Rešenja zadataka za vežbu na relacionoj algebri i relacionom računu
|
|
- Kerry Bond
- 6 years ago
- Views:
Transcription
1 Rešenja zadataka za vežbu na relacionoj algebri i relacionom računu 1. Izdvojiti ime i prezime studenata koji su rođeni u Beogradu. (DOSIJE WHERE MESTO_RODJENJA='Beograd')[IME, PREZIME] where mesto_rodjenja='beograd' 2. Prikazati ime i prezime studenta koji je polagao predmet sa identifikatorom ((ISPIT WHERE ID_PREDMETA=2001) JOIN DOSIJE)[IME, PREZIME] where exists ix (ix.indeks=dx.indeks and ix.id_predmeta=2001) 3. Prikazati nazive svih predmeta koje je položio student Nikola Vukovic. ((DOSIJE WHERE IME='Nikola' AND PREZIME='Vukovic')[INDEKS] JOIN (ISPIT WHERE OCENA>5)[INDEKS, ID_PREDMETA] JOIN PREDMET) [NAZIV] px.naziv
2 where exists ix(ix.id_predmeta=px.id_predmeta and ix.ocena>5 and exists dx(dx.indeks=ix.indeks and dx.ime='nikola' and dx.prezime='vukovic')) 4. Prikazati šifre svih predmeta koji nose 6 bodova ili ih je neko položio u roku Januar (PREDMET WHERE BODOVI=6)[SIFRA] UNION ((ISPIT WHERE OZNAKA_ROKA='jan' AND GODINA_ROKA=2015 AND OCENA>5) [ID_PREDMETA] JOIN PREDMET)[SIFRA] px.sifra where px.bodovi=6 or exists ix(ix.id_predmeta=px.id_predmeta and ix.godina_roka=2015 and ix.oznaka_roka='jan' and ix.ocena>5) 5. Prikazati imena i prezimena studenata koji imaju bar jedan ispit položen sa ocenom 6 i bar jedan ispit položen sa ocenom 10. (((ISPIT WHERE OCENA=6)[INDEKS] INTERSECT (ISPIT WHERE OCENA=10)[INDEKS]) JOIN DOSIJE)[IME, PREZIME] where exists ix(ix.indeks=dx.indeks and ix.ocena=6) and exists ix(ix.indeks=dx.indeks and ix.ocena=10) 6. Izdvojiti ime i prezime studenata koji nisu polagali predmet sa identifikatorom 2001.
3 ((DOSIJE[INDEKS] (ISPIT WHERE ID_PREDMETA=2001)[INDEKS]) JOIN DOSIJE)[IME, PREZIME] where not exists ix (ix.indeks=dx.indeks and ix.id_predmeta=2001) 7. Izdvojiti parove studenata za koje važi da su rođeni u istom mestu. Izdoviji indekse studenata. DEFINE ALIAS D FOR DOSIJE ((D TIMES DOSIJE) WHERE D.MESTO_RODJENJA=DOSIJE.MESTO_RODJENJA AND D.INDEKS<DOSIJE.INDEKS) [D.INDEKS, DOSIJE.INDEKS] range of dx, dy is dosije dx.indeks, dy.indeks where dx.mesto_rodjenja=dy.mesto_rodjenja and dx.indeks<dy.indeks 8. Izdvojiti nazive ispitnih rokova u kojima je polagan predmet Uvod u Veb i Internet tehnologije. ((PREDMET WHERE NAZIV='Uvod u Veb i Internet tehnologije')[id_predmeta] JOIN ISPIT JOIN ISPITNI_ROK) [NAZIV] range of irx is ispitni_rok irx.naziv
4 where exists ix(ix.godina_roka=irx.godina_roka and ix.oznaka_roka=irx.oznaka_roka and exists px( px.id_predmeta=ix.id_predmeta and px.naziv='uvod u Veb i Internet tehnologije')) 9. Izdvojiti oznake i godine ispitnih rokova u kojima nijedan student iz Beograda nije položio predmet koji nosi 4 boda. ISPITNI_ROK[GODINA_ROKA, OZNAKA_ROKA] ((DOSIJE WHERE MESTO_RODJENJA='Beograd') JOIN (ISPIT WHERE OCENA>5) JOIN (PREDMET WHERE BODOVI=4)[ID_PREDMETA]])[GODINA_ROKA, OZNAKA_ROKA] range of irx is ispitni_rok irx.godina_roka, irx.oznaka_roka where not exists ix (ix.godina_roka=irx.godina_roka and ix.oznaka_roka=irx.oznaka_roka and exists px(px.id_predmeta=ix.id_predmeta and px.bodovi=4) and exists dx(ix.indeks=dx.indeks and dx.mesto_rodjenja='beograd')) 10. Izdvojiti indeks, ime i prezime studenta koji a. je položio Programiranje 1 ali nije položio Analizu 1 ((PREDMET WHERE NAZIV='Programiranje 1')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5) JOIN DOSIJE)[INDEKS, IME, PREZIME] ((PREDMET WHERE NAZIV='Analiza 1')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5) JOIN DOSIJE)[INDEKS, IME, PREZIME] dx.indeks,
5 where exists ix( ix.indeks=dx.indeks and ix.ocena>5 and exists px ( px.id_predmeta=ix.id_predmeta and px.naziv='programiranje 1')) and not exists ix(ix.indeks=dx.indeks and ix.ocena>5 and exists px (px.id_predmeta=ix.id_predmeta and px.naziv='analiza 1')) b. je položio Programiranje 1 i Analizu 1 ((PREDMET WHERE NAZIV='Programiranje 1')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5) JOIN DOSIJE)[INDEKS, IME, PREZIME] INTERSECT ((PREDMET WHERE NAZIV='Analiza 1')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5) JOIN DOSIJE)[INDEKS, IME, PREZIME] dx.indeks, where exists ix(ix.indeks=dx.indeks and ix.ocena>5 and exists px (px.id_predmeta=ix.id_predmeta and px.naziv='programiranje 1')) and exists ix(ix.indeks=dx.indeks and ix.ocena>5 and exists px (px.id_predmeta=ix.id_predmeta and px.naziv='analiza 1')) c. nije položio Programiranje 1 ni Analizu 1. DOSIJE[INDEKS, IME, PREZIME] ((PREDMET WHERE NAZIV='Programiranje 1')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5) JOIN DOSIJE)[INDEKS, IME, PREZIME] ((PREDMET WHERE NAZIV='Analiza 1')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5) JOIN DOSIJE)[INDEKS, IME, PREZIME] dx.indeks,
6 where not exists ix(ix.indeks=dx.indeks and ix.ocena>5 and exists px (px.id_predmeta=ix.id_predmeta and px.naziv='programiranje 1')) and not exists ix(ix.indeks=dx.indeks and ix.ocena>5 and exists px (px.id_predmeta=ix.id_predmeta and px.naziv='analiza 1')) 11. Izdvojiti sve položene predmete studenata koji su položili Analizu 2. Izdvojiti indeks i naziv predmeta. (((PREDMET WHERE NAZIV='Analiza 2')[ID_PREDMETA] JOIN (ISPIT WHERE OCENA>5))[INDEKS] JOIN (ISPIT WHERE OCENA>5)[INDEKS, ID_PREDMETA] JOIN PREDMET) [INDEKS, NAZIV] range of px,py is predmet dx.indeks, px.naziv where exists ix( ix.indeks=dx.indeks and ix.id_predmeta=px.id_predmeta and ix.ocena>5) and exists ix( ix.indeks=dx.indeks and ix.ocena>5 and exists py (py.id_predmeta=ix.id_predmeta and py.naziv='analiza 2')) 12. Izdvojiti nazive ispitnih rokova u kojima su polagali svi studenti rođeni u Beogradu ili Kraljevu, a nije polagao nijedan student rođen u Novom Sadu. (((ISPIT[GODINA_ROKA, OZNAKA_ROKA, INDEKS] DIVIDEBY (DOSIJE WHERE MESTO_RODJENJA='Beograd' OR MESTO_RODJENJA='Kraljevo')[INDEKS]) ((DOSIJE WHERE MESTO_RODJENJA='Novi Sad')[INDEKS] JOIN ISPIT)[GODINA_ROKA, OZNAKA_ROKA]) JOIN ISPITNI_ROK)[NAZIV]
7 range of px,py is predmet range of irx is ispitni_rok irx.naziv where forall dx(if dx.mesto_rodjenja='beograd' or dx.mesto_rodjenja='kraljevo' then exists ix(ix.indeks=dx.indeks and ix.godina_roka=irx.godina_roka and ix.oznaka_roka=irx.oznaka_roka) ) and not exists dx(dx.mesto_rodjenja='novi Sad' and exists ix(ix.indeks=dx.indeks and ix.godina_roka=irx.godina_roka and ix.oznaka_roka=irx.oznaka_roka)) 13. Izdvojiti indeks, ime i prezime studenta koji je položio sve predmete koje su položili studenti rođeni u Novom Sadu. (((ISPIT WHERE OCENA>5)[INDEKS, ID_PREDMETA] DIVIDEBY (((DOSIJE WHERE MESTO_RODJENJA='Novi Sad') JOIN (ISPIT WHERE OCENA>5))[ID_PREDMETA])) JOIN DOSIJE)[INDEKS, IME, PREZIME] dx.indeks, where forall px(if exists dy(dy.mesto_rodjenja='novi Sad' and exists ix(ix.indeks=dy.indeks and ix.id_predmeta=px.id_predmeta and ix.ocena>5)) then exists ix(ix.indeks=dx.indeks and ix.id_predmeta=px.id_predmeta and ix.ocena>5)) 14. Izdvojiti ime i prezime studenta koji je položio samo jedan predmet. DEFINE ALIAS I FOR ISPIT (((ISPIT WHERE OCENA>5)[INDEKS] ((ISPIT TIMES I) WHERE ISPIT.OCENA>5 AND I.OCENA>5 AND ISPIT.INDEKS=I.INDEKS AND
8 ISPIT.ID_PREDMETA<>I.ID_PREDMETA)[I.INDEKS]) JOIN DOSIJE)[IME, PREZIME] range of ix, iy is ispit where exists ix(ix.indeks=dx.indeks and ix.ocena>5 and not exists iy(iy.indeks=dx.indeks and iy.ocena>5 and iy.id_predmeta<>ix.id_predmeta)) 15. Izdvojiti parove studenata koji imaju istu ocenu iz istog predmeta. Izdvojiti indekse, imena i prezimena studenata, naziv predmeta i ocenu. DEFINE ALIAS D FOR DOSIJE DEFINE ALIAS I FOR ISPIT ((DOSIJE TIMES ISPIT TIMES D TIMES I TIMES PREDMET) WHERE DOSIJE.INDEKS=ISPIT.INDEKS AND D.INDEKS=I.INDEKS AND I.ID_PREDMETA=ISPIT.ID_PREDMETA AND I.OCENA=ISPIT.OCENA AND DOSIJE.INDEKS<D.INDEKS AND I.ID_PREDMETA=PREDMET.ID_PREDMETA) [D.INDEKS, D.IME, D.PREZIME, DOSIJE.INDEKS, DOSIJE.IME, DOSIJE.PREZIME, PREDMET.NAZIV, I.OCENA] range of dx, dy is dosije range of ix, iy is ispit dx.indeks,, dy.indeks, dy.ime, dy.prezime, ix.ocena, px.naziv where dx.indeks=ix.indeks and px.id_predmeta=ix.id_predmeta and dx.indeks<dy.indeks and exists iy(iy.indeks=dy.indeks and iy.id_predmeta=px.id_predmeta and ix.ocena=iy.ocena)
Uvod u relacione baze podataka
Uvod u relacione baze podataka Ana Spasić 2. čas 1 Mala studentska baza dosije (indeks, ime, prezime, datum rodjenja, mesto rodjenja, datum upisa) predmet (id predmeta, sifra, naziv, bodovi) ispitni rok
More information1a select indeks from dosije where mesto_rodjenja='beograd' union select indeks from ispit where ocena=10 order by indeks desc;
1a union b intersect c except 2 select d.indeks, count(*) br_ispita d join ispit i on d.indeks=i.indeks group by d.indeks union, 0 d where not exists ( select * i where d.indeks=i.indeks); 3, id_predmeta,
More informationALGORITMI I STRUKTURE PODATAKA
Sveučilište u Rijeci ODJEL ZA INFORMATIKU Omladinska 14, Rijeka Akademska 2017/2018. godina ALGORITMI I STRUKTURE PODATAKA Studij: Preddiplomski studij MATEMATIKE (jednopredmetni) Web stranica predmeta:
More informationTEORIJA SKUPOVA Zadaci
TEORIJA SKUPOVA Zadai LOGIKA 1 I. godina 1. Zapišite simbolima: ( x nije element skupa S (b) d je član skupa S () F je podskup slupa S (d) Skup S sadrži skup R 2. Neka je S { x;2x 6} = = i neka je b =
More informationKevin James. MTHSC 206 Section 16.4 Green s Theorem
MTHSC 206 Section 16.4 Green s Theorem Theorem Let C be a positively oriented, piecewise smooth, simple closed curve in R 2. Let D be the region bounded by C. If P(x, y)( and Q(x, y) have continuous partial
More informationu Novom Sadu na Tehnološkom fakultetu od Septembra održava Workshop pod nazivom:
Poštovani, Obaveštavamo Vas da se u okviru COST Projekta MP0701 koji nosi naziv: Composites with novel functional and structural properties by nanoscale materials (Nano Composite Materials NCM) http://www.nanocomposites-cost.eu.
More information3. If a choice is broken down into two successive choices, the original H should be the weighted sum of the individual values of H.
Appendix A Information Theory A.1 Entropy Shannon (Shanon, 1948) developed the concept of entropy to measure the uncertainty of a discrete random variable. Suppose X is a discrete random variable that
More informationCOMPSCI 650 Applied Information Theory Jan 21, Lecture 2
COMPSCI 650 Applied Information Theory Jan 21, 2016 Lecture 2 Instructor: Arya Mazumdar Scribe: Gayane Vardoyan, Jong-Chyi Su 1 Entropy Definition: Entropy is a measure of uncertainty of a random variable.
More informationMath 240 Calculus III
Calculus III Summer 2015, Session II Monday, August 3, 2015 Agenda 1. 2. Introduction The reduction of technique, which applies to second- linear differential equations, allows us to go beyond equations
More informationSOLUTION FOR HOMEWORK 12, STAT 4351
SOLUTION FOR HOMEWORK 2, STAT 435 Welcome to your 2th homework. It looks like this is the last one! As usual, try to find mistakes and get extra points! Now let us look at your problems.. Problem 7.22.
More informationEdExcel Further Pure 2
EdExcel Further Pure 2 Complex Numbers Section : Loci in the Argand diagram Multiple Choice Test Questions 1 are about the following loci: P: z i = 2 Q: z i = z R: arg( z i) = S: z i = 2 z 1) Which of
More informationSolutions 1. Introduction to Coding Theory - Spring 2010 Solutions 1. Exercise 1.1. See Examples 1.2 and 1.11 in the course notes.
Solutions 1 Exercise 1.1. See Exaples 1.2 and 1.11 in the course notes. Exercise 1.2. Observe that the Haing distance of two vectors is the iniu nuber of bit flips required to transfor one into the other.
More informationSOLUTION FOR HOMEWORK 11, ACTS 4306
SOLUTION FOR HOMEWORK, ACTS 36 Welcome to your th homework. This is a collection of transformation, Central Limit Theorem (CLT), and other topics.. Solution: By definition of Z, Var(Z) = Var(3X Y.5). We
More informationLecture 5 - Fundamental Theorem for Line Integrals and Green s Theorem
Lecture 5 - Fundamental Theorem for Line Integrals and Green s Theorem Math 392, section C September 14, 2016 392, section C Lect 5 September 14, 2016 1 / 22 Last Time: Fundamental Theorem for Line Integrals:
More informationMA : Introductory Probability
MA 320-001: Introductory Probability David Murrugarra Department of Mathematics, University of Kentucky http://www.math.uky.edu/~dmu228/ma320/ Spring 2017 David Murrugarra (University of Kentucky) MA 320:
More informationor we could divide the total time T into N steps, with δ = T/N. Then and then we could insert the identity everywhere along the path.
D. L. Rubin September, 011 These notes are based on Sakurai,.4, Gottfried and Yan,.7, Shankar 8 & 1, and Richard MacKenzie s Vietnam School of Physics lecture notes arxiv:quanth/0004090v1 1 Path Integral
More informationMath 185 Homework Exercises II
Math 185 Homework Exercises II Instructor: Andrés E. Caicedo Due: July 10, 2002 1. Verify that if f H(Ω) C 2 (Ω) is never zero, then ln f is harmonic in Ω. 2. Let f = u+iv H(Ω) C 2 (Ω). Let p 2 be an integer.
More informationTOPOLOGY HW 2. x x ± y
TOPOLOGY HW 2 CLAY SHONKWILER 20.9 Show that the euclidean metric d on R n is a metric, as follows: If x, y R n and c R, define x + y = (x 1 + y 1,..., x n + y n ), cx = (cx 1,..., cx n ), x y = x 1 y
More informationEXAM # 3 PLEASE SHOW ALL WORK!
Stat 311, Summer 2018 Name EXAM # 3 PLEASE SHOW ALL WORK! Problem Points Grade 1 30 2 20 3 20 4 30 Total 100 1. A socioeconomic study analyzes two discrete random variables in a certain population of households
More informationGeometry. Class Examples (July 29) Paul Yiu. Department of Mathematics Florida Atlantic University. Summer 2014
Geometry lass Examples (July 29) Paul Yiu Department of Mathematics Florida tlantic University c a Summer 2014 1 The Pythagorean Theorem Theorem (Pythagoras). The lengths a
More informationLecture Wise Questions from 23 to 45 By Virtualians.pk. Q105. What is the impact of double integration in finding out the area and volume of Regions?
Lecture Wise Questions from 23 to 45 By Virtualians.pk Q105. What is the impact of double integration in finding out the area and volume of Regions? Ans: It has very important contribution in finding the
More informationRed veze za benzen. Slika 1.
Red veze za benzen Benzen C 6 H 6 je aromatično ciklično jedinjenje. Njegove dve rezonantne forme (ili Kekuléove structure), prema teoriji valentne veze (VB) prikazuju se uobičajeno kao na slici 1 a),
More information2010 GCE A Level H2 Maths Solution Paper 2 Section A: Pure Mathematics. 1i) x 2 6x + 34 = 0 6 ± x = 2
00 GCE A Level H Maths Solution Paper Section A: Pure Mathematics i) x 6x + 34 0 6 ± 36 36 x 6 ± 0i 3 ± 5i (ii) Since the coefficients are all real, another root of the equation is x i. [ x ( + i) ] [
More informationMTH301 Calculus II Solved Final Term Papers For Final Term Exam Preparation
MTH301 Calculus II Solved Final Term Papers For Final Term Exam Preparation Question No: 1 Laplace transform of t is 1 s 1 s 2 e s s Question No: 2 Symmetric equation for the line through (1,3,5) and (2,-2,3)
More information1. Exercise on Page 8: 2. Exercise on Page 8: (b)c 1 (C 2 C 3 ) and (C 1 C 2 ) (C 1 C 3 ) (C 1 C 2 ) (C 2 C 3 ) Problem Set 1 Fall 2017
. Exercise.2. on Page 8: Find the union C C 2 and the intersection C C 2 of the two sets C and C 2, where (a) C = {0,, 2}, C 2 = {2, 3, 4} Answer(a): C C 2 = {0,, 2, 3, 4}, C C 2 = {2} (b) C = {x : 0
More informationInformation Theory. Coding and Information Theory. Information Theory Textbooks. Entropy
Coding and Information Theory Chris Williams, School of Informatics, University of Edinburgh Overview What is information theory? Entropy Coding Information Theory Shannon (1948): Information theory is
More informationSolution/Correction standard, second Test Mathematics A + B1; November 7, 2014.
Solution/Correction standard, second Test Mathematics A + B1; November 7, 014. Kenmerk : Leibniz/toetsen/Re-Exam-Math-A-B1-141-Solutions Course : Mathematics A + B1 (Leibniz) Vakcode : 1911010 Date : November
More information(x + y) ds. 2 (1) dt = p Find the work done by the force eld. yzk
MATH Final Exam (Version 1) Solutions May 4, 11 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation.
More informationECE 302 Division 2 Exam 2 Solutions, 11/4/2009.
NAME: ECE 32 Division 2 Exam 2 Solutions, /4/29. You will be required to show your student ID during the exam. This is a closed-book exam. A formula sheet is provided. No calculators are allowed. Total
More informationGraphs with the Same Detour Matrix
CROATICA CHEMICA ACTA CCACAA 71 (1) 53 68 (1998) ISSN-0011-1643 CCA-2477 Original Scientific Paper Graphs with the Same Detour Matrix Milan Randi}, a Luz M. DeAlba, a and Frank E. Harris b a Department
More informationLecture 7: The Beam Element Equations.
4.1 Beam Stiffness. A Beam: A long slender structural component generally subjected to transverse loading that produces significant bending effects as opposed to twisting or axial effects. MECH 40: Finite
More informationSTA2603/205/1/2014 /2014. ry II. Tutorial letter 205/1/
STA263/25//24 Tutorial letter 25// /24 Distribution Theor ry II STA263 Semester Department of Statistics CONTENTS: Examination preparation tutorial letterr Solutions to Assignment 6 2 Dear Student, This
More informationMultiple Integrals. Chapter 4. Section 7. Department of Mathematics, Kookmin Univerisity. Numerical Methods.
4.7.1 Multiple Integrals Chapter 4 Section 7 4.7.2 Double Integral R f ( x, y) da 4.7.3 Double Integral Apply Simpson s rule twice R [ a, b] [ c, d] a x, x,..., x b, c y, y,..., y d 0 1 n 0 1 h ( b a)
More informationCapacity of a channel Shannon s second theorem. Information Theory 1/33
Capacity of a channel Shannon s second theorem Information Theory 1/33 Outline 1. Memoryless channels, examples ; 2. Capacity ; 3. Symmetric channels ; 4. Channel Coding ; 5. Shannon s second theorem,
More informationStatistical Learning Theory
Statistical Learning Theory Part I : Mathematical Learning Theory (1-8) By Sumio Watanabe, Evaluation : Report Part II : Information Statistical Mechanics (9-15) By Yoshiyuki Kabashima, Evaluation : Report
More informationMATH 106 HOMEWORK 4 SOLUTIONS. sin(2z) = 2 sin z cos z. (e zi + e zi ) 2. = 2 (ezi e zi )
MATH 16 HOMEWORK 4 SOLUTIONS 1 Show directly from the definition that sin(z) = ezi e zi i sin(z) = sin z cos z = (ezi e zi ) i (e zi + e zi ) = sin z cos z Write the following complex numbers in standard
More informationTHE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA hollscoile, CORCAIGH UNIVERSITY COLLEGE, CORK. Summer Examination 2009.
OLLSCOIL NA héireann, CORCAIGH THE NATIONAL UNIVERSITY OF IRELAND, CORK COLÁISTE NA hollscoile, CORCAIGH UNIVERSITY COLLEGE, CORK Summer Examination 2009 First Engineering MA008 Calculus and Linear Algebra
More informationApplications of Homotopy
Chapter 9 Applications of Homotopy In Section 8.2 we showed that the fundamental group can be used to show that two spaces are not homeomorphic. In this chapter we exhibit other uses of the fundamental
More informationPENRITH HIGH SCHOOL MATHEMATICS EXTENSION HSC Trial
PENRITH HIGH SCHOOL MATHEMATICS EXTENSION 013 Assessor: Mr Ferguson General Instructions: HSC Trial Total marks 100 Reading time 5 minutes Working time 3 hours Write using black or blue pen. Black pen
More informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART III MATHEMATICS
R Prerna Tower, Road No, Contractors Area, Bistupur, Jamshedpur 8300, Tel (0657)89, www.prernaclasses.com Jee Advance 03 Mathematics Paper I PART III MATHEMATICS SECTION : (Only One Option Correct Type)
More informationAnalysis of Experimental Designs
Analysis of Experimental Designs p. 1/? Analysis of Experimental Designs Gilles Lamothe Mathematics and Statistics University of Ottawa Analysis of Experimental Designs p. 2/? Review of Probability A short
More informationMath General Topology Fall 2012 Homework 6 Solutions
Math 535 - General Topology Fall 202 Homework 6 Solutions Problem. Let F be the field R or C of real or complex numbers. Let n and denote by F[x, x 2,..., x n ] the set of all polynomials in n variables
More informationCPT Solved Scanner (English) : Appendix 71
CPT Solved Scanner (English) : Appendix 71 Paper-4: Quantitative Aptitude Chapter-1: Ratio and Proportion, Indices and Logarithm [1] (b) The integral part of a logarithms is called Characteristic and the
More informationEGR 544 Communication Theory
EGR 544 Communcaton Theory. Informaton Sources Z. Alyazcoglu Electrcal and Computer Engneerng Department Cal Poly Pomona Introducton Informaton Source x n Informaton sources Analog sources Dscrete sources
More informationMathcad sa algoritmima
P R I M J E R I P R I M J E R I Mathcad sa algoritmima NAREDBE - elementarne obrade - sekvence Primjer 1 Napraviti algoritam za sabiranje dva broja. NAREDBE - elementarne obrade - sekvence Primjer 1 POČETAK
More informationComplex Analysis - Final exam - Answers
Complex Analysis - Final exam - Answers Exercise : (0 %) Let r, s R >0. Let f be an analytic function defined on D(0, r) and g be an analytic function defined on D(0, s). Prove that f +g is analytic on
More informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE NORMAL ACADEMIC LEVEL (016) (Syllabus 4044) CONTENTS Page INTRODUCTION AIMS ASSESSMENT OBJECTIVES SCHEME OF ASSESSMENT 3 USE OF CALCULATORS 3 SUBJECT CONTENT 4 MATHEMATICAL FORMULAE
More information24. Balkanska matematiqka olimpijada
4. Balkanska matematika olimpijada Rodos, Gka 8. apil 007 1. U konveksnom etvoouglu ABCD vaжi AB = BC = CD, dijagonale AC i BD su azliite duжine i seku se u taki E. Dokazati da je AE = DE ako i samo ako
More informationMath 416 Lecture 2 DEFINITION. Here are the multivariate versions: X, Y, Z iff P(X = x, Y = y, Z =z) = p(x, y, z) of X, Y, Z iff for all sets A, B, C,
Math 416 Lecture 2 DEFINITION. Here are the multivariate versions: PMF case: p(x, y, z) is the joint Probability Mass Function of X, Y, Z iff P(X = x, Y = y, Z =z) = p(x, y, z) PDF case: f(x, y, z) is
More informationMIL-DTL-5015 Style Circular Connectors
--01 y i oo /- i ooi --01 /- i i oi i --01 oi iio oo. io oiio o, oi i o i o o - -o-. /- i i oi i 12 i o iz o 10 o, i o o iz o #1 o #0 7 i o i o oo i iy o iio. o, i oo, i, oiio i i i o y oi --01, - o: i
More informationChapter 6. Basic triangle centers. 6.1 The Euler line The centroid
hapter 6 asic triangle centers 6.1 The Euler line 6.1.1 The centroid Let E and F be the midpoints of and respectively, and G the intersection of the medians E and F. onstruct the parallel through to E,
More informationINTRODUCTION TO LOW FREQUENCY LOCAL PLASMONS IN BULK EXTRINSIC SEMICONDUCTORS UDC 538.9; Yuri Kornyushin
FACTA UNIVERSITATIS Series: Physics, Chemistry and Technology Vol. 2, N o 5, 2003, pp. 253-258 INTRODUCTION TO LOW FREQUENCY LOCAL PLASMONS IN BULK EXTRINSIC SEMICONDUCTORS UDC 538.9; 621.315.5 Yuri Kornyushin
More informationMA4001 Engineering Mathematics 1 Lecture 15 Mean Value Theorem Increasing and Decreasing Functions Higher Order Derivatives Implicit Differentiation
MA4001 Engineering Mathematics 1 Lecture 15 Mean Value Theorem Increasing and Decreasing Functions Higher Order Derivatives Implicit Differentiation Dr. Sarah Mitchell Autumn 2014 Rolle s Theorem Theorem
More informationLab 3: measurement of Laser Gaussian Beam Profile Lab 3: basic experience working with laser (1) To create a beam expander for the Argon laser (2) To
Lab 3: measurement of Laser Gaussian Beam Profile Lab 3: basic experience working with laser (1) To create a beam expander for the Argon laser () To measure the spot size and profile of the Argon laser
More informationA Common FIXED POINT THEOREM for weakly compatible mappings in 2-metric Spaces
American Journal of Mathematics and Sciences Vol. 5, No.1, (January-December, 2016) Copyright Mind Reader Publications ISSN No: 2250-3102 www.journalshub.com A Common FIXED POINT THEOREM for weakly compatible
More informationIntroduction to Information Entropy Adapted from Papoulis (1991)
Introduction to Information Entropy Adapted from Papoulis (1991) Federico Lombardo Papoulis, A., Probability, Random Variables and Stochastic Processes, 3rd edition, McGraw ill, 1991. 1 1. INTRODUCTION
More informationLinear Models for Regression
Linear Models for Regression Seungjin Choi Department of Computer Science and Engineering Pohang University of Science and Technology 77 Cheongam-ro, Nam-gu, Pohang 37673, Korea seungjin@postech.ac.kr
More informationEXPERIMENTAL INVESTIGATION OF EXTRUSION SPEED AND TEMPERATURE EFFECTS ON ARITHMETIC MEAN SURFACE ROUGHNESS IN FDM- BUILT SPECIMENS
EXPERIMENTAL INVESTIGATION OF EXTRUSION SPEED AND TEMPERATURE EFFECTS ON ARITHMETIC MEAN SURFACE ROUGHNESS IN FDM- BUILT SPECIMENS Ognjan Lužanin *, Dejan Movrin, Miroslav Plančak University of Novi Sad,
More informationName: Block: Unit 2 Inequalities
Name: Block: Unit 2 Inequalities 2.1 Graphing and Writing Inequalities 2.2 Solving by Adding and Subtracting 2.3 Solving by Multiplying and Dividing 2.4 Solving Two Step and Multi Step Inequalities 2.5
More informationCourse 212: Academic Year Section 1: Metric Spaces
Course 212: Academic Year 1991-2 Section 1: Metric Spaces D. R. Wilkins Contents 1 Metric Spaces 3 1.1 Distance Functions and Metric Spaces............. 3 1.2 Convergence and Continuity in Metric Spaces.........
More informationRandom Variables. Cumulative Distribution Function (CDF) Amappingthattransformstheeventstotherealline.
Random Variables Amappingthattransformstheeventstotherealline. Example 1. Toss a fair coin. Define a random variable X where X is 1 if head appears and X is if tail appears. P (X =)=1/2 P (X =1)=1/2 Example
More informationMultivariate probability distributions and linear regression
Multivariate probability distributions and linear regression Patrik Hoyer 1 Contents: Random variable, probability distribution Joint distribution Marginal distribution Conditional distribution Independence,
More informationSection 5.8. (i) ( 3 + i)(14 2i) = ( 3)(14 2i) + i(14 2i) = {( 3)14 ( 3)(2i)} + i(14) i(2i) = ( i) + (14i + 2) = i.
1. Section 5.8 (i) ( 3 + i)(14 i) ( 3)(14 i) + i(14 i) {( 3)14 ( 3)(i)} + i(14) i(i) ( 4 + 6i) + (14i + ) 40 + 0i. (ii) + 3i 1 4i ( + 3i)(1 + 4i) (1 4i)(1 + 4i) (( + 3i) + ( + 3i)(4i) 1 + 4 10 + 11i 10
More informationMATH 31BH Homework 1 Solutions
MATH 3BH Homework Solutions January 0, 04 Problem.5. (a) (x, y)-plane in R 3 is closed and not open. To see that this plane is not open, notice that any ball around the origin (0, 0, 0) will contain points
More informationDETALJNI IZVEDBENI NASTAVNI PLAN PREDMETA
DETALJNI IZVEDBENI NASTAVNI PLAN PREDMETA Naziv predmeta Studijski program Godina 1 Status predmeta Web stranica predmeta/merlin Mogućnost izvođenja nastave na engleskom jeziku Bodovna vrijednost i način
More informationDirectional Derivative and the Gradient Operator
Chapter 4 Directional Derivative and the Gradient Operator The equation z = f(x, y) defines a surface in 3 dimensions. We can write this as z f(x, y) = 0, or g(x, y, z) = 0, where g(x, y, z) = z f(x, y).
More information7.13 7.14 7.15 J J WHERE CITY = 'London' ( SPJ WHERE J# = J# ( 'J1' ) ) { S# } 7.16 SPJ WHERE QTY QTY ( 300 ) AND QTY QTY ( 750 ) 7.17 7.18 7.19 7.20 7.21 P { COLOR, CITY } ( S JOIN P JOIN J ) { S#, P#,
More informationADDITIONAL MATHEMATICS
ADDITIONAL MATHEMATICS GCE Ordinary Level (Syllabus 4018) CONTENTS Page NOTES 1 GCE ORDINARY LEVEL ADDITIONAL MATHEMATICS 4018 2 MATHEMATICAL NOTATION 7 4018 ADDITIONAL MATHEMATICS O LEVEL (2009) NOTES
More informationScripture quotations marked cev are from the Contemporary English Version, Copyright 1991, 1992, 1995 by American Bible Society. Used by permission.
N Ra: E K B Da a a B a a, a-a- a aa, a a. T, a a. 2009 Ba P, I. ISBN 978-1-60260-296-0. N a a a a a, a,. C a a a Ba P, a 500 a a aa a. W, : F K B Da, Ba P, I. U. S a a a a K Ja V B. S a a a a N K Ja V.
More informationUnit 2 Maths Methods (CAS) Exam
Name: Teacher: Unit 2 Maths Methods (CAS) Exam 2 2014 Monday November 17 (1.50 pm) Reading time: 15 Minutes Writing time: 60 Minutes Instruction to candidates: Students are only permitted to bring into
More informationTV Breakaway Fail-Safe Lanyard Release Plug Military (D38999/29 & D38999/30)
y il- y l l iliy (/9 & /0) O O O -..... 6.. O ix i l ll iz y o l yi oiio / 9. O / i --, i, i- oo. i lol il l li, oi ili i 6@0 z iiio i., o l y, 00 i ooio i oli i l li, 00 o x l y, 0@0 z iiio i.,. &. ll
More informationMath 185 Fall 2015, Sample Final Exam Solutions
Math 185 Fall 2015, Sample Final Exam Solutions Nikhil Srivastava December 12, 2015 1. True or false: (a) If f is analytic in the annulus A = {z : 1 < z < 2} then there exist functions g and h such that
More informationWhen Are Two Random Variables Independent?
When Are Two Random Variables Independent? 1 Introduction. Almost all of the mathematics of inferential statistics and sampling theory is based on the behavior of mutually independent random variables,
More informationMAT 570 REAL ANALYSIS LECTURE NOTES. Contents. 1. Sets Functions Countability Axiom of choice Equivalence relations 9
MAT 570 REAL ANALYSIS LECTURE NOTES PROFESSOR: JOHN QUIGG SEMESTER: FALL 204 Contents. Sets 2 2. Functions 5 3. Countability 7 4. Axiom of choice 8 5. Equivalence relations 9 6. Real numbers 9 7. Extended
More informationSTUDENT NAME: STUDENT SIGNATURE: STUDENT ID NUMBER: SECTION NUMBER RECITATION INSTRUCTOR:
MA262 EXAM I SPRING 2016 FEBRUARY 25, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and
More information2) Let X be a compact space. Prove that the space C(X) of continuous real-valued functions is a complete metric space.
University of Bergen General Functional Analysis Problems with solutions 6 ) Prove that is unique in any normed space. Solution of ) Let us suppose that there are 2 zeros and 2. Then = + 2 = 2 + = 2. 2)
More informationNPTEL web course on Complex Analysis. A. Swaminathan I.I.T. Roorkee, India. and. V.K. Katiyar I.I.T. Roorkee, India
NPTEL web course on Complex Analysis A. Swaminathan I.I.T. Roorkee, India and V.K. Katiyar I.I.T. Roorkee, India A.Swaminathan and V.K.Katiyar (NPTEL) Complex Analysis 1 / 28 Complex Analysis Module: 6:
More informationIdz[3a y a x ] H b = c. Find H if both filaments are present:this will be just the sum of the results of parts a and
Chapter 8 Odd-Numbered 8.1a. Find H in cartesian components at P (, 3, 4) if there is a current filament on the z axis carrying 8mAinthea z direction: Applying the Biot-Savart Law, we obtain H a = IdL
More informationFunctional Analysis
The Hahn Banach Theorem : Functional Analysis 1-9-06 Extensions of Linear Forms and Separation of Convex Sets Let E be a vector space over R and F E be a subspace. A function f : F R is linear if f(αx
More information1 Chapter 1: SETS. 1.1 Describing a set
1 Chapter 1: SETS set is a collection of objects The objects of the set are called elements or members Use capital letters :, B, C, S, X, Y to denote the sets Use lower case letters to denote the elements:
More informationNAPREDNI FIZIČKI PRAKTIKUM II studij Geofizika MODUL ELASTIČNOSTI
NAPREDNI FIZIČKI PRAKTIKUM II studij Geofizika MODUL ELASTIČNOSTI studij Geofizika NFP II 1 ZADACI 1. Izmjerite ovisnost savijenosti šipki o: primijenjenoj sili debljini šipke širini šipke udaljenosti
More informationUsing Complex Weighted Centroids to Create Homothetic Polygons. Harold Reiter. Department of Mathematics, University of North Carolina Charlotte,
Using Complex Weighted Centroids to Create Homothetic Polygons Harold Reiter Department of Mathematics, University of North Carolina Charlotte, Charlotte, NC 28223, USA hbreiter@emailunccedu Arthur Holshouser
More informationTHE RDA MODEL OF SCALING AND SIZE EFFECT OF NANOCOMPOSITES
THE RDA MODEL OF SCALING AND SIZE EFFECT OF NANOCOMPOSITES prof.dr.sc. Dragan Milašinović, dipl.ing.građ. Građevinski fakultet Subotica Univerzitet u Novom Sadu Abstract: This paper presents an application
More informationOLLSCOIL NA heireann MA NUAD THE NATIONAL UNIVERSITY OF IRELAND MAYNOOTH MATHEMATICAL PHYSICS EE112. Engineering Mathematics II.
OLLSCOIL NA heireann MA NUAD THE NATIONAL UNIVERSITY OF IRELAND MAYNOOTH MATHEMATICAL PHYSICS EE112 Engineering Mathematics II Lines and Planes Prof. D. M. Heffernan and Mr. S. Pouryahya 1 4 Equations
More informationDESIGN OF THE QUESTION PAPER
SET-II DESIGN OF THE QUESTION PAPER MATHEMATICS CLASS IX Time : 3 Hours Maximum Marks : 80 The weightage or the distribution of marks over different dimensions of the question paper shall be as follows:
More informationChapter 1.4 Student Notes. Presenting Scientific Data
Chapter 1.4 Student Notes Presenting Scientific Data Line Graph Type Described Use Line Compares 2 variables Shows trends Bar Graph Type Described Use Bar Compares Shows Data Bar Graph Type Described Use
More informationMath 341: Convex Geometry. Xi Chen
Math 341: Convex Geometry Xi Chen 479 Central Academic Building, University of Alberta, Edmonton, Alberta T6G 2G1, CANADA E-mail address: xichen@math.ualberta.ca CHAPTER 1 Basics 1. Euclidean Geometry
More informationA2H Assignment #8 Cramer s Rule Unit 2: Matrices and Systems. DUE Date: Friday 12/2 as a Packet. 3x 2y = 10 5x + 3y = 4. determinant.
A2H Assignment #8 Cramer s Rule Unit 2: Matrices and Systems Name: DUE Date: Friday 12/2 as a Packet What is the Cramer s Rule used for? à Another method to solve systems that uses matrices and determinants.
More informationAPPM/MATH 4/5520 Solutions to Exam I Review Problems. f X 1,X 2. 2e x 1 x 2. = x 2
APPM/MATH 4/5520 Solutions to Exam I Review Problems. (a) f X (x ) f X,X 2 (x,x 2 )dx 2 x 2e x x 2 dx 2 2e 2x x was below x 2, but when marginalizing out x 2, we ran it over all values from 0 to and so
More informationGCE AS. Mathematics. Mark Schemes. January 2010
GCE AS Mathematics January 00 Mark Schemes Issued: April 00 NORTHERN IRELAND GENERAL CERTIFICATE OF SECONDARY EDUCATION (GCSE) AND NORTHERN IRELAND GENERAL CERTIFICATE OF EDUCATION (GCE) Introduction
More informationarxiv: v3 [math.co] 18 Jul 2014
Cop and robber game and hyperbolicity Jérémie Chalopin 1, Victor Chepoi 1, Panos Papasoglu 2, and Timothée Pecatte 3 arxiv:1308.3987v3 [math.co] 18 Jul 2014 1 Laboratoire d Informatique Fondamentale, Aix-Marseille
More informationTopic 1 Part 3 [483 marks]
Topic Part 3 [483 marks] The complex numbers z = i and z = 3 i are represented by the points A and B respectively on an Argand diagram Given that O is the origin, a Find AB, giving your answer in the form
More informationADDITIONAL MATHEMATICS 4037/01
Cambridge O Level *0123456789* ADDITIONAL MATHEMATICS 4037/01 Paper 1 For examination from 2020 SPECIMEN PAPER 2 hours You must answer on the question paper. No additional materials are needed. INSTRUCTIONS
More informationHomework 1 Due: Thursday 2/5/2015. Instructions: Turn in your homework in class on Thursday 2/5/2015
10-704 Homework 1 Due: Thursday 2/5/2015 Instructions: Turn in your homework in class on Thursday 2/5/2015 1. Information Theory Basics and Inequalities C&T 2.47, 2.29 (a) A deck of n cards in order 1,
More informationVARIS DODATNA OPREMA. Alu naplatak Podium anthracite. Alu naplatak 15 11, Light Grey PZ49P-B0671-CE. Sigumosne matice. Krovni nosac (3 vrata)
VARIS DODATNA OPREMA TOYOTA ALWAYS A BETTER WAY Alu naplatak 15 11 Podium anthracite PZ406-B067B-ZG 3.029,85kn 390,00kn Samo za vozila sa original 15" naplatcima. Cijena za 4 naplatka 3.419,85 kn Alu naplatak
More information26.2. Cauchy-Riemann Equations and Conformal Mapping. Introduction. Prerequisites. Learning Outcomes
Cauchy-Riemann Equations and Conformal Mapping 26.2 Introduction In this Section we consider two important features of complex functions. The Cauchy-Riemann equations provide a necessary and sufficient
More information1 Basics of vector space
Linear Algebra- Review And Beyond Lecture 1 In this lecture, we will talk about the most basic and important concept of linear algebra vector space. After the basics of vector space, I will introduce dual
More informationEven-Numbered Homework Solutions
-6 Even-Numbered Homework Solutions Suppose that the matric B has λ = + 5i as an eigenvalue with eigenvector Y 0 = solution to dy = BY Using Euler s formula, we can write the complex-valued solution Y
More informationLecture 21: Isoparametric Formulation of Plane Elements.
6.6. Rectangular Plane Stress/Strain Element. he CS element uses a triangular shape. he 3 nodes of the CS element allow us to employ linear multivariate approximations to the u and v displacements. he
More information