Search results for: convex feasibility problem
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3932

Search results for: convex feasibility problem

2372 Security Risk Analysis Based on the Policy Formalization and the Modeling of Big Systems

Authors: Luc Cessieux, French Navy, Adrien Derock, DCNS/IMATH

Abstract:

Security risk models have been successful in estimating the likelihood of attack for simple security threats. However, modeling complex system and their security risk is even a challenge. Many methods have been proposed to face this problem. Often difficult to manipulate, and not enough all-embracing they are not as famous as they should with administrators and deciders. We propose in this paper a new tool to model big systems on purpose. The software, takes into account attack threats and security strength.

Keywords: Security, risk management, threat, modelization.

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2371 Project Selection by Using Fuzzy AHP and TOPSIS Technique

Authors: S. Mahmoodzadeh, J. Shahrabi, M. Pariazar, M. S. Zaeri

Abstract:

In this article, by using fuzzy AHP and TOPSIS technique we propose a new method for project selection problem. After reviewing four common methods of comparing alternatives investment (net present value, rate of return, benefit cost analysis and payback period) we use them as criteria in AHP tree. In this methodology by utilizing improved Analytical Hierarchy Process by Fuzzy set theory, first we try to calculate weight of each criterion. Then by implementing TOPSIS algorithm, assessment of projects has been done. Obtained results have been tested in a numerical example.

Keywords: Fuzzy AHP, Project Selection, TOPSIS Technique.

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2370 A Protocol for Applied Consumer Behavior Research in Academia

Authors: A. Otjen, S. Keller

Abstract:

A Montana university has used applied consumer research in experiential learning with non-profit clients for over a decade. Through trial and error, a successful protocol has been established from problem statement through formative research to integrated marketing campaign execution. In this paper, we describe the protocol and its applications. Analysis was completed to determine the effectiveness of the campaigns and the results of how pre- and post-consumer research mark societal change because of media.

Keywords: Marketing, experiential learning, consumer behavior, community partner.

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2369 The Internet, its Social and Ethical Problem to the Young and How Curriculum Can Address the Issue

Authors: R. Ramli

Abstract:

The impact of the information revolution is double edged. While it is applauded for its versatility and performance robustness and acclaimed for making life smooth and easy, on the other hand people are concerned about its dark side especially to younger generations. The education system should extend its educating role beyond the school to home. Parents should be included in forming the policies of Internet use as well as in the curriculum delivery. This paper discusses how curriculum can be instrumental in addressing social and ethical issues resulted from the Internet.

Keywords: Curriculum, Ethics, Internet Addiction, Social Issues

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2368 A Optimal Subclass Detection Method for Credit Scoring

Authors: Luciano Nieddu, Giuseppe Manfredi, Salvatore D'Acunto, Katia La Regina

Abstract:

In this paper a non-parametric statistical pattern recognition algorithm for the problem of credit scoring will be presented. The proposed algorithm is based on a clustering k- means algorithm and allows for the determination of subclasses of homogenous elements in the data. The algorithm will be tested on two benchmark datasets and its performance compared with other well known pattern recognition algorithm for credit scoring.

Keywords: Constrained clustering, Credit scoring, Statistical pattern recognition, Supervised classification.

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2367 Heuristic Optimization Techniques for Network Reconfiguration in Distribution System

Authors: A. Charlangsut, N. Rugthaicharoencheep, S. Auchariyamet

Abstract:

Network reconfiguration is an operation to modify the network topology. The implementation of network reconfiguration has many advantages such as loss minimization, increasing system security and others. In this paper, two topics about the network reconfiguration in distribution system are briefly described. The first topic summarizes its impacts while the second explains some heuristic optimization techniques for solving the network reconfiguration problem.

Keywords: Network Reconfiguration, Optimization Techniques, Distribution System

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2366 Selection and Design of an Axial Flow Fan

Authors: D. Almazo, C. Rodríguez, M. Toledo

Abstract:

This work presents a methodology for the selection and design of propeller oriented to the experimental verification of theoretical results. The problem of propeller selection and design usually present itself in the following manner: a certain air volume and static pressure are required for a certain system. Once the necessity of fan design on a theoretical basis has been recognized, it is possible to determinate the dimensions for a fan unit so that it will perform in accordance with a certain set of specifications. The same procedures in this work then can be applied in other propeller selection.

Keywords: airfoil, axial flow, blade, fan, hub, mathematical algorithm, propeller design, simulation, wheel.

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2365 Rotary Machine Sealing Oscillation Frequencies and Phase Shift Analysis

Authors: Liliia N. Butymova, Vladimir Ya Modorskii

Abstract:

To ensure the gas transmittal GCU's efficient operation, leakages through the labyrinth packings (LP) should be minimized. Leakages can be minimized by decreasing the LP gap, which in turn depends on thermal processes and possible rotor vibrations and is designed to ensure absence of mechanical contact. Vibration mitigation allows to minimize the LP gap. It is advantageous to research influence of processes in the dynamic gas-structure system on LP vibrations. This paper considers influence of rotor vibrations on LP gas dynamics and influence of the latter on the rotor structure within the FSI unidirectional dynamical coupled problem. Dependences of nonstationary parameters of gas-dynamic process in LP on rotor vibrations under various gas speeds and pressures, shaft rotation speeds and vibration amplitudes, and working medium features were studied. The programmed multi-processor ANSYS CFX was chosen as a numerical computation tool. The problem was solved using PNRPU high-capacity computer complex. Deformed shaft vibrations are replaced with an unyielding profile that moves in the fixed annulus "up-and-down" according to set harmonic rule. This solves a nonstationary gas-dynamic problem and determines time dependence of total gas-dynamic force value influencing the shaft. Pressure increase from 0.1 to 10 MPa causes growth of gas-dynamic force oscillation amplitude and frequency. The phase shift angle between gas-dynamic force oscillations and those of shaft displacement decreases from 3π/4 to π/2. Damping constant has maximum value under 1 MPa pressure in the gap. Increase of shaft oscillation frequency from 50 to 150 Hz under P=10 MPa causes growth of gas-dynamic force oscillation amplitude. Damping constant has maximum value at 50 Hz equaling 1.012. Increase of shaft vibration amplitude from 20 to 80 µm under P=10 MPa causes the rise of gas-dynamic force amplitude up to 20 times. Damping constant increases from 0.092 to 0.251. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the minimum gas-dynamic force persistent oscillating amplitude under P=0.1 MPa being observed in methane, and maximum in the air. Frequency remains almost unchanged and the phase shift in the air changes from 3π/4 to π/2. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the maximum gas-dynamic force oscillating amplitude under P=10 MPa being observed in methane, and minimum in the air. Air demonstrates surging. Increase of leakage speed from 0 to 20 m/s through LP under P=0.1 MPa causes the gas-dynamic force oscillating amplitude to decrease by 3 orders and oscillation frequency and the phase shift to increase 2 times and stabilize. Increase of leakage speed from 0 to 20 m/s in LP under P=1 MPa causes gas-dynamic force oscillating amplitude to decrease by almost 4 orders. The phase shift angle increases from π/72 to π/2. Oscillations become persistent. Flow rate proved to influence greatly on pressure oscillations amplitude and a phase shift angle. Work medium influence depends on operation conditions. At pressure growth, vibrations are mostly affected in methane (of working substances list considered), and at pressure decrease, in the air at 25 ˚С.

Keywords: Aeroelasticity, labyrinth packings, oscillation phase shift, vibration.

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2364 Interactive Concept-based Search using MOEA:The Hierarchical Preferences Case

Authors: Gideon Avigad, Amiram Moshaiov, Neima Brauner

Abstract:

An IEC technique is described for a multi-objective search of conceptual solutions. The survivability of solutions is influenced by both model-based fitness and subjective human preferences. The concepts- preferences are articulated via a hierarchy of sub-concepts. The suggested method produces an objectivesubjective front. Academic example is employed to demonstrate the proposed approach.

Keywords: Conceptual solution, engineering design, hierarchical planning, multi-objective search, problem reduction.

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2363 Dynamic Network Routing Method Based on Chromosome Learning

Authors: Xun Liang

Abstract:

In this paper, we probe into the traffic assignment problem by the chromosome-learning-based path finding method in simulation, which is to model the driver' behavior in the with-in-a-day process. By simply making a combination and a change of the traffic route chromosomes, the driver at the intersection chooses his next route. The various crossover and mutation rules are proposed with extensive examples.

Keywords: Chromosome learning, crossover, mutation, traffic path finding.

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2362 An Approach for Ensuring Data Flow in Freight Delivery and Management Systems

Authors: Aurelija Burinskienė, Dalė Dzemydienė, Arūnas Miliauskas

Abstract:

This research aims at developing the approach for more effective freight delivery and transportation process management. The road congestions and the identification of causes are important, as well as the context information recognition and management. The measure of many parameters during the transportation period and proper control of driver work became the problem. The number of vehicles per time unit passing at a given time and point for drivers can be evaluated in some situations. The collection of data is mainly used to establish new trips. The flow of the data is more complex in urban areas. Herein, the movement of freight is reported in detail, including the information on street level. When traffic density is extremely high in congestion cases, and the traffic speed is incredibly low, data transmission reaches the peak. Different data sets are generated, which depend on the type of freight delivery network. There are three types of networks: long-distance delivery networks, last-mile delivery networks and mode-based delivery networks; the last one includes different modes, in particular, railways and other networks. When freight delivery is switched from one type of the above-stated network to another, more data could be included for reporting purposes and vice versa. In this case, a significant amount of these data is used for control operations, and the problem requires an integrated methodological approach. The paper presents an approach for providing e-services for drivers by including the assessment of the multi-component infrastructure needed for delivery of freights following the network type. The construction of such a methodology is required to evaluate data flow conditions and overloads, and to minimize the time gaps in data reporting. The results obtained show the possibilities of the proposing methodological approach to support the management and decision-making processes with functionality of incorporating networking specifics, by helping to minimize the overloads in data reporting.

Keywords: Transportation networks, freight delivery, data flow, monitoring, e-services.

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2361 Fuzzy Power Controller Design for Purdue University Research Reactor-1

Authors: Oktavian Muhammad Rizki, Appiah Rita, Lastres Oscar, Miller True, Chapman Alec, Tsoukalas Lefteri H.

Abstract:

The Purdue University Research Reactor-1 (PUR-1) is a 10 kWth pool-type research reactor located at Purdue University’s West Lafayette campus. The reactor was recently upgraded to use entirely digital instrumentation and control systems. However, currently, there is no automated control system to regulate the power in the reactor. We propose a fuzzy logic controller as a form of digital twin to complement the existing digital instrumentation system to monitor and stabilize power control using existing experimental data. This work assesses the feasibility of a power controller based on a Fuzzy Rule-Based System (FRBS) by modelling and simulation with a MATLAB algorithm. The controller uses power error and reactor period as inputs and generates reactivity insertion as output. The reactivity insertion is then converted to control rod height using a logistic function based on information from the recorded experimental reactor control rod data. To test the capability of the proposed fuzzy controller, a point-kinetic reactor model is utilized based on the actual PUR-1 operation conditions and a Monte Carlo N-Particle simulation result of the core to numerically compute the neutronics parameters of reactor behavior. The Point Kinetic Equation (PKE) was employed to model dynamic characteristics of the research reactor since it explains the interactions between the spatial and time varying input and output variables efficiently. The controller is demonstrated computationally using various cases: startup, power maneuver, and shutdown. From the test results, it can be proved that the implemented fuzzy controller can satisfactorily regulate the reactor power to follow demand power without compromising nuclear safety measures.

Keywords: Fuzzy logic controller, power controller, reactivity, research reactor.

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2360 Optimal Energy Management System for Electrical Vehicles to Further Extend the Range

Authors: M. R. Rouhi, S. Shafiei, A. Taghavipour, H. Adibi-Asl, A. Doosthoseini

Abstract:

This research targets at alleviating the problem of range anxiety associated with the battery electric vehicles (BEVs) by considering mechanical and control aspects of the powertrain. In this way, all the energy consuming components and their effect on reducing the range of the BEV and battery life index are identified. On the other hand, an appropriate control strategy is designed to guarantee the performance of the BEV and the extended electric range which is evaluated by an extensive simulation procedure and a real-world driving schedule.

Keywords: Battery, electric vehicles EV, ultra-capacitor.

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2359 Temperature-Based Detection of Initial Yielding Point in Loading of Tensile Specimens Made of Structural Steel

Authors: Aqsa Jamil, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

Abstract:

Yield point represents the upper limit of forces which can be applied on a specimen without causing any permanent deformation. After yielding, the behavior of specimen suddenly changes including the possibility of cracking or buckling. So, the accumulation of damage or type of fracture changes depending on this condition. As it is difficult to accurately detect yield points of the several stress concentration points in structural steel specimens, an effort has been made in this research work to develop a convenient technique using thermography (temperature-based detection) during tensile tests for the precise detection of yield point initiation. To verify the applicability of thermography camera, tests were conducted under different loading conditions and measuring the deformation by installing various strain gauges and monitoring the surface temperature with the help of thermography camera. The yield point of specimens was estimated by the help of temperature dip which occurs due to the thermoelastic effect during the plastic deformation. The scattering of the data has been checked by performing repeatability analysis. The effect of temperature imperfection and light source has been checked by carrying out the tests at daytime as well as midnight and by calculating the signal to noise ratio (SNR) of the noised data from the infrared thermography camera, it can be concluded that the camera is independent of testing time and the presence of a visible light source. Furthermore, a fully coupled thermal-stress analysis has been performed by using Abaqus/Standard exact implementation technique to validate the temperature profiles obtained from the thermography camera and to check the feasibility of numerical simulation for the prediction of results extracted with the help of thermographic technique.

Keywords: Signal to noise ratio, thermoelastic effect, thermography, yield point.

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2358 A Multi-Signature Scheme based on Coding Theory

Authors: Mohammed Meziani, Pierre-Louis Cayrel

Abstract:

In this paper we propose two first non-generic constructions of multisignature scheme based on coding theory. The first system make use of the CFS signature scheme and is secure in random oracle while the second scheme is based on the KKS construction and is a few times. The security of our construction relies on a difficult problems in coding theory: The Syndrome Decoding problem which has been proved NP-complete [4].

Keywords: Post-quantum cryptography, Coding-based cryptography, Digital signature, Multisignature scheme.

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2357 Flexible Communication Platform for Crisis Management

Authors: Jiří Barta, Tomáš Ludík, Jiří Urbánek

Abstract:

Topics Disaster and Emergency Management are highly debated among experts. Fast communication will help to deal with emergencies. Problem is with the network connection and data exchange. The paper suggests a solution, which allows possibilities and perspectives of new flexible communication platform to the protection of communication systems for crisis management. This platform is used for everyday communication and communication in crisis situations too.

Keywords: Communication Platform, Crisis Management, Crisis Communication, Information Systems, Interoperability, Security Environment.

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2356 Networks with Unreliable Nodes and Edges: Monte Carlo Lifetime Estimation

Authors: Y. Shpungin

Abstract:

Estimating the lifetime distribution of computer networks in which nodes and links exist in time and are bound for failure is very useful in various applications. This problem is known to be NP-hard. In this paper we present efficient combinatorial approaches to Monte Carlo estimation of network lifetime distribution. We also present some simulation results.

Keywords: Combinatorial spectrum, Monte Carlo, Networklifetime, Unreliable nodes and edges.

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2355 The Growth of E-Commerce and Online Dispute Resolution in Developing Nations: An Analysis

Authors: Robin V. Cupido

Abstract:

Online dispute resolution has been identified in many countries as a viable alternative for resolving conflicts which have arisen in the so-called digital age. This system of dispute resolution is developing alongside the Internet, and as new types of transactions are made possible by our increased connectivity, new ways of resolving disputes must be explored. Developed nations, such as the United States of America and the European Union, have been involved in creating these online dispute resolution mechanisms from the outset, and currently have sophisticated systems in place to deal with conflicts arising in a number of different fields, such as e-commerce, domain name disputes, labour disputes and conflicts arising from family law. Specifically, in the field of e-commerce, the Internet’s borderless nature has served as a way to promote cross-border trade, and has created a global marketplace. Participation in this marketplace boosts a country’s economy, as new markets are now available, and consumers can transact from anywhere in the world. It would be especially advantageous for developing nations to be a part of this global marketplace, as it could stimulate much-needed investment in these nations, and encourage international co-operation and trade. However, for these types of transactions to proliferate, an effective system for resolving the inevitable disputes arising from such an increase in e-commerce is needed. Online dispute resolution scholarship and practice is flourishing in developed nations, and it is clear that the gap is widening between developed and developing nations in this regard. The potential for implementing online dispute resolution in developing countries has been discussed, but there are a number of obstacles that have thus far prevented its continued development. This paper aims to evaluate the various political, infrastructural and socio-economic challenges faced in developing nations, and to question how these have impacted the acceptance and development of online dispute resolution, scholarship and training of online dispute resolution practitioners and, ultimately, developing nations’ readiness to participate in cross-border e-commerce.

Keywords: Developing countries, feasibility, online dispute resolution, progress.

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2354 Advanced Technologies and Algorithms for Efficient Portfolio Selection

Authors: Konstantinos Liagkouras, Konstantinos Metaxiotis

Abstract:

In this paper we present a classification of the various technologies applied for the solution of the portfolio selection problem according to the discipline and the methodological framework followed. We provide a concise presentation of the emerged categories and we are trying to identify which methods considered obsolete and which lie at the heart of the debate. On top of that, we provide a comparative study of the different technologies applied for efficient portfolio construction and we suggest potential paths for future work that lie at the intersection of the presented techniques.

Keywords: Portfolio selection, optimization techniques, financial models, stochastics, heuristics.

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2353 Dynamics and Control of Bouncing Ball

Authors: A. K. Kamath, N. M. Singh, R. Pasumarthy

Abstract:

This paper investigates the control of a bouncing ball using Model Predictive Control. Bouncing ball is a benchmark problem for various rhythmic tasks such as juggling, walking, hopping and running. Humans develop intentions which may be perceived as our reference trajectory and tries to track it. The human brain optimizes the control effort needed to track its reference; this forms the central theme for control of bouncing ball in our investigations.

Keywords: Bouncing Ball, impact dynamics, intermittent control, model predictive control.

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2352 Using Artificial Neural Networks for Optical Imaging of Fluorescent Biomarkers

Authors: K. A. Laptinskiy, S. A. Burikov, A. M. Vervald, S. A. Dolenko, T. A. Dolenko

Abstract:

The article presents the results of the application of artificial neural networks to separate the fluorescent contribution of nanodiamonds used as biomarkers, adsorbents and carriers of drugs in biomedicine, from a fluorescent background of own biological fluorophores. The principal possibility of solving this problem is shown. Use of neural network architecture let to detect fluorescence of nanodiamonds against the background autofluorescence of egg white with high accuracy - better than 3 ug/ml.

Keywords: Artificial neural networks, fluorescence, data aggregation.

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2351 Computing Center Conditions for Non-analytic Vector Fields with Constant Angular Speed

Authors: Li Feng

Abstract:

We investigate the planar quasi-septic non-analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The system could be changed into an analytic system by two transformations, with the help of computer algebra system MATHEMATICA, the conditions of uniform isochronous center are obtained.

Keywords: Non-analytic, center–focus problem, Lyapunov constant, uniform isochronous center.

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2350 New Stability Analysis for Neural Networks with Time-Varying Delays

Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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2349 Recursive Similarity Hashing of Fractal Geometry

Authors: Timothee G. Leleu

Abstract:

A new technique of topological multi-scale analysis is introduced. By performing a clustering recursively to build a hierarchy, and analyzing the co-scale and intra-scale similarities, an Iterated Function System can be extracted from any data set. The study of fractals shows that this method is efficient to extract self-similarities, and can find elegant solutions the inverse problem of building fractals. The theoretical aspects and practical implementations are discussed, together with examples of analyses of simple fractals.

Keywords: hierarchical clustering, multi-scale analysis, Similarity hashing.

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2348 Joint Training Offer Selection and Course Timetabling Problems: Models and Algorithms

Authors: Gianpaolo Ghiani, Emanuela Guerriero, Emanuele Manni, Alessandro Romano

Abstract:

In this article, we deal with a variant of the classical course timetabling problem that has a practical application in many areas of education. In particular, in this paper we are interested in high schools remedial courses. The purpose of such courses is to provide under-prepared students with the skills necessary to succeed in their studies. In particular, a student might be under prepared in an entire course, or only in a part of it. The limited availability of funds, as well as the limited amount of time and teachers at disposal, often requires schools to choose which courses and/or which teaching units to activate. Thus, schools need to model the training offer and the related timetabling, with the goal of ensuring the highest possible teaching quality, by meeting the above-mentioned financial, time and resources constraints. Moreover, there are some prerequisites between the teaching units that must be satisfied. We first present a Mixed-Integer Programming (MIP) model to solve this problem to optimality. However, the presence of many peculiar constraints contributes inevitably in increasing the complexity of the mathematical model. Thus, solving it through a general-purpose solver may be performed for small instances only, while solving real-life-sized instances of such model requires specific techniques or heuristic approaches. For this purpose, we also propose a heuristic approach, in which we make use of a fast constructive procedure to obtain a feasible solution. To assess our exact and heuristic approaches we perform extensive computational results on both real-life instances (obtained from a high school in Lecce, Italy) and randomly generated instances. Our tests show that the MIP model is never solved to optimality, with an average optimality gap of 57%. On the other hand, the heuristic algorithm is much faster (in about the 50% of the considered instances it converges in approximately half of the time limit) and in many cases allows achieving an improvement on the objective function value obtained by the MIP model. Such an improvement ranges between 18% and 66%.

Keywords: Heuristic, MIP model, Remedial course, School, Timetabling.

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2347 Adomian Method for Second-order Fuzzy Differential Equation

Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

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2346 Application of MoM-GEC Method for Electromagnetic Study of Planar Microwave Structures: Shielding Application

Authors: Ahmed Nouainia, Mohamed Hajji, Taoufik Aguili

Abstract:

In this paper, an electromagnetic analysis is presented for describing the influence of shielding in a rectangular waveguide. A hybridization based on the method of moments combined to the generalized equivalent circuit MoM-GEC is used to model the problem. This is validated by applying the MoM-GEC hybridization to investigate a diffraction structure. It consists of electromagnetic diffraction by an iris in a rectangular waveguide. Numerical results are shown and discussed and a comparison with FEM and Marcuvitz methods is achieved.

Keywords: Inductive irises, MoM-GEC, waveguide, shielding.

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2345 Futures Trading: Design of a Strategy

Authors: Jan Zeman

Abstract:

The paper describes the futures trading and aims to design the speculators trading strategy. The problem is formulated as the decision making task and such as is solved. The solution of the task leads to complex mathematical problems and the approximations of the decision making is demanded. Two kind of approximation are used in the paper: Monte Carlo for the multi-step prediction and iteration spread in time for the optimization. The solution is applied to the real-market data and the results of the off-line experiments are presented.

Keywords: futures trading, decision making

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2344 Robust Artificial Neural Network Architectures

Authors: A. Schuster

Abstract:

Many artificial intelligence (AI) techniques are inspired by problem-solving strategies found in nature. Robustness is a key feature in many natural systems. This paper studies robustness in artificial neural networks (ANNs) and proposes several novel, nature inspired ANN architectures. The paper includes encouraging results from experimental studies on these networks showing increased robustness.

Keywords: robustness, robust artificial neural networks architectures.

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2343 Some Applications of Transition Matrices via Eigen Values

Authors: Adil AL-Rammahi

Abstract:

In this short paper, new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, and information theory via channel entropy. The implemented test examples were promised for usages.

Keywords: Eigen value problem, transition matrix, state vector, information theory.

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