Search results for: Integral Max Flow Problem

Authors: Geeta Sikka, Arvinder Kaur Takkar, Moin Uddin

Abstract:

Missing data is a persistent problem in almost all areas of empirical research. The missing data must be treated very carefully, as data plays a fundamental role in every analysis. Improper treatment can distort the analysis or generate biased results. In this paper, we compare and contrast various imputation techniques on missing data sets and make an empirical evaluation of these methods so as to construct quality software models. Our empirical study is based on NASA-s two public dataset. KC4 and KC1. The actual data sets of 125 cases and 2107 cases respectively, without any missing values were considered. The data set is used to create Missing at Random (MAR) data Listwise Deletion(LD), Mean Substitution(MS), Interpolation, Regression with an error term and Expectation-Maximization (EM) approaches were used to compare the effects of the various techniques.

Keywords: Missing data, Imputation, Missing Data Techniques.

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Authors: Lillian Gungat, Meor Othman Hamzah, Mohd Rosli Mohd Hasan, Jan Valentin

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Utilization of a high percentage of reclaimed asphalt pavement (RAP) requires higher production temperatures and consumes more energy. High production temperature expedites the aging of bitumen in RAP, which could affect the mixture performance. Warm mix asphalt (WMA) additive enables reduced production temperatures as a result of viscosity reduction. This paper evaluates the integration of a high percentage of RAP with a WMA additive known as RH-WMA. The optimum dosage of RH-WMA was determined from basic properties tests. A total of 0%, 30% and 50% RAP contents from two roads sources were modified with RH-WMA. The modified RAP bitumen were examined for viscosity, stiffness, rutting resistance and greenhouse gas emissions. The addition of RH-WMA improved the flow of bitumen by reducing the viscosity, and thus, decreased the construction temperature. The stiffness of the RAP modified bitumen reduced with the incorporation of RH-WMA. The positive improvement in rutting resistance was observed on bitumen with the addition of RAP and RH-WMA in comparison with control. It was estimated that the addition of RH-WMA could potentially reduce fuel usage and GHG emissions by 22 %. Hence, the synergy of RAP and WMA technology can be an alternative in green road construction.

Keywords: Reclaimed asphalt pavement, WMA additive, viscosity, stiffness, emissions.

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Authors: Ashraf Anwar

Abstract:

In this work, I present a review on Sparse Distributed Memory for Small Cues (SDMSCue), a variant of Sparse Distributed Memory (SDM) that is capable of handling small cues. I then conduct and show some cognitive experiments on SDMSCue to test its cognitive soundness compared to SDM. Small cues refer to input cues that are presented to memory for reading associations; but have many missing parts or fields from them. The original SDM failed to handle such a problem. SDMSCue handles and overcomes this pitfall. The main idea in SDMSCue; is the repeated projection of the semantic space on smaller subspaces; that are selected based on the input cue length and pattern. This process allows for Read/Write operations using an input cue that is missing a large portion. SDMSCue is augmented with the use of genetic algorithms for memory allocation and initialization. I claim that SDM functionality is a subset of SDMSCue functionality.

Keywords: Artificial intelligence, recall, recognition, SDM, SDMSCue.

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Authors: Manoj Kumar Dutta

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Wavelength Division Multiplexing (WDM) technology is the most promising technology for the proper utilization of huge raw bandwidth provided by an optical fiber. One of the key problems in implementing the all-optical WDM network is the packet contention. This problem can be solved by several different techniques. In time domain approach the packet contention can be reduced by incorporating Fiber Delay Lines (FDLs) as optical buffer in the switch architecture. Different types of buffering architectures are reported in literatures. In the present paper a comparative performance analysis of three most popular FDL architectures are presented in order to obtain the best contention resolution performance. The analysis is further extended to consider the effect of different fiber non-linearities on the network performance.

Keywords: WDM network, contention resolution, optical buffering, non-linearity, throughput.

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Authors: Tawiwat V., Phermsak S., Noppasit C.

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This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.

Keywords: Under actuator, Dynamic optimal control, Minimumjerk, Minimum energy.

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Authors: Nihan Cinar

Abstract:

Location selection is one of the most important decision making process which requires to consider several criteria based on the mission and the strategy. This study-s object is to provide a decision support model in order to help the bank selecting the most appropriate location for a bank-s branch considering a case study in Turkey. The object of the bank is to select the most appropriate city for opening a branch among six alternatives in the South-Eastern of Turkey. The model in this study was consisted of five main criteria which are Demographic, Socio-Economic, Sectoral Employment, Banking and Trade Potential and twenty one subcriteria which represent the bank-s mission and strategy. Because of the multi-criteria structure of the problem and the fuzziness in the comparisons of the criteria, fuzzy AHP is used and for the ranking of the alternatives, TOPSIS method is used.

Keywords: MCDM, bank branch location, fuzzy AHP, TOPSIS.

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Authors: X. Z. Gao, S. J. Ovaska, X. Wang

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Prediction of sinusoidal signals with time-varying frequencies has been an important research topic in power electronics systems. To solve this problem, we propose a new fuzzy predictive filtering scheme, which is based on a Finite Impulse Response (FIR) filter bank. Fuzzy logic is introduced here to provide appropriate interpolation of individual filter outputs. Therefore, instead of regular 'hard' switching, our method has the advantageous 'soft' switching among different filters. Simulation comparisons between the fuzzy predictive filtering and conventional filter bank-based approach are made to demonstrate that the new scheme can achieve an enhanced prediction performance for slowly changing sinusoidal input signals.

Keywords: Predictive filtering, fuzzy logic, sinusoidal signals, time-varying frequencies.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

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This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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Authors: Patsaraporn Somboonsak, Mud-Armeen Munlin

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The P-Bigram method is a string comparison methods base on an internal two characters-based similarity measure. The edit distance between two strings is the minimal number of elementary editing operations required to transform one string into the other. The elementary editing operations include deletion, insertion, substitution two characters. In this paper, we address the P-Bigram method to sole the similarity problem in DNA sequence. This method provided an efficient algorithm that locates all minimum operation in a string. We have been implemented algorithm and found that our program calculated that smaller distance than one string. We develop PBigram edit distance and show that edit distance or the similarity and implementation using dynamic programming. The performance of the proposed approach is evaluated using number edit and percentage similarity measures.

Keywords: Edit distance, String Matching, String Similarity

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Authors: Mohammad Syuhaimi Ab-Rahman, Boonchuan Ng, Kasmiran Jumari

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This paper presented a new approach for centralized monitoring and self-protected against fiber fault in fiber-to-the-home (FTTH) access network by using Smart Access Network Testing, Analyzing and Database (SANTAD). SANTAD will be installed with optical line terminal (OLT) at central office (CO) for in-service transmission surveillance and fiber fault localization within FTTH with point-to-multipoint (P2MP) configuration downwardly from CO towards customer residential locations based on the graphical user interface (GUI) processing capabilities of MATLAB software. SANTAD is able to detect any fiber fault as well as identify the failure location in the network system. SANTAD enable the status of each optical network unit (ONU) connected line is displayed onto one screen with capability to configure the attenuation and detect the failure simultaneously. The analysis results and information will be delivered to the field engineer for promptly actions, meanwhile the failure line will be diverted to protection line to ensure the traffic flow continuously. This approach has a bright prospect to improve the survivability and reliability as well as increase the efficiency and monitoring capabilities in FTTH.

Keywords: Fiber fault, FTTH, SANTAD, transmission surveillance, MATLAB.

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Authors: Savita K.S, Hazwani H., Kalid K. S.

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This paper presents a narrative management system for organizations to capture organization's tacit knowledge through stories. The intention of capturing tacit knowledge is to address the problem that comes with the mobility of workforce in organisation. Storytelling in knowledge management context is seen as a powerful management tool to communicate tacit knowledge in organization. This narrative management system is developed firstly to enable uploading of many types of knowledge sharing stories, from general to work related-specific stories and secondly, each video has comment functionality where knowledge users can post comments to other knowledge users. The narrative management system allows the stories to browse, search and view by the users. In the system, stories are stored in a video repository. Stories that were produced from this framework will improve learning, knowledge transfer facilitation and tacit knowledge quality in an organization.

Keywords: Knowledge Management, Storytelling, Stories, Tacit Knowledge

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Authors: Mohammed A. Elhaj, Jamal S. Yassin

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This paper presents the exergy analysis of a desalination unit using humidification-dehumidification process. Here, this unit is considered as a thermal system with three main components, which are the heating unit by using a solar collector, the evaporator or the humidifier, and the condenser or the dehumidifier. In these components the exergy is a measure of the quality or grade of energy and it can be destroyed in them. According to the second law of thermodynamics this destroyed part is due to irreversibilities which must be determined to obtain the exergetic efficiency of the system. In the current paper a computer program has been developed using visual basic to determine the exergy destruction and the exergetic efficiencies of the components of the desalination unit at variable operation conditions such as feed water temperature, outlet air temperature, air to feed water mass ratio and salinity, in addition to cooling water mass flow rate and inlet temperature, as well as quantity of solar irradiance. The results obtained indicate that the exergy efficiency of the humidifier increases by increasing the mass ratio and decreasing the outlet air temperature. In the other hand the exergy efficiency of the condenser increases with the increase of this ratio and also with the increase of the outlet air temperature.

Keywords: Exergy analysis, desalination, solar, humidifier, condenser.

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Authors: Kaveh Shahi, Helmi Z. M. Shafri, Ebrahim Taherzadeh

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In remote sensing, shadow causes problems in many applications such as change detection and classification. It is caused by objects which are elevated, thus can directly affect the accuracy of information. For these reasons, it is very important to detect shadows particularly in urban high spatial resolution imagery which created a significant problem. This paper focuses on automatic shadow detection based on a new spectral index for multispectral imagery known as Shadow Detection Index (SDI). The new spectral index was tested on different areas of WorldView-2 images and the results demonstrated that the new spectral index has a massive potential to extract shadows with accuracy of 94% effectively and automatically. Furthermore, the new shadow detection index improved road extraction from 82% to 93%.

Keywords: Spectral index, shadow detection, remote sensing images, WorldView-2.

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Authors: Nadjah Chergui, Narhimene Boustia

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Intrusion Detection Systems are an essential tool for network security infrastructure. However, IDSs have a serious problem which is the generating of massive number of alerts, most of them are false positive ones which can hide true alerts and make the analyst confused to analyze the right alerts for report the true attacks. The purpose behind this paper is to present a formalism model to perform correlation engine by the reduction of false positive alerts basing on vulnerability contextual information. For that, we propose a formalism model based on non-monotonic JClassicδє description logic augmented with a default (δ) and an exception (є) operator that allows a dynamic inference according to contextual information.

Keywords: Context, exception, default, IDS, Non-monotonic Description Logic JClassicδє, vulnerability.

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Authors: Eakong Atiptamvaree, Twittie Senivongse

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Process-oriented software development is a new software development paradigm in which software design is modeled by a business process which is in turn translated into a process execution language for execution. The building blocks of this paradigm are software units that are composed together to work according to the flow of the business process. This new paradigm still exhibits the characteristic of the applications built with the traditional software component technology. This paper discusses an approach to apply a traditional technique for software component fabrication to the design of process-oriented software units, called process components. These process components result from decomposing a business process of a particular application domain into subprocesses, and these process components can be reused to design the business processes of other application domains. The decomposition considers five managerial goals, namely cost effectiveness, ease of assembly, customization, reusability, and maintainability. The paper presents how to design or decompose process components from a business process model and measure some technical features of the design that would affect the managerial goals. A comparison between the measurement values from different designs can tell which process component design is more appropriate for the managerial goals that have been set. The proposed approach can be applied in Web Services environment which accommodates process-oriented software development.

Keywords: Business Process Model, Managerial Goals, ProcessComponent.

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Authors: Sheng Fu, Yinbo Gao, Hao Lin

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In the current mine air compressors monitoring system, there are some difficulties in the installation and maintenance because of the wired connection. To solve the problem, this paper introduces a new air compressors monitoring system based on ZigBee in which the monitoring parameters are transmitted wirelessly. The collecting devices are designed to form a cluster network to collect vibration, temperature, and pressure of air cylinders and other parameters. All these devices are battery-powered. Besides, the monitoring software in PC is developed using MFC. Experiments show that the designed wireless sensor network works well in the site environmental condition and the system is very convenient to be installed since the wireless connection. This monitoring system will have a wide application prospect in the upgrade of the old monitoring system of the air compressors.

Keywords: Condition monitoring, wireless sensor network, air compressor, ZigBee, data collecting

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Authors: Suresh S. Salankar, Balasaheb M. Patre

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Research into the problem of classification of sonar signals has been taken up as a challenging task for the neural networks. This paper investigates the design of an optimal classifier using a Multi layer Perceptron Neural Network (MLP NN) and Support Vector Machines (SVM). Results obtained using sonar data sets suggest that SVM classifier perform well in comparison with well-known MLP NN classifier. An average classification accuracy of 91.974% is achieved with SVM classifier and 90.3609% with MLP NN classifier, on the test instances. The area under the Receiver Operating Characteristics (ROC) curve for the proposed SVM classifier on test data set is found as 0.981183, which is very close to unity and this clearly confirms the excellent quality of the proposed classifier. The SVM classifier employed in this paper is implemented using kernel Adatron algorithm is seen to be robust and relatively insensitive to the parameter initialization in comparison to MLP NN.

Keywords: Classification, MLP NN, backpropagation algorithm, SVM, Receiver Operating Characteristics.

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Authors: Toshinori Nawata

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In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input using weighted gradient optimization automatic choosing functions. Constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Hee-Choul Kwon, Heeyong Kwon

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Image rotation is one of main pre-processing steps for image processing or image pattern recognition. It is implemented with a rotation matrix multiplication. It requires a lot of floating point arithmetic operations and trigonometric calculations, so it takes a long time to execute. Therefore, there has been a need for a high speed image rotation algorithm without two major time-consuming operations. However, the rotated image has a drawback, i.e. distortions. We solved the problem using an augmented two-step shear transform. We compare the presented algorithm with the conventional rotation with images of various sizes. Experimental results show that the presented algorithm is superior to the conventional rotation one.

Keywords: High speed rotation operation, image rotation, transform matrix, image processing, pattern recognition.

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Authors: Tu Kun, Gu Nai-jie, Bi Kun, Liu Gang, Dong Wan-li

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As a structure for processing string problem, suffix array is certainly widely-known and extensively-studied. But if the string access pattern follows the “90/10" rule, suffix array can not take advantage of the fact that we often find something that we have just found. Although the splay tree is an efficient data structure for small documents when the access pattern follows the “90/10" rule, it requires many structures and an excessive amount of pointer manipulations for efficiently processing and searching large documents. In this paper, we propose a new and conceptually powerful data structure, called splay suffix arrays (SSA), for string search. This data structure combines the features of splay tree and suffix arrays into a new approach which is suitable to implementation on both conventional and clustered computers.

Keywords: suffix arrays, splay tree, string search, distributedalgorithm

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Authors: Yang Weiping, Zhang Zhilong, Zhang Yan, Chen Zengping

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Infrared focal plane arrays (IRFPA) sensors, due to their high sensitivity, high frame frequency and simple structure, have become the most prominently used detectors in military applications. However, they suffer from a common problem called the fixed pattern noise (FPN), which severely degrades image quality and limits the infrared imaging applications. Therefore, it is necessary to perform non-uniformity correction (NUC) on IR image. The algorithms of non-uniformity correction are classified into two main categories, the calibration-based and scene-based algorithms. There exist some shortcomings in both algorithms, hence a novel non-uniformity correction algorithm based on non-linear fit is proposed, which combines the advantages of the two algorithms. Experimental results show that the proposed algorithm acquires a good effect of NUC with a lower non-uniformity ratio.

Keywords: Non-uniformity correction, non-linear fit, two-point correction, temporal Kalman filter.

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Authors: Tao Quang Bang, Insu Jeon

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Most CT reconstruction system x-ray computed tomography (CT) is a well established visualization technique in medicine and nondestructive testing. However, since CT scanning requires sampling of radiographic projections from different viewing angles, common CT systems with mechanically moving parts are too slow for dynamic imaging, for instance of multiphase flows or live animals. A large number of X-ray projections are needed to reconstruct CT images, so the collection and calculation of the projection data consume too much time and harmful for patient. For the purpose of solving the problem, in this study, we proposed a method for tomographic reconstruction of a sample from a limited number of x-ray projections by using linear interpolation method. In simulation, we presented reconstruction from an experimental x-ray CT scan of a Aluminum phantom that follows to two steps: X-ray projections will be interpolated using linear interpolation method and using it for CT reconstruction based upon Ordered Subsets Expectation Maximization (OSEM) method.

Keywords: CT reconstruction, X-ray projections, Interpolation technique, OSEM

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

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In this paper, an analytical approach for free vibration analysis of rectangular and circular membranes is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for rectangular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of membranes. Subsequently, the eigenvalue problem for free vibration of membrane is formulated and the equation of membrane natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Rectangular and circular membranes, propagation matrix, reflection matrix, vibration analysis.

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Authors: Rafiziana M. Kasmani, Gordon E. Andrews, Herodotos N. Phylaktou, Norazana Ibrahim, Roshafima R. Ali

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An experiment of vented gas explosions involving two different cylinder vessel volumes (0.2 and 0.0065 m3) was reported, with equivalence ratio (Φ) ranged from 0.3 to 1.6. Both vessels were closed at the rear end and fitted at the other side with a circular orifice plate that gives a constant vent coefficient (K =Av/V2/3) of 16.4. It was shown that end ignition gives higher overpressures than central ignition, even though most of the published work on venting uses central ignition. For propane and ethylene, it is found that rich mixtures gave the highest overpressures and these mixtures are not considered in current vent design guidance; which the guideline is based on mixtures giving the maximum flame temperature. A strong influence of the vessel volume at constant K was found for methane, propane, ethylene and hydrogen-air explosions. It can be concluded that self- acceleration of the flame, which is dependent on the distance of a flame from the ignition and the ‘suction’ at the vent opening are significant factors affecting the vent flow during explosion development in vented gas explosion. This additional volume influence on vented explosions is not taken into account in the current vent design guidance.

Keywords: Equivalence ratio, ignition position, self-acceleration flame, vented gas explosion.

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Authors: A. V. Dolzhikova

Abstract:

The article deals with the problems of labour migration in the Russian Federation in the context of Russia's national security, provides the typology of migrants residing in the territory of the Russian Federation and analyzes the risk factors. The author considers the structure of migration flows and the terms of legal, economic and socio-cultural adaptation of migrants in the Russian Federation. In this connection, the status of the Russian migration legislation, the concept of the comprehensive exam in Russian as a foreign language, history of Russia and the basics of the Russian Federation legislation for foreign citizens which was introduced in Russia on January 1, 2015, are analyzed. The article discloses its role as the adaptation strategy and the factor of Russia's migration security.

Keywords: Comprehensive exam, migration policy, migration legislation, Russia's national security.

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Authors: Kashif Bilal, Tassawar Iqbal, Asad Ali Safi, Nadeem Daudpota

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This paper deals with dynamic load balancing using PVM. In distributed environment Load Balancing and Heterogeneity are very critical issues and needed to drill down in order to achieve the optimal results and efficiency. Various techniques are being used in order to distribute the load dynamically among different nodes and to deal with heterogeneity. These techniques are using different approaches where Process Migration is basic concept with different optimal flavors. But Process Migration is not an easy job, it impose lot of burden and processing effort in order to track each process in nodes. We will propose a dynamic load balancing technique in which application will intelligently balance the load among different nodes, resulting in efficient use of system and have no overheads of process migration. It would also provide a simple solution to problem of load balancing in heterogeneous environment.

Keywords: PVM, load balancing, task allocation, intelligent application.

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Authors: M. Kowalski, M. Kastek, M. Szustakowski

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Multispectral screening systems are becoming more popular because of their very interesting properties and applications. One of the most significant applications of multispectral screening systems is prevention of terrorist attacks. There are many kinds of threats and many methods of detection. Visual detection of objects hidden under clothing of a person is one of the most challenging problems of threats detection. There are various solutions of the problem; however, the most effective utilize multispectral surveillance imagers. The development of imaging devices and exploration of new spectral bands is a chance to introduce new equipment for assuring public safety. We investigate the possibility of long lasting detection of potentially dangerous objects covered with various types of clothing. In the article we present the results of comparative studies of passive imaging in three spectrums – visible, infrared and terahertz.

Keywords: Infrared, image processing, object detection, screening camera, terahertz.

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Authors: S. N. Deepa, A. D. Srinivasan, K. T. Veeramanju, R. Sandeep Kumar, Ashwini Mathapati

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Power transformer is a vital element in a power system as it continuously regulates power flow, maintaining good voltage regulation. The working of transformer much depends on the oil insulation, the oil insulation also decides the aging of transformer and hence its reliability. The mineral oil based liquid insulation is globally accepted for power transformer insulation; however it is potentially hazardous due to its non-biodegradability. In this work efficient alternative biodegradable insulating fluid is presented as a replacement to conventional mineral oil. Dielectric tests are performed as distinct alternating fluid to evaluate the suitability for transformer insulation. The selection of the distinct natural esters for an insulation system is carried out by the laboratory investigation of Breakdown voltage, Oxidation stability, Dissipation factor, Permittivity, Viscosity, Flash and Fire point. It is proposed to study and characterize the properties of natural esters to be used in power transformer. Therefore for the investigation of the dielectric behavior rice bran oil, sesame oil, and sunflower oil are considered for the study. The investigated results have been compared with the mineral oil to validate the dielectric behavior of natural esters.

Keywords: Alternative insulating fluid, dielectric properties, natural esters, power transformers.

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Authors: Aqeel-ur-Rehman, Zubair A. Shaikh

Abstract:

This paper is to present context-aware sensor grid framework for agriculture and its design challenges. Use of sensor networks in the domain of agriculture is not new. However, due to the unavailability of any common framework, solutions that are developed in this domain are location, environment and problem dependent. Keeping the need of common framework for agriculture, Context-Aware Sensor Grid Framework is proposed. It will be helpful in developing solutions for majority of the problems related to irrigation, pesticides spray, use of fertilizers, regular monitoring of plot and yield etc. due to the capability of adjusting according to location and environment. The proposed framework is composed of three layer architecture including context-aware application layer, grid middleware layer and sensor network layer.

Keywords: Agriculture, Context-Awareness, Grid Computing, and Sensor Grid.

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Authors: Oshmita Dey, Debjani Chakraborty

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In this paper, a single period inventory model with resalable returns has been analyzed in an imprecise and uncertain mixed environment. Demand has been introduced as a fuzzy random variable. In this model, a single order is placed before the start of the selling season. The customer, for a full refund, may return purchased products within a certain time interval. Returned products are resalable, provided they arrive back before the end of the selling season and are found to be undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. The probabilities that a sold product is returned and that a returned product is resalable, both imprecise in a real situation, have been assumed to be fuzzy in nature.

Keywords: Fuzzy random variable, Modified graded meanintegration, Internet mail order, Inventory.

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