Integrating Customer Requirements into Data Product Design

Size: px
Start display at page:

Download "Integrating Customer Requirements into Data Product Design"

Transcription

1 114 Econom Informatics, 2003 Integrating Customer Requirements into Data Product Design Ec., Ph.D. candidate Otilia PÎRLOG Successful data products are ones that meet customer needs, are innovative and that offer value. Qualit Function Deploment offers a continuous process for en suring that all the different qualit issues are considered during the whole design and production chain. It provides a plane view of designed process and is tpicall applied to small sstems. Its etension for large sstems consists of few tree-dimensional cascading structures. This is an important tool for understanding the customer and deploing a structured manner throughout the data life ccle. A set of matries links customer desires, data qualit and sstem functions with subsstems / procedures dedicated to generate data product desired. The formaliation of the methodolog given here demonstrates the capacit of using it like a ke component to assist in creative thinking and problem solving. The subsstems / procedures proposed to be used are related with the corresponded costs. D ata Qualit Function Deploment for Large Sstems The compleit of data product administration involves man sstems. The main goal of data qualit is to translate the customer s demands (Voice of Customer) into designed targets. Qualit Function Deploment (QFD) invests time in planning to reap a profit in a shorter overall development ccle. The requirements are decomposed in a logical fashion, from the level of customer wants to the detailed process, using a set of correlated matries. The central matri mediates the customer wants with supplier plans to provide them. This basic matri can be epanded to provide additional insight to the supplier and cascaded to identif process parameters that must be controlled. There are man varieties of QFD and man variations of the charts used. Data Qualit Function Deploment (DQFD) is a method of translating customer desires throughout the entire data product ccle. It relates ideas to ideas, ideas to data, data to data process. This is one of the most powerful approaches for delivering a valuable data product to customers. It helps to achieve high qualit data products b improving data design and process qualit. It can also be viewed as the allocation of requirements to subsstems in that a subsstem must meet a set of requirements. DQFD is a pointed wa of listening to customers to understand eactl what the want and then, using a logical sstem, to determine how to best fulfill those requirements with available recourses. B relating these customer demands to the technical requirements (Voice of Developer), a set of target values for each technical requirement is logicall derived. It addresses a set of dimensions: customer desire, data qualit, functions, subsstems, procedures. Since requirements and technolog largel dictate the compleit of the sstem, analsis is focused on the compleit of data. Because the performance increases, the first unit cost of large sstems has been escala t- ing. The primar cost parameters are the sie and the compleit of sstems. In order to estimate and optimie the cost of data product, we have to anale a lot of. The solution is Data Qualit Function Deploment for Large Sstems (DQFDLS). It links the concurrent engineering process, the robust design process and the costing process to the data qualit features. The effect is to generate a tightl project management process of high dimensionalit which flushes out issues earl to provide a high qualit, low cost, and, hence, competitive data product. The Three -dimensional Model The first understanding of the basic structure for DQFD is giving a plane view with multi-

2 Econom Informatics, ple correlations in all directions. This tec h- nique demonstra tes the meaning of its name, a matri of matries. With regard to DQFDLS, the picture is changed in a set of three-dimensional derived each-another shapes. This offers the possibilit of a better Customer desires look inside the sstem and to decide witch wa is the best one for our design. Ever le - vel of anale consists of a tree -dimensional representation (figure 1) in which are presented those categories of information that are correlated at that moment. Sstem functions B1 The start is represented b the customer desires, the qualit demanded b him. The customer desires are placed on the ais of a matri. A data qualit characteristic is a mea s- urable attribute b which one can measure whether a customer is getting the demanded qualit. For each customer desire are settled the data qualit. Qualit cha r- acteristics are defined through brainstorming to generate an affinit diagram. After forming a tree diagram of the chosen data qualit, those on the lowest level are placed on the other ais of the analing matri. Each data qualit are compared with each customer desire to determine the tpe of correlation: there is no correlation (value=0), a weak correlation (value=1), a moderate correlation (value=3) or a strong correlation (value=5). B summariing the customer desires for the specific data qualit characteristic it provided a value for that characteristic. This ma be interpreted as the value of a data qualit characteristic for a specific customer desire valuation. Mathematicall speaking, the vector of values of customer desires is transformed into vector values for data qualit, using the customer desire / data qualit correlation matri (A1 matri). A1 C1 Requirement Fig. 1. Requirement Definition The process is continued with identifing functions. A function is something the sstem must do to ensure the demanded qualit. Usuall it is defined in the form <verb, noun>. Qualit and sstem functions intersect and define a requirement variable of the form <function, attribute> (C1 matri). Each requirement variable is a measurable attribute for which a correlation eists between the function and the data qualit characteristic. Requirement can be fied to create requirements or the can be used as design guidelines for improving the sstem. If these can be related through equations, the provide a parametric behavioral description of the product. and functions can be ranked in terms of transformed customer value to determine which are the most important. If resources are constrained, then the most priorit can be given to those with the highest customer value. The same wa is followed to correlate the functions with customer desires using the customer desire/function correlation matri (B1 matri). The determined ais for the first stage of anale are: - of data product for satisfing customer desires; - customer desires;

3 116 Econom Informatics, functions used to achieve data. The process is continued b earmarking subsstems / procedures to the determined functions. This forms the new spatial structure of Subsstems/ Procedures the model (figure 2). It can also be viewed as the allocation of requirements to subsstems in that a subsstem must meet a set of requirement var iables. Sstem functions B2 Now we are able to see the correlation that eists between data and subsstems / procedures allocated to rea lie them (A2 matri). Because of the wa we used, the result of these designed subsstems / procedures will be qualitative data that will satisf the customer requirements. A2 C1 Requirement Fig. 2. Allocated Procedural Support Subsstems/ Procedures Ever designed project has to take into account the level of necessar resources. The new step of the analing process is given b the replacing of the sstem functions with the other dimension consist of the cost of qualit (Figure 3). Cost of data qualit COST1 This tree-dimensional picture praises costs in two appearances: first, the relationship that eists between costs and subsstems / procedures (COST1 matri) and secondaril, between costs and the obtained result, data qualit (COST2 matri). The first aspect shown represents an eas support for appling the activit based costing methodolog. A2 COST2 Cost Fig.3. The Cost of Data Qualit All these spatial structures finalie the prototpe support sstem. The team involved in the design of data product will evaluate it and will simulate different alternatives. This isn t a difficult approach because of the fleibilit delivered b the prototpe support sstem. In the same time, the result of this methodolog allows the suitable maintenance. Because of the wide range of epertise required for large sstems, it becomes evident

4 Econom Informatics, the need to decentralie the approach b decomposing the sstem into meaningful subgroups with lower interaction. The geometric nature of the method represents a natural medium in which to perform this decomposition and manage the interaction. The Formaliation of the Method A ver important aspect of using DQFDLS is the capabilit to translate the formal relatio n- ships in a mathematical form. The correlative method we provide here can be used as a real instrument in order to simulate different alternatives of the designed project. Finall, the best one will be select. Ever spatial structure presented above is corresponded with a set of tree correlated matries. To advance from one stage to the other means to change onl a spatial dimension. From mathematical point of view this is similarl with the keeping of one matri like support for the new representation and to add to it the two new derived matries. The first set of matries is shown in Figure 4. Let F1 Fn2 be sstem functions, Char 1 Char n1 be data qualit and Des 1 Des n3 customer desires. Therefore n1 denote the number of data qualit identified, n2 denote the number of sstem functions and n3 the range of the set of customer desires. To individualie a variable we will use i=1 n1 for data qualit, j=1 n2 for sstem functions and k=1 n3 corresponding to customer demands.. Sstem functions F 1 F n2 Customer desires Des 1 Des n3 C1(1,1) C1(1,n2) A1(1,1) A1(1,n3) C1( i, j ) A1( i, k ) Char 1 Char n1 C1(n1,1) C1(n1,n2) A1(n1,1) A1(n1,n3) B1(1,1) B1(1,n2) Customer desires Des 1 Des n3 B1(n3,1) B1( k, j ) B1(n3,n2) Fig. 4. Set of es to Anale Customer Desires The net set of matries is built accordingl with the previous manner, b recovering the place of customer desires with subsstems / procedures decided (P 1 P n4 ). Figure 5 presents the new set of determined matries, where n4 denote the number of subsstems / procedures and p is used to identif an element, p=1 n4. Sstem functions F 1 F n2 Subsstems / procedures P 1 P n4 C1(1,1) C1(1,n2) A2(1,1) A2(1,n4) C1( i, j ) A2( i, p ) Char 1 Char n1 C1(n1,1) C1(n1,n2) A2(n1,1) A2(n1,n4) Subsstems / procedures B2(1,1) B2(1,n2) P 1 P n4 B2( p, j ) B2(n4,1) B2(n4,n2) Fig. 5. Set of es to Anale Subsstems / Procedures The last step of anale involves the cost of data qualit. The connection between the last and the actual stage is given b A2 matri. It will be the base of the new structure. In this case n5 is the range of ident ified categories of cost and c particularies an element of the added matries, where c=1 n5 (Figure 6). Using the double view of projected costs,

5 118 Econom Informatics, 2003 matries COST1 and COST2, it is possible to simulate multiple scenarios and evaluate them in order to identif the best technical solution with the lowest cost level. Subsstems / procedures P1 Pn4 costs Cost1 Costn5 Char1 Charn1 costs Cost 1 Cost n5 A2(1,1) A2(1,n4) COST1(1,1) COST1(1,n5) A2( i, p ) COST1( i, c) A2(n1,1) A2(n1,n4) COST1(n1,1) COST1(n1,n5) COST2(1,1) COST2(1,n4) COST2( c, p) COST2(n5,1) COST2(n5,n4) Fig. 6. Set of es to Anale the Data Qualit Cost The adherent cost to a data characteristic is computed b summariing corresponding costs: COST1 j = COST1( i, c ) The level of cost for ever subsstems / procedures is computed in the same manner: COST2 p = COST2( c, p ) These sets of matries denote the eas maintenance of designed sstem. Regarding to large sstems, this approach delivers also a strong support for decomposing the designed sstem. This is a ver important appearance for the designing team. It suggests also the capacit of using the accumulated eperience for some data qualit and to pa more attention for the rest of them. There are evident benefits of presented method: - improves focus on customer needs: - helps prioritie customer requirements; - helps identif competitive gaps (benchmarking); - reduce late design changes; - promotes teamwork; - ensures inter-departmental communication; - facilitates concurrent engineering. References [Aung02] Aungst,S.,Barton,R.,Wilson,D.T.: Integrating Marketing Models, Institute for the Stud of Business Markets, The Pennslvania State Universit, ISBN Report [Dean98] Dean, E.B.: Qualit Function Deploment from the Perspective of Co mpetitive Advantage, 1998, akao.larc.nasa.gov/dfc/ qfd.html [Daha02] Dahan,E.,Hauser,J.: The Virtual Customer, Journal of Product Innova tion Management, September, [Fran02] Franke,N.,Von Hipped,E.: Satisfing Heterogeneous User Needs via Innovation Toolkits: The Case of Apache Securit Software, Massachusetts Institute of Tec h- nolog (MIT) Sloan School of Management, Cambridge, MA, W orking Paper, [Rolp00] Rolph, P., and Bartram, P.: The Information Agenda: Harnessing Relevant Information in a Changing Business Environment, London, Management Books, 2000.

Section 9.3: Functions and their Graphs

Section 9.3: Functions and their Graphs Section 9.: Functions and their Graphs Graphs provide a wa of displaing, interpreting, and analzing data in a visual format. In man problems, we will consider two variables. Therefore, we will need to

More information

D-Calib: Calibration Software for Multiple Cameras System

D-Calib: Calibration Software for Multiple Cameras System D-Calib: Calibration Software for Multiple Cameras Sstem uko Uematsu Tomoaki Teshima Hideo Saito Keio Universit okohama Japan {u-ko tomoaki saito}@ozawa.ics.keio.ac.jp Cao Honghua Librar Inc. Japan cao@librar-inc.co.jp

More information

PATTERNS AND ALGEBRA. He opened mathematics to many discoveries and exciting applications.

PATTERNS AND ALGEBRA. He opened mathematics to many discoveries and exciting applications. PATTERNS AND ALGEBRA The famous French philosopher and mathematician René Descartes (596 65) made a great contribution to mathematics in 67 when he published a book linking algebra and geometr for the

More information

High Dimensional Rendering in OpenGL

High Dimensional Rendering in OpenGL High Dimensional Rendering in OpenGL Josh McCo December, 2003 Description of Project Adding high dimensional rendering capabilit to the OpenGL graphics programming environment is the goal of this project

More information

y = f(x) x (x, f(x)) f(x) g(x) = f(x) + 2 (x, g(x)) 0 (0, 1) 1 3 (0, 3) 2 (2, 3) 3 5 (2, 5) 4 (4, 3) 3 5 (4, 5) 5 (5, 5) 5 7 (5, 7)

y = f(x) x (x, f(x)) f(x) g(x) = f(x) + 2 (x, g(x)) 0 (0, 1) 1 3 (0, 3) 2 (2, 3) 3 5 (2, 5) 4 (4, 3) 3 5 (4, 5) 5 (5, 5) 5 7 (5, 7) 0 Relations and Functions.7 Transformations In this section, we stud how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations

More information

A New Concept on Automatic Parking of an Electric Vehicle

A New Concept on Automatic Parking of an Electric Vehicle A New Concept on Automatic Parking of an Electric Vehicle C. CAMUS P. COELHO J.C. QUADRADO Instituto Superior de Engenharia de Lisboa Rua Conselheiro Emídio Navarro PORTUGAL Abstract: - A solution to perform

More information

Lines and Their Slopes

Lines and Their Slopes 8.2 Lines and Their Slopes Linear Equations in Two Variables In the previous chapter we studied linear equations in a single variable. The solution of such an equation is a real number. A linear equation

More information

7.5. Systems of Inequalities. The Graph of an Inequality. What you should learn. Why you should learn it

7.5. Systems of Inequalities. The Graph of an Inequality. What you should learn. Why you should learn it 0_0705.qd /5/05 9:5 AM Page 5 Section 7.5 7.5 Sstems of Inequalities 5 Sstems of Inequalities What ou should learn Sketch the graphs of inequalities in two variables. Solve sstems of inequalities. Use

More information

Chain Pattern Scheduling for nested loops

Chain Pattern Scheduling for nested loops Chain Pattern Scheduling for nested loops Florina Ciorba, Theodore Andronikos and George Papakonstantinou Computing Sstems Laborator, Computer Science Division, Department of Electrical and Computer Engineering,

More information

Tubes are Fun. By: Douglas A. Ruby Date: 6/9/2003 Class: Geometry or Trigonometry Grades: 9-12 INSTRUCTIONAL OBJECTIVES:

Tubes are Fun. By: Douglas A. Ruby Date: 6/9/2003 Class: Geometry or Trigonometry Grades: 9-12 INSTRUCTIONAL OBJECTIVES: Tubes are Fun B: Douglas A. Rub Date: 6/9/2003 Class: Geometr or Trigonometr Grades: 9-2 INSTRUCTIONAL OBJECTIVES: Using a view tube students will conduct an eperiment involving variation of the viewing

More information

Matrix Representations

Matrix Representations CONDENSED LESSON 6. Matri Representations In this lesson, ou Represent closed sstems with transition diagrams and transition matrices Use matrices to organize information Sandra works at a da-care center.

More information

Think About. Unit 5 Lesson 3. Investigation. This Situation. Name: a Where do you think the origin of a coordinate system was placed in creating this

Think About. Unit 5 Lesson 3. Investigation. This Situation. Name: a Where do you think the origin of a coordinate system was placed in creating this Think About This Situation Unit 5 Lesson 3 Investigation 1 Name: Eamine how the sequence of images changes from frame to frame. a Where do ou think the origin of a coordinate sstem was placed in creating

More information

Graphs, Linear Equations, and Functions

Graphs, Linear Equations, and Functions Graphs, Linear Equations, and Functions. The Rectangular R. Coordinate Fractions Sstem bjectives. Interpret a line graph.. Plot ordered pairs.. Find ordered pairs that satisf a given equation. 4. Graph

More information

Learning Objectives for Section Graphs and Lines. Cartesian coordinate system. Graphs

Learning Objectives for Section Graphs and Lines. Cartesian coordinate system. Graphs Learning Objectives for Section 3.1-2 Graphs and Lines After this lecture and the assigned homework, ou should be able to calculate the slope of a line. identif and work with the Cartesian coordinate sstem.

More information

Precision Peg-in-Hole Assembly Strategy Using Force-Guided Robot

Precision Peg-in-Hole Assembly Strategy Using Force-Guided Robot 3rd International Conference on Machiner, Materials and Information Technolog Applications (ICMMITA 2015) Precision Peg-in-Hole Assembl Strateg Using Force-Guided Robot Yin u a, Yue Hu b, Lei Hu c BeiHang

More information

Graphs and Functions

Graphs and Functions CHAPTER Graphs and Functions. Graphing Equations. Introduction to Functions. Graphing Linear Functions. The Slope of a Line. Equations of Lines Integrated Review Linear Equations in Two Variables.6 Graphing

More information

Clustering Part 2. A Partitional Clustering

Clustering Part 2. A Partitional Clustering Universit of Florida CISE department Gator Engineering Clustering Part Dr. Sanja Ranka Professor Computer and Information Science and Engineering Universit of Florida, Gainesville Universit of Florida

More information

Chapter 3: Section 3-2 Graphing Linear Inequalities

Chapter 3: Section 3-2 Graphing Linear Inequalities Chapter : Section - Graphing Linear Inequalities D. S. Malik Creighton Universit, Omaha, NE D. S. Malik Creighton Universit, Omaha, NE Chapter () : Section - Graphing Linear Inequalities / 9 Geometric

More information

Lecture 12 Date:

Lecture 12 Date: Information Technolog Delhi Lecture 2 Date: 3.09.204 The Signal Flow Graph Information Technolog Delhi Signal Flow Graph Q: Using individual device scattering parameters to analze a comple microwave network

More information

Statistically Analyzing the Impact of Automated ETL Testing on Data Quality

Statistically Analyzing the Impact of Automated ETL Testing on Data Quality Chapter 5 Statisticall Analzing the Impact of Automated ETL Testing on Data Qualit 5.0 INTRODUCTION In the previous chapter some prime components of hand coded ETL prototpe were reinforced with automated

More information

LINEAR PROGRAMMING. Straight line graphs LESSON

LINEAR PROGRAMMING. Straight line graphs LESSON LINEAR PROGRAMMING Traditionall we appl our knowledge of Linear Programming to help us solve real world problems (which is referred to as modelling). Linear Programming is often linked to the field of

More information

Pre-Algebra Notes Unit 8: Graphs and Functions

Pre-Algebra Notes Unit 8: Graphs and Functions Pre-Algebra Notes Unit 8: Graphs and Functions The Coordinate Plane A coordinate plane is formed b the intersection of a horizontal number line called the -ais and a vertical number line called the -ais.

More information

GLOBAL EDITION. Interactive Computer Graphics. A Top-Down Approach with WebGL SEVENTH EDITION. Edward Angel Dave Shreiner

GLOBAL EDITION. Interactive Computer Graphics. A Top-Down Approach with WebGL SEVENTH EDITION. Edward Angel Dave Shreiner GLOBAL EDITION Interactive Computer Graphics A Top-Down Approach with WebGL SEVENTH EDITION Edward Angel Dave Shreiner This page is intentionall left blank. 4.10 Concatenation of Transformations 219 in

More information

E V ER-growing global competition forces. Accuracy Analysis and Improvement for Direct Laser Sintering

E V ER-growing global competition forces. Accuracy Analysis and Improvement for Direct Laser Sintering Accurac Analsis and Improvement for Direct Laser Sintering Y. Tang 1, H. T. Loh 12, J. Y. H. Fuh 2, Y. S. Wong 2, L. Lu 2, Y. Ning 2, X. Wang 2 1 Singapore-MIT Alliance, National Universit of Singapore

More information

Developed in Consultation with Tennessee Educators

Developed in Consultation with Tennessee Educators Developed in Consultation with Tennessee Educators Table of Contents Letter to the Student........................................ Test-Taking Checklist........................................ Tennessee

More information

A CW-SSIM Kernel-based Nearest Neighbor Method for Handwritten Digit Classification

A CW-SSIM Kernel-based Nearest Neighbor Method for Handwritten Digit Classification A CW-SSIM Kernel-based Nearest Neighbor Method for Handwritten Digit Classification Jiheng Wang Dept. of Statistics and Actuarial Science, Univ. of Waterloo, Waterloo, ON, Canada j237wang@uwaterloo.ca

More information

12.4 The Ellipse. Standard Form of an Ellipse Centered at (0, 0) (0, b) (0, -b) center

12.4 The Ellipse. Standard Form of an Ellipse Centered at (0, 0) (0, b) (0, -b) center . The Ellipse The net one of our conic sections we would like to discuss is the ellipse. We will start b looking at the ellipse centered at the origin and then move it awa from the origin. Standard Form

More information

9/17/2009. Wenyan Li (Emily Li) Sep. 15, Introduction to Clustering Analysis

9/17/2009. Wenyan Li (Emily Li) Sep. 15, Introduction to Clustering Analysis Introduction ti to K-means Algorithm Wenan Li (Emil Li) Sep. 5, 9 Outline Introduction to Clustering Analsis K-means Algorithm Description Eample of K-means Algorithm Other Issues of K-means Algorithm

More information

Partial Fraction Decomposition

Partial Fraction Decomposition Section 7. Partial Fractions 53 Partial Fraction Decomposition Algebraic techniques for determining the constants in the numerators of partial fractions are demonstrated in the eamples that follow. Note

More information

Scientific Manual FEM-Design 16.0

Scientific Manual FEM-Design 16.0 1.4.6 Calculations considering diaphragms All of the available calculation in FEM-Design can be performed with diaphragms or without diaphragms if the diaphragms were defined in the model. B the different

More information

Appendix F: Systems of Inequalities

Appendix F: Systems of Inequalities A0 Appendi F Sstems of Inequalities Appendi F: Sstems of Inequalities F. Solving Sstems of Inequalities The Graph of an Inequalit The statements < and are inequalities in two variables. An ordered pair

More information

Grid and Mesh Generation. Introduction to its Concepts and Methods

Grid and Mesh Generation. Introduction to its Concepts and Methods Grid and Mesh Generation Introduction to its Concepts and Methods Elements in a CFD software sstem Introduction What is a grid? The arrangement of the discrete points throughout the flow field is simpl

More information

ξ ζ P(s) l = [ l x, l y, l z ] y (s)

ξ ζ P(s) l = [ l x, l y, l z ] y (s) Modeling of Linear Objects Considering Bend, Twist, and Etensional Deformations Hidefumi Wakamatsu, Shinichi Hirai, and Kauaki Iwata Dept. of Mechanical Engineering for Computer-Controlled Machiner, Osaka

More information

Max-Flow Min-Cost Algorithm for A Supply Chain Network

Max-Flow Min-Cost Algorithm for A Supply Chain Network APDSI Full Paper (Jul, ) Ma-Flow Min-Cost Algorithm for A Suppl Chain Network Shu-Yi Chen ), Ching-Chin Chern ) ) Dept. of Information Management, National Taiwan Universit (d455@im.ntu.edu.tw) ) Dept.

More information

Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Unit 04: Geometr: Coordinate Plane, Graphing Transformations, and Perspectives (9 das) Possible Lesson 0 (6 das) Possible Lesson

More information

Modeling and Simulation Exam

Modeling and Simulation Exam Modeling and Simulation am Facult of Computers & Information Department: Computer Science Grade: Fourth Course code: CSC Total Mark: 75 Date: Time: hours Answer the following questions: - a Define the

More information

2.8 Distance and Midpoint Formulas; Circles

2.8 Distance and Midpoint Formulas; Circles Section.8 Distance and Midpoint Formulas; Circles 9 Eercises 89 90 are based on the following cartoon. B.C. b permission of Johnn Hart and Creators Sndicate, Inc. 89. Assuming that there is no such thing

More information

More on Transformations. COS 426, Spring 2019 Princeton University

More on Transformations. COS 426, Spring 2019 Princeton University More on Transformations COS 426, Spring 2019 Princeton Universit Agenda Grab-bag of topics related to transformations: General rotations! Euler angles! Rodrigues s rotation formula Maintaining camera transformations!

More information

NUMERICAL PERFORMANCE OF COMPACT FOURTH ORDER FORMULATION OF THE NAVIER-STOKES EQUATIONS

NUMERICAL PERFORMANCE OF COMPACT FOURTH ORDER FORMULATION OF THE NAVIER-STOKES EQUATIONS Published in : Communications in Numerical Methods in Engineering (008 Commun.Numer.Meth.Engng. 008; Vol : pp 003-019 NUMERICAL PERFORMANCE OF COMPACT FOURTH ORDER FORMULATION OF THE NAVIER-STOKES EQUATIONS

More information

THE INVERSE GRAPH. Finding the equation of the inverse. What is a function? LESSON

THE INVERSE GRAPH. Finding the equation of the inverse. What is a function? LESSON LESSON THE INVERSE GRAPH The reflection of a graph in the line = will be the graph of its inverse. f() f () The line = is drawn as the dotted line. Imagine folding the page along the dotted line, the two

More information

NUMB3RS Activity: The Center of it All. Episode: Pilot

NUMB3RS Activity: The Center of it All. Episode: Pilot NUMBRS Activit Teacher Page NUMBRS Activit: The Center of it All Topic: Circles Grade Level: 9 - Objective: Eplore the circumcenter and investigate the relationship between the position of the circumcenter

More information

The Graph of an Equation

The Graph of an Equation 60_0P0.qd //0 :6 PM Page CHAPTER P Preparation for Calculus Archive Photos Section P. RENÉ DESCARTES (96 60) Descartes made man contributions to philosoph, science, and mathematics. The idea of representing

More information

Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide Enhanced Instructional Transition Guide Grade / Unit : Suggested Duration: das Unit : Statistics ( das) Possible Lesson 0 ( das) Possible Lesson 0 ( das) POSSIBLE LESSON 0 ( das) This lesson is one approach

More information

SECTION 3-4 Rational Functions

SECTION 3-4 Rational Functions 20 3 Polnomial and Rational Functions 0. Shipping. A shipping bo is reinforced with steel bands in all three directions (see the figure). A total of 20. feet of steel tape is to be used, with 6 inches

More information

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Eponential and Logarithmic Functions Figure Electron micrograph of E. Coli bacteria (credit: Mattosaurus, Wikimedia Commons) Chapter Outline. Eponential Functions. Logarithmic Properties. Graphs of Eponential

More information

Towards a unified measurement of quality for mixed elements

Towards a unified measurement of quality for mixed elements Towards a unified measurement of qualit for mixed elements technical report n 015/01, di utfsm Claudio Lobos Departmento de Informática Universidad Técnica Federico Santa María Santiago, Chile clobos@inf.utfsm.cl

More information

Roberto s Notes on Differential Calculus Chapter 8: Graphical analysis Section 5. Graph sketching

Roberto s Notes on Differential Calculus Chapter 8: Graphical analysis Section 5. Graph sketching Roberto s Notes on Differential Calculus Chapter 8: Graphical analsis Section 5 Graph sketching What ou need to know alread: How to compute and interpret limits How to perform first and second derivative

More information

KINEMATICS STUDY AND WORKING SIMULATION OF THE SELF- ERECTION MECHANISM OF A SELF-ERECTING TOWER CRANE, USING NUMERICAL AND ANALYTICAL METHODS

KINEMATICS STUDY AND WORKING SIMULATION OF THE SELF- ERECTION MECHANISM OF A SELF-ERECTING TOWER CRANE, USING NUMERICAL AND ANALYTICAL METHODS The rd International Conference on Computational Mechanics and Virtual Engineering COMEC 9 9 OCTOBER 9, Brasov, Romania KINEMATICS STUY AN WORKING SIMULATION OF THE SELF- ERECTION MECHANISM OF A SELF-ERECTING

More information

[ ] [ ] Orthogonal Transformation of Cartesian Coordinates in 2D & 3D. φ = cos 1 1/ φ = tan 1 [ 2 /1]

[ ] [ ] Orthogonal Transformation of Cartesian Coordinates in 2D & 3D. φ = cos 1 1/ φ = tan 1 [ 2 /1] Orthogonal Transformation of Cartesian Coordinates in 2D & 3D A vector is specified b its coordinates, so it is defined relative to a reference frame. The same vector will have different coordinates in

More information

Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1)

Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1) Unit 4 Trigonometr Stud Notes 1 Right Triangle Trigonometr (Section 8.1) Objective: Evaluate trigonometric functions of acute angles. Use a calculator to evaluate trigonometric functions. Use trigonometric

More information

7. f(x) = 1 2 x f(x) = x f(x) = 4 x at x = 10, 8, 6, 4, 2, 0, 2, and 4.

7. f(x) = 1 2 x f(x) = x f(x) = 4 x at x = 10, 8, 6, 4, 2, 0, 2, and 4. Section 2.2 The Graph of a Function 109 2.2 Eercises Perform each of the following tasks for the functions defined b the equations in Eercises 1-8. i. Set up a table of points that satisf the given equation.

More information

IJSRD - International Journal for Scientific Research & Development Vol. 4, Issue 04, 2016 ISSN (online):

IJSRD - International Journal for Scientific Research & Development Vol. 4, Issue 04, 2016 ISSN (online): IJSRD - International Journal for Scientific Research & Development Vol. 4, Issue 04, 2016 ISSN (online): 2321-0613 Stabilit Analsis of Multi- Building with Underneath Satellite Bus Stand Having Intermediate

More information

Systems of Linear Equations

Systems of Linear Equations Sstems of Linear Equations Gaussian Elimination Tpes of Solutions A linear equation is an equation that can be written in the form: a a a n n b The coefficients a i and the constant b can be real or comple

More information

Quad-Tree Based Geometric-Adapted Cartesian Grid Generation

Quad-Tree Based Geometric-Adapted Cartesian Grid Generation Quad-Tree Based Geometric-Adapted Cartesian Grid Generation EMRE KARA1, AHMET ĐHSAN KUTLAR1, MEHMET HALUK AKSEL 1Department of Mechanical Engineering Universit of Gaziantep 7310 Gaziantep TURKEY Mechanical

More information

Appendix F: Systems of Inequalities

Appendix F: Systems of Inequalities Appendi F: Sstems of Inequalities F. Solving Sstems of Inequalities The Graph of an Inequalit What ou should learn The statements < and ⱖ are inequalities in two variables. An ordered pair 共a, b兲 is a

More information

NEW. Plug & Automate 3D Machine Vision Product Line Ready-To-Use for Factory Automation. Scalable & Configurable. From Sensor to Software

NEW. Plug & Automate 3D Machine Vision Product Line Ready-To-Use for Factory Automation. Scalable & Configurable. From Sensor to Software NEW Plug & Automate 3D Machine Vision Product Line Read-To-Use for Factor Automation Scalable & Configurable. From Sensor to Software Plug & Automate NEW Plug & Automa Best Practice 3D Machine Vision Sensors

More information

Section 2.2: Absolute Value Functions, from College Algebra: Corrected Edition by Carl Stitz, Ph.D. and Jeff Zeager, Ph.D. is available under a

Section 2.2: Absolute Value Functions, from College Algebra: Corrected Edition by Carl Stitz, Ph.D. and Jeff Zeager, Ph.D. is available under a Section.: Absolute Value Functions, from College Algebra: Corrected Edition b Carl Stitz, Ph.D. and Jeff Zeager, Ph.D. is available under a Creative Commons Attribution-NonCommercial-ShareAlike.0 license.

More information

1-1. Functions. Lesson 1-1. What You ll Learn. Active Vocabulary. Scan Lesson 1-1. Write two things that you already know about functions.

1-1. Functions. Lesson 1-1. What You ll Learn. Active Vocabulary. Scan Lesson 1-1. Write two things that you already know about functions. 1-1 Functions What You ll Learn Scan Lesson 1- Write two things that ou alread know about functions. Lesson 1-1 Active Vocabular New Vocabular Write the definition net to each term. domain dependent variable

More information

Thermo vision system with embedded digital signal processor for real time objects detection

Thermo vision system with embedded digital signal processor for real time objects detection Thermo vision sstem with embedded digital signal processor for real time objects detection Snejana Pleshova, Aleander Beiarsi, Department of Telecommunications Technical Universit Kliment Ohridsi, 8 Sofia

More information

Two Dimensional Viewing

Two Dimensional Viewing Two Dimensional Viewing Dr. S.M. Malaek Assistant: M. Younesi Two Dimensional Viewing Basic Interactive Programming Basic Interactive Programming User controls contents, structure, and appearance of objects

More information

1. We ll look at: Types of geometrical transformation. Vector and matrix representations

1. We ll look at: Types of geometrical transformation. Vector and matrix representations Tob Howard COMP272 Computer Graphics and Image Processing 3: Transformations Tob.Howard@manchester.ac.uk Introduction We ll look at: Tpes of geometrical transformation Vector and matri representations

More information

XML-Based Hierarchical Description of 3D Systems and SIP

XML-Based Hierarchical Description of 3D Systems and SIP XML-Based Hierarchical Description of 3D Sstems and SIP Susann Wolf, And Heinig, Uwe Knöchel Fraunhofer Institute for Integrated Circuits, Design Automation Division (IIS/EAS), Dresden, German (Susann.Wolf

More information

Developing a Tracking Algorithm for Underwater ROV Using Fuzzy Logic Controller

Developing a Tracking Algorithm for Underwater ROV Using Fuzzy Logic Controller 5 th Iranian Conference on Fuzz Sstems Sept. 7-9, 2004, Tehran Developing a Tracking Algorithm for Underwater Using Fuzz Logic Controller M.H. Saghafi 1, H. Kashani 2, N. Mozaani 3, G. R. Vossoughi 4 mh_saghafi@ahoo.com

More information

Discussion: Clustering Random Curves Under Spatial Dependence

Discussion: Clustering Random Curves Under Spatial Dependence Discussion: Clustering Random Curves Under Spatial Dependence Gareth M. James, Wenguang Sun and Xinghao Qiao Abstract We discuss the advantages and disadvantages of a functional approach to clustering

More information

Concept: Slope of a Line

Concept: Slope of a Line Concept: Slope of a Line Warm Up Name: The following suggested activities would serve as a review to consolidate previous learning. While promoting rich mathematical dialog, the will also provide students

More information

PARAMETRIC EQUATIONS AND POLAR COORDINATES

PARAMETRIC EQUATIONS AND POLAR COORDINATES 9 ARAMETRIC EQUATIONS AND OLAR COORDINATES So far we have described plane curves b giving as a function of f or as a function of t or b giving a relation between and that defines implicitl as a function

More information

This lesson gives students practice in graphing

This lesson gives students practice in graphing NATIONAL MATH + SCIENCE INITIATIVE Mathematics 9 7 5 1 1 5 7 LEVEL Grade, Algebra 1, or Math 1 in a unit on solving sstems of equations MODULE/CONNECTION TO AP* Areas and Volumes *Advanced Placement and

More information

Conceptual Design of Planar Retainer Mechanisms for Bottom-Opening SMIF Environment

Conceptual Design of Planar Retainer Mechanisms for Bottom-Opening SMIF Environment Proceedings of the th World Congress in Mechanism and Machine Science August 8~, 003, Tianjin, China China Machiner Press, edited b Tian Huang Conceptual Design of Planar Retainer Mechanisms for Bottom-Opening

More information

A new Adaptive PID Control Approach Based on Closed-Loop Response Recognition

A new Adaptive PID Control Approach Based on Closed-Loop Response Recognition roceedings of the 7th WSEAS nternational Conference on Automation & nformation, Cavtat, Croatia, June 13-15, 2006 (pp156-160) A Adaptive Control Approach Based on Closed-Loop Response Recognition MARTN

More information

EELE 482 Lab #3. Lab #3. Diffraction. 1. Pre-Lab Activity Introduction Diffraction Grating Measure the Width of Your Hair 5

EELE 482 Lab #3. Lab #3. Diffraction. 1. Pre-Lab Activity Introduction Diffraction Grating Measure the Width of Your Hair 5 Lab #3 Diffraction Contents: 1. Pre-Lab Activit 2 2. Introduction 2 3. Diffraction Grating 4 4. Measure the Width of Your Hair 5 5. Focusing with a lens 6 6. Fresnel Lens 7 Diffraction Page 1 (last changed

More information

Using the same procedure that was used in Project 5, enter matrix A and its label into an Excel spreadsheet:

Using the same procedure that was used in Project 5, enter matrix A and its label into an Excel spreadsheet: Math 6: Ecel Lab 6 Summer Inverse Matrices, Determinates and Applications: (Stud sections, 6, 7 and in the matri book in order to full understand the topic.) This Lab will illustrate how Ecel can help

More information

Unit 2: Function Transformation Chapter 1

Unit 2: Function Transformation Chapter 1 Basic Transformations Reflections Inverses Unit 2: Function Transformation Chapter 1 Section 1.1: Horizontal and Vertical Transformations A of a function alters the and an combination of the of the graph.

More information

What are the rules of elementary algebra

What are the rules of elementary algebra What are the rules of elementar algebra James Davenport & Chris Sangwin Universities of Bath & Birmingham 7 Jul 2010 Setting A relativel traditional mathematics course, at, sa first-ear undergraduate level.

More information

Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things

Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things . Rotations object in a plane? What are the three basic was to move an Rotate A biccle wheel can rotate clockwise or counterclockwise. 0 0 0 9 9 9 8 8 8 7 6 7 6 7 6 ACTIVITY: Three Basic Was to Move Things

More information

Fractal Interpolation Representation of A Class of Quadratic Functions

Fractal Interpolation Representation of A Class of Quadratic Functions ISSN 1749-3889 (print, 1749-3897 (online International Journal of Nonlinear Science Vol.24(2017 No.3, pp.175-179 Fractal Interpolation Representation of A Class of Quadratic Functions Chengbin Shen, Zhigang

More information

Contents. How You May Use This Resource Guide

Contents. How You May Use This Resource Guide Contents How You Ma Use This Resource Guide ii 0 Trigonometric Formulas, Identities, and Equations Worksheet 0.: Graphical Analsis of Trig Identities.............. Worksheet 0.: Verifing Trigonometric

More information

8.6 Three-Dimensional Cartesian Coordinate System

8.6 Three-Dimensional Cartesian Coordinate System SECTION 8.6 Three-Dimensional Cartesian Coordinate Sstem 69 What ou ll learn about Three-Dimensional Cartesian Coordinates Distance and Midpoint Formulas Equation of a Sphere Planes and Other Surfaces

More information

Complex-beam migration: non-recursive and recursive implementations

Complex-beam migration: non-recursive and recursive implementations Comple-beam migration: non-recursive and recursive implementations Tianfei Zhu*, CGGVeritas, Calgar AB, Canada Tianfei.Zhu@cggveritas.com Summar We have developed a comple-beam method for shot-domain prestack

More information

2.2 Absolute Value Functions

2.2 Absolute Value Functions . Absolute Value Functions 7. Absolute Value Functions There are a few was to describe what is meant b the absolute value of a real number. You ma have been taught that is the distance from the real number

More information

Non-linear models. Basis expansion. Overfitting. Regularization.

Non-linear models. Basis expansion. Overfitting. Regularization. Non-linear models. Basis epansion. Overfitting. Regularization. Petr Pošík Czech Technical Universit in Prague Facult of Electrical Engineering Dept. of Cbernetics Non-linear models Basis epansion.....................................................................................................

More information

A Hierarchical Multiprocessor Scheduling System for DSP Applications

A Hierarchical Multiprocessor Scheduling System for DSP Applications Presented at the Twent-Ninth Annual Asilomar Conference on Signals, Sstems, and Computers - October 1995 A Hierarchical Multiprocessor Scheduling Sstem for DSP Applications José Luis Pino, Shuvra S Bhattachara

More information

Linear Programming. Revised Simplex Method, Duality of LP problems and Sensitivity analysis

Linear Programming. Revised Simplex Method, Duality of LP problems and Sensitivity analysis Linear Programming Revised Simple Method, Dualit of LP problems and Sensitivit analsis Introduction Revised simple method is an improvement over simple method. It is computationall more efficient and accurate.

More information

Image Metamorphosis By Affine Transformations

Image Metamorphosis By Affine Transformations Image Metamorphosis B Affine Transformations Tim Mers and Peter Spiegel December 16, 2005 Abstract Among the man was to manipulate an image is a technique known as morphing. Image morphing is a special

More information

Introduction to Homogeneous Transformations & Robot Kinematics

Introduction to Homogeneous Transformations & Robot Kinematics Introduction to Homogeneous Transformations & Robot Kinematics Jennifer Ka Rowan Universit Computer Science Department. Drawing Dimensional Frames in 2 Dimensions We will be working in -D coordinates,

More information

20 Calculus and Structures

20 Calculus and Structures 0 Calculus and Structures CHAPTER FUNCTIONS Calculus and Structures Copright LESSON FUNCTIONS. FUNCTIONS A function f is a relationship between an input and an output and a set of instructions as to how

More information

3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately.

3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately. Math 65 Weekl Activit 1 (50 points) Name: Simplif the following epressions. Make sure to use the = smbol appropriatel. Due (1) (a) - 4 (b) ( - ) 4 () 8 + 5 6 () 1 5 5 Evaluate the epressions when = - and

More information

Chap 7, 2009 Spring Yeong Gil Shin

Chap 7, 2009 Spring Yeong Gil Shin Three-Dimensional i Viewingi Chap 7, 29 Spring Yeong Gil Shin Viewing i Pipeline H d fi i d? How to define a window? How to project onto the window? Rendering "Create a picture (in a snthetic camera) Specification

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Polnomial and Rational Functions Figure -mm film, once the standard for capturing photographic images, has been made largel obsolete b digital photograph. (credit film : modification of work b Horia Varlan;

More information

World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:10, No:4, 2016

World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:10, No:4, 2016 World Academ of Science, Engineering and Technolog X-Corner Detection for Camera Calibration Using Saddle Points Abdulrahman S. Alturki, John S. Loomis Abstract This paper discusses a corner detection

More information

Mathematics Stage 5 PAS5.1.2 Coordinate geometry

Mathematics Stage 5 PAS5.1.2 Coordinate geometry Mathematics Stage PAS.. Coordinate geometr Part Graphing lines Acknowledgments This publication is copright New South Wales Department of Education and Training (DET), however it ma contain material from

More information

Math 1050 Lab Activity: Graphing Transformations

Math 1050 Lab Activity: Graphing Transformations Math 00 Lab Activit: Graphing Transformations Name: We'll focus on quadratic functions to eplore graphing transformations. A quadratic function is a second degree polnomial function. There are two common

More information

Determine Whether Two Functions Are Equivalent. Determine whether the functions in each pair are equivalent by. and g (x) 5 x 2

Determine Whether Two Functions Are Equivalent. Determine whether the functions in each pair are equivalent by. and g (x) 5 x 2 .1 Functions and Equivalent Algebraic Epressions On September, 1999, the Mars Climate Orbiter crashed on its first da of orbit. Two scientific groups used different measurement sstems (Imperial and metric)

More information

Section 4.3 Features of a Line

Section 4.3 Features of a Line Section.3 Features of a Line Objectives In this section, ou will learn to: To successfull complete this section, ou need to understand: Identif the - and -intercepts of a line. Plotting points in the --plane

More information

science. In this course we investigate problems both algebraically and graphically.

science. In this course we investigate problems both algebraically and graphically. Section. Graphs. Graphs Much of algebra is concerned with solving equations. Man algebraic techniques have been developed to provide insights into various sorts of equations and those techniques are essential

More information

All in Focus Image Generation based on New Focusing Measure Operators

All in Focus Image Generation based on New Focusing Measure Operators (JACSA nternational Journal of Advanced Computer Science and Applications, Vol 7, No, 06 All in Focus mage Generation based on New Focusing Measure Operators Hossam Eldeen M Shamardan epartment of nmation

More information

2-1. The Language of Functions. Vocabulary

2-1. The Language of Functions. Vocabulary Chapter Lesson -1 BIG IDEA A function is a special tpe of relation that can be described b ordered pairs, graphs, written rules or algebraic rules such as equations. On pages 78 and 79, nine ordered pairs

More information

1 Teaching Objective(s) *Lesson Plan designed for 3-5 days The student will: II (c): complete a function based on a given rule.

1 Teaching Objective(s) *Lesson Plan designed for 3-5 days The student will: II (c): complete a function based on a given rule. ! "# Teaching Objective(s) *Lesson Plan designed for 3-5 das The student will: II (c): complete a function based on a given rule. II (e): appl the principles of graphing in the coordinate sstem. II (f):

More information

CS770/870 Spring 2017 Transformations

CS770/870 Spring 2017 Transformations CS770/870 Spring 2017 Transformations Coordinate sstems 2D Transformations Homogeneous coordinates Matrices, vectors, points Coordinate Sstems Coordinate sstems used in graphics Screen coordinates: the

More information

B + -trees. Kerttu Pollari-Malmi

B + -trees. Kerttu Pollari-Malmi B + -trees Kerttu Pollari-Malmi This tet is based partl on the course tet book b Cormen and partl on the old lecture slides written b Matti Luukkainen and Matti Nkänen. 1 Introduction At first, read the

More information

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology Intermediate Algebra Gregg Waterman Oregon Institute of Technolog c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license

More information