Search results for: contact problem
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4001

Search results for: contact problem

3281 Algorithmic Method for Efficient Cruise Program

Authors: Pelaez Verdet, Antonio, Loscertales Sanchez, Pilar

Abstract:

One of the mayor problems of programming a cruise circuit is to decide which destinations to include and which don-t. Thus a decision problem emerges, that might be solved using a linear and goal programming approach. The problem becomes more complex if several boats in the fleet must be programmed in a limited schedule, trying their capacity matches best a seasonal demand and also attempting to minimize the operation costs. Moreover, the programmer of the company should consider the time of the passenger as a limited asset, and would like to maximize its usage. The aim of this work is to design a method in which, using linear and goal programming techniques, a model to design circuits for the cruise company decision maker can achieve an optimal solution within the fleet schedule.

Keywords: Itinerary design, cruise programming, goalprogramming, linear programming

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3280 Touching Interaction: An NFC-RFID Combination

Authors: Eduardo Álvarez, Gerardo Quiroga, Jorge Orozco, Gabriel Chavira

Abstract:

AmI proposes a new way of thinking about computers, which follows the ideas of the Ubiquitous Computing vision of Mark Weiser. In these, there is what is known as a Disappearing Computer Initiative, with users immersed in intelligent environments. Hence, technologies need to be adapted so that they are capable of replacing the traditional inputs to the system by embedding these in every-day artifacts. In this work, we present an approach, which uses Radiofrequency Identification (RFID) and Near Field Communication (NFC) technologies. In the latter, a new form of interaction appears by contact. We compare both technologies by analyzing their requirements and advantages. In addition, we propose using a combination of RFID and NFC.

Keywords: Touching interaction, ambient intelligence, NFC, RFID.

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3279 The Exploitation of Balancing an Inverted Pendulum System Using Sliding Mode Control

Authors: Sheren H. Salah, Ahmed Y. Ben Sasi

Abstract:

The inverted pendulum system is a classic control problem that is used in universities around the world. It is a suitable process to test prototype controllers due to its high non-linearities and lack of stability. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. This paper presents the possibility of balancing an inverted pendulum system using sliding mode control (SMC). The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart's position. Therefore, proportional-integral-derivative (PID) is used for comparison. Results have proven SMC control produced better response compared to PID control in both normal and noisy systems.

Keywords: Inverted pendulum (IP) proportional-integralderivative (PID), sliding mode control (SMC).

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3278 Optimal Control of Volterra Integro-Differential Systems Based On Legendre Wavelets and Collocation Method

Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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3277 Spatio-Temporal Video Slice Edges Analysis for Shot Transition Detection and Classification

Authors: Aissa Saoudi, Hassane Essafi

Abstract:

In this work we will present a new approach for shot transition auto-detection. Our approach is based on the analysis of Spatio-Temporal Video Slice (STVS) edges extracted from videos. The proposed approach is capable to efficiently detect both abrupt shot transitions 'cuts' and gradual ones such as fade-in, fade-out and dissolve. Compared to other techniques, our method is distinguished by its high level of precision and speed. Those performances are obtained due to minimizing the problem of the boundary shot detection to a simple 2D image partitioning problem.

Keywords: Boundary shot detection, Shot transition detection, Video analysis, Video indexing.

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3276 Discrete Element Modeling on Bearing Capacity Problems

Authors: N. Li, Y. M. Cheng

Abstract:

In this paper, the classical bearing capacity problem is re-considered from discrete element analysis. In the discrete element approach, the bearing capacity problem is considered from the elastic stage to plastic stage to rupture stage (large displacement). The bearing capacity failure mechanism of a strip footing on soil is investigated, and the influence of micro-parameters on the bearing capacity of soil is also observed. It is found that the distinct element method (DEM) gives very good visualized results, and basically coincides well with that derived by the classical methods.

Keywords: Bearing capacity, distinct element method, failure mechanism, large displacement.

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3275 Efficient Broadcasting in Wireless Sensor Networks

Authors: Min Kyung An, Hyuk Cho

Abstract:

In this paper, we study the Minimum Latency Broadcast Scheduling (MLBS) problem in wireless sensor networks (WSNs). The main issue of the MLBS problem is to compute schedules with the minimum number of timeslots such that a base station can broadcast data to all other sensor nodes with no collisions. Unlike existing works that utilize the traditional omni-directional WSNs, we target the directional WSNs where nodes can collaboratively determine and orientate their antenna directions. We first develop a 7-approximation algorithm, adopting directional WSNs. Our ratio is currently the best, to the best of our knowledge. We then validate the performance of the proposed algorithm through simulation.

Keywords: Broadcast, collision-free, directional antenna, approximation, wireless sensor networks.

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3274 On an Open Problem for Definable Subsets of Covering Approximation Spaces

Authors: Mei He, Ying Ge, Jingyu Qian

Abstract:

Let (U;D) be a Gr-covering approximation space (U; C) with covering lower approximation operator D and covering upper approximation operator D. For a subset X of U, this paper investigates the following three conditions: (1) X is a definable subset of (U;D); (2) X is an inner definable subset of (U;D); (3) X is an outer definable subset of (U;D). It is proved that if one of the above three conditions holds, then the others hold. These results give a positive answer of an open problem for definable subsets of covering approximation spaces.

Keywords: Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.

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3273 Two Area Power Systems Economic Dispatch Problem Solving Considering Transmission Capacity Constraints

Authors: M. Zarei, A. Roozegar, R. Kazemzadeh, J.M. Kauffmann

Abstract:

This paper describes an efficient and practical method for economic dispatch problem in one and two area electrical power systems with considering the constraint of the tie transmission line capacity constraint. Direct search method (DSM) is used with some equality and inequality constraints of the production units with any kind of fuel cost function. By this method, it is possible to use several inequality constraints without having difficulty for complex cost functions or in the case of unavailability of the cost function derivative. To minimize the number of total iterations in searching, process multi-level convergence is incorporated in the DSM. Enhanced direct search method (EDSM) for two area power system will be investigated. The initial calculation step size that causes less iterations and then less calculation time is presented. Effect of the transmission tie line capacity, between areas, on economic dispatch problem and on total generation cost will be studied; line compensation and active power with reactive power dispatch are proposed to overcome the high generation costs for this multi-area system.

Keywords: Economic dispatch, Power System Operation, Direct Search Method, Transmission Capacity Constraint.

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3272 Fuzzy Based Problem-Solution Data Structureas a Data Oriented Model for ABS Controlling

Authors: Ahmad Habibizad Navin, Mehdi Naghian Fesharaki, Mohamad Teshnelab, Ehsan Shahamatnia

Abstract:

The anti-lock braking systems installed on vehicles for safe and effective braking, are high-order nonlinear and timevariant. Using fuzzy logic controllers increase efficiency of such systems, but impose a high computational complexity as well. The main concept introduced by this paper is reducing computational complexity of fuzzy controllers by deploying problem-solution data structure. Unlike conventional methods that are based on calculations, this approach is based on data oriented modeling.

Keywords: ABS, Fuzzy controller, PSDS, Time-Memory tradeoff, Data oriented modeling.

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3271 Hybrid of Hunting Search and Modified Simplex Methods for Grease Position Parameter Design Optimisation

Authors: P. Luangpaiboon, S. Boonhao

Abstract:

This study proposes a multi-response surface optimization problem (MRSOP) for determining the proper choices of a process parameter design (PPD) decision problem in a noisy environment of a grease position process in an electronic industry. The proposed models attempts to maximize dual process responses on the mean of parts between failure on left and right processes. The conventional modified simplex method and its hybridization of the stochastic operator from the hunting search algorithm are applied to determine the proper levels of controllable design parameters affecting the quality performances. A numerical example demonstrates the feasibility of applying the proposed model to the PPD problem via two iterative methods. Its advantages are also discussed. Numerical results demonstrate that the hybridization is superior to the use of the conventional method. In this study, the mean of parts between failure on left and right lines improve by 39.51%, approximately. All experimental data presented in this research have been normalized to disguise actual performance measures as raw data are considered to be confidential.

Keywords: Grease Position Process, Multi-response Surfaces, Modified Simplex Method, Hunting Search Method, Desirability Function Approach.

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3270 Optimal Design of Two-Channel Recursive Parallelogram Quadrature Mirror Filter Banks

Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

This paper deals with the optimal design of two-channel recursive parallelogram quadrature mirror filter (PQMF) banks. The analysis and synthesis filters of the PQMF bank are composed of two-dimensional (2-D) recursive digital all-pass filters (DAFs) with nonsymmetric half-plane (NSHP) support region. The design problem can be facilitated by using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters. For finding the coefficients of the 2-D recursive NSHP DAFs, we appropriately formulate the design problem to result in an optimization problem that can be solved by using a weighted least-squares (WLS) algorithm in the minimax (L) optimal sense. The designed 2-D recursive PQMF bank achieves perfect magnitude response and possesses satisfactory phase response without requiring extra phase equalizer. Simulation results are also provided for illustration and comparison.

Keywords: Parallelogram Quadrature Mirror Filter Bank, Doubly Complementary Filter, Nonsymmetric Half-Plane Filter, Weighted Least Squares Algorithm, Digital All-Pass Filter.

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3269 Modelling Sudoku Puzzles as Block-world Problems

Authors: Cecilia Nugraheni, Luciana Abednego

Abstract:

Sudoku is a kind of logic puzzles. Each puzzle consists of a board, which is a 9×9 cells, divided into nine 3×3 subblocks and a set of numbers from 1 to 9. The aim of this puzzle is to fill in every cell of the board with a number from 1 to 9 such that in every row, every column, and every subblock contains each number exactly one. Sudoku puzzles belong to combinatorial problem (NP complete). Sudoku puzzles can be solved by using a variety of techniques/algorithms such as genetic algorithms, heuristics, integer programming, and so on. In this paper, we propose a new approach for solving Sudoku which is by modelling them as block-world problems. In block-world problems, there are a number of boxes on the table with a particular order or arrangement. The objective of this problem is to change this arrangement into the targeted arrangement with the help of two types of robots. In this paper, we present three models for Sudoku. We modellized Sudoku as parameterized multi-agent systems. A parameterized multi-agent system is a multi-agent system which consists of several uniform/similar agents and the number of the agents in the system is stated as the parameter of this system. We use Temporal Logic of Actions (TLA) for formalizing our models.

Keywords: Sudoku puzzle, block world problem, parameterized multi agent systems modelling, Temporal Logic of Actions.

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3268 Reducing Variation of Dyeing Process in Textile Manufacturing Industry

Authors: M. Zeydan, G. Toğa

Abstract:

This study deals with a multi-criteria optimization problem which has been transformed into a single objective optimization problem using Response Surface Methodology (RSM), Artificial Neural Network (ANN) and Grey Relational Analyses (GRA) approach. Grey-RSM and Grey-ANN are hybrid techniques which can be used for solving multi-criteria optimization problem. There have been two main purposes of this research as follows. 1. To determine optimum and robust fiber dyeing process conditions by using RSM and ANN based on GRA, 2. To obtain the best suitable model by comparing models developed by different methodologies. The design variables for fiber dyeing process in textile are temperature, time, softener, anti-static, material quantity, pH, retarder, and dispergator. The quality characteristics to be evaluated are nominal color consistency of fiber, maximum strength of fiber, minimum color of dyeing solution. GRA-RSM with exact level value, GRA-RSM with interval level value and GRA-ANN models were compared based on GRA output value and MSE (Mean Square Error) performance measurement of outputs with each other. As a result, GRA-ANN with interval value model seems to be suitable reducing the variation of dyeing process for GRA output value of the model.

Keywords: Artificial Neural Network, Grey Relational Analysis, Optimization, Response Surface Methodology

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3267 Strategy Analysis and Creation by Simulation in the General Game

Authors: Gábor Szűcs, Gábor Neszveda, Xin Fang

Abstract:

In this paper the General Game problem is described. In this problem the competition or cooperation dilemma occurs as the two basic types of strategies. The strategy possibilities have been analyzed for finding winning strategy in uncertain situations (no information about the number of players and their strategy types). The winning strategy is missing, but a good solution can be found by simulation by varying the ratio of the two types of strategies. This new method has been used in a real contest with human players, where the created strategies by simulation have reached very good ranks. This construction can be applied in other real social games as well.

Keywords: competition, cooperation, finding good strategy, General Game

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3266 The Competence of Solving Mathematical Problems in the Formation of Ethical Values

Authors: Veronica Diaz Quezada

Abstract:

A study and its preliminary results are presented. The research is descriptive and exploratory and it is still in process. Its objective is to develop an assessment method in the field of fostering values using competence mathematics problem solving. This is part of a more extensive research that aims at contributing to educational integration in Latin America, particularly to the development of proposals to link education for citizenship and the mathematics lessons. This is being carried out by research teams of University of Barcelona-España; University Nacional of Costa Rica; University Autónoma of Querétaro-México; Pontificia University Católica of Perú, University Nacional of Villa María- Argentina and University of Los Lagos-Chile, in the context of Andrés Bello Chair for the Association of Latin American Universities. This research was developed and implemented in Chile in 2016, using mixed research methods. It included interviews and a problem-solving math test with ethical values that was administered to students of the secondary education of the regions of Los Ríos and of the Lakes of Chile. The results show the lack of integration between the teaching of values and science discipline.

Keywords: Citizenship, ethical values, mathematics, secondary school, solving problem.

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3265 Beginner Physical Sciences Teacher’s Implementation of Problem-Based Learning in Promoting Creativity as a 21st-Century Skill on Learners: A Case Study

Authors: Motlhale Judicial Sebatana, Washington Takawira Dudu

Abstract:

This study investigated how one beginner Physical Sciences teacher implemented Problem-Based Learning (PBL) strategy in the teaching and learning of Particulate Nature of Matter (PNM) in the Grade 10 classroom. PBL was implemented to explore how it can promote a 21st-century skill of creativity and enhance understanding of PNM. This study was guided by theoretical framework of Social Interdependence Theory (SIT). This exploratory qualitative case study was conveniently conducted in the North West province, South Africa, where one Physical Sciences teacher was purposefully sampled. A self-developed open-ended questionnaire, portfolio and individual semi-structured interview were used as the methods of generating data for this study. The results show that the participant of this study had no prior knowledge of utilising PBL in the teaching and learning of PNM before the Teacher Professional Development (TPD) programme, no knowledge of creativity as a 21st-century skill, and a successful PBL implementation post TPD to promote creativity.

Keywords: Beginner teachers, physical sciences teachers, problem-based learning, 21st-century skills, creativity skill, particulate nature of matter.

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3264 Modeling Methodologies for Optimization and Decision Support on Coastal Transport Information System (Co.Tr.I.S.)

Authors: Vassilios Moussas, Dimos N. Pantazis, Panagiotis Stratakis

Abstract:

The aim of this paper is to present the optimization methodology developed in the frame of a Coastal Transport Information System. The system will be used for the effective design of coastal transportation lines and incorporates subsystems that implement models, tools and techniques that may support the design of improved networks. The role of the optimization and decision subsystem is to provide the user with better and optimal scenarios that will best fulfill any constrains, goals or requirements posed. The complexity of the problem and the large number of parameters and objectives involved led to the adoption of an evolutionary method (Genetic Algorithms). The problem model and the subsystem structure are presented in detail, and, its support for simulation is also discussed.

Keywords: Coastal transport, modeling, optimization.

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3263 Stability of Fractional Differential Equation

Authors: Rabha W. Ibrahim

Abstract:

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.

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3262 Multiple Regression based Graphical Modeling for Images

Authors: Pavan S., Sridhar G., Sridhar V.

Abstract:

Super resolution is one of the commonly referred inference problems in computer vision. In the case of images, this problem is generally addressed using a graphical model framework wherein each node represents a portion of the image and the edges between the nodes represent the statistical dependencies. However, the large dimensionality of images along with the large number of possible states for a node makes the inference problem computationally intractable. In this paper, we propose a representation wherein each node can be represented as acombination of multiple regression functions. The proposed approach achieves a tradeoff between the computational complexity and inference accuracy by varying the number of regression functions for a node.

Keywords: Belief propagation, Graphical model, Regression, Super resolution.

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3261 An Augmented Beam-search Based Algorithm for the Strip Packing Problem

Authors: Hakim Akeb, Mhand Hifi

Abstract:

In this paper, the use of beam search and look-ahead strategies for solving the strip packing problem (SPP) is investigated. Given a strip of fixed width W, unlimited length L, and a set of n circular pieces of known radii, the objective is to determine the minimum length of the initial strip that packs all the pieces. An augmented algorithm which combines beam search and a look-ahead strategies is proposed. The look-ahead is used in order to evaluate the nodes at each level of the tree search. The best nodes are then retained for branching. The computational investigation showed that the proposed augmented algorithm is able to improve the best known solutions of the literature on most instances used.

Keywords: Combinatorial optimization, cutting and packing, beam search, heuristic, look-ahead strategy.

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3260 Modeling of Co-Cu Elution From Clinoptilolite using Neural Network

Authors: John Kabuba, Antoine Mulaba-Bafubiandi

Abstract:

The elution process for the removal of Co and Cu from clinoptilolite as an ion-exchanger was investigated using three parameters: bed volume, pH and contact time. The present paper study has shown quantitatively that acid concentration has a significant effect on the elution process. The favorable eluant concentration was found to be 2 M HCl and 2 M H2SO4, respectively. The multi-component equilibrium relationship in the process can be very complex, and perhaps ill-defined. In such circumstances, it is preferable to use a non-parametric technique such as Neural Network to represent such an equilibrium relationship.

Keywords: Clinoptilolite, elution, modeling, neural network.

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3259 Comparative Analysis of Classical and Parallel Inpainting Algorithms Based on Affine Combinations of Projections on Convex Sets

Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

Abstract:

The paper is a comparative study of two classical vari-ants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time, in classical CPU and, alternativaly, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, ınpainting, parallel projection methods

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3258 Technology of Thermal Spray Coating Machining

Authors: Jana Petrů, Tomáš Zlámal, Robert Čep, Lenka Čepová

Abstract:

This article is focused on the thermal spray coating machining issue. Those are irreplaceable in many areas of nowadays industrial branches such as aerospace industry, mostly thanks to their excellent qualities in production and also in renovation of machinery parts. The principals of thermal spraying and elementary diversification are described in introduction. Plasma coating method of composite materials – cermets – is described more thoroughly. The second part describes thermal spray coating machining and grinding in detail. This part contains suggestion of appropriate grinding tool and assessment of cutting conditions used for grinding a given part. Conclusion describes a problem which occurred while grinding a cermet thermal spray coating with a specially designed grindstone and a way to solve this problem.

Keywords: Coating, aerospace, plasma, grinding.

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3257 Addressing the Oracle Problem: Decentralized Authentication in Blockchain-Based Green Hydrogen Certification

Authors: Volker Wannack

Abstract:

The aim of this paper is to present a concept for addressing the Oracle Problem in the context of hydrogen production using renewable energy sources. The proposed approach relies on the authentication of the electricity used for hydrogen production by multiple surrounding actors with similar electricity generation facilities, which attest to the authenticity of the electricity production. The concept introduces an Authenticity Score assigned to each certificate, as well as a Trust Score assigned to each witness. Each certificate must be attested by different actors with a sufficient Trust Score to achieve an Authenticity Score above a predefined threshold, thereby demonstrating that the produced hydrogen is indeed "green."

Keywords: Hydrogen, blockchain, sustainability, structural change.

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3256 An Output Oriented Super-Efficiency Model for Considering Time Lag Effect

Authors: Yanshuang Zhang, Byungho Jeong

Abstract:

There exists some time lag between the consumption of inputs and the production of outputs. This time lag effect should be considered in calculating efficiency of decision making units (DMU). Recently, a couple of DEA models were developed for considering time lag effect in efficiency evaluation of research activities. However, these models can’t discriminate efficient DMUs because of the nature of basic DEA model in which efficiency scores are limited to ‘1’. This problem can be resolved a super-efficiency model. However, a super efficiency model sometimes causes infeasibility problem. This paper suggests an output oriented super-efficiency model for efficiency evaluation under the consideration of time lag effect. A case example using a long term research project is given to compare the suggested model with the MpO model.

Keywords: DEA, Super-efficiency, Time Lag.

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3255 Oxide Based Resistive Random Access Memory Device for High Density Non Volatile Memory Applications

Authors: Z. Fang, X. P. Wang, G. Q. Lo, D. L. Kwong

Abstract:

In this work, we demonstrated vertical RRAM device fabricated at the sidewall of contact hole structures for possible future 3-D stacking integrations. The fabricated devices exhibit polarity dependent bipolar resistive switching with small operation voltage of less than 1V for both set and reset process. A good retention of memory window ~50 times is maintained after 1000s voltage bias.

Keywords: Bipolar switching, non volatile memory, resistive random access memory, 3-D stacking.

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3254 Creating or Destroying Objects Plan in the Graphplan Framework

Authors: Wen-xiang Gu, Zeng-yu Cai, Xin-mei Zhang, Gui-dong Jiang

Abstract:

At present, intelligent planning in the Graphplan framework is a focus of artificial intelligence. While the Creating or Destroying Objects Planning (CDOP) is one unsolved problem of this field, one of the difficulties, too. In this paper, we study this planning problem and bring forward the idea of transforming objects to propositions, based on which we offer an algorithm, Creating or Destroying Objects in the Graphplan framework (CDOGP). Compared to Graphplan, the new algorithm can solve not only the entire problems that Graphplan do, but also a part of CDOP. It is for the first time that we introduce the idea of object-proposition, and we emphasize the discussion on the representations of creating or destroying objects operator and an algorithm in the Graphplan framework. In addition, we analyze the complexity of this algorithm.

Keywords: Graphplan, object_proposition, Creating or destroying objects, CDOGP.

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3253 Testing of Electronic Control Unit Communication Interface

Authors: Petr Šimek, Kamil Kostruk

Abstract:

This paper deals with the problem of testing the Electronic Control Unit (ECU) for the specified function validation. Modern ECUs have many functions which need to be tested. This process requires tracking between the test and the specification. The technique discussed in this paper explores the system for automating this process. The paper focuses on the introduction to the problem in general, then it describes the proposed test system concept and its principle. It looks at how the process of the ECU interface specification file for automated interface testing and test tracking works. In the end, the future possible development of the project is discussed.

Keywords: Electronic control unit testing, embedded system, test generate, test automation, process automation, CAN bus, Ethernet.

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3252 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption

Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.

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