Abstract: The univariate integration of a function over a closed interval can be realized through various analytical or numerical methods. Almost all numerical methods assume the continuity and the smoothness of the function under consideration and tries to use somehow a polynomial approximation. They fail if the function has nonintegrable singularity in the integration interval. In the case of integrable singularities in the interval the numerical methods may become slowly converging. They may be negatively affected even from the singularities outside the integration domain. Hence, to remove or to decrease these types of negative effects, one can use a weight function which somehow reflects and compensates the singular nature of the function to be integrated.

Fluctuation expansion uses sharply localized weight functions representable by Dirac's delta function which picks the value of a function at a given point. Dirac’s delta function can be approximated by appropriately defined projection operator kernels. Fluctuation expansion is based on these types of approximations. It expands and approximates the weight function in this way and produces a Gauss quadrature like approximation formula with universal weight coefficients which are different for different weights. The accuracy can be controlled by monitoring the number of the terms in expansion of weight in terms of projection operator kernels.

Fluctuation expansion can also be applied to multivariate integration. The basic philosophy remains same in this case. Only difference is the multivariance in various entities and as long as sufficient care is paid for possible complications the efficiency is again powerful and the method remains promising.

All linear partial differential equations describing probabilistic events can be handled by using fluctuation expansion. This is because of the fact that the existence of probability in the event description implies the utilization of the expectation values like in quantum mechanics or nonequilibrium statistical mechanics via Liuouville equation. If the expectation values are considered instead of the probability describing entities then the multivariate integrals in the representations of expectation values can be approximated by using the fluctuation expansion.

Plenary Lecture 2

Incomplete inventory information - the next challenge

Professor Suresh P. Sethi

Charles & Nancy Davidson Distinguished Professor

Director, Center for Intelligent Supply Networks

School of Management

University of Texas at Dallas

Richardson, TX 75080, USA

Abstract: The purpose of this lecture is to review recent developments in the analysis of partially observed optimal control problems that arise in the management of inventory systems.

Inventory control is one of the most important topics in management science/operations research. A systematic analysis of inventory problems began with the development of the classical EOQ formula of Harris in 1913. Since then, an enormous amount of literature has accumulated on inventory control problems.

One of the critical assumptions in this vast literature has been that the current level of inventory is fully observed. Some of the most celebrated results such as optimality of base-stock or (s,S) policies have been obtained under the assumption of full observation. Yet it is often the case in practice that the inventory level is only partially observed. Most of the well-known inventory policies are not only non-optimal, but are also not applicable in the partial observation environment.

The reasons for partial observation of the current inventory level are many. Inventory records or cash register information differ from actual inventory because of a variety of factors including transaction errors, theft, spoilage, misplacement, unobserved lost demands, and information delays. As a result, what are usually observed are some events or surrogate measures, called signals, related to the inventory level. At best, these relationships may provide only the distribution of current inventory levels.

In the best case, therefore, the relevant state in the inventory control problems is not the current inventory level, but rather its distribution given the observed signals. Thus, the analysis for finding optimal production or ordering policies takes place generally in the space of infinite-dimensional probability distributions.

SESSION: Probabilities, Statistics and Operational Research

Chair: Alexey Sadovski, Remi Leandre

On Arrow Paradox: Preference Ranking and Decision Making Mechanism Based on Rating Method and Expert Information	Alexey Sadovski	567-258
The division method in semi-group theory	Remi Leandre	567-136
Road traffic modelling and simulating with fluid-dynamic approach	Ciro D'Apice, Annunziata Cascone	567-310
The Study of Fuzzy Performance Evaluation	Ching-Cheng Shen, Kun-Lin Hsieh	567-128
Finding the Population Variance of Costs over the Solution Space of the TSP in Polynomial Time	Paul Sutcliffe, Andrew Solomon, Jenny Edwards	567-180
Improvement of Performance in a maintenance Job Shop	V. S. Chandra sekhar, M. Pramila Devi	567-253

Friday, March 23, 2007

SESSION: Computational Algorithms and Applications

Chair: Toshinori Yamada, Mihai Bugaru

Fault Identification Algorithms in the Presence of Intermittent Faults	Toshinori Yamada, Daisuke Kiri	567-185
Transfer Matrix Method For A Single-Chamber Mufflers	Mihai Bugaru, Ovidiu Vasile	567-215
On generalized quantum Turing machine and its language classes	Satoshi Iriyama and Masanori Ohya	567-277
Economic Comparison of Waste Water Cleaning for Central Waste Water Treatment Plant and Decentralised System with Smaller Waste Water Treatment Plants	J. Zorko, D. Goricanec	567-089
Cost-Effectiveness of Heat Pump Heating and of other Heating Systems	Matavz E., Krope J., Goricanec D.	567-090

SESSION: Control Methods and Optimization Techniques

Chair: Yezid Donoso, Kuang Yuan Kung

Multiobjective Optimization to schedule The Economic Operation of Colombian Atlantic Coast under insulation conditions from National Land	Johanna Amaya, Luceny Guzman, Yezid Donoso	567-220
Application of Grey-based Taguchi methods on Determining Process Parameter of linear motion guide with Multiple Performance Characteristics	Y.F. Hsiao , Y.S. Tarng and K. Y. Kung	567-115
A control method with brain machine interface for man-machine systems	Tohru Kawabe	567-148
The Notion of Stability Defect in Game Control Problems	Vladimir Ushakov, Sergey Brykalov, Yaroslav Latushkin	567-237
Sensor-target and weapon-target pairings based on auction algorithm	Zbigniew Bogdanowicz, Norman Coleman	567-103
Linear programming formulation of the travelling salesman problem	Moustapha Diaby	567-112

Symposium: Management, Marketing and Finances (MMF '07)

Chair: Richard Ehrhardt, Chih-Hung Hsu

The DEA Method In Economical Efficiency Analysis (Micro-Level)	Iurie Caraus, Tkacenko Alexandra, Nikos E. Mastorakis	567-099
The Forward ARD Input-Oriented Efficiency Analysis Of Moldavian Micro-Level Economy	Iurie Caraus, Tkacenko Alexandra, Nikos E. Mastorakis	567-095
Describing Service in Independent Demand Inventory Systems	Richard Ehrhardt	567-301
Offshoring Decision Making in the Logistics of the Norwegian Shipbuilding Yards	Maryna Solesvik and Sylvia Encheva	567-285
Using Innovative Technology in QFD To Improve Marketing Quality	Chih-Hung Hsu, Shih -Yuan Wang, Liang-Tzung Lin	567-127
Multifactor performance measure model with an application to Semiconductor industry Performance	Chuan-Chun Wu, Chang-Chun Li, Tsan-Hun Wang	567-286
Information technology support system of supply chain management	Jing Yang, Hua Jiang	567-155
Evolution structure of a process and resource models-based simulation for the supply chain management	Pyoung Yol Jang	567-302
General and Specific Objectives of the Phare Waste Management Programme In the Cisnadie Area, Sibiu County, Romania	Dan D. Dumitrascu, Radu V. Pascu, Codruta L. Dumitrascu	535-328

Saturday, March 24, 2007

SESSION: Numerical Analysis, Linear Algebra and Applications

Chair: Vasilis Zafiris, Jianfeng Li

A Novel LBG algorithm for Image Compression in Wavelet Transform Domain	Somphob Soongsathitanon	567-167
Numerical Scheme of Magnetic Monopoles	M. Affouf	567-265
Remarks on the Geometric Properties of Trivariate Maps	Vasilis Zafiris	567-088 pp162-167
Application of fuzzy clustering in financial analysis of logistic companies	Jianfeng Li, Xusheng Cui	567-255
Simple model for convective free boundary mass transfer inside square capillary tube	Damelys Zabala, Aura L. López de Ramos	567-125
An Lw₁w₁ Axiomatization of the Linear Archimedean Continua as Merely Relational Structures	Milos Arsenijevic, Miodrag Kapetanovic	567-161
Implications of a Scale Invariant Model of Statistical Mechanics to Nonstandard Analysis and the Wave Equation	Siavash H. Sohrab	567-266
Meshless Analysis of Linear Elastostatic Plane Problems	M.Riyad Abdelkader , A.Sahli , O.Rahmani	567-294

SESSION: Educational Methods

Chair: Felipe Jiménez, Sylvia Encheva

A Model of Technological Course of using Information Science and Technology	Rong-Jyue Fang, Hung Jen Yang, Hua Lin Tsai, Chi Jen Lee,Tien-Sheng Tsai,Dai-Hua Li	567-190
New Geometric Constructions to Determine the Radius of Curvature of Conics at any Point	Felipe Jiménez, Francisco Granero	567-181
Many-Valued Logic in an Intelligent Tutoring System	Sylvia Encheva, Sharil Tumin	567-245

SESSION: Differential Equations and Applications

Chair: Stanislaw Kasperczuk, Katarina Jegdic

Effective Potential Energy Expression for Cell Membrane Transport	Robert Finkel	567-308
A note on Kowalevski exponents and polynomial integrals for differential systems	Stanislaw Kasperczuk	567-107
Quantum Potential Swarm Optimization of PD Controller for Cargo Ship Steering	C. K. Loo, Nikos, E. Mastorakis	567-313
On the subharmonicity of separately subharmonic functions	Juhani Riihentaus	567-120
Numerical solutions to a Riemann problem for gas dynamics equations	Katarina Jegdic	567-306
New development for expansion of semigroups and application	Xu Gen Qi and Nikos E. Mastorakis	567-119
Conversion of First Order Linear Vector Differential Equations With Polynomial Coefficient Matrix To Okubo Form	Metin Demiralp	567-188
Simulation of Wind Pressure on Circular Cylinder at Super-Critical Reynolds Number	Saeed-Reza, Sabbagh-Yazdi, Farzad, Meysami Azad, Nikos E. Mastorakis	567-154
Thermophysical Property Influence in Model Accuracy for the Sterilization Process	Pedro Vargas, Damelys Zabala, Aura Lopez de Ramos	567-186