Image Enhancement: Histogram-based methods
|
|
|
- Marshall Cox
- 5 years ago
- Views:
Transcription
1 Image Enhancement: Hitogam-baed method The hitogam of a digital image with gayvalue, i the dicete function,, L n n # ixel with value Total # ixel image The function eeent the faction of the total numbe of ixel with gayvalue. Hitogam ovide a global decition of the aeaance of the image. If we conide the gayvalue the image a ealiation of a andom vaiable R, with ome obability denity, hitogam ovide an aoximation to thi obability denity. In othe wod, P[ R ]
2 Some tyical Hitogam The hae of a hitogam ovide ueful fomation fo contat enhancement Da Image.9.8. Bight Image High Contat Image Low Contat Image
3 Hitogam Equaliation Let u aume fo the moment that the ut image to be enhanced ha contuou gayvalue, with eeentg blac and eeentg white. We need to deign a gayvalue tanfomation T, baed on the hitogam of the ut image, which will enhance the image. A befoe, we aume that: T i a monotonically ceag function fo eeve ode fom blac to white T ma [,] to [,] eeve the ange of allowed gayvalue. Outut gayvalue T Inut gayvalue nomalied
4 Let u denote the vee tanfomation by T. We aume that the vee tanfomation alo atifie the above two condition. We conide the gayvalue the ut image and ut image a andom vaiable the teval [, ]. Let and denote the obability denity of the gayvalue the ut and ut image. If and T ae nown, and T atifie condition, we can wite eult fom obability theoy: d d T One way to enhance the image i to deign a tanfomation T. uch that the gayvalue the ut i unifomly ditibuted [, ], i.e., In tem of hitogam, the ut image will have all gayvalue equal ootion. Thi technique i called hitogam equaliation.
5 Conide the tanfomation T w dw, Note that thi i the cumulative ditibution function CDF of and atifie the eviou two condition. Fom the eviou equation and ug the fundamental theoem of calculu, d d Theefoe, the ut hitogam i given by [ ], fo T T The ut obability denity function i unifom, egadle of the ut.
6 Thu, ug a tanfomation function equal to the CDF of ut gayvalue, we can obta an image with unifom gayvalue. Thi uually eult an enhanced image, with an ceae the dynamic ange of ixel value. Examle: Read examle age 6 of text. Fo image with dicete gayvalue, we have n, fo, and L n L: Total numbe of gaylevel n : Numbe of ixel with gayvalue n: Total numbe of ixel the image The dicete veion of the eviou tanfomation baed on CDF i given by: T n n, fo L
7 Examle Conide an 8-level 64 x 64 image with gayvalue,,,. The nomalied gayvalue ae, /, 2/,,. The nomalied hitogam i given below: n n /n 9.9 / / / / / / Hitogam unnomalied.25 Nomalied Hitogam.2 8 # ixel faction of # ixel ayvalue.5 Nomalied ayvalue
8 Alyg the eviou tanfomation, we have afte oundg off to neaet gaylevel: Notice that thee ae only five ditct gaylevel --- /, 3/, 5/, 6/, the ut image. We will elabel them a,,, T T T T T T T T
9 With thi tanfomation, the ut image will have hitogam n n /n / 9.9 3/ / / Hitogam of ut image 8 # ixel gayvalue Note that the hitogam of ut image i only aoximately, and not exactly, unifom. Thi hould not be uig, ce thee i no eult that claim unifomity the dicete cae.
10 Examle Oigal image and it hitogam aimead tie.tif ; imhita; Hitogam equalied image and it hitogam bhiteqa; imhitb;
11 Hitogam equaliation may not alway oduce deiable eult, aticulaly if the given hitogam i vey naow. It can oduce fale edge and egion. It can alo ceae image gae and atche.
12 Oigal Image and it hitogam Hitogam equalied image and it hitogam
13 Hitogam Secification Hitogam equaliation yield an image whoe ixel ae theoy unifomly ditibuted among all gaylevel. Sometime, thi may not be deiable. Intead, we may want a tanfomation that yield an ut image with a eecified hitogam. Thi technique i called hitogam ecification. Aga, we will aume, fo the moment, contuougayvalue. Suoe, the ut image ha obability denity. We want to fd a tanfomation H, uch that the obability denity of the new image obtaed by thi tanfomation i, which i not neceaily unifom. Fit aly the tanfomation T w dw, Thi give an image with a unifom obability denity. * If the deied ut image wee available, then the followg tanfomation would geneate an image with unifom denity:
14 ν w dw, Fom the gayvalue ν we can obta the gayvalue by ug the vee tanfomation, ν. If tead of ug the gayvalue ν obtaed fom **, we ue the gayvalue obtaed fom * above both ae unifomly ditibuted!, then the ot tanfomation ** H [ T ] will geneate an image with the ecified denity, fom an ut image with denity! Fo dicete gaylevel, we have T n n, fo L and ν, fo L If the tanfomation i one-to-one, the vee tanfomation, can be eaily detemed, ce we ae dealg with a mall et of dicete gayvalue.
15 In actice, thi i not uually the cae i.e., i not one-to-one and we aign gayvalue to match the given hitogam, a cloely a oible.
16 Examle Conide the eviou 8-gaylevel 64 x 64 image hitogam: n n /n 9.9 / / / / / / el x i # gayvalue It i deied to tanfom thi image to a new image, ug a tanfomation H [ T ], with hitogam a ecified below: 4. /. 2 2/. 3 3/.5 4 4/.2 5 5/.3 6 6/.2.5 e l x i # gayvalue
17 The tanfomation T wa obtaed ealie eoduced below: n / 9.9 3/ / , / , , 6 4
18 Next we comute the tanfomation a befoe ν ν ν ν ν ν ν ν
19 Notice that i not vetible. But we will do the bet oible by ettg? / 3/ 2/ 4/ 3/ 4/ 4/? 5/ 5/ 6/ 6/ thi doe not matte, ce thi doe not matte, ce 2/ thi i not defed, but we ue a cloe match thi doe not matte, ce 4/ Combg the two tanfomation T and -, we get ou equied tanfomation H T [ T ] H /? 3 3/ / 3/ / 3 / / 4 4 / 2 2 / 5/ 2 / 4 / 2 2 / 5 5/ 3 3/ 6 / 3/ 4 / 3 3/ 6 6 / 4 4 / 6 / 4 /? 4 4 / 6 6 / 5 5 / 5 / 5 / 5 5/ 6 6 / 6 / 6 / 6 6 /
20 Alyg the tanfomation H to the oigal image yield an image with hitogam a below: n n /n actual hit. ecified hit... /.. 2 2/.. 3 3/ / / / Oigal hitogam 4 Secified hitogam 2 Outut hitogam e l x i # gayvalue 5 gayvalue 5 gayvalue
21 Aga, the actual hitogam of the ut image doe not exactly but only aoximately matche with the ecified hitogam. Thi i becaue we ae dealg with dicete hitogam.
22 Examle Oigal image and it hitogam Hitogam equalied image, Actual hitogam of ut Hitogam ecified image, Actual Hitogam, and Secified Hitogam
Histogram Processing
Hitogam Poceing Lectue 4 (Chapte 3) Hitogam Poceing The hitogam of a digital image with gay level fom to L- i a dicete function h( )=n, whee: i the th gay level n i the numbe of pixel in the image with
Basic propositional and. The fundamentals of deduction
Baic ooitional and edicate logic The fundamental of deduction 1 Logic and it alication Logic i the tudy of the atten of deduction Logic lay two main ole in comutation: Modeling : logical entence ae the
Chapter 8 Sampling. Contents. Dr. Norrarat Wattanamongkhol. Lecturer. Department of Electrical Engineering, Engineering Faculty, sampling
Content Chate 8 Samling Lectue D Noaat Wattanamongkhol Samling Theoem Samling of Continuou-Time Signal 3 Poceing Continuou-Time Signal 4 Samling of Dicete-Time Signal 5 Multi-ate Samling Deatment of Electical
Analysis of Arithmetic. Analysis of Arithmetic. Analysis of Arithmetic Round-Off Errors. Analysis of Arithmetic. Analysis of Arithmetic
In the fixed-oint imlementation of a digital filte only the esult of the multilication oeation is quantied The eesentation of a actical multilie with the quantie at its outut is shown below u v Q ^v The
Then the number of elements of S of weight n is exactly the number of compositions of n into k parts.
Geneating Function In a geneal combinatoial poblem, we have a univee S of object, and we want to count the numbe of object with a cetain popety. Fo example, if S i the et of all gaph, we might want to
Online-routing on the butterfly network: probabilistic analysis
Online-outing on the buttefly netwok: obabilistic analysis Andey Gubichev 19.09.008 Contents 1 Intoduction: definitions 1 Aveage case behavio of the geedy algoithm 3.1 Bounds on congestion................................
Chapter 19 Webassign Help Problems
Chapte 9 Webaign Help Poblem 4 5 6 7 8 9 0 Poblem 4: The pictue fo thi poblem i a bit mileading. They eally jut give you the pictue fo Pat b. So let fix that. Hee i the pictue fo Pat (a): Pat (a) imply
Inference for A One Way Factorial Experiment. By Ed Stanek and Elaine Puleo
Infeence fo A One Way Factoial Expeiment By Ed Stanek and Elaine Puleo. Intoduction We develop etimating equation fo Facto Level mean in a completely andomized one way factoial expeiment. Thi development
Fall 2004/05 Solutions to Assignment 5: The Stationary Phase Method Provided by Mustafa Sabri Kilic. I(x) = e ixt e it5 /5 dt (1) Z J(λ) =
8.35 Fall 24/5 Solution to Aignment 5: The Stationay Phae Method Povided by Mutafa Sabi Kilic. Find the leading tem fo each of the integal below fo λ >>. (a) R eiλt3 dt (b) R e iλt2 dt (c) R eiλ co t dt
Basic Gray Level Transformations (2) Negative
Gonzalez & Woods, 22 Basic Gay Level Tansfomations (2) Negative 23 Basic Gay Level Tansfomations (3) Log Tansfomation (Example fo Fouie Tansfom) Fouie spectum values ~1 6 bightest pixels dominant display
Estimation and Confidence Intervals: Additional Topics
Chapte 8 Etimation and Confidence Inteval: Additional Topic Thi chapte imply follow the method in Chapte 7 fo foming confidence inteval The text i a bit dioganized hee o hopefully we can implify Etimation:
Precision Spectrophotometry
Peciion Spectophotomety Pupoe The pinciple of peciion pectophotomety ae illutated in thi expeiment by the detemination of chomium (III). ppaatu Spectophotomete (B&L Spec 20 D) Cuvette (minimum 2) Pipet:
Physics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
New On-Line Algorithms for the Page Replication Problem. Susanne Albers y Hisashi Koga z. Abstract
New On-Line Algoithm fo the Page Replication Poblem Suanne Albe y Hiahi Koga z Abtact We peent impoved competitive on-line algoithm fo the page eplication poblem and concentate on impotant netwok topologie
Simulation of Spatially Correlated Large-Scale Parameters and Obtaining Model Parameters from Measurements
Simulation of Spatially Coelated Lage-Scale Paamete and Obtaining Model Paamete fom PER ZETTERBERG Stockholm Septembe 8 TRITA EE 8:49 Simulation of Spatially Coelated Lage-Scale Paamete and Obtaining Model
Section 25 Describing Rotational Motion
Section 25 Decibing Rotational Motion What do object do and wh do the do it? We have a ve thoough eplanation in tem of kinematic, foce, eneg and momentum. Thi include Newton thee law of motion and two
Let {X n, n 1} be a sequence of independent and identically distributed random variables with a common cdf F (x) and pdf f(x).
Kangweon-Kyungki Math Jou 2 24, No, pp 5 22 RCURRNC RLATION FOR QUOTINTS OF TH POWR DISTRIBUTION BY RCORD VALUS Min-Young Lee and Se-Kyung Chang Abtact In thi pape we etablih ome ecuence elation atified
Gravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003
avity David Bawacz 7778 Thonapple Bayou, and Rapid, MI 495 David Bawacz /3/3 http://membe.titon.net/daveb Uing the concept dicued in the peceding pape ( http://membe.titon.net/daveb ), I will now deive
9.1 The multiplicative group of a finite field. Theorem 9.1. The multiplicative group F of a finite field is cyclic.
Chapte 9 Pimitive Roots 9.1 The multiplicative goup of a finite fld Theoem 9.1. The multiplicative goup F of a finite fld is cyclic. Remak: In paticula, if p is a pime then (Z/p) is cyclic. In fact, this
Honors Classical Physics I
Hono Claical Phyic I PHY141 Lectue 9 Newton Law of Gavity Pleae et you Clicke Channel to 1 9/15/014 Lectue 9 1 Newton Law of Gavity Gavitational attaction i the foce that act between object that have a
Chapter Eight Notes N P U1C8S4-6
Chapte Eight Notes N P UC8S-6 Name Peiod Section 8.: Tigonometic Identities An identit is, b definition, an equation that is alwas tue thoughout its domain. B tue thoughout its domain, that is to sa that
Analysis of Finite Word-Length Effects
T-6.46 Digital Signal Pocessing and Filteing 8.9.4 Intoduction Analysis of Finite Wod-Length Effects Finite wodlength effects ae caused by: Quantization of the filte coefficients ounding / tuncation of
V V The circumflex (^) tells us this is a unit vector
Vecto Vecto have Diection and Magnitude Mike ailey mjb@c.oegontate.edu Magnitude: V V V V x y z vecto.pptx Vecto Can lo e Defined a the oitional Diffeence etween Two oint 3 Unit Vecto have a Magnitude
Σr2=0. Σ Br. Σ br. Σ r=0. br = Σ. Σa r-s b s (1.2) s=0. Σa r-s b s-t c t (1.3) t=0. cr = Σ. dr = Σ. Σa r-s b s-t c t-u d u (1.4) u =0.
0 Powe of Infinite Seie. Multiple Cauchy Poduct The multinomial theoem i uele fo the powe calculation of infinite eie. Thi i becaue the polynomial theoem depend on the numbe of tem, o it can not be applied
11.5 MAP Estimator MAP avoids this Computational Problem!
.5 MAP timator ecall that the hit-or-mi cot function gave the MAP etimator it maimize the a oteriori PDF Q: Given that the MMS etimator i the mot natural one why would we conider the MAP etimator? A: If
FI 2201 Electromagnetism
FI Electomagnetim Aleande A. Ikanda, Ph.D. Phyic of Magnetim and Photonic Reeach Goup ecto Analyi CURILINEAR COORDINAES, DIRAC DELA FUNCION AND HEORY OF ECOR FIELDS Cuvilinea Coodinate Sytem Cateian coodinate:
Eddy Currents in Permanent Magnets of a Multi-pole Direct Drive Motor
Acta Technica Jauineni Vol. 6. No. 1. 2013 Eddy Cuent in Pemanent Magnet of a Multi-pole Diect Dive Moto G. Gotovac 1, G. Lampic 1, D. Miljavec 2 Elaphe Ltd. 1, Univeity of Ljubljana, Faculty of Electical
556: MATHEMATICAL STATISTICS I
556: MATHEMATICAL STATISTICS I CHAPTER 5: STOCHASTIC CONVERGENCE The following efinitions ae state in tems of scala anom vaiables, but exten natually to vecto anom vaiables efine on the same obability
Solutions Practice Test PHYS 211 Exam 2
Solution Pactice Tet PHYS 11 Exam 1A We can plit thi poblem up into two pat, each one dealing with a epaate axi. Fo both the x- and y- axe, we have two foce (one given, one unknown) and we get the following
Rotational Kinetic Energy
Add Impotant Rotational Kinetic Enegy Page: 353 NGSS Standad: N/A Rotational Kinetic Enegy MA Cuiculum Famewok (006):.1,.,.3 AP Phyic 1 Leaning Objective: N/A, but olling poblem have appeaed on peviou
ASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4.
ASTR 3740 Relativity & Comology Sping 019. Anwe to Poblem Set 4. 1. Tajectoie of paticle in the Schwazchild geomety The equation of motion fo a maive paticle feely falling in the Schwazchild geomety ae
one primary direction in which heat transfers (generally the smallest dimension) simple model good representation for solving engineering problems
CHAPTER 3: One-Dimenional Steady-State Conduction one pimay diection in which heat tanfe (geneally the mallet dimenion) imple model good epeentation fo olving engineeing poblem 3. Plane Wall 3.. hot fluid
A note on rescalings of the skew-normal distribution
Poyeccione Jounal of Mathematic Vol. 31, N o 3, pp. 197-07, Septembe 01. Univeidad Católica del Note Antofagata - Chile A note on ecaling of the kew-nomal ditibution OSVALDO VENEGAS Univeidad Católica
On the Efficiency of Markets with Two-sided Proportional Allocation Mechanisms
On the Efficiency of Maket with Two-ided Pootional Allocation Mechanim Volodymy Kulehov and Adian Vetta Deatment of Mathematic and Statitic, and School of Comute Science, McGill Univeity volodymy.kulehov@mail.mcgill.ca,
Solution to HW 3, Ma 1a Fall 2016
Solution to HW 3, Ma a Fall 206 Section 2. Execise 2: Let C be a subset of the eal numbes consisting of those eal numbes x having the popety that evey digit in the decimal expansion of x is, 3, 5, o 7.
3.6 Applied Optimization
.6 Applied Optimization Section.6 Notes Page In this section we will be looking at wod poblems whee it asks us to maimize o minimize something. Fo all the poblems in this section you will be taking the
Effect of Graph Structures on Selection for a Model of a Population on an Undirected Graph
Effect of Gah Stuctue o Selectio fo a Model of a Poulatio o a Udiected Gah Watig Che Advio: Jao Schweibeg May 0, 206 Abtact Thi eeach focue o aalyzig electio amlifie i oulatio geetic. Sice the tuctue of
3.1 Random variables
3 Chapte III Random Vaiables 3 Random vaiables A sample space S may be difficult to descibe if the elements of S ae not numbes discuss how we can use a ule by which an element s of S may be associated
Noether Theorem, Noether Charge and All That
Noethe Theoem, Noethe Chage and All That Ceated fo PF by Samalkhaiat 10 Tanfomation Let G be a Lie goup whoe action on Minkowki pace-time fomally ealized by coodinate tanfomation ( ) ( 1,3,η) M i Infiniteimally,
TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the
Chapte 15 RAVELING WAVES 15.1 Simple Wave Motion Wave in which the ditubance i pependicula to the diection of popagation ae called the tanvee wave. Wave in which the ditubance i paallel to the diection
The Substring Search Problem
The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is
Auchmuty High School Mathematics Department Advanced Higher Notes Teacher Version
The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!
Figure 1 Siemens PSSE Web Site
Stability Analyi of Dynamic Sytem. In the lat few lecture we have een how mall ignal Lalace domain model may be contructed of the dynamic erformance of ower ytem. The tability of uch ytem i a matter of
On the quadratic support of strongly convex functions
Int. J. Nonlinea Anal. Appl. 7 2016 No. 1, 15-20 ISSN: 2008-6822 electonic http://dx.doi.og/10.22075/ijnaa.2015.273 On the quadatic uppot of tongly convex function S. Abbazadeh a,b,, M. Ehaghi Godji a
6 PROBABILITY GENERATING FUNCTIONS
6 PROBABILITY GENERATING FUNCTIONS Cetain deivations pesented in this couse have been somewhat heavy on algeba. Fo example, detemining the expectation of the Binomial distibution (page 5.1 tuned out to
ψ - exponential type orbitals, Frictional
ew develoment in theoy of Laguee olynomial I. I. Gueinov Deatment of Phyic, Faculty of At and Science, Onekiz Mat Univeity, Çanakkale, Tukey Abtact The new comlete othonomal et of L -Laguee tye olynomial
Notes on McCall s Model of Job Search. Timothy J. Kehoe March if job offer has been accepted. b if searching
Notes on McCall s Model of Job Seach Timothy J Kehoe Mach Fv ( ) pob( v), [, ] Choice: accept age offe o eceive b and seach again next peiod An unemployed oke solves hee max E t t y t y t if job offe has
Errata for Edition 1 of Coding the Matrix, January 13, 2017
Eata fo Edition of Coding the Matix, Januay 3, 07 You coy might not contain some of these eos. Most do not occu in the coies cuently being sold as Ail 05. Section 0.3:... the inut is a e-image of the inut...
Section 11. Timescales Radiation transport in stars
Section 11 Timescales 11.1 Radiation tanspot in stas Deep inside stas the adiation eld is vey close to black body. Fo a black-body distibution the photon numbe density at tempeatue T is given by n = 2
Chapter 3: Theory of Modular Arithmetic 38
Chapte 3: Theoy of Modula Aithmetic 38 Section D Chinese Remainde Theoem By the end of this section you will be able to pove the Chinese Remainde Theoem apply this theoem to solve simultaneous linea conguences
1. The F-test for Equality of Two Variances
. The F-tet for Equality of Two Variance Previouly we've learned how to tet whether two population mean are equal, uing data from two independent ample. We can alo tet whether two population variance are
INFLUENCE OF DESIGN DATA OF INDUCTION MOTOR ON EFFECTS OF CAGE ASYMMETRY
Pace Nauowe Intytutu Mazyn, Naędów i Pomiaów Eletycznych N 66 Politechnii Wocławiej N 66 Studia i Mateiały N 3 1 Alejando FERNANDEZ GOMEZ* Tadeuz J. SOBCZYK* induction moto, oto cage aymmety, cage moto
of the contestants play as Falco, and 1 6
JHMT 05 Algeba Test Solutions 4 Febuay 05. In a Supe Smash Bothes tounament, of the contestants play as Fox, 3 of the contestants play as Falco, and 6 of the contestants play as Peach. Given that thee
Static Electric Fields. Coulomb s Law Ε = 4πε. Gauss s Law. Electric Potential. Electrical Properties of Materials. Dielectrics. Capacitance E.
Coulomb Law Ε Gau Law Electic Potential E Electical Popetie of Mateial Conducto J σe ielectic Capacitance Rˆ V q 4πε R ρ v 2 Static Electic Field εe E.1 Intoduction Example: Electic field due to a chage
EC381/MN308 Probability and Some Statistics. Lecture 7 - Outline. Chapter Cumulative Distribution Function (CDF) Continuous Random Variables
EC38/MN38 Probability and Some Statitic Yanni Pachalidi yannip@bu.edu, http://ionia.bu.edu/ Lecture 7 - Outline. Continuou Random Variable Dept. of Manufacturing Engineering Dept. of Electrical and Computer
Theorem 2: Proof: Note 1: Proof: Note 2:
A New 3-Dimenional Polynomial Intepolation Method: An Algoithmic Appoach Amitava Chattejee* and Rupak Bhattachayya** A new 3-dimenional intepolation method i intoduced in thi pape. Coeponding to the method
Impulse and Momentum
Impule and Momentum 1. A ca poee 20,000 unit of momentum. What would be the ca' new momentum if... A. it elocity wee doubled. B. it elocity wee tipled. C. it ma wee doubled (by adding moe paenge and a
Determining the Best Linear Unbiased Predictor of PSU Means with the Data. included with the Random Variables. Ed Stanek
Detemining te Bet Linea Unbiaed Pedicto of PSU ean wit te Data included wit te andom Vaiable Ed Stanek Intoduction We develop te equation fo te bet linea unbiaed pedicto of PSU mean in a two tage andom
Estimating Conditional Mean and Difference Between Conditional Mean and Conditional Median
Etimating Conditional Mean and Difference Between Conditional Mean and Conditional Median Liang Peng Deartment of Ri Management and Inurance Georgia State Univerity and Qiwei Yao Deartment of Statitic,
Several new identities involving Euler and Bernoulli polynomials
Bull. Math. Soc. Sci. Math. Roumanie Tome 9107 No. 1, 016, 101 108 Seveal new identitie involving Eule and Benoulli polynomial by Wang Xiaoying and Zhang Wenpeng Abtact The main pupoe of thi pape i uing
Bogoliubov Transformation in Classical Mechanics
Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How
Internet Appendix for A Bayesian Approach to Real Options: The Case of Distinguishing Between Temporary and Permanent Shocks
Intenet Appendix fo A Bayesian Appoach to Real Options: The Case of Distinguishing Between Tempoay and Pemanent Shocks Steven R. Genadie Gaduate School of Business, Stanfod Univesity Andey Malenko Gaduate
Probabilistic number theory : A report on work done. What is the probability that a randomly chosen integer has no square factors?
Pobabilistic numbe theoy : A eot on wo done What is the obability that a andomly chosen intege has no squae factos? We can constuct an initial fomula to give us this value as follows: If a numbe is to
The Normal Stress Dıstribution in an Infinite. Elastic Body with a Locally Curved and Hollow. Fiber under Geometrical Nonlinear Statement
Nonlinea Analyi and Diffeential quation Vol. 4 06 no. 6 95-04 HIKARI td www.m-hikai.com htt://dx.doi.og/0.988/nade.06.656 The Nomal Ste Dıtibution in an Infinite latic Body with a ocally Cuved and Hollow
Data Structures and Algorithm Analysis (CSC317) Randomized algorithms (part 2)
Data Stuctues and Algoithm Analysis (CSC317) Randomized algoithms (at 2) Hiing oblem - eview c Cost to inteview (low i ) Cost to fie/hie (exensive ) n Total numbe candidates m Total numbe hied c h O(c
(n 1)n(n + 1)(n + 2) + 1 = (n 1)(n + 2)n(n + 1) + 1 = ( (n 2 + n 1) 1 )( (n 2 + n 1) + 1 ) + 1 = (n 2 + n 1) 2.
Paabola Volume 5, Issue (017) Solutions 151 1540 Q151 Take any fou consecutive whole numbes, multiply them togethe and add 1. Make a conjectue and pove it! The esulting numbe can, fo instance, be expessed
Computational Geometry. Kirkpatrick-Seidel s Prune-and-Search Convex Hull Algorithm
COSC 6114 Coutational Geoety Kikatick-Seidel Pune-and-Seach Convex Hull Algoith Intoduction Thi note concen the coutation of the convex hull of a given et P ={ 1, 2,..., n }of n oint in the lane. et h
Lecture 4 Topic 3: General linear models (GLMs), the fundamentals of the analysis of variance (ANOVA), and completely randomized designs (CRDs)
Lecture 4 Topic 3: General linear model (GLM), the fundamental of the analyi of variance (ANOVA), and completely randomized deign (CRD) The general linear model One population: An obervation i explained
Divisibility. c = bf = (ae)f = a(ef) EXAMPLE: Since 7 56 and , the Theorem above tells us that
Divisibility DEFINITION: If a and b ae integes with a 0, we say that a divides b if thee is an intege c such that b = ac. If a divides b, we also say that a is a diviso o facto of b. NOTATION: d n means
Supplemental Materials. Advanced Thermoelectrics Governed by Single Parabolic Band Model:
Electonic Supplementay Mateial (ESI) fo Phyical Chemity Chemical Phyic. Thi jounal i The Royal Society of Chemity 04 Supplemental Mateial Advanced Themoelectic Govened by Single Paabolic and Model: Mg
B da = 0. Q E da = ε. E da = E dv
lectomagnetic Theo Pof Ruiz, UNC Asheville, doctophs on YouTube Chapte Notes The Maxwell quations in Diffeential Fom 1 The Maxwell quations in Diffeential Fom We will now tansfom the integal fom of the
defined on a domain can be expanded into the Taylor series around a point a except a singular point. Also, f( z)
08 Tylo eie nd Mcluin eie A holomophic function f( z) defined on domin cn be expnded into the Tylo eie ound point except ingul point. Alo, f( z) cn be expnded into the Mcluin eie in the open dik with diu
1 Notes on Order Statistics
1 Notes on Ode Statistics Fo X a andom vecto in R n with distibution F, and π S n, define X π by and F π by X π (X π(1),..., X π(n) ) F π (x 1,..., x n ) F (x π 1 (1),..., x π 1 (n)); then the distibution
μ + = σ = D 4 σ = D 3 σ = σ = All units in parts (a) and (b) are in V. (1) x chart: Center = μ = 0.75 UCL =
Our online Tutor are available 4*7 to provide Help with Proce control ytem Homework/Aignment or a long term Graduate/Undergraduate Proce control ytem Project. Our Tutor being experienced and proficient
10/04/18. P [P(x)] 1 negl(n).
![10/04/18. P [P(x)] 1 negl(n).](/thumbs/92/110495316.jpg "10/04/18. P [P(x)] 1 negl(n).")
Mastemath, Sping 208 Into to Lattice lgs & Cypto Lectue 0 0/04/8 Lectues: D. Dadush, L. Ducas Scibe: K. de Boe Intoduction In this lectue, we will teat two main pats. Duing the fist pat we continue the
Sinusoidal Oscillators
Sinuoidal Ocillato Signal geneato: inuoidal, ectangula, tiangula, aw-tooth, etc. Obtaining a ine wave: tiangle functional tanf. ine ine wave geneation: fequency elective netwok in a feedback loo of a PF
On a quantity that is analogous to potential and a theorem that relates to it
Su une quantité analogue au potential et su un théoème y elatif C R Acad Sci 7 (87) 34-39 On a quantity that is analogous to potential and a theoem that elates to it By R CLAUSIUS Tanslated by D H Delphenich
AE 423 Space Technology I Chapter 2 Satellite Dynamics
AE 43 Space Technology I Chapte Satellite Dynamic.1 Intoduction In thi chapte we eview ome dynamic elevant to atellite dynamic and we etablih ome of the baic popetie of atellite dynamic.. Dynamic of a
Design By Emulation (Indirect Method)
Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal
NCAAPMT Calculus Challenge Challenge #3 Due: October 26, 2011
NCAAPMT Calculu Challenge 011 01 Challenge #3 Due: October 6, 011 A Model of Traffic Flow Everyone ha at ome time been on a multi-lane highway and encountered road contruction that required the traffic
Dorin Andrica Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania
#A INTEGERS 5A (05) THE SIGNUM EQUATION FOR ERDŐS-SURÁNYI SEQUENCES Doin Andica Faculty of Mathematics and Comute Science, Babeş-Bolyai Univesity, Cluj-Naoca, Romania dandica@math.ubbcluj.o Eugen J. Ionascu
EE Control Systems LECTURE 14
Updated: Tueday, March 3, 999 EE 434 - Control Sytem LECTURE 4 Copyright FL Lewi 999 All right reerved ROOT LOCUS DESIGN TECHNIQUE Suppoe the cloed-loop tranfer function depend on a deign parameter k We
Boise State University Department of Electrical and Computer Engineering ECE470 Electric Machines
Boie State Univeity Depatment of Electical and Compute Engineeing ECE470 Electic Machine Deivation of the Pe-Phae Steady-State Equivalent Cicuit of a hee-phae Induction Machine Nomenclatue θ: oto haft
DESIGN OF BEAMS FOR MOMENTS
CHAPTER Stuctual Steel Design RFD ethod Thid Edition DESIGN OF BEAS FOR OENTS A. J. Clak School of Engineeing Deatment of Civil and Envionmental Engineeing Pat II Stuctual Steel Design and Analysis 9 FA
Physics 6A. Angular Momentum. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Phyic 6A Angular Momentum For Campu earning Angular Momentum Thi i the rotational equivalent of linear momentum. t quantifie the momentum of a rotating object, or ytem of object. f we imply tranlate the
Chapter 2: Descriptive Statistics
Chapte : Decptve Stattc Peequte: Chapte. Revew of Uvaate Stattc The cetal teecy of a oe o le yetc tbuto of a et of teval, o hghe, cale coe, ofte uaze by the athetc ea, whch efe a We ca ue the ea to ceate
Kepler s problem gravitational attraction
Kele s oblem gavitational attaction Summay of fomulas deived fo two-body motion Let the two masses be m and m. The total mass is M = m + m, the educed mass is µ = m m /(m + m ). The gavitational otential
arxiv: v1 [math.cv] 7 Nov 2018
![arxiv: v1 [math.cv] 7 Nov 2018](/thumbs/90/101586781.jpg "arxiv: v1 [math.cv] 7 Nov 2018")
INTERMEDIATE HANKEL OPERATORS ON THE FOCK SPACE OLIVIA CONSTANTIN axiv:181103137v1 [mathcv] 7 Nov 2018 Abtact We contuct a natual equence of middle Hankel opeato on the Fock pace, ie opeato which ae intemediate
Goodness-of-fit for composite hypotheses.
Section 11 Goodness-of-fit fo composite hypotheses. Example. Let us conside a Matlab example. Let us geneate 50 obsevations fom N(1, 2): X=nomnd(1,2,50,1); Then, unning a chi-squaed goodness-of-fit test
Design of Two-Channel Low-Delay FIR Filter Banks Using Constrained Optimization
contrained otimization, CIT Journal of Comuting and Information Technology, vol. 8, no 4,. 34 348, 2. Deign of Two-Channel Low-Delay FIR Filter Bank Uing Contrained Otimization Abtract Robert Bregović
New problems in universal algebraic geometry illustrated by boolean equations
New poblems in univesal algebaic geomety illustated by boolean equations axiv:1611.00152v2 [math.ra] 25 Nov 2016 Atem N. Shevlyakov Novembe 28, 2016 Abstact We discuss new poblems in univesal algebaic
γ from B D(Kπ)K and B D(KX)K, X=3π or ππ 0
fom and X, X= o 0 Jim Libby, Andew Powell and Guy Wilkinon Univeity of Oxfod 8th Januay 007 Gamma meeting 1 Outline The AS technique to meaue Uing o 0 : intoducing the coheence facto Meauing the coheence
( ) F α. a. Sketch! r as a function of r for fixed θ. For the sketch, assume that θ is roughly the same ( )
. An acoustic a eflecting off a wav bounda (such as the sea suface) will see onl that pat of the bounda inclined towad the a. Conside a a with inclination to the hoizontal θ (whee θ is necessail positive,
In the previous section we considered problems where the
5.4 Hydodynamically Fully Developed and Themally Developing Lamina Flow In the pevious section we consideed poblems whee the velocity and tempeatue pofile wee fully developed, so that the heat tansfe coefficient
763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012
763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012 1. Continuous Random Walk Conside a continuous one-dimensional andom walk. Let w(s i ds i be the pobability that the length of the i th displacement
into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get
Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}
rad rev 60sec p sec 2 rad min 2 2
NAME: EE 459/559, Exa 1, Fall 2016, D. McCalley, 75 inute allowed (unle othewie diected) Cloed Book, Cloed Note, Calculato Peitted, No Counication Device. The following infoation ay o ay not be ueful fo
k. s k=1 Part of the significance of the Riemann zeta-function stems from Theorem 9.2. If s > 1 then 1 p s
9 Pimes in aithmetic ogession Definition 9 The Riemann zeta-function ζs) is the function which assigns to a eal numbe s > the convegent seies k s k Pat of the significance of the Riemann zeta-function
Problem Set 8 Solutions
Deign and Analyi of Algorithm April 29, 2015 Maachuett Intitute of Technology 6.046J/18.410J Prof. Erik Demaine, Srini Devada, and Nancy Lynch Problem Set 8 Solution Problem Set 8 Solution Thi problem
22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 18
.65, MHD Theoy of Fuion Sytem Pof. Feidbeg Lectue 8. Deive δw fo geneal cew pinch. Deive Suydam citeion Scew Pinch Equilibia μ p + + ( ) = μ J = μ J= Stability ( ) m k ξ=ξ e ι +ι ξ=ξ e +ξ e +ξ e =ξ +ξ