Search results for: Systems engineering

Authors: Sahar S. Tabrizi, Dogan Ibrahim

Abstract:

Cloud Computing is a convenient model for on-demand networks that uses shared pools of virtual configurable computing resources, such as servers, networks, storage devices, applications, etc. The cloud serves as an environment for companies and organizations to use infrastructure resources without making any purchases and they can access such resources wherever and whenever they need. Cloud computing is useful to overcome a number of problems in various Information Technology (IT) domains such as Geographical Information Systems (GIS), Scientific Research, e-Governance Systems, Decision Support Systems, ERP, Web Application Development, Mobile Technology, etc. Companies can use Cloud Computing services to store large amounts of data that can be accessed from anywhere on Earth and also at any time. Such services are rented by the client companies where the actual rent depends upon the amount of data stored on the cloud and also the amount of processing power used in a given time period. The resources offered by the cloud service companies are flexible in the sense that the user companies can increase or decrease their storage requirements or the processing power requirements at any time, thus minimizing the overall rental cost of the service they receive. In addition, the Cloud Computing service providers offer fast processors and applications software that can be shared by their clients. This is especially important for small companies with limited budgets which cannot afford to purchase their own expensive hardware and software. This paper is an overview of the Cloud Computing, giving its types, principles, advantages, and disadvantages. In addition, the paper gives some example engineering applications of Cloud Computing and makes suggestions for possible future applications in the field of engineering.

Keywords: Cloud computing, cloud services, IaaS, PaaS, SaaS, IoT.

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Authors: Liqiang Duan, Ma Jingkai, Lv Zhipeng, Haifan Cai

Abstract:

The integrated solar combined cycle (ISCC) system has a series of advantages such as increasing the system power generation, reducing the cost of solar power generation, less pollutant and CO₂ emission. In this paper, the parabolic trough collectors with direct steam generation (DSG) technology are considered to replace the heat load of heating surfaces in heat regenerator steam generation (HRSG) of a conventional natural gas combined cycle (NGCC) system containing a PG9351FA gas turbine and a triple pressure HRSG with reheat. The detailed model of the NGCC system is built in ASPEN PLUS software and the parabolic trough collectors with DSG technology is modeled in EBSILON software. ISCC-DSG systems with the replacement of single, two, three and four heating surfaces are studied in this paper. Results show that: (1) the ISCC-DSG systems with the replacement heat load of HPB, HPB+LPE, HPE2+HPB+HPS, HPE1+HPE2+ HPB+HPS are the best integration schemes when single, two, three and four stages of heating surfaces are partly replaced by the parabolic trough solar energy collectors with DSG technology. (2) Both the changes of feed water flow and the heat load of the heating surfaces in ISCC-DSG systems with the replacement of multi-stage heating surfaces are smaller than those in ISCC-DSG systems with the replacement of single heating surface. (3) ISCC-DSG systems with the replacement of HPB+LPE heating surfaces can increase the solar power output significantly. (4) The ISCC-DSG systems with the replacement of HPB heating surfaces has the highest solar-thermal-to-electricity efficiency (47.45%) and the solar radiation energy-to-electricity efficiency (30.37%), as well as the highest exergy efficiency of solar field (33.61%).

Keywords: HRSG, integration scheme, parabolic trough collectors with DSG technology, solar power generation.

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Authors: Li Xu, Shouming Zhong

Abstract:

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: Reachable set, Distributed delay, Lyapunov-Krasovskii function, Polytopic uncertainties.

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Authors: Caigen Zhou, Haibo Jiang

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The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: Irina Pyrlina

Abstract:

This article presents the results of a study conducted to identify operational risks for information systems (IS) with service-oriented architecture (SOA). Analysis of current approaches to risk and system error classifications revealed that the system error classes were never used for SOA risk estimation. Additionally system error classes are not normallyexperimentally supported with realenterprise error data. Through the study several categories of various existing error classifications systems are applied and three new error categories with sub-categories are identified. As a part of operational risks a new error classification scheme is proposed for SOA applications. It is based on errors of real information systems which are service providers for application with service-oriented architecture. The proposed classification approach has been used to classify SOA system errors for two different enterprises (oil and gas industry, metal and mining industry). In addition we have conducted a research to identify possible losses from operational risks.

Keywords: Enterprise architecture, Error classification, Oil&Gas and Metal&Mining industries, Operational risks, Serviceoriented architecture

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Authors: Vijay Janyani, Neetu Joshi, Jigyasa Pagaria, Parul Pathak

Abstract:

Photonic Crystal (PhC) based devices are being increasingly used in multifunctional, compact devices in integrated optical communication systems. They provide excellent controllability of light, yet maintaining the small size required for miniaturization. In this paper, the band gap properties of PhCs and their typical applications in optical waveguiding are considered. Novel PhC based applications such as nonlinear switching and tapers are considered and simulation results are shown using the accurate time-domain numerical method based on Finite Difference Time Domain (FDTD) scheme. The suitability of these devices for novel applications is discussed and evaluated.

Keywords: Band gap engineering, Nonlinear switching, Photonic crystals, PhC tapers, waveguides.

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Authors: Md. Mahmudul Hasan

Abstract:

OFDM systems are known to have a high PAPR (Peak-to-Average Power Ratio) compared with single-carrier systems. In fact, the high PAPR is one of the most detrimental aspects in the OFDM system, as it can cause power degradation (Inband distortion) and spectral spreading (Out-of-band radiation). In this paper, from the foundation of the PAPR analysis an effective method of PAPR reduction has been proposed based on Orthogonal Eigenvector Matrix (OEM) transform. Extensive computer simulations show that a PAPR reduction of up to 4.4 dB can be obtained without introducing in-band distortion or out-of-band radiation in the system.

Keywords: Orthogonal frequency division multiplexing (OFDM), peak-to-average power ratio (PAPR), Orthogonal Eigenvector Matrix (OEM).

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Authors: Cherif Haddad, Faouzi Ben Charrada

Abstract:

On a such wide-area environment as a Grid, data placement is an important aspect of distributed database systems. In this paper, we address the problem of initial placement of database no-replicated fragments in Grid architecture. We propose a graph based approach that considers resource restrictions. The goal is to optimize the use of computing, storage and communication resources. The proposed approach is developed in two phases: in the first phase, we perform fragment grouping using knowledge about fragments dependency and, in the second phase, we determine an efficient placement of the fragment groups on the Grid. We also show, via experimental analysis that our approach gives solutions that are close to being optimal for different databases and Grid configurations.

Keywords: Grid computing, Distributed systems, Data resourcesmanagement, Database systems, Database placement.

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Authors: Yifan Fan, Xudong Luo, Pingping Lin

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Nowadays, dialogue systems increasingly become the way for humans to access many computer systems. So, humans can interact with computers in natural language. A dialogue system consists of three parts: understanding what humans say in natural language, managing dialogue, and generating responses in natural language. In this paper, we survey deep learning based methods for dialogue management, response generation and dialogue evaluation. Specifically, these methods are based on neural network, long short-term memory network, deep reinforcement learning, pre-training and generative adversarial network. We compare these methods and point out the further research directions.

Keywords: Dialogue management, response generation, reinforcement learning, deep learning, evaluation.

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Authors: Kazuo Komatsu, Hitoshi Takata

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In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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Authors: Ghalem Belalem, Yahya Slimani

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Large scale systems such as computational Grid is a distributed computing infrastructure that can provide globally available network resources. The evolution of information processing systems in Data Grid is characterized by a strong decentralization of data in several fields whose objective is to ensure the availability and the reliability of the data in the reason to provide a fault tolerance and scalability, which cannot be possible only with the use of the techniques of replication. Unfortunately the use of these techniques has a height cost, because it is necessary to maintain consistency between the distributed data. Nevertheless, to agree to live with certain imperfections can improve the performance of the system by improving competition. In this paper, we propose a multi-layer protocol combining the pessimistic and optimistic approaches conceived for the data consistency maintenance in large scale systems. Our approach is based on a hierarchical representation model with tree layers, whose objective is with double vocation, because it initially makes it possible to reduce response times compared to completely pessimistic approach and it the second time to improve the quality of service compared to an optimistic approach.

Keywords: Data Grid, replication, consistency, optimistic approach, pessimistic approach.

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Authors: Thang Manh Hoang

Abstract:

Recent research result has shown that two multidelay feedback systems can synchronize each other under different schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating synchronization. There, the driving signal is significantly complex due that it is constituted by multiple nonlinear transformations of delayed state variable. In this paper, a secure communication model is proposed based on synchronization of coupled multidelay feedback systems, in which the plain signal is mixed with a complex signal at the transmitter side and it is precisely retrieved at the receiver side. The effectiveness of the proposed model is demonstrated and verified in the specific example, where the message signal is masked directly by the complex signal and security is examined under the breaking method of power spectrum analysis.

Keywords: chaos synchronization, time-delayed system, chaosbasedsecure communications

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Authors: Woo Young Jung, Min Ho Kwon, Bu Seog Ju

Abstract:

The primary objective of this research is to improve the flexural capacity of FRP strengthened RC Beam structures with Aluminum and Titanium laminates. FRP rupture of flexural strengthened RC beams using FRP plates generally occurs at the interface between FRP plate and the beam. Therefore, in order to prevent brittle rupture and improve the ductility of the system, this research was performed by using Aluminum and Titanium materials between the two different structural systems. The research also aims to provide various strengthening/retrofitting methods for RC beam structures and to conduct a preliminary analysis of the demands on the structural systems. This was achieved by estimation using the experimental data from this research to identify a flexural capacity for the systems. Ultimately, the preliminary analysis of current study showed that the flexural capacity and system demand ductility was significantly improved by the systems inserted with Aluminum and Titanium anchor plates. Further verification of the experimental research is currently on its way to develop a new or reliable design guideline to retrofit/strengthen the concrete-FRP structural system can be evaluated.

Keywords: Reinforced Concrete, FRP Laminate, Flexural Capacity, Ductility.

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Authors: Andrei A. Kolyshkin

Abstract:

In the present paper some recommendations for the use of software package “Mathematica" in a basic numerical analysis course are presented. The methods which are covered in the course include solution of systems of linear equations, nonlinear equations and systems of nonlinear equations, numerical integration, interpolation and solution of ordinary differential equations. A set of individual assignments developed for the course covering all the topics is discussed in detail.

Keywords: Numerical methods, "Mathematica", e-learning.

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Authors: A. Vasan

Abstract:

Particle swarm optimization (PSO) technique is applied to design the water distribution pipeline network. A simulation-optimization model is formulated with the objective of minimizing cost and is applied to a benchmark water distribution system optimization problem. The benchmark problem taken for the application of PSO technique to optimize the pipe size of the water distribution network is New York City water supply system problem. The results from the analysis infer that PSO is a potential alternative optimization technique when compared to other heuristic techniques for optimal sizing of water distribution systems.

Keywords: Water distribution systems, Optimization, Particle swarm optimization, Swarm intelligence, New York water supply system.

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Authors: H. T. Barney, G. C. Low

Abstract:

The design of distributed systems involves dividing the system into partitions (or components) and then allocating these partitions to physical nodes. There have been several techniques proposed for both the partitioning and allocation processes. These existing techniques suffer from a number of limitations including lack of support for replication. Replication is difficult to use effectively but has the potential to greatly improve the performance of a distributed system. This paper presents a new technique technique for allocating objects in order to improve performance in a distributed system that supports replication. The performance of the proposed technique is demonstrated and tested on an example system. The performance of the new technique is compared with the performance of an existing technique in order to demonstrate both the validity and superiority of the new technique when developing a distributed system that can utilise object replication.

Keywords: Allocation, Distributed Systems, Replication.

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Authors: Zach-Amaury Boufoy-Bastick, Lenandlar Singh

Abstract:

Computer-mediated communication technologies which provide for virtual communities have typically evolved in a cross-dichotomous manner, such that technical constructs of the technology have evolved independently from the social environment of the community. The present paper analyses some limitations of current implementations of computer-mediated communication technology that are implied by such a dichotomy, and discusses their inhibiting effects on possible developments of virtual communities. A Socio-Technical Indicator Model is introduced that utilizes integrated feedback to describe, simulate and operationalise increasing representativeness within a variety of structurally and parametrically diverse systems. In illustration, applications of the model are briefly described for financial markets and for eco-systems. A detailed application is then provided to resolve the aforementioned technical limitations of moderation on the evolution of virtual communities. The application parameterises virtual communities to function as self-transforming social-technical systems which are sensitive to emergent and shifting community values as products of on-going communications within the collective.

Keywords: Virtual community, e-democracy, feedback systems, moderation.

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Authors: Federico Valenzuela-Beltran, Sonia E. Ruiz, Alfredo Reyes-Salazar, Juan Bojorquez

Abstract:

A reliability-based methodology which uses structural demand hazard curves to consider the increment of the ductility demands of structures with tilting is proposed. The approach considers the effect of two orthogonal components of the ground motions as well as the influence of soil-structure interaction. The approach involves the calculation of ductility demand hazard curves for symmetric systems and, alternatively, for systems with different degrees of asymmetry. To get this objective, demand hazard curves corresponding to different global ductility demands of the systems are calculated. Next, Uniform Exceedance Rate Spectra (UERS) are developed for a specific mean annual rate of exceedance value. Ratios between UERS corresponding to asymmetric and to symmetric systems located in soft soil of the valley of Mexico are obtained. Results indicate that the ductility demands corresponding to tilted structures may be several times higher than those corresponding to symmetric structures, depending on several factors such as tilting angle and vibration period of structure and soil.

Keywords: Asymmetric yielding, tilted structures, seismic performance, structural reliability

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Authors: Hoda Aslani, Mohammad Moghiman, Mohammad Aslani

Abstract:

Considering the demand to reduce global warming potential and importance of solidification in various applications, there is an increasing interest in energy storage systems to find the efficient phase change materials. Therefore, this paper presents an experimental study and comparison on the potential of titania nanofluids with and without surfactant for cooling energy storage systems. A designed cooling generation device based on compression refrigeration cycle is used to explore nanofluids solidification characteristics. In this work, titania nanoparticles of 0.01, 0.02 and 0.04 wt.% are dispersed in deionized water as base fluid. Measurement of phase change parameters of nanofluids illustrates that the addition of polyvinylpyrrolidone (PVP) as surfactant to titania nanofluids advances the onset nucleation time and leads to lower solidification time. Also, the experimental results show that only adding 0.02 wt.% titania nanoparticles, especially in the case of nanofluids with a surfactant, can evidently reduce the supercooling degree by nearly 70%. Hence, it is concluded that there is a great energy saving potential in the energy storage systems using titania nanofluid with PVP.

Keywords: Cooling energy storage, nanofluid, PVP, solidification, titania.

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Authors: B. Chandra, P. Paul Varghese

Abstract:

Crypto System Identification is one of the challenging tasks in Crypt analysis. The paper discusses the possibility of employing Neural Networks for identification of Cipher Systems from cipher texts. Cascade Correlation Neural Network and Back Propagation Network have been employed for identification of Cipher Systems. Very large collection of cipher texts were generated using a Block Cipher (Enhanced RC6) and a Stream Cipher (SEAL). Promising results were obtained in terms of accuracy using both the Neural Network models but it was observed that the Cascade Correlation Neural Network Model performed better compared to Back Propagation Network.

Keywords: Back Propagation Neural Networks, CascadeCorrelation Neural Network, Crypto systems, Block Cipher, StreamCipher.

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Authors: Mykola S. Shestavin

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A strategy for the creation of a Virtual Interactive Platform (or Networking Platform) to combine the four web-baseness of expert systems on the transfer and diffusion of low-carbon technologies. It used the concept of “Open Innovation” and “Triple Helix” with regard to theories of “Green Growth” and “Carbon Footprint”. Interpreters expert systems operate on the basis of models of the “Predator-Prey” for the process of transfer and diffusion of technologies, taking into account the features caused by the need to mitigate the effects of climate change.

Keywords: Climate Change, Expert Systems, Low-Carbon Technology, Open Innovation, Virtual Interactive Platform.

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Authors: A. Ghodbane, M. Saad, J.-F. Boland, C. Thibeault

Abstract:

Historically, actuators’ redundancy was used to deal with faults occurring suddenly in flight systems. This technique was generally expensive, time consuming and involves increased weight and space in the system. Therefore, nowadays, the on-line fault diagnosis of actuators and accommodation plays a major role in the design of avionic systems. These approaches, known as Fault Tolerant Flight Control systems (FTFCs) are able to adapt to such sudden faults while keeping avionics systems lighter and less expensive. In this paper, a (FTFC) system based on the Geometric Approach and a Reconfigurable Flight Control (RFC) are presented. The Geometric approach is used for cosmic ray fault reconstruction, while Sliding Mode Control (SMC) based on Lyapunov stability theory is designed for the reconfiguration of the controller in order to compensate the fault effect. Matlab®/Simulink® simulations are performed to illustrate the effectiveness and robustness of the proposed flight control system against actuators’ faulty signal caused by cosmic rays. The results demonstrate the successful real-time implementation of the proposed FTFC system on a non-linear 6 DOF aircraft model.

Keywords: Actuators’ faults, Fault detection and diagnosis, Fault tolerant flight control, Sliding mode control, Geometric approach for fault reconstruction, Lyapunov stability.

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Authors: Keiko Shimazu, Yasuhiro Maida, Tetsuya Sugata, Daisuke Tamakoshi, Kenji Makabe, Haruki Suzuki

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In this paper, we report how to acquire serious victims’ locations in the Acute Stage of Large-scale Disasters, in an Emergency Information Network System designed by us. The background of our concept is based on the Great East Japan Earthquake occurred on March 11^th, 2011. Through many experiences of national crises caused by earthquakes and tsunamis, we have established advanced communication systems and advanced disaster medical response systems. However, Japan was devastated by huge tsunamis swept a vast area of Tohoku causing a complete breakdown of all the infrastructures including telecommunications. Therefore, we noticed that we need interdisciplinary collaboration between science of disaster medicine, regional administrative sociology, satellite communication technology and systems engineering experts. Communication of emergency information was limited causing a serious delay in the initial rescue and medical operation. For the emergency rescue and medical operations, the most important thing is to identify the number of casualties, their locations and status and to dispatch doctors and rescue workers from multiple organizations. In the case of the Tohoku earthquake, the dispatching mechanism and/or decision support system did not exist to allocate the appropriate number of doctors and locate disaster victims. Even though the doctors and rescue workers from multiple government organizations have their own dedicated communication system, the systems are not interoperable.

Keywords: Crisis management, disaster mitigation, messing, MGRS, Satellite communication system.

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Authors: A. Aissani, H. Benaoudia

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Stochastic comparison has been an important direction of research in various area. This can be done by the use of the notion of stochastic ordering which gives qualitatitive rather than purely quantitative estimation of the system under study. In this paper we present applications of comparison based uncertainty related to entropy in Reliability analysis, for example to design better systems. These results can be used as a priori information in simulation studies.

Keywords: Uncertainty, Stochastic comparison, Reliability, serie's system, imperfect repair.

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Authors: Kazuyoshi Mori, Keisuke Hashimoto

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In this paper, we consider the two-stage compensator designs of SISO plants. As an investigation of the characteristics of the two-stage compensator designs, which is not well investigated yet, of SISO plants, we implement three dimensional visualization systems of output signals and optimization system for SISO plants by the parametrization of stabilizing controllers based on the two-stage compensator design. The system runs on Mathematica by using “Three Dimensional Surface Plots,” so that the visualization can be interactively manipulated by users. In this paper, we use the discrete-time LTI system model. Even so, our approach is the factorization approach, so that the result can be applied to many linear models.

Keywords: Linear systems, visualization, optimization, two-Stage compensator design, Mathematica.

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Authors: S. J. Hosseini Ghoncheh, M. Paripour

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In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: Arvind Kumar, Rajoo Pandey

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For broadband wireless mobile communication systems the orthogonal frequency division multiplexing (OFDM) is a suitable modulation scheme. The frequency offset between transmitter and receiver local oscillator is main drawback of OFDM systems, which causes intercarrier interference (ICI) in the subcarriers of the OFDM system. This ICI degrades the bit error rate (BER) performance of the system. In this paper an improved self-ICI cancellation scheme is proposed to improve the system performance. The proposed scheme is based on discrete Fourier transform-inverse discrete Fourier transform (DFT-IDFT). The simulation results show that there is satisfactory improvement in the bit error rate (BER) performance of the present scheme.

Keywords: OFDM, Intercarrier Interference, InterferenceCoefficients, DFT based Self-ICI Cancellation.

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Authors: Mohammad Reza Kangavari, Samira Ghandchi, Manak Golpour

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Question answering (QA) aims at retrieving precise information from a large collection of documents. Most of the Question Answering systems composed of three main modules: question processing, document processing and answer processing. Question processing module plays an important role in QA systems to reformulate questions. Moreover answer processing module is an emerging topic in QA systems, where these systems are often required to rank and validate candidate answers. These techniques aiming at finding short and precise answers are often based on the semantic relations and co-occurrence keywords. This paper discussed about a new model for question answering which improved two main modules, question processing and answer processing which both affect on the evaluation of the system operations. There are two important components which are the bases of the question processing. First component is question classification that specifies types of question and answer. Second one is reformulation which converts the user's question into an understandable question by QA system in a specific domain. The objective of an Answer Validation task is thus to judge the correctness of an answer returned by a QA system, according to the text snippet given to support it. For validating answers we apply candidate answer filtering, candidate answer ranking and also it has a final validation section by user voting. Also this paper described new architecture of question and answer processing modules with modeling, implementing and evaluating the system. The system differs from most question answering systems in its answer validation model. This module makes it more suitable to find exact answer. Results show that, from total 50 asked questions, evaluation of the model, show 92% improving the decision of the system.

Keywords: Answer processing, answer validation, classification, question answering, query reformulation.

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Authors: Sandeep Khimta, Parvinder S. Sandhu, Amanpreet Singh Brar

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The traditional software product and process metrics are neither suitable nor sufficient in measuring the complexity of software components, which ultimately is necessary for quality and productivity improvement within organizations adopting CBSE. Researchers have proposed a wide range of complexity metrics for software systems. However, these metrics are not sufficient for components and component-based system and are restricted to the module-oriented systems and object-oriented systems. In this proposed study it is proposed to find the complexity of the JavaBean Software Components as a reflection of its quality and the component can be adopted accordingly to make it more reusable. The proposed metric involves only the design issues of the component and does not consider the packaging and the deployment complexity. In this way, the software components could be kept in certain limit which in turn help in enhancing the quality and productivity.

Keywords: JavaBean Components, Complexity, Metrics, Validation.

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: Meshless spectrally convergent, partial differential equations, extended arithmetic precision, no branching.

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