Search results for: Discrete boundary value problems

Authors: Y.Bakhshan, H.Ashoori

Abstract:

In this research, a 2-D computational analysis of steady state free convection in a rectangular enclosure filled with an electrically conducting fluid under Effect of Magnetic Field has been performed. The governing equations (mass, momentum, and energy) are formulated and solved by a finite volume method (FVM) subjected to different boundary conditions. A parametric study has been conducted to consider the influence of Grashof number (Gr), Prantdl number (Pr) and the orientation of magnetic field on the flow and heat transfer characteristics. It is observed that Nusselt number (Nu) and heat flux will increase with increasing Grashof and Prandtl numbers and decreasing the slope of the orientation of magnetic field.

Keywords: Rectangular Cavity, magneto-hydrodynamic, free convection, simulation

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Authors: M. B. Meenavathi, K. Rajesh

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Color image segmentation plays an important role in computer vision and image processing areas. In this paper, the features of Volterra filter are utilized for color image segmentation. The discrete Volterra filter exhibits both linear and nonlinear characteristics. The linear part smoothes the image features in uniform gray zones and is used for getting a gross representation of objects of interest. The nonlinear term compensates for the blurring due to the linear term and preserves the edges which are mainly used to distinguish the various objects. The truncated quadratic Volterra filters are mainly used for edge preserving along with Gaussian noise cancellation. In our approach, the segmentation is based on K-means clustering algorithm in HSI space. Both the hue and the intensity components are fully utilized. For hue clustering, the special cyclic property of the hue component is taken into consideration. The experimental results show that the proposed technique segments the color image while preserving significant features and removing noise effects.

Keywords: Color image segmentation, HSI space, K–means clustering, Volterra filter.

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Authors: D. I. De Souza, G. P. Azevedo, R. Rocha

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The State of Rio de Janeiro, Brazil, will hold two important events in the nearby future. In 2014 it will have the final game of the Football World Cup, and in 2016 it will be holding the Olympic Games. Therefore, the public transportation system (mainly buses) is of a major concern to the Rio de Janeiro State authorities-. The main objective of this work is to compare the quality of service of the bus companies operating in the cities of ItaperunaandCampos, both cities situated in the state of Rio de Janeiro, Brazil. The outcome of thiscomparison, based on the opinion of the bus users, has shownthemdispleased with the quality of the service provided by the bus companies operating in both cities. It is urgent the need to find possible practical alternatives to minimize the consequences of the main problems detected in this work. With these practical alternatives available, we will be able to offer to the Rio de Janeiro State authorities- suggestions about possible solutions to the main problems identified in this survey, as well as the time of implantation and costs of these solutions.

Keywords: Public Transportation, Quality of Service, Riders' Opinion, Bus Companies, Practical Alternatives.

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Authors: K. Diwakar, K. Aanandha Saravanan, C. Senthilpari

Abstract:

Higher order ΔΣ Modulator (DSM) is basically an unstable system. The approximate conditions for stability cannot be used for the design of a DSM for industrial applications where risk is involved. The existing second order, single stage, single bit, unity feedback gain , discrete DSM cannot be used for the normalized full range (-1 to +1) of an input signal since the DSM becomes unstable when the input signal is above ±0.55. The stability is also not guaranteed for input signals of amplitude less than ±0.55. In the present paper, the above mentioned second order DSM is modified with input signal dependent forward path gain. The proposed DSM is suitable for industrial applications where one needs the digital representation of the analog input signal, during each sampling period. The proposed DSM can operate almost for the full range of input signals (-0.95 to +0.95) without causing instability, assuming that the second integrator output should not exceed the circuit supply voltage, ±15 Volts.

Keywords: DSM, stability, SNR, state variables.

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Authors: Aritras Roy, Rinku Mukherjee

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The current study couples a quasi-steady Vortex Lattice Method and a camber correcting technique, ‘Decambering’ for unsteady post-stall flow prediction. The wake is force-free and discrete such that the wake lattices move with the free-stream once shed from the wing. It is observed that the time-averaged unsteady coefficient of lift sees a relative drop at post-stall angles of attack in comparison to its steady counterpart for some angles of attack. Multiple solutions occur at post-stall and three different algorithms to choose solutions in these regimes show both unsteadiness and non-convergence of the iterations. The distribution of coefficient of lift on the wing span also shows sawtooth. Distribution of vorticity changes both along span and in the direction of the free-stream as the wake develops over time with distinct roll-up, which increases with time.

Keywords: Post-stall, unsteady, wing, aerodynamics.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

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The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: Vijay Gajanan Neve, Pallavi V. Pullawar, G. M. Dhole

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Modern industrial processes are based on a large amount of electronic devices such as programmable logic controllers and adjustable speed drives. Unfortunately, electronic devices are sensitive to disturbances, and thus, industrial loads become less tolerant to power quality problems such as sags, swells, and harmonics. Voltage sags are an important power quality problem. In this paper proposed a new configuration of Static Var Compensator (SVC) considering three different conditions named as topologies and Booster transformer with fuzzy logic based controller, capable of compensating for power quality problems associated with voltage sags and maintaining a prescribed level of voltage profile. Fuzzy logic controller is designed to achieve the firing angles for SVC such that it maintains voltage profile. The online monitoring system for voltage sag mitigation in the laboratory using the hardware is used. The results are presented from the performance of each topology and Booster transformer considered in this paper.

Keywords: Booster Transformer, Fuzzy logic, Static Var Compensator, Voltage sag.

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Authors: M. Kotobuki, M. Koishi

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Li1.5Al0.5Ti1.5 (PO4)3(LATP) has received much attention as a solid electrolyte for lithium batteries. In this study, the LATP solid electrolyte is prepared by the co-precipitation method using Li3PO4 as a Li source. The LATP is successfully prepared and the Li ion conductivities of bulk (inner crystal) and total (inner crystal and grain boundary) are 1.1 × 10-3 and 1.1 × 10-4 S cm-1, respectively. These values are comparable to the reported values, in which Li2C2O4 is used as the Li source. It is conclude that the LATP solid electrolyte can be prepared by the co-precipitation method using Li3PO4 as the Li source and this procedure has an advantage in mass production over previous procedure using Li2C2O4 because Li3PO4 is lower price reagent compared with Li2C2O4.

Keywords: Co-precipitation method, lithium battery, NASICON-type electrolyte, solid electrolyte.

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Authors: Tirthankar Ghosh, Dilip Roy, Nimai Kumar Chandra

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Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.

Keywords: Discretization, Reversed Hazard Rate, Exponential distribution, reliability approximation, engineering item.

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Authors: Sherin M. Youssef, Ahmed Abouelfarag, Noha M. Ghatwary

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An adaptive Fuzzy Inference Perceptual model has been proposed for watermarking of digital images. The model depends on the human visual characteristics of image sub-regions in the frequency multi-resolution wavelet domain. In the proposed model, a multi-variable fuzzy based architecture has been designed to produce a perceptual membership degree for both candidate embedding sub-regions and strength watermark embedding factor. Different sizes of benchmark images with different sizes of watermarks have been applied on the model. Several experimental attacks have been applied such as JPEG compression, noises and rotation, to ensure the robustness of the scheme. In addition, the model has been compared with different watermarking schemes. The proposed model showed its robustness to attacks and at the same time achieved a high level of imperceptibility.

Keywords: Watermarking, The human visual system (HVS), Fuzzy Inference System (FIS), Local Binary Pattern (LBP), Discrete Wavelet Transform (DWT).

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Authors: B. S. Jayashankarbabu, Karisiddappa

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The finite element method is used to obtain the elastic buckling load factor for square isotropic plate containing circular, square and rectangular cutouts. ANSYS commercial finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and the influence of plate edge conditions, such as SSSS, CCCC and mixed boundary condition SCSC on the plate buckling strength have been considered in the analysis.

Keywords: Concentric cutout, Elastic buckling, Finite element method, Inplane loads, Thickness ratio.

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Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue

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A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.

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Authors: Fridhi Hadia, Soua Wadhah, Hidouri Ammar, Omri Ahmed

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In this paper, the effect of the intake temperature (IT) and intake pressure (IP) on ignition timing and pollutants emission of Homogeneous Charge Compression Ignition (HCCI) engine is investigated. Numerical computations are performed using the CHEMKIN computer code. The numerical temperature obtained using different boundary conditions is compared to published data and a good agreement is assigned. Results show that the HCCI combustion engine is significantly improved by increasing the IT. With a value of IT lower than 390 K, combustion cannot occur. However, with an IT greater than 420 K, the cylinder pressure decreases. An optimum crank rotation angle is achieved by using IT of 420 K. So, we can conclude that the variation of the IT and IP influence notably the emission concentration.

Keywords: HCCI engine, CEMKIN, intake temperature, intake pressure.

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Authors: M. Vijaya Kini, R. S. Pai, D. Srikanth Rao, Satish Shenoy B, R. Pai

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The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.

Keywords: 3-axial groove, dynamic characteristics, groovelocation, water lubricated bearings.

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Authors: Mustahsan Mir, Ahmed Hassanin, Mohammed A. Al-Saleh

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The layout optimization of building blocks of unequal areas has applications in many disciplines including VLSI floorplanning, macrocell placement, unequal-area facilities layout optimization, and plant or machine layout design. A number of heuristics and some analytical and hybrid techniques have been published to solve this problem. This paper presents an efficient high-quality building-block layout design technique especially suited for solving large-size problems. The higher efficiency and improved quality of optimized solutions are made possible by introducing the concept of Promising Infant Clusters in a constructive placement procedure. The results presented in the paper demonstrate the improved performance of the presented technique for benchmark problems in comparison with published heuristic, analytic, and hybrid techniques.

Keywords: Block layout problem, building-block layout design, CAD, optimization, search techniques.

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: Engineering education, errors, limits, mathematics competences, problem solving.

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Authors: Shen-Kuei Du, Jen-Chieh Chang, Chia-Hong Kao, Tzu-Chen Hung, Chii-Ray Lin

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This study experimentally investigates the heat transfer effects of forced convection and natural convection under different substrate openings design. A computational fluid dynamics (CFD) model was established and implemented to verify and explain the experimental results and heat transfer behavior. It is found that different opening position will destroy the growth of the boundary layer on substrates to alter the cooling ability for both forced under low Reynolds number and natural convection. Nevertheless, having too many opening may reduce heat conduction and affect the overall heat transfer performance. This study provides future researchers with a guideline on designing and electronic package manufacturing.

Keywords: electronic cooling, experiment, opening concept, CFD.

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Authors: Sedighe Arabameri, Nasser Salmasi

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In this researcha particle swarm optimization (PSO) algorithm is proposedfor no-wait flowshopsequence dependent setuptime scheduling problem with weighted earliness-tardiness penalties as the criterion (
|, |Σ   " ).The smallestposition value (SPV) rule is applied to convert the continuous value of position vector of particles in PSO to job permutations.A timing algorithm is generated to find the optimal schedule and calculate the objective function value of a given sequence in PSO algorithm. Twodifferent neighborhood structures are applied to improve the solution quality of PSO algorithm.The first one is based on variable neighborhood search (VNS) and the second one is a simple one with invariable structure. In order to compare the performance of two neighborhood structures, random test problems are generated and solved by both neighborhood approaches.Computational results show that the VNS algorithmhas better performance than the other one especially for the large sized problems.

Keywords: minimization of summation of weighed earliness and tardiness, no-wait flowshop scheduling, particle swarm optimization, sequence dependent setup times

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Authors: Jinghua Zhang, Charles B. Owen, Jinsheng Xu

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A new hybrid coding method for compressing animated polygonal meshes is presented. This paper assumes the simplistic representation of the geometric data: a temporal sequence of polygonal meshes for each discrete frame of the animated sequence. The method utilizes a delta coding and an octree-based method. In this hybrid method, both the octree approach and the delta coding approach are applied to each single frame in the animation sequence in parallel. The approach that generates the smaller encoded file size is chosen to encode the current frame. Given the same quality requirement, the hybrid coding method can achieve much higher compression ratio than the octree-only method or the delta-only method. The hybrid approach can represent 3D animated sequences with higher compression factors while maintaining reasonable quality. It is easy to implement and have a low cost encoding process and a fast decoding process, which make it a better choice for real time application.

Keywords: animated polygonal meshes, compression, deltacoding, octree.

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Authors: He YuanYan

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In recent years, China has implemented the reform of land and space planning. As an important public policy, land and space planning plays a vital role in the construction and development of cities. Land and space planning throughout the country is in full swing, but there are still many disputes from all walks of life. The content, scope, and specific implementation process of land and space planning are also ambiguous, leading to the integration of multiple regulation problems such as unclear authority, unclear responsibilities, and poor planning results during the implementation of land and space planning. Therefore, it is necessary to sort out the development and evolution of domestic and foreign land space planning, clarify the problems and cruxes from the current situation of China's land space planning, and sort out the obstacles and countermeasures to the implementation of this policy, so as to deepen the understanding of the connotation of land space planning. It is of great practical significance for all planners to correctly understand and clarify the specific contents and methods of land space planning and to smoothly promote the implementation of land space planning at all levels.

Keywords: Territorial spatial planning, public policy, land space, overall planning.

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Authors: Mohammad Taghi Shervani Tabar, Zahra Poursharifi

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The interaction of the blade tip with the casing boundary layer and the leakage flow may lead to a kind of cavitation namely tip vortex cavitation. In this study, the onset of tip vortex cavitation was experimentally investigated in an axial flow pump. For a constant speed and a fixed angle of attack and by changing the flow rate, the pump head, input power, output power and efficiency were calculated and the pump characteristic curves were obtained. The cavitation phenomenon was observed with a camera and a stroboscope. Finally, the critical flow region, which tip vortex cavitation might have occurred, was identified. The results show that just by adjusting the flow rate, out of the specified region, the possibility of occurring tip vortex cavitation, decreases to a great extent.

Keywords: Axial flow pump, Gap cavitation, Leakage vortex, Tip vortex cavitation.

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Authors: Rumyana Peytcheva-Forsyth, Blagovesna Yovkova

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This paper presents the outcomes of a qualitative study which aims to investigate the pedagogical potentials of serious games in the preparation of future teachers. The authors discuss the existing problems and barriers associated with the organization of teaching practices in Bulgaria as part of the pre-service teacher training, as well as the attitudes and perceptions of the interviewed academics, teachers and trainees concerning the integration of serious games in the teaching practicum. The study outcomes strongly confirm the positive attitudes of the respondents to the introduction of virtual learning environments for the development of professional skills of future teachers as a supplement to the traditional forms of education. Through the inclusion of serious games it is expected to improve the quality of practical training of pre-service teachers as they overcome many of the problems identified in the existing teaching practices. The outcomes of the study will inform the design of the educational simulation software which is part of the project SimAula Tomorrow's Teachers Training.

Keywords: pre-service teacher training, serious games, virtual practicum, simulations

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Authors: Wook-Won Kim, Sung-Yul Kim, Jin-O Kim

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The fault current levels through the electric devices have a significant impact on failure probability. New fault current results in exceeding the rated capacity of circuit breaker and switching equipments and changes operation characteristic of overcurrent relay. In order to solve these problems, SFCL (Superconducting Fault Current Limiter) has rising as one of new alternatives so as to improve these problems. A fault current reduction differs depending on installed location. Therefore, a location of SFCL is very important. Also, SFCL decreases the fault current, and it prevents surrounding protective devices to be exposed to fault current, it then will bring a change of reliability. In this paper, we propose method which determines the optimal location when SFCL is installed in power system. In addition, the reliability about the power system which SFCL was installed is evaluated. The efficiency and effectiveness of this method are also shown by numerical examples and the reliability indices are evaluated in this study at each load points. These results show a reliability change of a system when SFCL was installed.

Keywords: Superconducting Fault Current Limiter, OptimalLocation, Reliability

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Authors: Pingping Lin, Xudong Luo, Yifan Fan

Abstract:

Sentiment analysis is a very active research topic. Every day, Facebook, Twitter, Weibo, and other social media, as well as significant e-commerce websites, generate a massive amount of comments, which can be used to analyse peoples opinions or emotions. The existing methods for sentiment analysis are based mainly on sentiment dictionaries, machine learning, and deep learning. The first two kinds of methods rely on heavily sentiment dictionaries or large amounts of labelled data. The third one overcomes these two problems. So, in this paper, we focus on the third one. Specifically, we survey various sentiment analysis methods based on convolutional neural network, recurrent neural network, long short-term memory, deep neural network, deep belief network, and memory network. We compare their futures, advantages, and disadvantages. Also, we point out the main problems of these methods, which may be worthy of careful studies in the future. Finally, we also examine the application of deep learning in multimodal sentiment analysis and aspect-level sentiment analysis.

Keywords: Natural language processing, sentiment analysis, document analysis, multimodal sentiment analysis, deep learning.

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Authors: Raja Muhammad Asif Zahoor, Junaid Ali Khan, I. M. Qureshi

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In this article an evolutionary technique has been used for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been successfully applied to solve the different forms of Riccati differential equations. The strength of proposed method has in its equal applicability for the integer order case, as well as, fractional order case. Comparison of the method has been made with standard numerical techniques as well as the analytic solutions. It is found that the designed method can provide the solution to the equation with better accuracy than its counterpart deterministic approaches. Another advantage of the given approach is to provide results on entire finite continuous domain unlike other numerical methods which provide solutions only on discrete grid of points.

Keywords: Riccati Equation, Non linear ODE, Fractional differential equation, Genetic algorithm.

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Authors: Venkatesh C., K. Shanti Swarup

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This paper investigates the impact on operating time delay and relay maloperation when 1st,2nd and 3rd order analog antialiasing filters are used in numerical distance protection. RC filter with cut-off frequency 90 Hz is used. Simulations are carried out for different SIR (Source to line Impedance Ratio), load, fault type and fault conditions using SIMULINK, where the voltage and current signals are fed online to the developed numerical distance relay model. Matlab is used for plotting the impedance trajectory. Investigation results shows that, about 75 % of the simulated cases, numerical distance relay operating time is not increased even-though there is a time delay when higher order filters are used. Relay maloperation (selectivity) also reduces (increases) when higher order filters are used in numerical distance protection.

Keywords: Antialiasing, capacitive voltage transformers, delay estimation, discrete Fourier transform (DFT), distance measurement, low-pass filters, source to line impedance ratio (SIR), protective relaying.

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Authors: Jinghao Sun, Guozhen Tan, Guangjian Hou

Abstract:

The Chinese Postman Problem (CPP) is one of the classical problems in graph theory and is applicable in a wide range of fields. With the rapid development of hybrid systems and model based testing, Chinese Postman Problem with Time Dependent Travel Times (CPPTDT) becomes more realistic than the classical problems. In the literature, we have proposed the first integer programming formulation for the CPPTDT problem, namely, circuit formulation, based on which some polyhedral results are investigated and a cutting plane algorithm is also designed. However, there exists a main drawback: the circuit formulation is only available for solving the special instances with all circuits passing through the origin. Therefore, this paper proposes a new integer programming formulation for solving all the general instances of CPPTDT. Moreover, the size of the circuit formulation is too large, which is reduced dramatically here. Thus, it is possible to design more efficient algorithm for solving the CPPTDT in the future research.

Keywords: Chinese Postman Problem, Time Dependent, Integer Programming, Upper Bound Analysis.

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Authors: Ayad Sleibi Mustafa, Ahmed Abdulkadhim Mohsin, Layth Noori Ali

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The deterioration of solid waste management in Baghdad city is considered as a great challenge in terms of human health and environment. Baghdad city is divided into thirteen districts which are distributed on both Tigris River banks. The west bank is Al-Karkh and the east bank is Al-Rusafa. Municipal Solid Waste Management is one of the most complicated problems facing the environment in Iraq. Population growth led to increase waste production and more load of the waste to the limited capacity infrastructure. The problems of municipal solid waste become more serious after the war in 2003. More waste is disposed in underground landfills in Baghdad with little or no concern for both human health and environment. The results showed that the total annually predicted solid waste is increasing for the period 2015-2030. Municipal solid waste in 2030 will be 6,427,773 tons in Baghdad city according to the population growth rate of 2.4%. This increase is estimated to be approximately 30%.

Keywords: Municipal solid waste, solid waste composition and characteristics, Baghdad city, environment, human health.

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Authors: Shivali D. Kulkarni, Ameya K. Naik, Nitin S. Nagori

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In this paper we present simulation results for the application of a bandwidth efficient algorithm (mapping algorithm) to an image transmission system. This system considers three different real valued transforms to generate energy compact coefficients. First results are presented for gray scale and color image transmission in the absence of noise. It is seen that the system performs its best when discrete cosine transform is used. Also the performance of the system is dominated more by the size of the transform block rather than the number of coefficients transmitted or the number of bits used to represent each coefficient. Similar results are obtained in the presence of additive white Gaussian noise. The varying values of the bit error rate have very little or no impact on the performance of the algorithm. Optimum results are obtained for the system considering 8x8 transform block and by transmitting 15 coefficients from each block using 8 bits.

Keywords: Additive white Gaussian noise channel, mapping algorithm, peak signal to noise ratio, transform encoding.

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Authors: A. Farshidianfar, P. Oliazadeh, M. H. Farshidianfar

Abstract:

In order to study the free vibration of simply supported circular cylindrical shells; an analytical procedure is developed and discussed in detail. To identify its’ validity, the exact technique was applied to four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter, and 4) Donnell. The exact procedure was compared favorably with experimental results and those obtained using the numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The effects of this approximate method were also investigated on the natural frequencies by comparing results with those of the exact analysis.

Keywords: Circular Cylindrical Shell, Free Vibration, Natural Frequency.

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