Contributions to Economics

Transcription

1 Contributions to Economics

2 Kesra Nermend Vector Calculus in Regional Development Analysis Comparative Regional Analysis Using the Example of Poland Physica Verlag A Springer Company

3 Dr. inž. Kesra Nermend Institute of Informatics in Management ul. Mickiewicza Szczecin Poland Book first published in Polish under the title Wydawnictwo Naukowe Uniwersytetu Szczecińskiego, Szczecin 2008 Rachunek wektorowy w analizie rozwoju regionalnego ISBN e-isbn DOI: / Contributions to Economics ISSN Library of Congress Control Number: # Physica-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Physica-Verlag. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Physica Verlag Berlin Heidelberg (

4 Contents List of Variables and Notation... vii Introduction Regional Development Economic Perspective Notion and Factors Determining Regional Development Data Monitoring for Regional Development Assesment Regional Development Indicators Methodical Dilemma Over Regional Development Analysis Organization of Analytical Processes in Regional Development Investigation Review of Methods Used for Regional Development Analysis Reasons Behind Using Vector Calculus for Regional Development Analysis Methodology of Vector Calculus in Regional Development Analysis Procedure for Applying Vector Calculus in Regional Development Analysis Taxonomic Vector Measure of Regional Development Interpretation of Data in Space Vector Component Along Another Vector Comparison of Vectors in Unitary Space Visualization of Local Development Measures in 3D Space Taxonomic Synthetic Vector Measure in the Assessment of Regional Development: Results of Empirical Research Selection of Diagnostic Variables Construction of the Standard Object v

5 vi Contents 4.3. Investigation of Spatial Relationships Between Groups of Variables Computer-Aided Regional Development Analysis Computer System for Regional Development Analysis as a Decision Support System Concept of Decision Support System in Regional Development Analysis Data-Base Management System (DBMS) System Functions Model-Base Management System (MBMS) Dialog Generation and Management System (DGMS) Functioning of Computer System for Regional Development Analysis Conclusions Bibliography List of Figures and Tables

6 List of Variables and Notation X Matrix of objects describing variables x ik Value of kth variable of ith object (first index object number, second index variable number) w Number of objects n Number of variables z ik Standardized value of kth variable of ith object s k Standard deviation of kth variable x k Mean value of kth variable v k Variability level measure of kth variable S i Standard deviation of ith object s variables I Stimulants set K Destimulant set L Nominants set P i Point representing ith object P o Point representing the standard d ij Similarity measure between ith and jth objects dðp i ; P j Þ Similarity measure between ith and jth points m i Development measure of ith object m Mean measure of development of all objects s m Standard deviation of synthetic measure wg k Weight of kth variable r k Coefficient of object s scale change along kth variable D k Coefficient of object s translation along kth variable ~A Designation of vector g ij Metric tensor gr ij Border between classes odl ijk Distance of ith object from the border between class jth and class kth odl wzgl jk Percentage distance of ith object from the border between class jth i and class kth pas Coefficient controlling width of border belt szer klas Mean width of class Percentage reliability of ith object membership of jth class pp i j vii

7 viii List of Variables and Notation roz ~ A~B Similarity between two objects represented by two vectors ~A and ~B calculated as length of their vectors difference ~A j~aj c ~A ~B j~aj j~bj reg k nreg i l klas Unit vector along vector ~A ~A Projection of unit vector onto unit vector ~B j~aj j~bj Value at point P k of regular grid Value at point P i of irregular grid Number of classes