L2 (R) Solutions of Dilation Equations and

Oracle Corporation

Description

• expression écrite

L2(R) Solutions of Dilation Equations and Fourier-like Transforms David Malone∗ December 6, 2000 Abstract We state a novel construction of the Fourier transform on L2(R) based on translation and dilation properties which makes use of the multiresolu- tion analysis structure commonly used in the design of wavelets. We ex- amine the conditions imposed by variants of these translation and dilation properties. This allows other characterisations of the Fourier transform to be given, and operators which have similar properties are classified.

• sets of the mul- tiresolution analysis
• dilation equations
• dilation property
• spirit of multiresolution analysis
• dilation property for scales
• various cases
• fourier transform
• linear
• structure

Sujets

• Transform
• Collège
• Dilation
• Analysis
• Fourier
• Structure
• Property
• Various
• Multirésolution
• Scales
• Linear

Informations

• Publié par: figas
• Nombre de lectures: 27
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

O R A C L E ® C R Y S T A L B A L L D E C I S I O N O P T I M I Z E R ,
F U S I O N E D I T I O N
R E L E A S E 1 1 . 1 . 1 . 3 . 0 0
O P T Q U E S T U S E R ' S G U I D ECrystal Ball Decision Optimizer OptQuest User's Guide, 11.1.1.3.00
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may incur from dealing with any third party.Contents
Chapter 1. Welcome ................................................................. 9
Introduction .......................................................... 9
How This Manual is Organized ............................................ 9
Screen Capture Notes .................................................. 10
Getting Help ......................................................... 10
Additional Resources 11
Chapter 2. Overview ................................................................ 13
Introduction 13
What OptQuest Does 13
How OptQuest Works ................................................. 14
About Optimization Models ............................................. 15
Optimization Objectives ................................................ 16
Forecast Statistics .................................................. 16
Minimizing or Maximizing ........................................... 16
Requirements ..................................................... 17
Decision Variables .................................................... 17
Constraints .......................................................... 18
Model and Solution Feasibility ............................................ 19
Efficient Frontier Analysis ............................................... 19
Efficient Portfolios ................................................. 20
OptQuest and Process Capability .......................................... 21
Chapter 3. Setting Up and Optimizing a Model .............................................. 23
Introduction ......................................................... 23
Overview ........................................................... 23
For Users of OptQuest Versions Earlier Than 11.1.1.x ........................ 24
Developing a Crystal Ball Optimization Model ................................ 24
Developing the Worksheet ............................................ 24
Defining Assumptions, Decision Variables, and Forecasts ..................... 25
Setting Crystal Ball Run Preferences ..................................... 25
Starting OptQuest ..................................................... 26
Contents iiiSelecting the Forecast Objective .......................................... 26
Selecting Decision Variables to Optimize .................................... 27
Specifying Constraints ................................................. 28
Specifying Constraints in Simple Entry Mode .............................. 29
Specifying Constraints in Advanced Entry Mode ............................ 29
Constraints Editor and Related Buttons .................................. 31
Constraint Rules and Syntax .......................................... 32
Constraints and Cell References in Advanced Entry Mode ..................... 33
Constraint Types .................................................. 34
Setting Options ....................................................... 34
Advanced Options ................................................. 35
Running Optimizations 35
OptQuest Control Panel Buttons and Commands ........................... 36
OptQuest Results Window ........................................... 36
Interpreting the Results 40
Viewing a Solution Analysis 40
Running a Longer Simulation of the Results ............................... 42
Printing OptQuest Results ............................................ 42
Viewing Charts in Crystal Ball ......................................... 42
Creating OptQuest Reports 42
Extracting OptQuest Data 44
Saving optimization models and settings .................................... 45
Closing OptQuest ..................................................... 45
Setting Up Efficient Frontier Analysis in OptQuest ............................. 46
Efficient Frontier Variable Bound Example ................................ 46
Transferring Settings from .opt Files ........................................ 46
Learning More About OptQuest .......................................... 48
Chapter 4. OptQuest Tutorials ......................................................... 49
Introduction 49
Tutorial 1 — Futura Apartments Model ..................................... 49
Running OptQuest ................................................. 50
Tutorial 2 — Portfolio Allocation Model .................................... 54
Problem Description ................................................ 55
Using OptQuest ................................................... 55
Chapter 5. Examples Using OptQuest .................................................... 67
Overview ........................................................... 67
Product Mix ......................................................... 69
Product Mix Problem Statement ....................................... 69
iv ContentsProduct Mix Spreadsheet Model ....................................... 70
Product Mix OptQuest Solution 70
Hotel Design and Pricing Problem ......................................... 72
Hotel Design Problem Statement 72
Hotel Design Spreadsheet Model 73
Hotel Design OptQuest Solution 73
Budget-constrained Project Selection ....................................... 75
Project Selection Problem Statement .................................... 75
Project Selection Spreadsheet Model 76
Project Selection OptQuest Solution 77
Groundwater Cleanup .................................................. 79
Groundwater Cleanup Problem Statement ................................ 79
Groundwater Cleanup Spreadsheet Model 79
Groundwater Cleanup OptQuest Solution 81
Oil Field Development ................................................. 83
Oil Field Development Problem Statement 83
Oil Field Development Spreadsheet Model 84
Oil Field Development OptQuest Solution ............