Search results for: wireless communication systems

Authors: Ragi Poyyara, Vivek V., Ashish Khaparde

Abstract:

The product development process (PDP) in the Technology group plays a very important role in the launch of any product. While a manufacturing process encourages the use of certain measures to reduce health, safety and environmental (HSE) risks on the shop floor, the PDP concentrates on the use of Geometric Dimensioning and Tolerancing (GD&T) to develop a flawless design. Furthermore, PDP distributes and coordinates activities between different departments such as marketing, purchasing, and manufacturing. However, it is seldom realized that PDP makes a significant contribution to developing a product that reduces HSE risks by encouraging the Technology group to use effective GD&T. The GD&T is a precise communication tool that uses a set of symbols, rules, and definitions to mathematically define parts to be manufactured. It is a quality assurance method widely used in the oil and gas sector. Traditionally it is used to ensure the interchangeability of a part without affecting its form, fit, and function. Parts that do not meet these requirements are rejected during quality audits. This paper discusses how the Technology group integrates this quality assurance tool into the PDP and how the tool plays a major role in helping the HSE department in its goal towards eliminating HSE incidents. The PDP involves a thorough risk assessment and establishes a method to address those risks during the design stage. An illustration shows how GD&T helped reduce safety risks by ergonomically improving assembling operations. A brief discussion explains how tolerances provided on a part help prevent finger injury. This tool has equipped Technology to produce fixtures, which are used daily in operations as well as manufacturing. By applying GD&T to create good fits, HSE risks are mitigated for operating personnel. Both customers and service providers benefit from reduced safety risks.

Keywords: HSE, PDP, GD&T, risks.

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Authors: M. Soryani, N. Rafat

Abstract:

Dealing with hundreds of features in character recognition systems is not unusual. This large number of features leads to the increase of computational workload of recognition process. There have been many methods which try to remove unnecessary or redundant features and reduce feature dimensionality. Besides because of the characteristics of Farsi scripts, it-s not possible to apply other languages algorithms to Farsi directly. In this paper some methods for feature subset selection using genetic algorithms are applied on a Farsi optical character recognition (OCR) system. Experimental results show that application of genetic algorithms (GA) to feature subset selection in a Farsi OCR results in lower computational complexity and enhanced recognition rate.

Keywords: Feature Subset Selection, Genetic Algorithms, Optical Character Recognition.

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Authors: M. Ouassaid, A. Nejmi, M. Cherkaoui, M. Maaroufi

Abstract:

The very nonlinear nature of the generator and system behaviour following a severe disturbance precludes the use of classical linear control technique. In this paper, a new approach of nonlinear control is proposed for transient and steady state stability analysis of a synchronous generator. The control law of the generator excitation is derived from the basis of Lyapunov stability criterion. The overall stability of the system is shown using Lyapunov technique. The application of the proposed controller to simulated generator excitation control under a large sudden fault and wide range of operating conditions demonstrates that the new control strategy is superior to conventional automatic voltage regulator (AVR), and show very promising results.

Keywords: Excitation control, Lyapunov technique, non linearcontrol, synchronous generator, transient stability, voltage regulation.

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Authors: Jadwiga Klukow, Anna Ksykiewicz-Dorota

Abstract:

An analysis of the distribution of nurses’ working time constitutes vital information for the management in planning employment. The objective of the study was to analyze the distribution of nurses’ working time in an emergency department. The study was conducted in an emergency department of a teaching hospital in Lublin, in Southeast Poland. The catalogue of activities performed by nurses was compiled by means of continuous observation. Identified activities were classified into four groups: Direct care, indirect care, coordination of work in the department and personal activities. Distribution of nurses’ working time was determined by work sampling observation (Tippett) at random intervals. The research project was approved by the Research Ethics Committee by the Medical University of Lublin (Protocol 0254/113/2010). On average, nurses spent 31% of their working time on direct care, 47% on indirect care, 12% on coordinating work in the department and 10% on personal activities. The most frequently performed direct care tasks were diagnostic activities – 29.23% and treatment-related activities – 27.69%. The study has provided information on the complexity of performed activities and utilization of nurses’ working time. Enhancing the effectiveness of nursing actions requires working out a strategy for improved management of the time nurses spent at work. Increasing the involvement of auxiliary staff and optimizing communication processes within the team may lead to reduction of the time devoted to indirect care for the benefit of direct care.

Keywords: Emergency nurses, nursing care, workload, work sampling.

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Authors: Ming-Ta Yang, Jin-Lung Guan, Jhy-Cherng Gu

Abstract:

The purpose of this paper is to solve the problem of protecting aerial lines from high impedance faults (HIFs) in distribution systems. This investigation successfully applies 3I0 zero sequence current to solve HIF problems. The feature extraction system based on discrete wavelet transform (DWT) and the feature identification technique found on statistical confidence are then applied to discriminate effectively between the HIFs and the switch operations. Based on continuous wavelet transform (CWT) pattern recognition of HIFs is proposed, also. Staged fault testing results demonstrate that the proposed wavelet based algorithm is feasible performance well.

Keywords: Continuous wavelet transform, discrete wavelet transform, high impedance faults, statistical confidence.

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA), is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: Balanced truncation, Clustering, Dominant pole, Hankel norm, Model reduction.

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Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

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The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Nikunj Agarwal, M. P. Sebastian

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Cloud computing can reduce the start-up expenses of implementing EHR (Electronic Health Records). However, many of the healthcare institutions are yet to implement cloud computing due to the associated privacy and security issues. In this paper, we analyze the challenges and opportunities of implementing cloud computing in healthcare. We also analyze data of over 5000 US hospitals that use Telemedicine applications. This analysis helps to understand the importance of smart phones over the desktop systems in different departments of the healthcare institutions. The wide usage of smartphones and cloud computing allows ubiquitous and affordable access to the health data by authorized persons, including patients and doctors. Cloud computing will prove to be beneficial to a majority of the departments in healthcare. Through this analysis, we attempt to understand the different healthcare departments that may benefit significantly from the implementation of cloud computing.

Keywords: Cloud computing, smart devices, healthcare, telemedicine.

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Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Based on the component approach, three kinds of dynamic load models, including a single –motor model, a two-motor model and composite load model have been developed for the stability studies of Khuzestan power system. The study results are presented in this paper. Voltage instability is a dynamic phenomenon and therefore requires dynamic representation of the power system components. Industrial loads contain a large fraction of induction machines. Several models of different complexity are available for the description investigations. This study evaluates the dynamic performances of several dynamic load models in combination with the dynamics of a load changing transformer. Case study is steel industrial substation in Khuzestan power systems.

Keywords: Dynamic load, modeling, Voltage Stability.

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Authors: Chin-Cheh Yi, Pei-Wen Liao, Chin-Feng Huang, I-Hui Hwang

Abstract:

With the proliferation of mobile computing technology, mobile learning (m-learning) will play a vital role in the rapidly growing electronic learning market. However, the acceptance of m-learning by individuals is critical to the successful implementation of m-learning systems. Thus, there is a need to research the factors that affect users- intention to use m-learning. Based on an updated information system (IS) success model, data collected from 350 respondents in Taiwan were tested against the research model using the structural equation modeling approach. The data collected by questionnaire were analyzed to check the validity of constructs. Then hypotheses describing the relationships between the identified constructs and users- satisfaction were formulated and tested.

Keywords: m-learning, information system success, users' satisfaction, perceived value.

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Authors: F. Pagliara, F. Mauriello

Abstract:

The objective of this paper is to investigate the relationship between the increase of accessibility brought by high speed rail (HSR) systems and the tourism market in Italy. The impacts of HSR projects on tourism can be quantified in different ways. In this manuscript, an empirical analysis has been carried out with the aid of a dataset containing information both on tourism and transport for 99 Italian provinces during the 2006-2016 period. Panel data regression models have been considered, since they allow modelling a wide variety of correlation patterns. Results show that HSR has an impact on the choice of a given destination for Italian tourists while the presence of a second level hub mainly affects foreign tourists. Attraction variables are also significant for both categories and the variables concerning security, such as number of crimes registered in a given destination, have a negative impact on the choice of a destination.

Keywords: Tourists, overnights, high speed rail, attractions, security.

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Authors: Yu-Cheng Lin

Abstract:

Construction project control attempts to obtain real-time information and effectively enhance dynamic control and management via information sharing and analysis among project participants to eliminate construction conflicts and project delays. However, survey results for Taiwan indicate that construction commercial project management software is not widely accepted for subcontractors and suppliers. To solve the project communications problems among participants, this study presents a novel system called the Construction Dynamic Teams Communication Management (Con-DTCM) system for small-to-medium sized subcontractors and suppliers in Taiwanese Construction industry, and demonstrates that the Con-DTCM system responds to the most recent project information efficiently and enhances management of project teams (general contractor, suppliers and subcontractors) through web-based environment. Web-based technology effectively enhances information sharing during construction project management, and generates cost savings via the Internet. The main unique characteristic of the proposed Con-DTCM system is extremely user friendly and easily design compared with current commercial project management applications. The Con-DTCM system is applied to a case study of construction of a building project in Taiwan to confirm the proposed methodology and demonstrate the effectiveness of information sharing during the construction phase. The advantages of the Con-DTCM system are in improving project control and management efficiency for general contractors, and in providing dynamic project tracking and management, which enables subcontractors and suppliers to acquire the most recent project-related information. Furthermore, this study presents and implements a generic system architecture.

Keywords: Construction project management, Information System, Portal, Web, Small-to-medium enterprises.

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Authors: Nasıf Ekiz, Tara Salih, Sibel Küçüköner, Kemal Fidanboylu

Abstract:

Continuation of an active call is one of the most important quality measurements in the cellular systems. Handoff process enables a cellular system to provide such a facility by transferring an active call from one cell to another. Different approaches are proposed and applied in order to achieve better handoff service. The principal parameters used to evaluate handoff techniques are: forced termination probability and call blocking probability. The mechanisms such as guard channels and queuing handoff calls decrease the forced termination probability while increasing the call blocking probability. In this paper we present an overview about the issues related to handoff initiation and decision and discuss about different types of handoff techniques available in the literature.

Keywords: Handoff, Forced Termination Probability, Blocking probability, Handoff Initiation, Handoff Decision, Handoff Prioritization Schemes.

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Authors: Hock Chuan, Lim

Abstract:

This paper presents an approach for identifying interactive effects using Network Science (NS) supported by Social Network Analysis (SNA) techniques. Based on general observations that learning processes and behaviors are shaped by the social relationships and influenced by learning environment, the central idea was to understand both the human and non-human interactive effects for a blended learning mode of delivery of computer science modules. Important findings include (a) the importance of non-human nodes to influence the centrality and transfer; (b) the degree of non-human and human connectivity impacts learning. This project reveals that the NS pattern and connectivity as measured by node relationships offer alternative approach for hypothesis generation and design of qualitative data collection. An iterative process further reinforces the analysis, whereas the experimental simulation option itself is an interesting alternative option, a hybrid combination of both experimental simulation and qualitative data collection presents itself as a promising and viable means to study complex scenario such as blended learning delivery mode. The primary value of this paper lies in the design of the approach for studying interactive effects of human (social nodes) and non-human (learning/study environment, Information and Communication Technologies (ICT) infrastructures nodes) components. In conclusion, this project adds to the understanding and the use of SNA to model and study interactive effects in blended social learning.

Keywords: Blended learning, network science, social learning, social network analysis, study environment.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

We model the process of a data center as a multi- objective problem of mapping independent tasks onto a set of data center machines that simultaneously minimizes the energy consump¬tion and response time (makespan) subject to the constraints of deadlines and architectural requirements. A simple technique based on multi-objective goal programming is proposed that guarantees Pareto optimal solution with excellence in convergence process. The proposed technique also is compared with other traditional approach. The simulation results show that the proposed technique achieves superior performance compared to the min-min heuristics, and com¬petitive performance relative to the optimal solution implemented in UNDO for small-scale problems.

Keywords: Energy-efficient computing, distributed systems, multi-objective optimization.

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Authors: W. Kiamouche, M. Benslama

Abstract:

This paper presents an alternative strategy of queuing handover called Pseudo Last Useful Instant PLUI scheme for Low Earth Orbit Mobile Satellite Systems LEO MSSs. The PLUI scheme uses the same approach as the Last Useful Instant LUI scheme previously proposed in literature, with less complex implementation. Simulation tests were carried out using Dynamic Channel Allocation DCA in order to evaluate the performance of this scheme and also an analytical approach has been presented to allow the performance evaluation of Fixed Channel Allocation FCA, with different handover queuing disciplines. The results show that performances achieved by the proposed strategy are close to those achieved using the LUI scheme.

Keywords: LEO mobile satellite networks, LUI and FIFOschemes, queuing handover.

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Authors: Yong-Je Choi, Moo-Seop Kim, Hang-Rok Lee, Ho-Won Kim

Abstract:

Polynomial bases and normal bases are both used for elliptic curve cryptosystems, but field arithmetic operations such as multiplication, inversion and doubling for each basis are implemented by different methods. In general, it is said that normal bases, especially optimal normal bases (ONB) which are special cases on normal bases, are efficient for the implementation in hardware in comparison with polynomial bases. However there seems to be more examined by implementing and analyzing these systems under similar condition. In this paper, we designed field arithmetic operators for each basis over GF(2233), which field has a polynomial basis recommended by SEC2 and a type-II ONB both, and analyzed these implementation results. And, in addition, we predicted the efficiency of two elliptic curve cryptosystems using these field arithmetic operators.

Keywords: Elliptic Curve Cryptosystem, Crypto Algorithm, Polynomial Basis, Optimal Normal Basis, Security.

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Authors: Khaled M. El Naggar

Abstract:

This paper introduces a digital method for fault section identification in transmission lines. The method uses digital set of the measured short circuit current to locate faults in electrical power systems. The digitized current is used to construct a set of overdetermined system of equations. The problem is then constructed and solved using the proposed digital optimization technique to find the fault distance. The proposed optimization methodology is an application of simulated annealing optimization technique. The method is tested using practical case study to evaluate the proposed method. The accurate results obtained show that the algorithm can be used as a powerful tool in the area of power system protection.

Keywords: Optimization, estimation, faults, measurement, high voltage, simulated annealing.

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Authors: Farag Azzedin, Ali Rizvi

Abstract:

In any trust model, the two information sources that a peer relies on to predict trustworthiness of another peer are direct experience as well as reputation. These two vital components evolve over time. Trust evolution is an important issue, where the objective is to observe a sequence of past values of a trust parameter and determine the future estimates. Unfortunately, trust evolution algorithms received little attention and the proposed algorithms in the literature do not comply with the conditions and the nature of trust. This paper contributes to this important problem in the following ways: (a) presents an algorithm that manages and models trust evolution in a P2P environment, (b) devises new mechanisms for effectively maintaining trust values based on the conditions that influence trust evolution , and (c) introduces a new methodology for incorporating trust-nurture incentives into the trust evolution algorithm. Simulation experiments are carried out to evaluate our trust evolution algorithm.

Keywords: P2P, Trust, Reputation, Incentives.

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Authors: Ivana Mokrá

Abstract:

The article deals with modelling of the fire pragmatism in the area of military management and its experimental verification. Potential approaches are based on the synergy of mathematical and theoretical ideas, operational and tactical requirements and the military decision-making process. This issue has taken on importance in recent times, particularly with the increasing trend of digitized battlefield, the development of C4ISR systems and intention to streamline the command and control process at the lowest levels of command. From fundamental and philosophical point of view, these new approaches seek to significantly upgrade and enhance the decision-making process of the tactical commanders.

Keywords: Military management, decision-making process, strike modeling, experimental evaluation, pragmatism, tactical strike modeling

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Authors: Y. Yudin, T. Krasikova, Y. Dorozhko, N. Currle-Linde

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Nowadays, HPC, Grid and Cloud systems are evolving very rapidly. However, the development of infrastructure solutions related to HPC is lagging behind. While the existing infrastructure is sufficient for simple cases, many computational problems have more complex requirements.Such computational experiments use different resources simultaneously to start a large number of computational jobs.These resources are heterogeneous. They have different purposes, architectures, performance and used software.Users need a convenient tool that allows to describe and to run complex computational experiments under conditions of HPC environment. This paper introduces a modularworkflow system called SEGL which makes it possible to run complex computational experiments under conditions of a real HPC organization. The system can be used in a great number of organizations, which provide HPC power. Significant requirements to this system are high efficiency and interoperability with the existing HPC infrastructure of the organization without any changes.

Keywords: HPC, Molecular Dynamics, Workflow Languages, Workflow Management.

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Authors: Sezen Yildirim, Tahir Çetin Akinci, Serhat Seker, Nazmi Ekren

Abstract:

Ferroresonance is an electrical phenomenon in nonlinear character, which frequently occurs in power system due to transmission line faults and single or more-phase switching on the lines as well as usage of the saturable transformers. In this study, the ferroresonance phenomena are investigated under the modeling of the West Anatolian Electric Power Network of 380 kV in Turkey. The ferroresonance event is observed as a result of removing the loads at the end of the lines. In this sense, two different cases are considered. At first, the switching is applied at 2nd second and the ferroresonance affects are observed between 2nd and 4th seconds in the voltage variations of the phase-R. Hence the ferroresonance and nonferroresonance parts of the overall data are compared with each others using the Fourier transform techniques to show the ferroresonance affects.

Keywords: Ferroresonance, West Anatolian Electric Power System, Power System Modeling, Switching, Spectral Analysis.

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Authors: Abbas Moshref Razavi, Rodina Ahmad

Abstract:

Organizations are supposed to be systems and consequently require defining the notion of equilibrium within. However, organizations comprise people and unavoidably entail their irrational aspects. Then, the question is what is the organizational equilibrium and equilibrating mechanisms considering these aspects. Hence, some arguments are provided here to conceptualize human unconsciousness, irrationalities and consequent uncertainties within organizations in the form of a system of psychic dynamism. The assumption is this dynamism maintains the psychic balance of the organization through a psychodynamic point of view. The resultant conceptualization expected to promote the understanding of such aspects in different organizational settings by hypothesizing organizational equilibration from this perspective. As a result, the main expectation is, if it is known that how the organization equilibrates in this sense, we can explain and deal with such irrationalities and unconsciousness by rational and, of course conscious, planning and accomplishing.

Keywords: Equilibration, General System Theory, Organization, Psychodynamic.

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Authors: Kleanthis Prekas, Maria Rangoussi, Savvas Vassiliadis, George Prekas

Abstract:

Intelligent tutoring systems constitute an evolution of computer-aided educational software. We present here the modules of an intelligent tutoring system for Automatic Control, developed in our department. Through the software application developed,students can perform complete automatic control laboratory experiments, either over the departmental local area network or over the Internet. Monitoring of access to the system (local as well as international), along with student performance statistics, has yielded strongly encouraging results (as of fall 2004), despite the advanced technical content of the presented paradigm, thus showing the potential of the system developed for education and for training.

Keywords: Automatic control, tutoring system, Internet access, laboratory experiments.

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Authors: Blesson Varghese, Gerard T. McKee

Abstract:

The work reported in this paper is motivated by the fact that there is a need to apply autonomic computing concepts to parallel computing systems. Advancing on prior work based on intelligent cores [36], a swarm-array computing approach, this paper focuses on 'Intelligent agents' another swarm-array computing approach in which the task to be executed on a parallel computing core is considered as a swarm of autonomous agents. A task is carried to a computing core by carrier agents and is seamlessly transferred between cores in the event of a predicted failure, thereby achieving self-ware objectives of autonomic computing. The feasibility of the proposed swarm-array computing approach is validated on a multi-agent simulator.

Keywords: Autonomic computing, intelligent agents, swarm-array computing.

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Authors: Dezhi Li, Peng Cui, Bo Zhang, Tengyuan Chang

Abstract:

In order to solve the housing problem for the low-income families, the construction of affordable housing is booming in China. However, due to various reasons, the service facilities and systems in the indemnificatory residential community meet many problems. This article established a Satisfaction Evaluation System of the Fundamental Public Services for Large-scale Indemnificatory Residential Community based on the national standards and local criteria and developed evaluation methods and processes. At last, in the case of Huagang project in Nanjing, the satisfaction of basic public service is calculated according to a survey of local residents.

Keywords: Indemnificatory residential community, public services, satisfaction evaluation, structural equation modeling.

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Authors: Omaima N. Ahmad AL-Allaf

Abstract:

Over communication networks, images can be easily copied and distributed in an illegal way. The copyright protection for authors and owners is necessary. Therefore, the digital watermarking techniques play an important role as a valid solution for authority problems. Digital image watermarking techniques are used to hide watermarks into images to achieve copyright protection and prevent its illegal copy. Watermarks need to be robust to attacks and maintain data quality. Therefore, we discussed in this paper two approaches for image watermarking, first is based on Particle Swarm Optimization (PSO) and the second approach is based on Genetic Algorithm (GA). Discrete wavelet transformation (DWT) is used with the two approaches separately for embedding process to cover image transformation. Each of PSO and GA is based on co-relation coefficient to detect the high energy coefficient watermark bit in the original image and then hide the watermark in original image. Many experiments were conducted for the two approaches with different values of PSO and GA parameters. From experiments, PSO approach got better results with PSNR equal 53, MSE equal 0.0039. Whereas GA approach got PSNR equal 50.5 and MSE equal 0.0048 when using population size equal to 100, number of iterations equal to 150 and 3×3 block. According to the results, we can note that small block size can affect the quality of image watermarking based PSO/GA because small block size can increase the search area of the watermarking image. Better PSO results were obtained when using swarm size equal to 100.

Keywords: Image watermarking, genetic algorithm, particle swarm optimization, discrete wavelet transform.

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Authors: F. Javier Benitez, Carolina Garcia, Juan Luis Acero, Francisco J. Real

Abstract:

Four phenylurea herbicides (isoproturon, chlortoluron, diuron and linuron) were dissolved in different water matrices in order to study their chemical degradation by using UV radiation, ozone and some advanced oxidation processes (UV/H2O2, O3/H2O2, Fenton reagent and the photo- Fenton system). The waters used were: ultra-pure water, a commercial mineral water, a groundwater and a surface water taken from a reservoir. Elimination levels were established for each herbicide and for several global quality parameters, and a kinetic study was performed in order to determine basic kinetic parameters of each reaction between the target phenylureas and these oxidizing systems.

Keywords: Phenylurea herbicides, UV radiation; Ozone, Fenton reagent, Hydroxyl radicals, Rate constants, Quantum yields

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Authors: Properties, Approximation Distribution Reductions in Multigranulation Rough Set Model

Abstract:

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

Keywords: Incomplete information system, maximal compatible class, multi-granulation rough set model, reduction.

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