Look over Chapter 7 Sectos -8 8, 0 eamples, 3, 4, 6, 7, 8,9, 0 ad How To ake Phscs Pa We wll ow look at a wa of calculatg where the
Lecture Notes Types of economic variables
Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte
On A Two Dimensional Finsler Space Whose Geodesics Are Semi- Elipses and Pair of Straight Lines
IOSR Joural of Mathematcs (IOSR-JM) e-issn: 78-578 -ISSN:39-765X Volume 0 Issue Ver VII (Mar-Ar 04) PP 43-5 wwwosrjouralsorg O A Two Dmesoal Fsler Sace Whose Geodescs Are Sem- Elses ad Par of Straght es
Sampling Theory MODULE V LECTURE - 14 RATIO AND PRODUCT METHODS OF ESTIMATION
Samplg Theor MODULE V LECTUE - 4 ATIO AND PODUCT METHODS OF ESTIMATION D. SHALABH DEPATMENT OF MATHEMATICS AND STATISTICS INDIAN INSTITUTE OF TECHNOLOG KANPU A mportat objectve a statstcal estmato procedure
[ L] υ = (3) [ L] n. Q: What are the units of K in Eq. (3)? (Why is units placed in quotations.) What is the relationship to K in Eq. (1)?
![[ L] υ = (3) [ L] n. Q: What are the units of K in Eq. (3)? (Why is units placed in quotations.) What is the relationship to K in Eq. (1)?](/thumbs/87/96901092.jpg "[ L] υ = (3) [ L] n. Q: What are the units of K in Eq. (3)? (Why is units placed in quotations.) What is the relationship to K in Eq. (1)?")
Chem 78 Spr. M. Wes Bdg Polyomals Bdg Polyomals We ve looked at three cases of lgad bdg so far: The sgle set of depedet stes (ss[]s [ ] [ ] Multple sets of depedet stes (ms[]s, or m[]ss All or oe, or two-state
Investigating Cellular Automata
Researcher: Taylor Dupuy Advsor: Aaro Wootto Semester: Fall 4 Ivestgatg Cellular Automata A Overvew of Cellular Automata: Cellular Automata are smple computer programs that geerate rows of black ad whte
DKA method for single variable holomorphic functions
DKA method for sgle varable holomorphc fuctos TOSHIAKI ITOH Itegrated Arts ad Natural Sceces The Uversty of Toushma -, Mamhosama, Toushma, 770-8502 JAPAN Abstract: - Durad-Kerer-Aberth (DKA method for
Transforming Numerical Methods Education for the STEM Undergraduate Torque (N-m)
Regresso Trasformg Numercal Methods Educato for the STEM udergraduate Applcatos Mousetrap Car Torsoal Stffess of a Mousetrap Sprg 0.4 Torque (N-m 0.3 0. T k 0 k1 θ 0.1 0.5 1 1.5 θ (radas 1 Stress vs Stra
Wu-Hausman Test: But if X and ε are independent, βˆ. ECON 324 Page 1
Wu-Hausma Test: Detectg Falure of E( ε X ) Caot drectly test ths assumpto because lack ubased estmator of ε ad the OLS resduals wll be orthogoal to X, by costructo as ca be see from the momet codto X'
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
Some Applications of the Resampling Methods in Computational Physics
Iteratoal Joural of Mathematcs Treds ad Techoloy Volume 6 February 04 Some Applcatos of the Resampl Methods Computatoal Physcs Sotraq Marko #, Lorec Ekoom * # Physcs Departmet, Uversty of Korca, Albaa,
Dimensionality reduction Feature selection
CS 750 Mache Learg Lecture 3 Dmesoalty reducto Feature selecto Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 750 Mache Learg Dmesoalty reducto. Motvato. Classfcato problem eample: We have a put data
ECONOMETRIC THEORY. MODULE VIII Lecture - 26 Heteroskedasticity
ECONOMETRIC THEORY MODULE VIII Lecture - 6 Heteroskedastcty Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur . Breusch Paga test Ths test ca be appled whe the replcated data
,...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
Carrier Action under Perturbation
Carrer Acto uder Perturbato Eulbrum: o curret ad o formato ca be represeted. Ferm-level s flat! Perturbato s ecessary to artfcally ecode formato perturbed states: electrc feld (drft), cocetrato gradet
Generative classification models
CS 75 Mache Learg Lecture Geeratve classfcato models Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square Data: D { d, d,.., d} d, Classfcato represets a dscrete class value Goal: lear f : X Y Bar classfcato
Taylor s Series and Interpolation. Interpolation & Curve-fitting. CIS Interpolation. Basic Scenario. Taylor Series interpolates at a specific
CIS 54 - Iterpolato Roger Crawfs Basc Scearo We are able to prod some fucto, but do ot kow what t really s. Ths gves us a lst of data pots: [x,f ] f(x) f f + x x + August 2, 25 OSU/CIS 54 3 Taylor s Seres
Regression and the LMS Algorithm
CSE 556: Itroducto to Neural Netorks Regresso ad the LMS Algorthm CSE 556: Regresso 1 Problem statemet CSE 556: Regresso Lear regresso th oe varable Gve a set of N pars of data {, d }, appromate d b a
CSE 5526: Introduction to Neural Networks Linear Regression
CSE 556: Itroducto to Neural Netorks Lear Regresso Part II 1 Problem statemet Part II Problem statemet Part II 3 Lear regresso th oe varable Gve a set of N pars of data , appromate d by a lear fucto
Third handout: On the Gini Index
Thrd hadout: O the dex Corrado, a tala statstca, proposed (, 9, 96) to measure absolute equalt va the mea dfferece whch s defed as ( / ) where refers to the total umber of dvduals socet. Assume that. The
MA/CSSE 473 Day 27. Dynamic programming
MA/CSSE 473 Day 7 Dyamc Programmg Bomal Coeffcets Warshall's algorthm (Optmal BSTs) Studet questos? Dyamc programmg Used for problems wth recursve solutos ad overlappg subproblems Typcally, we save (memoze)
Periodic Table of Elements. EE105 - Spring 2007 Microelectronic Devices and Circuits. The Diamond Structure. Electronic Properties of Silicon
EE105 - Srg 007 Mcroelectroc Devces ad Crcuts Perodc Table of Elemets Lecture Semcoductor Bascs Electroc Proertes of Slco Slco s Grou IV (atomc umber 14) Atom electroc structure: 1s s 6 3s 3 Crystal electroc
1. BLAST (Karlin Altschul) Statistics
Parwse seuece algmet global ad local Multple seuece algmet Substtuto matrces Database searchg global local BLAST Seuece statstcs Evolutoary tree recostructo Gee Fdg Prote structure predcto RNA structure
CS 2750 Machine Learning. Lecture 7. Linear regression. CS 2750 Machine Learning. Linear regression. is a linear combination of input components x
CS 75 Mache Learg Lecture 7 Lear regresso Mlos Hauskrecht los@cs.ptt.edu 59 Seott Square CS 75 Mache Learg Lear regresso Fucto f : X Y s a lear cobato of put copoets f + + + K d d K k - paraeters eghts
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
SPECIAL CONSIDERATIONS FOR VOLUMETRIC Z-TEST FOR PROPORTIONS
SPECIAL CONSIDERAIONS FOR VOLUMERIC Z-ES FOR PROPORIONS Oe s stctve reacto to the questo of whether two percetages are sgfcatly dfferet from each other s to treat them as f they were proportos whch the