ON SOME PROPERTIES OF KANTOROVICH BIVARIATE OPERATORS

Size: px
Start display at page:

Download "ON SOME PROPERTIES OF KANTOROVICH BIVARIATE OPERATORS"

Transcription

1 Proceedigs of the Iteratioal Coferece o Theory ad Applicatios of Matheatics ad Iforatics ICTAMI 3 Alba Iulia ON SOME PROPERTIES OF KANTOROVICH BIVARIATE OPERATORS by Lucia A. Căbulea ad Mihaela Aldea Abstract. I this paper we cotiue our earlier ivestigatios cocerig the use of probabilistic ethods for costructig liear positive operators useful i approxiatio theory of fuctios. The ai result of this paper cosists i itroducig ad ivestigatig the approxiatio properties of Katorovich bivariate operator which is a itegral liear positive operator reproducig the liear fuctios. Keywords: bivariate operator. THE OPERATORS OF KANTOROVICH Let N be fixed. The operators K : L ([] C([] defied by ( K f x ( x ( x ( f ( t dt (. are the operators of Katorovich. If we oticed χ the characteristic fuctio of the the operators (. ca be defie ( f ( t χ t dt (. ( K f x ( p ( x where p x x ( x [] are the Berstei polyoials. Lea[]. The operators of Katorovich satisfy the relatios i ( e ( x K 6

2 Lucia A. Căbulea Mihaela Aldea - O soe properties of Katorovich K ( x x ( ii ( e ( K e ( x x x. ( ( 3( iii ( iv For all f ([ ] ( K f ( x ( B F ( x L ( B f ( x x ( x f [ ] d where F( x dx x f ( t dt ad x are the operators of Berstei. Theore [8]. The operators of Katorovich have the properties li uiforly o [] ( f C[ ] i f f K. ii K li f f f L [ ] p. ( p. THE OPERATORS OF STANCU-KANTOROVICH The Stacu polyoials [7] defied by S ( f ; x w ( x f I [ ] x ( ( x ( x where w ( x ( ( x x( x...( x ( used for costructig the operators of Stacu-Katorovich[5] ca be K ( f ; x ( w ( x f ( t dt. (. It is clear that the operators defied by (. are liear ad positive too. I the th particular case the operator reduces obviously to the classical Katorovich operator defied by (.. Lea [3]. The operators defied by (. satisfy the relatios 6

3 Lucia A. Căbulea Mihaela Aldea - O soe properties of Katorovich K x i ( ; ii K ( t x; x x ( iii ( t x K ( ; x x( x ( 3( iv If C with C a positive costat it follows where ( x ( t x ; x ( x x K ( C ψ x ( x E A A ψ with E x I \ E ad A > fixed. Theore. Let ( ( K be defied by (. ad ( p ( ( β. ( / p p 3( / r If r 3 is a iteger uber ad ( p fuctio f [ ] we have with L p ( / r f f C β ( p f ω r ( p β N the for every r ( r ( f K p r β p C p r a positive costat idepedet of f ad. p 3.THE BIVARIATE OPERATORS OF KANTOROVICH We cosider the operators defied by 63

4 Lucia A. Căbulea Mihaela Aldea - O soe properties of Katorovich h h ( K f ( x y ( ( x ( x y ( y f ( u v h where f belogs to the spaces ([ ] [ ] L. The operators defied by (3. are the of Katorovich. Lea. The of Ktorovich satisfy the relatios: i ( e ( x y K K x ( ii ( e ( x y K ( x y y ( iii ( e K iv ( e ( x y x y ( ( ( K ( ( 3( v ( e ( x y x x ( K. ( ( 3( vi ( e ( x y y y Theore. The of Katorovich have the properties li uiforly o [ ] [ ] ( C( [ ] [ ] i f f K f h h dudv ii li f f ( f L ([ ] [ ] p. K p 4.THE BIVARIATE OPERATORS OF STANCU KANTOROVICH Now we cosider the operators defied by 64

5 Lucia A. Căbulea Mihaela Aldea - O soe properties of Katorovich K h h ( f ; x y ( ( w ( x w ( y f ( u v h dudv (4. ( ( x ( x ( where w ( x ( x x( x...( x ( ad ( h ( h y ( y ( w h ( x ( y h y( y...( y ( h. h The operators defied by (4. are the of Stacu- Katorovich. Lea. The operators defied by (4. satisfy the relatios K i ( ; x y ii ( u x; x y K x ( iii ( v y; x y K y ( iv (( u x( v y ; x y K x y ( ( ( ; x y x( x v ( u x K ( 3( vi ( v y K ( ; x y y( y ( 3(. REFERENCES []. Agratii O. Aproxiare pri operatori liiari Presa Uiversitară Clujeaă. []. Căbulea L. Aldea M. Geeralizatios of Katorovich type Aalele Uiversităţii Aurel Vlaicu Arad Seria Mateatica Arad 7-3. [3]. Della Vechia B. O the approxiatio offuctios by eas ofthe operators of D. 65

6 Lucia A. Căbulea Mihaela Aldea - O soe properties of Katorovich D. Stacu Studia Uiv. Babeş-Bolyai Math. XXXVII ( [4]. Della Vechia B. Mache D. H. O approxiatio properties of Stacu-Katorovich operators Rev. D'Aalyse Nu. Et de Théorie de L'Approx. 7(998 o [5]. Katorovich L. V. Surcertais dévelopets suivat Ies polyôes de la fore de S. Bestei I II C. R. Acad. URSS ( [6]. Razi Q. Approxiatio of a fuctio by Katorovich type operators Mat. Veşic. 4( [7]. Sedov B. Popov V. A. The Averaged Moduli of Soothess Pure ad Applied Matheatics Joh Wiley & Soos 988. [8]. Stacu D. D. Approxiatio of fuctios by a ew class of liear polyoial operators Rev. Rouaie Math. Pures Appl. 8( [9]. Stacu D. D. Coa Gh. Agratii O. Trîbiţaş R. Aaliză uerică şi teoria aproxiării voi. l Presa Uiversitară Clujeaă. Authors: Lucia A. Căbulea " Decebrie 98" Uiversity of Alba lulia Roâia. Departaet of Matheatics e-ail: lcabulea@uab.ro Mihaela Aldea " Decebrie 98" Uiversity of Alba lulia Roâia. Departaet of Matheatics e-ail: todea@uab.ro. 66

ON AN INTEGRAL OPERATOR WHICH PRESERVE THE UNIVALENCE

ON AN INTEGRAL OPERATOR WHICH PRESERVE THE UNIVALENCE Proceedigs of the Iteratioal Coferece o Theory ad Applicatios of Mathematics ad Iformatics ICTAMI 3, Alba Iulia ON AN INTEGRAL OPERATOR WHICH PRESERVE THE UNIVALENCE by Maria E Gageoea ad Silvia Moldoveau

More information

Degree of Approximation of Continuous Functions by (E, q) (C, δ) Means

Degree of Approximation of Continuous Functions by (E, q) (C, δ) Means Ge. Math. Notes, Vol. 11, No. 2, August 2012, pp. 12-19 ISSN 2219-7184; Copyright ICSRS Publicatio, 2012 www.i-csrs.org Available free olie at http://www.gema.i Degree of Approximatio of Cotiuous Fuctios

More information

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL. Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio - Israel Istitute of Techology, 3000, Haifa, Israel I memory

More information

A Faster Clause-Shortening Algorithm for SAT with No Restriction on Clause Length

A Faster Clause-Shortening Algorithm for SAT with No Restriction on Clause Length Joural o Satisfiability, Boolea Modelig ad Computatio 1 2005) 49-60 A Faster Clause-Shorteig Algorithm for SAT with No Restrictio o Clause Legth Evgey Datsi Alexader Wolpert Departmet of Computer Sciece

More information

A zero one programming model for RNA structures with arc length 4

A zero one programming model for RNA structures with arc length 4 Iraia Joural of Matheatical Cheistry, Vol. 3, No.2, Septeber 22, pp. 85 93 IJMC A zero oe prograig odel for RNA structures with arc legth 4 G. H. SHIRDEL AND N. KAHKESHANI Departet of Matheatics, Faculty

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Our aim is to show that under reasonable assumptions a given 2π-periodic function f can be represented as convergent series

Our aim is to show that under reasonable assumptions a given 2π-periodic function f can be represented as convergent series 8 Fourier Series Our aim is to show that uder reasoable assumptios a give -periodic fuctio f ca be represeted as coverget series f(x) = a + (a cos x + b si x). (8.) By defiitio, the covergece of the series

More information

the product of the hook-lengths is over all boxes of the diagram. We denote by d (n) the number of semi-standard tableaux:

the product of the hook-lengths is over all boxes of the diagram. We denote by d (n) the number of semi-standard tableaux: O Represetatio Theory i Coputer Visio Probles Ao Shashua School of Coputer Sciece ad Egieerig Hebrew Uiversity of Jerusale Jerusale 91904, Israel eail: shashua@cs.huji.ac.il Roy Meshula Departet of Matheatics

More information

Entropy of bi-capacities

Entropy of bi-capacities Etropy of bi-capacities Iva Kojadiovic LINA CNRS FRE 2729 Site école polytechique de l uiv. de Nates Rue Christia Pauc 44306 Nates, Frace iva.kojadiovic@uiv-ates.fr Jea-Luc Marichal Applied Mathematics

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

Asymptotic Growth of Functions

Asymptotic Growth of Functions CMPS Itroductio to Aalysis of Algorithms Fall 3 Asymptotic Growth of Fuctios We itroduce several types of asymptotic otatio which are used to compare the performace ad efficiecy of algorithms As we ll

More information

Numerical Analysis for Characterization of a Salty Water Meter

Numerical Analysis for Characterization of a Salty Water Meter Nuerical Aalysis for Characterizatio of a Salty Water Meter José Erique Salias Carrillo Departaeto de Ciecias Básicas Istituto Tecológico de Tehuacá Bolio Arago Perdoo Departaeto de Mecatróica Istituto

More information

AP Calculus AB 2006 Scoring Guidelines Form B

AP Calculus AB 2006 Scoring Guidelines Form B AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a ot-for-profit membership associatio whose missio is to coect studets to college success

More information

The Binomial Multi- Section Transformer

The Binomial Multi- Section Transformer 4/15/21 The Bioial Multisectio Matchig Trasforer.doc 1/17 The Bioial Multi- Sectio Trasforer Recall that a ulti-sectio atchig etwork ca be described usig the theory of sall reflectios as: where: Γ ( ω

More information

S. Tanny MAT 344 Spring 1999. be the minimum number of moves required.

S. Tanny MAT 344 Spring 1999. be the minimum number of moves required. S. Tay MAT 344 Sprig 999 Recurrece Relatios Tower of Haoi Let T be the miimum umber of moves required. T 0 = 0, T = 7 Iitial Coditios * T = T + $ T is a sequece (f. o itegers). Solve for T? * is a recurrece,

More information

A Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design

A Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design A Combied Cotiuous/Biary Geetic Algorithm for Microstrip Atea Desig Rady L. Haupt The Pesylvaia State Uiversity Applied Research Laboratory P. O. Box 30 State College, PA 16804-0030 haupt@ieee.org Abstract:

More information

Section 11.3: The Integral Test

Section 11.3: The Integral Test Sectio.3: The Itegral Test Most of the series we have looked at have either diverged or have coverged ad we have bee able to fid what they coverge to. I geeral however, the problem is much more difficult

More information

THE HEIGHT OF q-binary SEARCH TREES

THE HEIGHT OF q-binary SEARCH TREES THE HEIGHT OF q-binary SEARCH TREES MICHAEL DRMOTA AND HELMUT PRODINGER Abstract. q biary search trees are obtaied from words, equipped with the geometric distributio istead of permutatios. The average

More information

Infinite Sequences and Series

Infinite Sequences and Series CHAPTER 4 Ifiite Sequeces ad Series 4.1. Sequeces A sequece is a ifiite ordered list of umbers, for example the sequece of odd positive itegers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...

More information

Research Article Sign Data Derivative Recovery

Research Article Sign Data Derivative Recovery Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov

More information

A note on the boundary behavior for a modified Green function in the upper-half space

A note on the boundary behavior for a modified Green function in the upper-half space Zhag ad Pisarev Boudary Value Problems (015) 015:114 DOI 10.1186/s13661-015-0363-z RESEARCH Ope Access A ote o the boudary behavior for a modified Gree fuctio i the upper-half space Yulia Zhag1 ad Valery

More information

Chapter 5 O A Cojecture Of Erdíos Proceedigs NCUR VIII è1994è, Vol II, pp 794í798 Jeærey F Gold Departmet of Mathematics, Departmet of Physics Uiversity of Utah Do H Tucker Departmet of Mathematics Uiversity

More information

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

More information

GOAL PROGRAMMING BASED MASTER PLAN FOR CYCLICAL NURSE SCHEDULING

GOAL PROGRAMMING BASED MASTER PLAN FOR CYCLICAL NURSE SCHEDULING Joural of Theoretical ad Applied Iforatio Techology 5 th Deceber 202. Vol. 46 No. 2005-202 JATIT & LLS. All rights reserved. ISSN: 992-8645 www.jatit.org E-ISSN: 87-395 GOAL PROGRAMMING BASED MASTER PLAN

More information

New exact solutions for the combined sinh-cosh-gordon equation

New exact solutions for the combined sinh-cosh-gordon equation Sociedad Colobiaa de Mateáticas XV Cogreso Nacioal de Mateáticas 2005 Aputes Lecturas Mateáticas Volue Especial (2006), págias 87 93 New exact solutios for the cobied sih-cosh-gordo equatio César A. Góez

More information

Running Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis

Running Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis Ruig Time ( 3.) Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Most algorithms trasform iput objects ito output objects.

More information

THE ABRACADABRA PROBLEM

THE ABRACADABRA PROBLEM THE ABRACADABRA PROBLEM FRANCESCO CARAVENNA Abstract. We preset a detailed solutio of Exercise E0.6 i [Wil9]: i a radom sequece of letters, draw idepedetly ad uiformly from the Eglish alphabet, the expected

More information

arxiv:0903.5136v2 [math.pr] 13 Oct 2009

arxiv:0903.5136v2 [math.pr] 13 Oct 2009 First passage percolatio o rado graphs with fiite ea degrees Shakar Bhaidi Reco va der Hofstad Gerard Hooghiestra October 3, 2009 arxiv:0903.536v2 [ath.pr 3 Oct 2009 Abstract We study first passage percolatio

More information

Uncertainty Chapter 13. Mausam (Based on slides by UW-AI faculty)

Uncertainty Chapter 13. Mausam (Based on slides by UW-AI faculty) Ucertait Chapter 3 Mausam Based o slides b UW-AI facult Kowledge Represetatio KR Laguage Otological Commitmet Epistemological Commitmet ropositioal Logic facts true false ukow First Order Logic facts objects

More information

Installment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate

Installment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate Iteratioal Coferece o Maagemet Sciece ad Maagemet Iovatio (MSMI 4) Istallmet Joit Life Isurace ctuarial Models with the Stochastic Iterest Rate Nia-Nia JI a,*, Yue LI, Dog-Hui WNG College of Sciece, Harbi

More information

Guido Walz. Nr.86. November 1988. Oll Generalized Bernstein Polynomials in CAGD , ' ;.' _. ",.' ",...,.,.'. 'i-'.,,~~...

Guido Walz. Nr.86. November 1988. Oll Generalized Bernstein Polynomials in CAGD , ' ;.' _. ,.' ,...,.,.'. 'i-'.,,~~... Oll Geeralized Berstei Polyomials i CAGD Guido Walz Nr.86 November 1988 'i-'.,,~~.......... :'>'-. "',.,- ~. ~,..._.. w. ",... -i. _. ",.' ",...,.,.'., ' ;.' ~-.,."""",:.... _...~...'-.... _,, O Geeralized

More information

Sequences and Series

Sequences and Series CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their

More information

Semiconductor Devices

Semiconductor Devices emicoductor evices Prof. Zbigiew Lisik epartmet of emicoductor ad Optoelectroics evices room: 116 e-mail: zbigiew.lisik@p.lodz.pl Uipolar devices IFE T&C JFET Trasistor Uipolar evices - Trasistors asic

More information

Review: Classification Outline

Review: Classification Outline Data Miig CS 341, Sprig 2007 Decisio Trees Neural etworks Review: Lecture 6: Classificatio issues, regressio, bayesia classificatio Pretice Hall 2 Data Miig Core Techiques Classificatio Clusterig Associatio

More information

Firewall Modules and Modular Firewalls

Firewall Modules and Modular Firewalls Firewall Modules ad Modular Firewalls H. B. Acharya Uiversity of Texas at Austi acharya@cs.utexas.edu Aditya Joshi Uiversity of Texas at Austi adityaj@cs.utexas.edu M. G. Gouda Natioal Sciece Foudatio

More information

A Fuzzy Model of Software Project Effort Estimation

A Fuzzy Model of Software Project Effort Estimation TJFS: Turkish Joural of Fuzzy Systems (eissn: 309 90) A Official Joural of Turkish Fuzzy Systems Associatio Vol.4, No.2, pp. 68-76, 203 A Fuzzy Model of Software Project Effort Estimatio Oumout Chouseioglou

More information

Department of Computer Science, University of Otago

Department of Computer Science, University of Otago Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS-2006-09 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly

More information

A probabilistic proof of a binomial identity

A probabilistic proof of a binomial identity A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two

More information

Digital Interactive Kanban Advertisement System Using Face Recognition Methodology

Digital Interactive Kanban Advertisement System Using Face Recognition Methodology Coputatioal Water, Eergy, ad Eviroetal Egieerig, 2013, 2, 26-30 doi:10.4236/cweee.2013.23b005 Published Olie July 2013 (http://www.scirp.org/joural/cweee) Digital Iteractive Kaba Advertiseet Syste Usig

More information

An Efficient Polynomial Approximation of the Normal Distribution Function & Its Inverse Function

An Efficient Polynomial Approximation of the Normal Distribution Function & Its Inverse Function A Efficiet Polyomial Approximatio of the Normal Distributio Fuctio & Its Iverse Fuctio Wisto A. Richards, 1 Robi Atoie, * 1 Asho Sahai, ad 3 M. Raghuadh Acharya 1 Departmet of Mathematics & Computer Sciece;

More information

THIN SEQUENCES AND THE GRAM MATRIX PAMELA GORKIN, JOHN E. MCCARTHY, SANDRA POTT, AND BRETT D. WICK

THIN SEQUENCES AND THE GRAM MATRIX PAMELA GORKIN, JOHN E. MCCARTHY, SANDRA POTT, AND BRETT D. WICK THIN SEQUENCES AND THE GRAM MATRIX PAMELA GORKIN, JOHN E MCCARTHY, SANDRA POTT, AND BRETT D WICK Abstract We provide a ew proof of Volberg s Theorem characterizig thi iterpolatig sequeces as those for

More information

On the L p -conjecture for locally compact groups

On the L p -conjecture for locally compact groups Arch. Math. 89 (2007), 237 242 c 2007 Birkhäuser Verlag Basel/Switzerlad 0003/889X/030237-6, ublished olie 2007-08-0 DOI 0.007/s0003-007-993-x Archiv der Mathematik O the L -cojecture for locally comact

More information

arxiv:0805.1434v1 [math.pr] 9 May 2008

arxiv:0805.1434v1 [math.pr] 9 May 2008 Degree-distribution stability of scale-free networs Zhenting Hou, Xiangxing Kong, Dinghua Shi,2, and Guanrong Chen 3 School of Matheatics, Central South University, Changsha 40083, China 2 Departent of

More information

ON THE DENSE TRAJECTORY OF LASOTA EQUATION

ON THE DENSE TRAJECTORY OF LASOTA EQUATION UNIVERSITATIS IAGELLONICAE ACTA MATHEMATICA, FASCICULUS XLIII 2005 ON THE DENSE TRAJECTORY OF LASOTA EQUATION by Atoi Leo Dawidowicz ad Najemedi Haribash Abstract. I preseted paper the dese trajectory

More information

Chapter 7 - Sampling Distributions. 1 Introduction. What is statistics? It consist of three major areas:

Chapter 7 - Sampling Distributions. 1 Introduction. What is statistics? It consist of three major areas: Chapter 7 - Samplig Distributios 1 Itroductio What is statistics? It cosist of three major areas: Data Collectio: samplig plas ad experimetal desigs Descriptive Statistics: umerical ad graphical summaries

More information

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad

More information

'rj /ifi a a2 a3 a4. (To = Vi/r/2h), are entered in the last column of Table I for different values ECONOMICS AND THE CALCULUS OF VARIATIONS

'rj /ifi a a2 a3 a4. (To = Vi/r/2h), are entered in the last column of Table I for different values ECONOMICS AND THE CALCULUS OF VARIATIONS 90 MA THEMA TICS: G. C. E VA NS PROC. N. A. S. ues for a show i the secod colum, the coefficiets of zi may be easily computed for ay specific value of V/w. The coefficiets A- satisfy the coditio i j! =

More information

Math 113 HW #11 Solutions

Math 113 HW #11 Solutions Math 3 HW # Solutios 5. 4. (a) Estimate the area uder the graph of f(x) = x from x = to x = 4 usig four approximatig rectagles ad right edpoits. Sketch the graph ad the rectagles. Is your estimate a uderestimate

More information

Irreducible polynomials with consecutive zero coefficients

Irreducible polynomials with consecutive zero coefficients Irreducible polyomials with cosecutive zero coefficiets Theodoulos Garefalakis Departmet of Mathematics, Uiversity of Crete, 71409 Heraklio, Greece Abstract Let q be a prime power. We cosider the problem

More information

Floating Codes for Joint Information Storage in Write Asymmetric Memories

Floating Codes for Joint Information Storage in Write Asymmetric Memories Floatig Codes for Joit Iformatio Storage i Write Asymmetric Memories Axiao (Adrew Jiag Computer Sciece Departmet Texas A&M Uiversity College Statio, TX 77843-311 ajiag@cs.tamu.edu Vaske Bohossia Electrical

More information

Mathematical Model for Forecasting and Estimating of Market Demand

Mathematical Model for Forecasting and Estimating of Market Demand Mathematical Model for Forecastig ad Estimatig of Market Demad Da Nicolae, Valeti Pau, Mihaela Jaradat, Mugurel Iout Adreica, Vasile Deac To cite this versio: Da Nicolae, Valeti Pau, Mihaela Jaradat, Mugurel

More information

Chair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics

Chair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics Chair for Network Architectures ad Services Istitute of Iformatics TU Müche Prof. Carle Network Security Chapter 2 Basics 2.4 Radom Number Geeratio for Cryptographic Protocols Motivatio It is crucial to

More information

Notes on exponential generating functions and structures.

Notes on exponential generating functions and structures. Notes o expoetial geeratig fuctios ad structures. 1. The cocept of a structure. Cosider the followig coutig problems: (1) to fid for each the umber of partitios of a -elemet set, (2) to fid for each the

More information

Data Analysis and Statistical Behaviors of Stock Market Fluctuations

Data Analysis and Statistical Behaviors of Stock Market Fluctuations 44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:

More information

Proof of Geeratig Fuctio For J.B.S.A.R.D.T.a.a.

Proof of Geeratig Fuctio For J.B.S.A.R.D.T.a.a. Ca. J. Math., Vol. XXXVII, No. 6, 1985, pp. 1201-1210 DIRECTED GRAPHS AND THE JACOBI-TRUDI IDENTITY I. P. GOULDEN 1. Itroductio. Let \a i L X deote the X determiat with (/', y)-etry a-, ad h k = h k (x

More information

Integer Factorization Algorithms

Integer Factorization Algorithms Iteger Factorizatio Algorithms Coelly Bares Departmet of Physics, Orego State Uiversity December 7, 004 This documet has bee placed i the public domai. Cotets I. Itroductio 3 1. Termiology 3. Fudametal

More information

This is a refereed journal and all articles are professionally screened and reviewed

This is a refereed journal and all articles are professionally screened and reviewed Advaces i Evirometal Biology, 7(9): 2509-2521, 2013 ISSN 1995-0756 2509 This is a refereed joural ad all articles are professioally screeed ad reviewed ORIGINAL ARTICLE A New Algorithm for ERP System Selectio

More information

Multiplexers and Demultiplexers

Multiplexers and Demultiplexers I this lesso, you will lear about: Multiplexers ad Demultiplexers 1. Multiplexers 2. Combiatioal circuit implemetatio with multiplexers 3. Demultiplexers 4. Some examples Multiplexer A Multiplexer (see

More information

Section 8.3 : De Moivre s Theorem and Applications

Section 8.3 : De Moivre s Theorem and Applications The Sectio 8 : De Moivre s Theorem ad Applicatios Let z 1 ad z be complex umbers, where z 1 = r 1, z = r, arg(z 1 ) = θ 1, arg(z ) = θ z 1 = r 1 (cos θ 1 + i si θ 1 ) z = r (cos θ + i si θ ) ad z 1 z =

More information

Investigation of Atwood s machines as Series and Parallel networks

Investigation of Atwood s machines as Series and Parallel networks Ivestiatio of Atwood s achies as Series ad Parallel etworks Jafari Matehkolaee, Mehdi; Bavad, Air Ahad Islaic Azad uiversity of Shahrood, Shahid Beheshti hih school i Sari, Mazadara, Ira ehdisaraviaria@yahoo.co

More information

Math 114- Intermediate Algebra Integral Exponents & Fractional Exponents (10 )

Math 114- Intermediate Algebra Integral Exponents & Fractional Exponents (10 ) Math 4 Math 4- Itermediate Algebra Itegral Epoets & Fractioal Epoets (0 ) Epoetial Fuctios Epoetial Fuctios ad Graphs I. Epoetial Fuctios The fuctio f ( ) a, where is a real umber, a 0, ad a, is called

More information

FIBONACCI NUMBERS: AN APPLICATION OF LINEAR ALGEBRA. 1. Powers of a matrix

FIBONACCI NUMBERS: AN APPLICATION OF LINEAR ALGEBRA. 1. Powers of a matrix FIBONACCI NUMBERS: AN APPLICATION OF LINEAR ALGEBRA. Powers of a matrix We begi with a propositio which illustrates the usefuless of the diagoalizatio. Recall that a square matrix A is diogaalizable if

More information

The Computational Rise and Fall of Fairness

The Computational Rise and Fall of Fairness Proceedigs of the Twety-Eighth AAAI Coferece o Artificial Itelligece The Coputatioal Rise ad Fall of Fairess Joh P Dickerso Caregie Mello Uiversity dickerso@cscuedu Joatha Golda Caregie Mello Uiversity

More information

Quantum bouncer with dissipation

Quantum bouncer with dissipation ENSEÑANZA REVISTA MEXICANA DE FÍSICA E5 ) 16 131 DICIEMBRE 006 Quatu boucer with dissipatio G. López G. Gozález Departaeto de Física de la Uiversidad de Guadalajara, Apartado Postal 4-137, 44410 Guadalajara,

More information

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 [C] Commuicatio Measuremet A1. Solve problems that ivolve liear measuremet, usig: SI ad imperial uits of measure estimatio strategies measuremet strategies.

More information

THE LEAST COMMON MULTIPLE OF A QUADRATIC SEQUENCE

THE LEAST COMMON MULTIPLE OF A QUADRATIC SEQUENCE THE LEAST COMMON MULTIPLE OF A QUADRATIC SEQUENCE JAVIER CILLERUELO Abstract. We obtai, for ay irreducible quadratic olyomial f(x = ax 2 + bx + c, the asymtotic estimate log l.c.m. {f(1,..., f(} log. Whe

More information

Incremental calculation of weighted mean and variance

Incremental calculation of weighted mean and variance Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

More information

1. MATHEMATICAL INDUCTION

1. MATHEMATICAL INDUCTION 1. MATHEMATICAL INDUCTION EXAMPLE 1: Prove that for ay iteger 1. Proof: 1 + 2 + 3 +... + ( + 1 2 (1.1 STEP 1: For 1 (1.1 is true, sice 1 1(1 + 1. 2 STEP 2: Suppose (1.1 is true for some k 1, that is 1

More information

Acta Acad. Paed. Agriensis, Sectio Mathematicae 29 (2002) 77 87. ALMOST SURE FUNCTIONAL LIMIT THEOREMS IN L p( ]0, 1[ ), WHERE 1 p <

Acta Acad. Paed. Agriensis, Sectio Mathematicae 29 (2002) 77 87. ALMOST SURE FUNCTIONAL LIMIT THEOREMS IN L p( ]0, 1[ ), WHERE 1 p < Acta Acad. Paed. Agriesis, Sectio Mathematicae 29 22) 77 87 ALMOST SUR FUNCTIONAL LIMIT THORMS IN L ], [ ), WHR < József Túri Nyíregyháza, Hugary) Dedicated to the memory of Professor Péter Kiss Abstract.

More information

AP Calculus BC 2003 Scoring Guidelines Form B

AP Calculus BC 2003 Scoring Guidelines Form B AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet

More information

Multiple Representations for Pattern Exploration with the Graphing Calculator and Manipulatives

Multiple Representations for Pattern Exploration with the Graphing Calculator and Manipulatives Douglas A. Lapp Multiple Represetatios for Patter Exploratio with the Graphig Calculator ad Maipulatives To teach mathematics as a coected system of cocepts, we must have a shift i emphasis from a curriculum

More information

Analytical Model of Modified Traffic Control in an ATM Computer Network J. Filip

Analytical Model of Modified Traffic Control in an ATM Computer Network J. Filip Acta Polytechica ol. 4 No. 6/2 Aalytical Model of Modified Traffic Cotrol i a ATM Coputer Networ J. Filip The ABR class of ATM coputer etwors uses feedbac iforatio that is geerated by et switches ad destiatio

More information

3 Energy. 3.3. Non-Flow Energy Equation (NFEE) Internal Energy. MECH 225 Engineering Science 2

3 Energy. 3.3. Non-Flow Energy Equation (NFEE) Internal Energy. MECH 225 Engineering Science 2 MECH 5 Egieerig Sciece 3 Eergy 3.3. No-Flow Eergy Equatio (NFEE) You may have oticed that the term system kees croig u. It is ecessary, therefore, that before we start ay aalysis we defie the system that

More information

On Formula to Compute Primes. and the n th Prime

On Formula to Compute Primes. and the n th Prime Applied Mathematical cieces, Vol., 0, o., 35-35 O Formula to Compute Primes ad the th Prime Issam Kaddoura Lebaese Iteratioal Uiversity Faculty of Arts ad cieces, Lebao issam.kaddoura@liu.edu.lb amih Abdul-Nabi

More information

Combinatorial Identities: Table I: Intermediate Techniques for Summing Finite Series

Combinatorial Identities: Table I: Intermediate Techniques for Summing Finite Series Combiatorial Idetities: Table I: Itermediate Techiques for Summig Fiite Series From the seve upublished mauscripts of H. W. Gould Edited ad Compiled by Jocely Quaitace May 3, 00 Coefficiet Compariso Remar.

More information

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chi-square (χ ) distributio.

More information

Convention Paper 6764

Convention Paper 6764 Audio Egieerig Society Covetio Paper 6764 Preseted at the 10th Covetio 006 May 0 3 Paris, Frace This covetio paper has bee reproduced from the author's advace mauscript, without editig, correctios, or

More information

1 Correlation and Regression Analysis

1 Correlation and Regression Analysis 1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

BINOMIAL EXPANSIONS 12.5. In this section. Some Examples. Obtaining the Coefficients

BINOMIAL EXPANSIONS 12.5. In this section. Some Examples. Obtaining the Coefficients 652 (12-26) Chapter 12 Sequeces ad Series 12.5 BINOMIAL EXPANSIONS I this sectio Some Examples Otaiig the Coefficiets The Biomial Theorem I Chapter 5 you leared how to square a iomial. I this sectio you

More information

Automatic Tuning for FOREX Trading System Using Fuzzy Time Series

Automatic Tuning for FOREX Trading System Using Fuzzy Time Series utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which

More information

Class Meeting # 16: The Fourier Transform on R n

Class Meeting # 16: The Fourier Transform on R n MATH 18.152 COUSE NOTES - CLASS MEETING # 16 18.152 Itroductio to PDEs, Fall 2011 Professor: Jared Speck Class Meetig # 16: The Fourier Trasform o 1. Itroductio to the Fourier Trasform Earlier i the course,

More information

I. Why is there a time value to money (TVM)?

I. Why is there a time value to money (TVM)? Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

WHEN IS THE (CO)SINE OF A RATIONAL ANGLE EQUAL TO A RATIONAL NUMBER?

WHEN IS THE (CO)SINE OF A RATIONAL ANGLE EQUAL TO A RATIONAL NUMBER? WHEN IS THE (CO)SINE OF A RATIONAL ANGLE EQUAL TO A RATIONAL NUMBER? JÖRG JAHNEL 1. My Motivatio Some Sort of a Itroductio Last term I tought Topological Groups at the Göttige Georg August Uiversity. This

More information

Permutations, the Parity Theorem, and Determinants

Permutations, the Parity Theorem, and Determinants 1 Permutatios, the Parity Theorem, ad Determiats Joh A. Guber Departmet of Electrical ad Computer Egieerig Uiversity of Wiscosi Madiso Cotets 1 What is a Permutatio 1 2 Cycles 2 2.1 Traspositios 4 3 Orbits

More information

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity

More information

Probabilistic Engineering Mechanics. Do Rosenblatt and Nataf isoprobabilistic transformations really differ?

Probabilistic Engineering Mechanics. Do Rosenblatt and Nataf isoprobabilistic transformations really differ? Probabilistic Egieerig Mechaics 4 (009) 577 584 Cotets lists available at ScieceDirect Probabilistic Egieerig Mechaics joural homepage: wwwelseviercom/locate/probegmech Do Roseblatt ad Nataf isoprobabilistic

More information

2-3 The Remainder and Factor Theorems

2-3 The Remainder and Factor Theorems - The Remaider ad Factor Theorems Factor each polyomial completely usig the give factor ad log divisio 1 x + x x 60; x + So, x + x x 60 = (x + )(x x 15) Factorig the quadratic expressio yields x + x x

More information

Research Article Analyzing Big Data with the Hybrid Interval Regression Methods

Research Article Analyzing Big Data with the Hybrid Interval Regression Methods Hidawi Publishig Corporatio e Scietific World Joural Volue 204, Article ID 24392, 8 pages http://dx.doi.org/0.55/204/24392 Research Article Aalyzig Big Data with the Hybrid Iterval Regressio Methods Chia-Hui

More information

Monitoring procedure for parameter change in causal time series

Monitoring procedure for parameter change in causal time series Moitorig procedure for parameter chage i causal time series Jea-Marc Bardet, William Chakry Kege To cite this versio: Jea-Marc Bardet, William Chakry Kege. Moitorig procedure for parameter chage i causal

More information

ë2ë P. Erdíos, Problems and results in additive number theory, in Colloque ë4ë P. Erdíos, Graph Theory and Probability II., Canad. J. Math.

ë2ë P. Erdíos, Problems and results in additive number theory, in Colloque ë4ë P. Erdíos, Graph Theory and Probability II., Canad. J. Math. ëë P. Erdíos, Probles ad results i additive uber theory, i Colloque sur la Thçeorie des Nobres ècbrmè, Bruxelles, 1955, 17-137. ë3ë P. Erdíos, Graph Theory ad Probability, Caad. J. Math. 11 è1959è, 34-38.

More information

Lecture 2: Karger s Min Cut Algorithm

Lecture 2: Karger s Min Cut Algorithm priceto uiv. F 3 cos 5: Advaced Algorithm Desig Lecture : Karger s Mi Cut Algorithm Lecturer: Sajeev Arora Scribe:Sajeev Today s topic is simple but gorgeous: Karger s mi cut algorithm ad its extesio.

More information

Transient Vibration of the single degree of freedom systems.

Transient Vibration of the single degree of freedom systems. Trasiet Vibratio of the sigle degree of freedo systes. 1. -INTRODUCTION. Trasiet vibratio is defied as a teporarily sustaied vibratio of a echaical syste. It ay cosist of forced or free vibratios, or both

More information

Domain 1: Configuring Domain Name System (DNS) for Active Directory

Domain 1: Configuring Domain Name System (DNS) for Active Directory Maual Widows Domai 1: Cofigurig Domai Name System (DNS) for Active Directory Cofigure zoes I Domai Name System (DNS), a DNS amespace ca be divided ito zoes. The zoes store ame iformatio about oe or more

More information

Perfect Packing Theorems and the Average-Case Behavior of Optimal and Online Bin Packing

Perfect Packing Theorems and the Average-Case Behavior of Optimal and Online Bin Packing SIAM REVIEW Vol. 44, No. 1, pp. 95 108 c 2002 Society for Idustrial ad Applied Mathematics Perfect Packig Theorems ad the Average-Case Behavior of Optimal ad Olie Bi Packig E. G. Coffma, Jr. C. Courcoubetis

More information

Domain 1 - Describe Cisco VoIP Implementations

Domain 1 - Describe Cisco VoIP Implementations Maual ONT (642-8) 1-800-418-6789 Domai 1 - Describe Cisco VoIP Implemetatios Advatages of VoIP Over Traditioal Switches Voice over IP etworks have may advatages over traditioal circuit switched voice etworks.

More information

arxiv:1506.03481v1 [stat.me] 10 Jun 2015

arxiv:1506.03481v1 [stat.me] 10 Jun 2015 BEHAVIOUR OF ABC FOR BIG DATA By Wetao Li ad Paul Fearhead Lacaster Uiversity arxiv:1506.03481v1 [stat.me] 10 Ju 2015 May statistical applicatios ivolve models that it is difficult to evaluate the likelihood,

More information