Search results for: fixed points

Authors: Sammani Danwawu Abdullahi

Abstract:

Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: Approximation, counting with uncertainties, mathematical programming, optimization, vertex enumeration.

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Authors: Chien-Song Chyang, Yu-Chi Wang

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For sludge disposal, incineration is considered to be better than direct burial because of regulations and space limitations in Taiwan. Additionally, burial after incineration can effectively prolong the lifespan of a landfill. Therefore, it is the most satisfactory method for treating sludge at present. Of the various incineration technologies, the fluidized bed incinerator is a suitable choice due to its fuel flexibility. In this work, sludge generated from industrial plants was treated in a pilot-scale vortexing fluidized bed. The moisture content of the sludge was 48.53%, and its LHV was 454.6 kcal/kg. Primary gas and secondary gas were fixed at 3 Nm³/min and 1 Nm³/min, respectively. Diesel burners with on-off controllers were used to control the temperature; the bed temperature was set to 750±20 °C, and the freeboard temperature was 850±20 °C. The experimental data show that the NO emission increased with bed temperature. The maximum NO emission is 139 ppm, which is in agreement with the regulation. The CO emission is low than 100 ppm through the operation period. The mean particle size of fly ash collected from baghouse decreased with operating time. The ration of bottom ash to fly ash is about 3. Compared with bottom ash, the potassium in the fly ash is much higher. It implied that the potassium content is not the key factor for aggregation of bottom ash.

Keywords: Sludge incineration, fluidized bed combustion, fly ash, bottom ash.

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Authors: Daniel Chen, George Mamic, Clinton Fookes, Sridha Sridharan

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An automatic method for the extraction of feature points for face based applications is proposed. The system is based upon volumetric feature descriptors, which in this paper has been extended to incorporate scale space. The method is robust to noise and has the ability to extract local and holistic features simultaneously from faces stored in a database. Extracted features are stable over a range of faces, with results indicating that in terms of intra-ID variability, the technique has the ability to outperform manual landmarking.

Keywords: Scale space volume descriptor, feature extraction, 3D facial landmarking

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Authors: Dimitrios Koukopoulos

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In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, p)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates p > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.

Keywords: Parallel computing, network stability, adversarial queuing theory, greedy scheduling protocols.

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Authors: Yury Nikulin

Abstract:

A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.

Keywords: Stability and accuracy, multicriteria optimization, lexicographic optimality.

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Authors: Nelson J. Cossa, Narayanan S. Potty, Mohd Shahir Liew, Arazi B. Idrus

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The oil and gas industry has moved towards Load and Resistance Factor Design through API RP2A - LRFD and the recently published international standard, ISO-19902, for design of fixed steel offshore structures. The ISO 19902 is intended to provide a harmonized design practice that offers a balanced structural fitness for the purpose, economy and safety. As part of an ongoing work, the reliability analysis of tubular joints of the jacket structure has been carried out to calibrate the load and resistance factors for the design of offshore platforms in Malaysia, as proposed in the ISO. Probabilistic models have been established for the load effects (wave, wind and current) and the tubular joints strengths. In this study the First Order Reliability Method (FORM), coded in MATLAB Software has been employed to evaluate the reliability index of the typical joints, designed using API RP2A - WSD and ISO 19902.

Keywords: FORM, Reliability Analysis, Tubular Joints

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Authors: Pilanee Vaithanomsat, Sinsupha Chuichulcherm, Waraporn Apiwatanapiwat

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Sunflower stalks were analysed for chemical compositions: pentosan 15.84%, holocellulose 70.69%, alphacellulose 45.74%, glucose 27.10% and xylose 7.69% based on dry weight of 100-g raw material. The most optimum condition for steam explosion pretreatment was as follows. Sunflower stalks were cut into small pieces and soaked in 0.02 M H2SO4 for overnight. After that, they were steam exploded at 207 C and 21 kg/cm2 for 3 minutes to fractionate cellulose, hemicellulose and lignin. The resulting hydrolysate, containing hemicellulose, and cellulose pulp contained xylose sugar at 2.53% and 7.00%, respectively.The pulp was further subjected to enzymatic saccharification at 50 C, pH 4.8 citrate buffer) with pulp/buffer 6% (w/w)and Celluclast 1.5L/pulp 2.67% (w/w) to obtain single glucose with maximum yield 11.97%. After fixed-bed fermentation under optimum condition using conventional yeast mixtures to produce bioethanol, it indicated maximum ethanol yield of 0.028 g/100 g sunflower stalk.

Keywords: Enzymatic, steam explosion, sunflower stalk, ethanol production.

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Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin

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Mostly the real life signals are time varying in nature. For proper characterization of such signals, time-frequency representation is required. The STFT (short-time Fourier transform) is a classical tool used for this purpose. The limitation of the STFT is its fixed time-frequency resolution. Thus, an enhanced version of the STFT, which is based on the cross-level sampling, is devised. It can adapt the sampling frequency and the window function length by following the input signal local variations. Therefore, it provides an adaptive resolution time-frequency representation of the input. The computational complexity of the proposed STFT is deduced and compared to the classical one. The results show a significant gain of the computational efficiency and hence of the processing power. The processing error of the proposed technique is also discussed.

Keywords: Level Crossing Sampling, Activity Selection, Adaptive Resolution Analysis, Computational Complexity

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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Authors: Françoise Petersen, Mike Pluke, Tatiana Kovacikova, Giovanni Bartolomeo

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As communications systems and technology become more advanced and complex, it will be increasingly important to focus on users- individual needs. Personalization and effective user profile management will be necessary to ensure the uptake and success of new services and devices and it is therefore important to focus on the users- requirements in this area and define solutions that meet these requirements. The work on personalization and user profiles emerged from earlier ETSI work on a Universal Communications Identifier (UCI) which is a unique identifier of the user rather than a range of identifiers of the many of communication devices or services (e.g. numbers of fixed phone at home/work, mobile phones, fax and email addresses). This paper describes work on personalization including standardized information and preferences and an architectural framework providing a description of how personalization can be integrated in Next Generation Networks, together with the UCI concept.

Keywords: Interoperability, Next Generation Network (NGN), Personalization, Universal Communications Identifier (UCI), User Profile Management (UPM)

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Authors: Yassine Meraihi, Dalila Acheli, Rabah Meraihi

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Vehicular Ad hoc Network (VANET) is a special case of Mobile Ad hoc Network (MANET) used to establish communications and exchange information among nearby vehicles and between vehicles and nearby fixed infrastructure. VANET is seen as a promising technology used to provide safety, efficiency, assistance and comfort to the road users. Routing is an important issue in Vehicular Ad Hoc Network to find and maintain communication between vehicles due to the highly dynamic topology, frequently disconnected network and mobility constraints.

This paper evaluates the performance of two most popular proactive routing protocols OLSR and DSDV in real city traffic scenario on the basis of three metrics namely Packet delivery ratio, throughput and average end to end delay by varying vehicles density and transmission range.

Keywords: DSDV, OLSR, Quality of service, Routing protocols, VANET.

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Authors: F.H.Wee, F. Malek

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This paper presents the utilizing of ferroelectric material on antenna application. There are two different ferroelectric had been used on the proposed antennas which include of Barium Strontium Titanate (BST) and Bismuth Titanate (BiT), suitable for Access Points operating in the WLAN IEEE 802.11 b/g and WiMAX IEEE 802.16 within the range of 2.3 GHz to 2.5 GHz application. BST, which had been tested to own a dielectric constant of εr = 15 while BiT has a dielectric constant that higher than BST which is εr = 21 and both materials are in rectangular shaped. The influence of various parameters on antenna characteristics were investigated extensively using commercial electromagnetic simulations software by Communication Simulation Technology (CST). From theoretical analysis and simulation results, it was demonstrated that ferroelectric material used have not only improved the directive emission but also enhanced the radiation efficiency.

Keywords: Ferroelectric material, WLAN, WiMAX, dielectric constant

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Authors: N. Arslanoglu

Abstract:

This paper deals with the optimum tilt angle for the solar collector in order to collect the maximum solar radiation. The optimum angle for tilted surfaces varying from 0^◦ to 90^◦ in steps of 1^◦ was computed. In present study, a theoretical model is used to predict the global solar radiation on a tilted surface and to obtain the optimum tilt angle for a solar collector in Bursa, Turkey. Global solar energy radiation on the solar collector surface with an optimum tilt angle is calculated for specific periods. It is determined that the optimum slope angle varies between 0^◦ (June) and 59^◦ (December) throughout the year. In winter (December, January, and February) the tilt should be 55^◦, in spring (March, April, and May) 19.6^◦, in summer (June, July, and August) 5.6^◦, and in autumn (September, October, and November) 44.3^◦. The yearly average of this value was obtained to be 31.1^◦ and this would be the optimum fixed slope throughout the year.

Keywords: Optimum tilt angle, global solar radiation, tilted surface.

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Authors: J. P. P. Andrade, V. A. F. Campos

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This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put the system in closed loop poles in a specific region of the complex plane. Test results using a dynamic model of the F-16 aircraft are presented and discussed.

Keywords: F-16 Aircraft, linear matrix inequalities, pole placement, robust control.

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Authors: Supriya Pal, Kalyan Adhikari, Somnath Mukherjee, Sudipta Ghosh

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This study presents the application of artificial neural network for modeling the phenolic compound migration through vertical soil column. A three layered feed forward neural network with back propagation training algorithm was developed using forty eight experimental data sets obtained from laboratory fixed bed vertical column tests. The input parameters used in the model were the influent concentration of phenol(mg/L) on the top end of the soil column, depth of the soil column (cm), elapsed time after phenol injection (hr), percentage of clay (%), percentage of silt (%) in soils. The output of the ANN was the effluent phenol concentration (mg/L) from the bottom end of the soil columns. The ANN predicted results were compared with the experimental results of the laboratory tests and the accuracy of the ANN model was evaluated.

Keywords: Modeling, Neural Networks, Phenol, Soil media

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Authors: A. Chellil, I. Gahlouz, S. Lecheb, A. Nour, S. Chellil, H. Mechakra, H. Kebir

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In this paper, the experimental study for the instability of a separator rotor is presented, under dynamic loading response in the harmonic analysis condition. The global measurement and analysis of vibration on the cement separator RC500 is carried, the points of measurement used are radial dots, vertical, horizontal and oblique. The measures of trends and spectral analysis for reconnaissance of the main anomalies, the main defects in the separator and manifestation, the results prove that the defects effect has a negative effect on the stability of the rotor. Experimentally the study of the rotor in transient system allowed to determine the vibratory responses due to the unbalances and various excitations.

Keywords: Rotor, experimental, defect, frequency, specter.

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Authors: V. Goremikins, K. Rocens, D. Serdjuks

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One of the main problems of suspended cable structures is initial shape change under the action of non uniform load. The problem can be solved by increasing of weight of construction or by using of prestressing. But this methods cause increasing of materials consumption of suspended cable structure. The cable truss usage is another way how the problem of shape change under the action of non uniform load can be fixed. The cable trusses with the vertical and inclined suspensions, cross web and single cable were analyzed as the main load-bearing structures of suspension bridge. It was shown, that usage of cable truss allows to reduce the vertical displacements up to 32% in comparison with the single cable in case of non uniformly distributed load. In case of uniformly distributed load single cable is preferable.

Keywords: Cable trusses, Non uniform load, Suspension bridge, Vertical displacements.

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Authors: Yi Liao, Wencheng Yang, Gangyi Jiang

Abstract:

According to investigating impact of complexity of stereoscopic frame pairs on stereoscopic video coding and transmission, a new rate control algorithm is presented. The proposed rate control algorithm is performed on three levels: stereoscopic group of pictures (SGOP) level, stereoscopic frame (SFrame) level and frame level. A temporal-spatial frame complexity model is firstly established, in the bits allocation stage, the frame complexity, position significance and reference property between the left and right frames are taken into account. Meanwhile, the target buffer is set according to the frame complexity. Experimental results show that the proposed method can efficiently control the bitrates, and it outperforms the fixed quantization parameter method from the rate distortion perspective, and average PSNR gain between rate-distortion curves (BDPSNR) is 0.21dB.

Keywords: Stereoscopic video coding, rate control, stereoscopic group of pictures, complexity of stereoscopic frame pairs.

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Authors: Dubbale Daniel A., Tsutsumi J., Michael J. Bendewald

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Addis Ababa is a seat of African Union (AU), United Nations Economic Commission for Africa (UN-ECA) and hundreds of embassies and consular representatives. Addis Ababa is one of the highest capitals in the world with an average 2400 meters above sea level. It is dichotomous city with a blend of modern high-rise and deteriorating slum quarters. Water supply and sanitation, waste management and housing are continuing to be serious problems. Forest wood based domestic energy use as well as uncontrolled emissions from mobile and fixed sources has endangered the state of the urban environment. Analysis based on satellite imagery has revealed the deteriorating urban environment within the last three decades. The recently restructured city administration has brought improvements in the condition of the urban environment. However, the overwhelming size of the challenges faced by the city dwarfed their fairly good results.

Keywords: Addis Ababa, Urban environment, Slum, Housing, Relocation

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Authors: Rasaki O. Olanrewaju

Abstract:

The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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Authors: Sharon S. Wu, Yong S. Park

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This project aims to study and evaluate the motorcycle crash bar, which is used to reduce injuries caused by side impacts to the motorcycle, and then develop an improved design using the engineering design process theory based on the current benchmark crash bar in order to lower the severity of motorcycle crash injuries. For this purpose, simulations for the crash bar are set up so that it travels at an angle towards a fixed concrete wall and collides at certain velocities. 3D CAD models are first designed in SolidWorks and dynamic crash simulations are then carried out using ANSYS to determine the lowest maximum Von-Mises stress over time and deformations by adjusting the parameters used in manufacturing the crash bar, including the velocity of the crash, material used, geometries with various radius fillets, and different thicknesses for the bar. The results of the simulation are used to determine the optimum parameters for a safer crash bar to withstand higher stress and deformation. Specifically, the von-Mises stress was reduced by at least 75% compared with the benchmark design by choosing aluminum alloy and a true unibar design.

Keywords: Crash bar, crash simulation, engineering design, motorcycle safety.

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Authors: Amir Reza Saffari Azar Alamdari

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In this paper, a model of self-organizing spiking neural networks is introduced and applied to mobile robot environment representation and path planning problem. A network of spike-response-model neurons with a recurrent architecture is used to create robot-s internal representation from surrounding environment. The overall activity of network simulates a self-organizing system with unsupervised learning. A modified A* algorithm is used to find the best path using this internal representation between starting and goal points. This method can be used with good performance for both known and unknown environments.

Keywords: Mobile Robot, Path Planning, Self-organization, Spiking Neural Networks.

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Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

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This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm² and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: Reconfigurable, fast Fourier transform, single-path delay feedback, 3GPP-LTE.

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Authors: Qian Wang, Sylvain Lassalle, Antony R. Mileham, Geraint W. Owen

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This paper mathematically analyses the varying magnitude of production loss, which may occur due to idle time (inprocess waiting time and traveling time) on a linear walking worker assembly line. Within this flexible and reconfigurable assembly system, each worker travels down the line carrying out each assembly task at each station; and each worker accomplishes the assembly of a unit from start to finish and then travels back to the first station to start the assembly of a new product. This strategy of system design attempts to combine the flexibility of the U-shaped moving worker assembly cell with the efficiency of the conventional fixed worker assembly line. The paper aims to evaluate the effect of idle time that may offset the labor efficiency of each walking worker providing an insight into the mechanism of such a flexible and reconfigurable assembly system.

Keywords: Production lines, manufacturing systems, assemblysystems, walking workers.

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Authors: Eakkasak Susakunphaisan, Pichai Namprakai, Withaya Puangsombut

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The objective of this paper was to designing a ventilation system to enhance the performance of roof solar collector (RSC) for reducing heat accumulation inside the house. The RSC has 1.8 m2 surface area made of CPAC monier roof tiles on the upper part and gypsum board on the lower part. The space between CPAC monier and gypsum board was fixed at 14 cm. Ventilation system of modified roof solar collector (modified RSC) consists of 9 tubes of 0.15m diameter and installed in the lower part of RSC. Experimental result showed that the temperature of the room, and attic temperature. The average temperature reduction of room of house used modified RSC is about 2oC. and the percentage of room temperature reduction varied between 0 to 10%. Therefore, modified RSC is an interesting option in the sense that it promotes solar energy and conserve energy.

Keywords: roof solar collector, heat accumulation

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Authors: D. Almazo, M. Toledo, C. Rodríguez

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This work presents a methodology for the design and manufacture of propellers oriented to the experimental verification of theoretical results based on the combined model. The design process begins by using algorithms in Matlab which output data contain the coordinates of the points that define the blade airfoils, in this case the NACA 6512 airfoil was used. The modeling for the propeller blade was made in NX7, through the imported files in Matlab and with the help of surfaces. Later, the hub and the clamps were also modeled. Finally, NX 7 also made possible to create post-processed files to the required machine. It is possible to find the block of numbers with G & M codes about the type of driver on the machine. The file extension is .ptp. These files made possible to manufacture the blade, and the hub of the propeller.

Keywords: Airfoil, CAM, manufacturing, mathematical algorithm, numeric control, propeller design, simulation.

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Authors: Mike Sewell, Jagath Samarabandu, Ranga Rodrigo, Kenneth McIsaac

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A novel method of individual level adaptive mutation rate control called the rank-scaled mutation rate for genetic algorithms is introduced. The rank-scaled mutation rate controlled genetic algorithm varies the mutation parameters based on the rank of each individual within the population. Thereby the distribution of the fitness of the papulation is taken into consideration in forming the new mutation rates. The best fit mutate at the lowest rate and the least fit mutate at the highest rate. The complexity of the algorithm is of the order of an individual adaptation scheme and is lower than that of a self-adaptation scheme. The proposed algorithm is tested on two common problems, namely, numerical optimization of a function and the traveling salesman problem. The results show that the proposed algorithm outperforms both the fixed and deterministic mutation rate schemes. It is best suited for problems with several local optimum solutions without a high demand for excessive mutation rates.

Keywords: Genetic algorithms, mutation rate control, adaptive mutation.

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Authors: Yongyoon Suh, Yongtae Park

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The interaction among information and communication technology (ICT) industries is a recently ubiquitous phenomenon through fixed-mobile integration. To monitor the impact of interaction, previous research has mainly focused on measuring spillover effect among ICT industries using various methods. Among others, inter-industry analysis is one of the useful methods for examining spillover effect between industries. However, more complex ICT industries become, more important the impact within an industry is. Inter-industry analysis is limited in mirroring intra-relationships within an industry. Thus, this study applies the analytic network process (ANP) to measure the spillover effect, capturing all of the intra and inter-relationships. Using ANP-based intra and inter-industry analysis, the spillover effect is effectively measured, mirroring the complex structure of ICT industries. A main ICT industry and its linkages are also explored to show the current structure of ICT industries. The proposed approach is expected to allow policy makers to understand interactions of ICT industries and their impact.

Keywords: ANP, intra and inter-industry analysis, spillover effect

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Authors: Shivakumar, G. S. Vijay, P. Srinivas Pai, B. R. Shrinivasa Rao

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In the present study, RBF neural networks were used for predicting the performance and emission parameters of a biodiesel engine. Engine experiments were carried out in a 4 stroke diesel engine using blends of diesel and Honge methyl ester as the fuel. Performance parameters like BTE, BSEC, Tex and emissions from the engine were measured. These experimental results were used for ANN modeling. RBF center initialization was done by random selection and by using Clustered techniques. Network was trained by using fixed and varying widths for the RBF units. It was observed that RBF results were having a good agreement with the experimental results. Networks trained by using clustering technique gave better results than using random selection of centers in terms of reduced MRE and increased prediction accuracy. The average MRE for the performance parameters was 3.25% with the prediction accuracy of 98% and for emissions it was 10.4% with a prediction accuracy of 80%.

Keywords: Radial Basis Function networks, emissions, Performance parameters, Fuzzy c means.

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Authors: Lívia B. Meirelles, Erika C. A. N. Chrisman, Flávia B. de Andrade, Lilian C. M. de Oliveira

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True Boiling Point distillation (TBP) is one of the most common experimental techniques for the determination of petroleum properties. This curve provides information about the performance of petroleum in terms of its cuts. The experiment is performed in a few days. Techniques are used to determine the properties faster with a software that calculates the distillation curve when a little information about crude oil is known. In order to evaluate the accuracy of distillation curve prediction, eight points of the TBP curve and specific gravity curve (348 K and 523 K) were inserted into the HYSYS Oil Manager, and the extended curve was evaluated up to 748 K. The methods were able to predict the curve with the accuracy of 0.6%-9.2% error (Software X ASTM), 0.2%-5.1% error (Software X Spaltrohr).

Keywords: Distillation curve, petroleum distillation, simulation, true boiling point curve.

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