Search results for: magnetic pole position.

Authors: Amirhossein Asadabadi, Amir Anvar

Abstract:

Small satellites have become increasingly popular recently as a means of providing educational institutes with the chance to design, construct, and test their spacecraft from beginning to the possible launch due to the low launching cost. This approach is remarkably cost saving because of the weight and size reduction of such satellites. Weight reduction could be realised by utilising electromagnetic coils solely, instead of different types of actuators. This paper describes the restrictions of using only “Electromagnetic" actuation for 3D stabilisation and how to make the magnetorquer based attitude control feasible using Fuzzy Logic Control (FLC). The design is developed to stabilize the spacecraft against gravity gradient disturbances with a three-axis stabilizing capability.

Keywords: Fuzzy, Attitude Control, Small Satellite, Fuzzy Logic Control, Electromagnetic, Magnetic Control.

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Authors: Tlotlollo Sidwell Hlalele, Shengzhi Du

Abstract:

High-voltage power transmission lines are the back bone of electrical power utilities. The stability and continuous monitoring of this critical infrastructure is pivotal. Nine-Sigma representing Eskom Holding SOC limited, South Africa has a major problem on proactive detection of fallen power lines and real time sagging measurement together with slipping of such conductors. The main objective of this research is to innovate RFID technology to solve this challenge. Various options and technologies such as GPS, PLC, image processing, MR sensors and etc., have been reviewed and draw backs were made. The potential of RFID to give precision measurement will be observed and presented. The future research will look at magnetic and electrical interference as well as corona effect on the technology.

Keywords: Precision Measurement, RFID and Sag.

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Authors: D. A. Binas, M. Konidari, C. Bourgioti, L. Angela Moulopoulou, T. L. Economopoulos, G. K. Matsopoulos

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High grade ovarian epithelial cancer (OEC) is the most fatal gynecological cancer and poor prognosis of this entity is closely related to considerable intratumoral genetic heterogeneity. By examining imaging data, it is possible to assess the heterogeneity of tumorous tissue. This study presents a methodology for aligning, segmenting and finally visualizing information from various magnetic resonance imaging series, in order to construct 3D models of heterogeneity maps from the same tumor in OEC patients. The proposed system may be used as an adjunct digital tool by health professionals for personalized medicine, as it allows for an easy visual assessment of the heterogeneity of the examined tumor.

Keywords: K-means segmentation, ovarian epithelial cancer, quantitative characteristics, registration, tumor visualization.

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Authors: Alaa E. Abdallah, Bajes Y. Alskarnah

Abstract:

Ant colony based routing algorithms are known to grantee the packet delivery, but they suffer from the huge overhead of control messages which are needed to discover the route. In this paper we utilize the network nodes positions to group the nodes in connected clusters. We use clusters-heads only on forwarding the route discovery control messages. Our simulations proved that the new algorithm has decreased the overhead dramatically without affecting the delivery rate.

Keywords: Ant colony-based routing, position-based routing, MANET.

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Authors: Praveen Saraswat, Rudraman Singh

Abstract:

In this paper, we have investigated the free convection MHD flow due to heat and mass transfer through porous medium bounded by an infinite vertical non-conducting porous plate with time dependent suction under the influence of uniform transverse magnetic field of strength H₀. When Temperature (T) and Concentration (C) at the plate is oscillatory with time about a constant non-zero mean. The velocity distribution, the temperature distribution, co-efficient of skin friction and role of heat transfer is investigated. Here the partial differential equations are involved. Exact solution is not possible so approximate solution is obtained and various graphs are plotted.

Keywords: Time Dependent Suction, Convection, MHD, Porous.

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Authors: Jhalique Jane R. Fojas, Rizalinda L. De Leon, Lucille V. Abad

Abstract:

The characterization of κ-carrageenan could provide a better understanding of its functions in biological, medical and industrial applications. Chemical and physical analyses of carrageenan from seaweeds, Euchema cottonii L., were done to offer information on its properties and the effects of Co-60 γ-irradiation on its thermochemical characteristics. The structural and morphological characteristics of κ-carrageenan were determined using scanning electron microscopy (SEM) while the composition, molecular weight and thermal properties were determined using attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), gel permeation chromatography (GPC), thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC). Further chemical analysis was done using hydrogen-1 nuclear magnetic resonance (1H NMR) and functional characteristics in terms of biocompatibility were evaluated using cytotoxicity test.

Keywords: Biocompatibility, carrageenan, DSC, FTIR, GPC, irradiation, NMR, physicochemical, SEM, TGA.

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Authors: Luka Pavlič, Marjan Heričko

Abstract:

E-services have significantly changed the way of doing business in recent years. We can, however, observe poor use of these services. There is a large gap between supply and actual eservices usage. This is why we started a project to provide an environment that will encourage the use of e-services. We believe that only providing e-service does not automatically mean consumers would use them. This paper shows the origins of our project and its current position. We discuss the decision of using semantic web technologies and their potential to improve e-services usage. We also present current knowledge base and its real-world classification. In the paper, we discuss further work to be done in the project. Current state of the project is promising.

Keywords: E-Services, E-Services Repository, Ontologies, Semantic Web

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Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

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This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: Kinematics, degree of freedom, optimization, robot manipulator.

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Authors: Mahmud Hesain ALdwaik, Omar Hsiain Eldwaik

Abstract:

This paper deals with tracking and estimating time delay between two signals. The simulation of this algorithm accomplished by using Mathcad package is carried out. The algorithm we will present adaptively controls and tracking the delay, so as to minimize the mean square of this error. Thus the algorithm in this case has task not only of seeking the minimum point of error but also of tracking the change of position, leading to a significant improving of performance. The flowchart of the algorithm is presented as well as several tests of different cases are carried out.

Keywords: Tracking time delay, Algorithm simulation, Mathcad, MSE

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Authors: Siddharth Ahuja, T. M. Muruganandam

Abstract:

An analytical investigation is performed to study the unsteady response of a one-dimensional, non-linear dynamic shock system to external downstream pressure perturbations in a supersonic flow in a varying area duct. For a given pressure ratio across a wind tunnel, the normal shock's location can be computed as per one-dimensional steady gas dynamics. Similarly, for some other pressure ratio, the location of the normal shock will change accordingly, again computed using one-dimensional gas dynamics. This investigation focuses on the small-time interval between the first steady shock location and the new steady shock location (corresponding to different pressure ratios). In essence, this study aims to shed light on the motion of the shock from one steady location to another steady location. Further, this study aims to create the foundation of the Unsteady Gas Dynamics field enabling further insight in future research work. According to the new pressure ratio, a pressure pulse, generated at the exit of the tunnel which travels and perturbs the shock from its original position, setting it into motion. During such activity, other numerous physical phenomena also happen at the same time. However, three broad phenomena have been focused on, in this study - Traversal of a Wave, Fluid Element Interactions and Wave Interactions. The above mentioned three phenomena create, alter and kill numerous waves for different conditions. The waves which are created by the above-mentioned phenomena eventually interact with the shock and set it into motion. Numerous such interactions with the shock will slowly make it settle into its final position owing to the new pressure ratio across the duct, as estimated by one-dimensional gas dynamics. This analysis will be extremely helpful in the prediction of inlet 'unstart' of the flow in a supersonic engine intake and its prominence with the incoming flow Mach number, incoming flow pressure and the external perturbation pressure is also studied to help design more efficient supersonic intakes for engines like ramjets and scramjets.

Keywords: Analytical investigation, compression and expansion waves, fluid element interactions, shock trajectory, supersonic flow, unsteady gas dynamics, varying area duct, wave interactions.

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Authors: Sebastien Harasse, Laurent Bonnaud, Michel Desvignes

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Counting people from a video stream in a noisy environment is a challenging task. This project aims at developing a counting system for transport vehicles, integrated in a video surveillance product. This article presents a method for the detection and tracking of multiple faces in a video by using a model of first and second order local moments. An iterative process is used to estimate the position and shape of multiple faces in images, and to track them. the trajectories are then processed to count people entering and leaving the vehicle.

Keywords: face detection, tracking, counting, local statistics

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Authors: Yuri Boiko, Iluju Kiringa, Tet Yeap

Abstract:

Current drainage attack suggested previously is further studied in regular settings of closed-loop controlled Brushless DC (BLDC) motor with Kalman filter in the feedback loop. Modeling and simulation experiments are conducted in a MATLAB environment, implementing the closed-loop control model of BLDC motor operation in position sensorless mode under Kalman filter drive. The current increase in the motor windings is caused by the controller (p-controller in our case) affected by false data injection of substitution of the angular velocity estimates with distorted values. Operation of multiplication to distortion coefficient, values of which are taken from the distortion function synchronized in its periodicity with the rotor’s position change. A saw function with a triangular tooth shape is studied herewith for the purpose of carrying out the bias injection with current drainage consequences. The specific focus here is on how the asymmetry of the tooth in the saw function affects the flow of current drainage. The purpose is two-fold: (i) to produce and collect the signature of an asymmetric saw in the attack for further pattern recognition process, and (ii) to determine conditions of improving stealthiness of such attack via regulating asymmetry in saw function used. It is found that modification of the symmetry in the saw tooth affects the periodicity of current drainage modulation. Specifically, the modulation frequency of the drained current for a fully asymmetric tooth shape coincides with the saw function modulation frequency itself. Increasing the symmetry parameter for the triangle tooth shape leads to an increase in the modulation frequency for the drained current. Moreover, such frequency reaches the switching frequency of the motor windings for fully symmetric triangular shapes, thus becoming undetectable and improving the stealthiness of the attack. Therefore, the collected signatures of the attack can serve for attack parameter identification via the pattern recognition route.

Keywords: Bias injection attack, Kalman filter, BLDC motor, control system, closed loop, P-controller, PID-controller, current drainage, saw-function, asymmetry.

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Authors: Afshin Moradi, Mohammad Hosain Teimourpour

Abstract:

We derive simple sets of equations to describe the microwave response of a thin film of magnetized hydrogen plasma in the presence of carbon nanotubes, which were grown by ironcatalyzed high-pressure disproportionation (HiPco). By considering the interference effects due to multiple reflections between thin plasma film interfaces, we present the effects of the continuously changing external magnetic field and plasma parameters on the reflected power, absorbed power, and transmitted power in the system. The simulation results show that the interference effects play an important role in the reflectance, transmittance and absorptance of microwave radiation at the magnetized plasma slab. As a consequence, the interference effects lead to a sinusoidal variation of the reflected intensity and can greatly reduce the amount of reflection power, but the absorption power increases.

Keywords:

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Authors: Noboru Abe, Yoshinori Amai, Toshinori Nakatake, Sumio Masuda, Kazuaki Yamaguchi

Abstract:

We consider the problem of placing labels of the points on a plane. For each point, its position, the size of its label and a priority are given. Moreover, several candidates of its label positions are prespecified, and each of such label positions is assigned a priority. The objective of our problem is to maximize the total sum of priorities of placed labels and their points. By refining a labeling algorithm that can use these priorities, we propose a new heuristic algorithm which is more suitable for treating the assigned priorities.

Keywords: Map labeling, greedy algorithm, heuristic algorithm, priority.

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Authors: João Cepeda

Abstract:

In crafting their way between theory and practice, authors and artists seem to be always immersed in a never-ending process of relating epochs, objects and images. Endless ‘affinities’ emerge, from a somewhat unexplainable (and intimate) magnetic relation. It is through this ‘warburgian’ assessment that two of the most prominent twentieth century modern architects from Japan and Portugal are put into perspective in this paper, focusing on their paths and thinking-practice, and on the research of their personal and professional archives. Moreover, this research especially aims its focus at essaying specifically on the possible ‘affinities’ between two of their most renowned architectural projects: the Kenzo Tange’s (demolished) Villa Seijo project in Tokyo (Japan), and Fernando Távora’s Tennis Pavilion design in Matosinhos (Portugal), respectively, side-by-side – through in-depth fieldwork in the sites, bibliographical and archival research, (unprecedented) material analysis, and a final critical consideration.

Keywords: Tange, Távora, architecture, affinities.

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Authors: Boo-Sung Koh, Seung-Eock Kim

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In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.

Keywords: Direct design, nonlinear inelastic analysis, residual stress, initial geometric imperfection.

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Authors: Do Hyeung Kim, Dae Hee Seo, Byung Doo Kim, Byung Gil Lee

Abstract:

As many recent researches being implemented in aviation and maritime aspects, strong doubts have been raised concerning the reliability of the estimation of collision risk. It is shown that using position and velocity of objects can lead to imprecise results. In this paper, therefore, a new approach to the estimation of collision risks using pose and shape of objects is proposed. Simulation results are presented validating the accuracy of the new criterion to adapt to collision risk algorithm based on fuzzy logic.

Keywords: Collision risk, Pose and shape, Fuzzy logic.

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Authors: Anna Avramenko, Heikki Haario

Abstract:

This paper reports the development and application of a 2D1 depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. κ − ε and 2D LES turbulence models were consider in this article. 2D CFD2 simulations for one hill was done to check the depth-averaged model in practise.

Keywords: Depth-averaged equations, numerical modeling, CFD

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Authors: Moussa Hamdan, Abdulati Abdullah

Abstract:

This paper presents an investigation of the fabrication of the optical devices in terms of their characteristics based on the use of the electromagnetic waves. Planar waveguides are used to examine the field modes (bound modes) and the parameters required for this structure. The modifications are conducted on surface plasmons based waveguides. Simple symmetric dielectric slab structure is used and analyzed in terms of transverse electric mode (TE-Mode) and transverse magnetic mode (TM-Mode. The paper presents mathematical and numerical solutions for solving simple symmetric plasmons and provides simulations of surface plasmons for field confinement. Asymmetric TM-mode calculations for dielectric surface plasmons are also provided.

Keywords: Surface plasmons, optical waveguides, semiconductor lasers, refractive index, slab dialectical.

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Authors: Marc Landry, Azeddine Kaddouri, Yassine Bouslimani, Mohsen Ghribi

Abstract:

In this paper, a new alignment method based on the particle swarm optimization (PSO) technique is presented. The PSO algorithm is used for locating the optimal coupling position with the highest optical power with three-degrees of freedom alignment. This algorithm gives an interesting results without a need to go thru the complex mathematical modeling of the alignment system. The proposed algorithm is validated considering practical tests considering the alignment of two Single Mode Fibers (SMF) and the alignment of SMF and PCF fibers.

Keywords: Particle-swarm optimization, optical fiber, automatic alignment.

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Authors: Ivan Yatchev, Ewen Ritchie

Abstract:

Comparison of two approaches for the simulation of the dynamic behaviour of a permanent magnet linear actuator is presented. These are full coupled model, where the electromagnetic field, electric circuit and mechanical motion problems are solved simultaneously, and decoupled model, where first a set of static magnetic filed analysis is carried out and then the electric circuit and mechanical motion equations are solved employing bi-cubic spline approximations of the field analysis results. The results show that the proposed decoupled model is of satisfactory accuracy and gives more flexibility when the actuator response is required to be estimated for different external conditions, e.g. external circuit parameters or mechanical loads.

Keywords: Coupled problems, dynamic models, finite elementanalysis, linear actuators, permanent magnets.

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Authors: Chanhoe Kang, Changhyun Lee, Seock-Hee Jun, Yeong-Tae Oh

Abstract:

Offshore floating structure under the various environmental conditions maintains a fixed position by mooring system. Environmental conditions, vessel motions and mooring loads are applied to mooring lines as the dynamic tension. Because global responses of mooring system in deep water are specified as wave frequency and low frequency response, they should be calculated from the time-domain analysis due to non-linear dynamic characteristics. To take into account all mooring loads, environmental conditions, added mass and damping terms at each time step, a lot of computation time and capacities are required. Thus, under the premise that reliable fatigue damage could be derived through reasonable analysis method, it is necessary to reduce the analysis cases through the sensitivity studies and appropriate assumptions. In this paper, effects in fatigue are studied for spread mooring system connected with oil FPSO which is positioned in deep water of West Africa offshore. The target FPSO with two Mbbls storage has 16 spread mooring lines (4 bundles x 4 lines). The various sensitivity studies are performed for environmental loads, type of responses, vessel offsets, mooring position, loading conditions and riser behavior. Each parameter applied to the sensitivity studies is investigated from the effects of fatigue damage through fatigue analysis. Based on the sensitivity studies, the following results are presented: Wave loads are more dominant in terms of fatigue than other environment conditions. Wave frequency response causes the higher fatigue damage than low frequency response. The larger vessel offset increases the mean tension and so it results in the increased fatigue damage. The external line of each bundle shows the highest fatigue damage by the governed vessel pitch motion due to swell wave conditions. Among three kinds of loading conditions, ballast condition has the highest fatigue damage due to higher tension. The riser damping occurred by riser behavior tends to reduce the fatigue damage. The various analysis results obtained from these sensitivity studies can be used for a simplified fatigue analysis of spread mooring line as the reference.

Keywords: Mooring system, fatigue analysis, time domain, non-linear dynamic characteristics.

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

Abstract:

This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.

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Authors: Fotios N. Vlachos, Anastasios D. Garetsos, Nikolaos K. Uzunoglu, Efstathios D. Gotsis

Abstract:

A four element prototype phased array surface probe has been designed and constructed to improve clinical human prostate spectroscopic data. The probe consists of two pairs of adjacent rectangular coils with an optimum overlap to reduce the mutual inductance. The two pairs are positioned on the anterior and the posterior pelvic region and two couples of varactors at the input of each coil undertake the procedures of tuning and matching. The probe switches off and on automatically during the consecutive phases of the MR experiment with the use of an analog switch that is triggered by a microcontroller. Experimental tests that were carried out resulted in high levels of tuning accuracy. Also, the switching mechanism functions properly for various applied loads and pulse sequence characteristics, producing only 10 μs of latency.

Keywords: Automatic tuning, prostate imaging, phased array, spectroscopy.

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Authors: George Charkoftakis, Panagiotis Liosatos, Nicolas-Alexander Tatlas, Dimitrios Goustouridis, Stelios M. Potirakis

Abstract:

E-maintenance is a relatively recent concept, generally referring to maintenance management by monitoring assets over the Internet. One of the key links in the chain of an e-maintenance system is data acquisition and transmission. Specifically for the case of a fleet of heavy-duty vehicles, where the main challenge is the diversity of the vehicles and vehicle-embedded self-diagnostic/reporting technologies, the design of the data acquisition and transmission unit is a demanding task. This is clear if one takes into account that a heavy-vehicles fleet assortment may range from vehicles with only a limited number of analog sensors monitored by dashboard light indicators and gauges to vehicles with plethora of sensors monitored by a vehicle computer producing digital reporting. The present work proposes an adaptable internet of things (IoT) sensor node that is capable of addressing this challenge. The proposed sensor node architecture is based on the increasingly popular single-board computer – expansion boards approach. In the proposed solution, the expansion boards undertake the tasks of position identification, cellular connectivity, connectivity to the vehicle computer, and connectivity to analog and digital sensors by means of a specially targeted design of expansion board. Specifically, the latter offers a number of adaptability features to cope with the diverse sensor types employed in different vehicles. In standard mode, the IoT sensor node communicates to the data center through cellular network, transmitting all digital/digitized sensor data, IoT device identity and position. Moreover, the proposed IoT sensor node offers connectivity, through WiFi and an appropriate application, to smart phones or tablets allowing the registration of additional vehicle- and driver-specific information and these data are also forwarded to the data center. All control and communication tasks of the IoT sensor node are performed by dedicated firmware.

Keywords: IoT sensor nodes, e-maintenance, single-board computers, sensor expansion boards, on-board diagnostics

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Authors: Tusharkanta Das, Tumbanath Samantara, Sukanta Kumar Sahoo

Abstract:

Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

Keywords: Heat transfer, radiation, MHD, free convection, porous medium, suction.

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Authors: Ahsan Bin Tufail, Ali Abidi, Adil Masood Siddiqui, Muhammad Shahzad Younis

Abstract:

An early and accurate detection of Alzheimer's disease (AD) is an important stage in the treatment of individuals suffering from AD. We present an approach based on the use of structural magnetic resonance imaging (sMRI) phase images to distinguish between normal controls (NC), mild cognitive impairment (MCI) and AD patients with clinical dementia rating (CDR) of 1. Independent component analysis (ICA) technique is used for extracting useful features which form the inputs to the support vector machines (SVM), K nearest neighbour (kNN) and multilayer artificial neural network (ANN) classifiers to discriminate between the three classes. The obtained results are encouraging in terms of classification accuracy and effectively ascertain the usefulness of phase images for the classification of different stages of Alzheimer-s disease.

Keywords: Biomedical image processing, classification algorithms, feature extraction, statistical learning.

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Authors: Guy Leshem, Ya'acov Ritov

Abstract:

Traffic Management and Information Systems, which rely on a system of sensors, aim to describe in real-time traffic in urban areas using a set of parameters and estimating them. Though the state of the art focuses on data analysis, little is done in the sense of prediction. In this paper, we describe a machine learning system for traffic flow management and control for a prediction of traffic flow problem. This new algorithm is obtained by combining Random Forests algorithm into Adaboost algorithm as a weak learner. We show that our algorithm performs relatively well on real data, and enables, according to the Traffic Flow Evaluation model, to estimate and predict whether there is congestion or not at a given time on road intersections.

Keywords: Machine Learning, Boosting, Classification, TrafficCongestion, Data Collecting, Magnetic Loop Detectors, SignalizedIntersections, Traffic Signal Timing Optimization.

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Authors: Anita D. Adamu, Winston M. W. Shakantu

Abstract:

Maintenance management is no longer a stand-alone activity. It has now assumed a strategic position in many organisations that have recognised its importance in achieving primary goals and a key aspect of effective management of facilities. This paper aims at providing an understanding of the role and function of strategic management in creating and sustaining an effective maintenance management system in an organisation. The background provides an articulated concept and principles of strategic management. The theoretical concepts paved way for a conceptual framework for which strategic management can be integrated into the maintenance management system of an organisation to improve effectiveness in the maintenance of facilities.

Keywords: Facilities, maintenance management, organisations, strategic management.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

The Algorithm 2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm 2 guarantees the reaching of a target position in a finite number of steps. The Algorithm 2 is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the Algorithm2 implementation are given.

Keywords: Manipulator, trajectory planning, unknown obstacles.

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