Search results for: mathematical modelling

Authors: Mohamed Dbouk, Ihab Sbeity

Abstract:

Spatial and mobile computing evolves. This paper describes a smart modeling platform called “GeoSEMA". This approach tends to model multidimensional GeoSpatial Evolutionary and Mobile Agents. Instead of 3D and location-based issues, there are some other dimensions that may characterize spatial agents, e.g. discrete-continuous time, agent behaviors. GeoSEMA is seen as a devoted design pattern motivating temporal geographic-based applications; it is a firm foundation for multipurpose and multidimensional special-based applications. It deals with multipurpose smart objects (buildings, shapes, missiles, etc.) by stimulating geospatial agents. Formally, GeoSEMA refers to geospatial, spatio-evolutive and mobile space constituents where a conceptual geospatial space model is given in this paper. In addition to modeling and categorizing geospatial agents, the model incorporates the concept of inter-agents event-based protocols. Finally, a rapid software-architecture prototyping GeoSEMA platform is also given. It will be implemented/ validated in the next phase of our work.

Keywords: Location-Trajectory management, GIS, Mobile- Moving Objects/Agents, Multipurpose/Spatiotemporal data, Multi- Agent Systems.

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Authors: Haziyah Hussin, Syazwan Abdul Samad, Rosnani Jusoh

Abstract:

This study is aimed towards the automisation of basic patternmaking for traditional clothes for the purpose of mass production using AutoCAD to apply AutoLISP feature under software Hazi Attire. A standard dress form (industrial form) with the size of small (S), medium (M) and large (L) size is measured using full body scanning machine. Later, the pattern for the clothes is designed parametrically based on the measured dress form. Hazi Attire program is used within the framework of AutoCAD to generate the basic pattern of front bodice, back bodice, front skirt, back skirt and sleeve block (sloper). The generation of pattern is based on the parameters inputted by user, whereby in this study, the parameters were determined based on the measured size of dress form. The finalized pattern parameter shows that the pattern fit perfectly on the dress form. Since the pattern is generated almost instantly, these proved that using the AutoLISP programming, the manufacturing lead time for the mass production of the traditional clothes can be decreased.

Keywords: Apparel, AutoLISP, Malay Traditional Clothes, Pattern Ganeration.

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Authors: Behrouz Afshar Nadjafi

Abstract:

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where production period length is constrained. In this paper, we address the problem of deciding the optimal production quantity and the number of minor setups within each cycle, in which, production period length is constrained but a minor setup is possible for pass the constraint. A mathematical model is developed and Iterated Local Search (ILS) is proposed to solve this problem. Finally, solution procedure illustrated with a numerical example and results are analyzed.

Keywords: EPQ, Inventory control, minor setup, ILS.

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Authors: Emad Alenany, M. Adel El-Baz

Abstract:

In this paper, the flow of different classes of patients into a hospital is modelled and analyzed by using the queueing network analyzer (QNA) algorithm and discrete event simulation. Input data for QNA are the rate and variability parameters of the arrival and service times in addition to the number of servers in each facility. Patient flows mostly match real flow for a hospital in Egypt. Based on the analysis of the waiting times, two approaches are suggested for improving performance: Separating patients into service groups, and adopting different service policies for sequencing patients through hospital units. The separation of a specific group of patients, with higher performance target, to be served separately from the rest of patients requiring lower performance target, requires the same capacity while improves performance for the selected group of patients with higher target. Besides, it is shown that adopting the shortest processing time and shortest remaining processing time service policies among other tested policies would results in, respectively, 11.47% and 13.75% reduction in average waiting time relative to first come first served policy.

Keywords: Queueing network, discrete-event simulation, health applications, SPT.

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Authors: A. Reyes-Salazar, M. D. Llanes-Tizoc, E. Bojorquez, F. Valenzuela-Beltran, J. Bojorquez, J. R. Gaxiola-Camacho, A. Haldar

Abstract:

Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated to lateral vibrations are commonly used to develop the matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the nonlinear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively, when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment resisting steel frames and the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: Moment-resisting steel frames, consistent and concentrated mass matrices, nonlinear seismic response, Rayleigh damping.

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Authors: Mujde Turkkan, Nurkan Yagiz

Abstract:

The vibrations, caused by the irregularities of the road surface, are to be suppressed via suspension systems. In this paper, sliding mode control for a half bus model with air suspension system is presented. The bus is modelled as five degrees of freedom (DoF) system. The mathematical model of the half bus is developed using Lagrange Equations. For time domain analysis, the bus model is assumed to travel at certain speed over the bump road. The numerical results of the analysis indicate that the sliding mode controllers can be effectively used to suppress the vibrations and to improve the ride comfort of the busses.

Keywords: Sliding mode control, bus model, air suspension.

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Authors: Sagaren Pillay

Abstract:

In this paper bi-annual time series data on unemployment rates (from the Labour Force Survey) are expanded to quarterly rates and linked to quarterly unemployment rates (from the Quarterly Labour Force Survey). The resultant linked series and the consumer price index (CPI) series are examined using Johansen’s cointegration approach and vector error correction modeling. The study finds that both the series are integrated of order one and are cointegrated. A statistically significant co-integrating relationship is found to exist between the time series of unemployment rates and the CPI. Given this significant relationship, the study models this relationship using Vector Error Correction Models (VECM), one with a restriction on the deterministic term and the other with no restriction.

A formal statistical confirmation of the existence of a unique linear and lagged relationship between inflation and unemployment for the period between September 2000 and June 2011 is presented. For the given period, the CPI was found to be an unbiased predictor of the unemployment rate. This relationship can be explored further for the development of appropriate forecasting models incorporating other study variables.

Keywords: Forecasting, lagged, linear, relationship.

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Authors: Wang Xingbo

Abstract:

Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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Authors: Y. Bi, T. Anderson, M. Huang

Abstract:

The use of technology is increasingly adopted to support flexible learning in Higher Education institutions. The adoption of more sophisticated technologies offers a broad range of facilities for communication and resource sharing, thereby creating a flexible learning environment that facilitates and even encourages students not to physically attend classes. However this emerging trend seems to contradict class attendance requirements within universities, inevitably leading to a dilemma between amending traditional regulations and creating new policies for the higher education institutions. This study presents an investigation into student engagement in a technology enhanced/driven flexible environment along with its relationship to attainment. We propose an approach to modelling engagement from different perspectives in terms of indicators and then consider what impact these indicators have on student academic performance. We have carried out a case study on the relation between attendance and attainment in a flexible environment. Although our preliminary results show attendance is quantitatively correlated with successful student development and learning outcomes, our results also indicate there is a cohort that did not follow such a pattern. Nevertheless the preliminary results could provide an insight into pilot studies in the wider deployment of new technology to support flexible learning.

Keywords: Engagement, flexible leaning, attendance and attainment.

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Authors: Sabah S. Al-Fedaghi

Abstract:

The technique of k-anonymization has been proposed to obfuscate private data through associating it with at least k identities. This paper investigates the basic tabular structures that underline the notion of k-anonymization using cell suppression. These structures are studied under idealized conditions to identify the essential features of the k-anonymization notion. We optimize data kanonymization through requiring a minimum number of anonymized values that are balanced over all columns and rows. We study the relationship between the sizes of the anonymized tables, the value k, and the number of attributes. This study has a theoretical value through contributing to develop a mathematical foundation of the kanonymization concept. Its practical significance is still to be investigated.

Keywords: Balanced tables, k-anonymization, private data

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Authors: Edward Guillén, Stephanne Rodríguez, Jhordany Rodríguez

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Throughput enhancement can be achieved with two main approaches. The first one is by the increase of transmission rate and the second one is reducing the control traffic. This paper focuses on how the throughput can be enhanced by increasing Maximum Transmission Unit -MTU. Transmission of larger packets can cause a throughput improvement by reducing IP overhead. Analysis results are obtained by a mathematical model and simulation tools with a main focus on wireless channels.

Keywords: 802.11, Maximum Transfer Unit, throughput enhancement, wireless networks.

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Authors: W. Mughees, M. Al-Ahmad, M. Naeem

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This research involves the design and analysis of pinch-based water/wastewater networks to minimize water utility in the petrochemical and petroleum industries. A study has been done on Tehran Oil Refinery to analyze feasibilities of regeneration, reuse and recycling of water network. COD is considered as a single key contaminant. Amount of freshwater was reduced about 149m3/h (43.8%) regarding COD. Re-design (or retrofitting) of water allocation in the networks was undertaken. The results were analyzed through graphical method and mathematical programming technique which clearly demonstrated that amount of required water would be determined by mass transfer of COD.

Keywords: Minimization, Water Pinch, Water Management, Pollution Prevention.

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Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

Abstract:

Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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Authors: M. A. Serag-Eldin

Abstract:

The paper presents the results of simple measurements conducted on a model of a wind-driven venturi-type room ventilator. The ventilator design is new and was developed employing mathematical modeling. However, the computational model was not validated experimentally for the particular application considered. The paper presents the performance of the ventilator model under laboratory conditions, for five different wind tunnel speeds. The results are used to both demonstrate the effectiveness of the new design and to validate the computational model employed to develop it.

Keywords: Venturi-flow, ventilation, Wind-energy, Wind flow.

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Authors: Mohamad Saab, Sidi Souvi

Abstract:

In a major nuclear accident, the released fission products (FPs) and the structural materials are likely to influence the transport of iodine in the reactor coolant system (RCS) of a pressurized water reactor (PWR). So far, the thermodynamic data on cesium and silver species used to estimate the magnitude of FP release show some discrepancies, data are scarce and not reliable. For this reason, it is crucial to review the thermodynamic values related to cesium and silver materials. To this end, we have used state-of-the-art quantum chemical methods to compute the formation enthalpies and entropies of AgHMoO₄, CsHMoO₄, and AgCsMoO₄ in the gas phase. Different quantum chemical methods have been investigated (DFT and CCSD(T)) in order to predict the geometrical parameters and the energetics including the correlation energy. The geometries were optimized with TPSSh-5%HF method, followed by a single point calculation of the total electronic energies using the CCSD(T) wave function method. We thus propose with a final uncertainty of about 2 kJmol⁻¹ standard enthalpies of formation of AgHMoO₄, CsHMoO₄, and AgCsMoO₄.

Keywords: ASTEC, Accident Source Term Evaluation Code, quantum chemical methods, severe nuclear accident, thermochemical database.

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Authors: Paulo S. Caparelli, Eduardo Costa, Alexsandro S. Soares, Hipolito Barbosa

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This paper presents an evolutionary method for designing electronic circuits and numerical methods associated with monitoring systems. The instruments described here have been used in studies of weather and climate changes due to global warming, and also in medical patient supervision. Genetic Programming systems have been used both for designing circuits and sensors, and also for determining sensor parameters. The authors advance the thesis that the software side of such a system should be written in computer languages with a strong mathematical and logic background in order to prevent software obsolescence, and achieve program correctness.

Keywords: Pattern recognition, evolutionary computation, biological signal, functional programming.

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Authors: Y. Lacroix, J.-F. Malbranque

Abstract:

We present a chronological evolution for naval telecommunication networks. We distinguish periods: with or without multiplexers, with switch systems, with federative systems, with medium switching, and with medium switching with wireless networks. This highlights the introduction of new layers and technology in the architecture. These architectures are presented using layer models of transmission, in a unified way, which enables us to integrate pre-existing models. A ship of a naval fleet has internal communications (i.e. applications' networks of the edge) and external communications (i.e. the use of the means of transmission between edges). We propose architectures, deduced from the layer model, which are the point of convergence between the networks on board and the HF, UHF radio, and satellite resources. This modelling allows to consider end-to-end naval communications, and in a more global way, that is from the user on board towards the user on shore, including transmission and networks on the shore side. The new architectures need take care of quality of services for end-to-end communications, the more remote control develops a lot and will do so in the future. Naval telecommunications will be more and more complex and will use more and more advanced technologies, it will thus be necessary to establish clear global communication schemes to grant consistency of the architectures. Our latest model has been implemented in a military naval situation, and serves as the basic architecture for the RIFAN2 network.

Keywords: Equilibrium beach profile, eastern tombolo of Giens, potential function, erosion.

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Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

Abstract:

In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.

Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection

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Authors: S. Ariffin, K. Hasnan, R.H. Weston

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A new generation of manufacturing machines so-called MIMCA (modular and integrated machine control architecture) capable of handling much increased complexity in manufacturing control-systems is presented. Requirement for more flexible and effective control systems for manufacturing machine systems is investigated and dimensioned-which highlights a need for improved means of coordinating and monitoring production machinery and equipment used to- transport material. The MIMCA supports simulation based on machine modeling, was conceived by the authors to address the issues. Essentially MIMCA comprises an organized unification of selected architectural frameworks and modeling methods, which include: NISTRCS, UMC and Colored Timed Petri nets (CTPN). The unification has been achieved; to support the design and construction of hierarchical and distributed machine control which realized the concurrent operation of reusable and distributed machine control components; ability to handle growing complexity; and support requirements for real- time control systems. Thus MIMCA enables mapping between 'what a machine should do' and 'how the machine does it' in a well-defined but flexible way designed to facilitate reconfiguration of machine systems.

Keywords: Machine control, architectures, Petri nets, modularity, modeling, simulation.

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

Abstract:

There exist a wide range of failure modes in composite structures due to the increased usage of the structures especially in aerospace industry. Moreover, temperature dependent wave response of composite and layered structures have been continuously studied, though still limited, in the last decade mainly due to the broad operating temperature range of aerospace structures. A wave finite element (WFE) and finite element (FE) based computational method is presented by which the temperature dependent wave dispersion characteristics and interaction phenomenon in composite structures can be predicted. Initially, the temperature dependent mechanical properties of the panel in the range of -100 ◦C to 150 ◦C are measured experimentally using the Thermal Mechanical Analysis (TMA). Temperature dependent wave dispersion characteristics of each waveguide of the structural system, which is discretized as a system of a number of waveguides coupled by a coupling element, is calculated using the WFE approach. The wave scattering properties, as a function of temperature, is determined by coupling the WFE wave characteristics models of the waveguides with the full FE modelling of the coupling element on which defect is included. Numerical case studies are exhibited for two waveguides coupled through a coupling element.

Keywords: Temperature dependent mechanical characteristics, wave propagation properties, damage detection, wave finite element, composite structure.

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Authors: Eleni Galiotou, Angela Ralli

Abstract:

In this paper we propose a computational model for the representation and processing of morpho-phonological phenomena in a natural language, like Modern Greek. We aim at a unified treatment of inflection, compounding, and word-internal phonological changes, in a model that is used for both analysis and generation. After discussing certain difficulties cuase by well-known finitestate approaches, such as Koskenniemi-s two-level model [7] when applied to a computational treatment of compounding, we argue that a morphology-based model provides a more adequate account of word-internal phenomena. Contrary to the finite state approaches that cannot handle hierarchical word constituency in a satisfactory way, we propose a unification-based word grammar, as the nucleus of our strategy, which takes into consideration word representations that are based on affixation and [stem stem] or [stem word] compounds. In our formalism, feature-passing operations are formulated with the use of the unification device, and phonological rules modeling the correspondence between lexical and surface forms apply at morpheme boundaries. In the paper, examples from Modern Greek illustrate our approach. Morpheme structures, stress, and morphologically conditioned phoneme changes are analyzed and generated in a principled way.

Keywords: Morpho-Phonology, Natural Language Processing.

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Authors: Petr Morávek, Miloš Šeda

Abstract:

In practice, we often come across situations where it is necessary to make decisions based on incomplete or uncertain data. In control systems it may be due to the unknown exact mathematical model, or its excessive complexity (e.g. nonlinearity) when it is necessary to simplify it, respectively, to solve it using a rule base. In the case of databases, searching data we compare a similarity measure with of the requirements of the selection with stored data, where both the select query and the data itself may contain vague terms, for example in the form of linguistic qualifiers. In this paper, we focus on the processing of uncertain data in databases and demonstrate it on the example multi-criteria decision making in the selection of variants, specified by higher number of technical parameters.

Keywords: fuzzy logic, linguistic variable, multicriteria decision

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: A. Deswal, N. S. Deora, H. N. Mishra

Abstract:

The aim of the present study was to develop a rapid method for electronic nose for online quality control of oat milk. Analysis by electronic nose and bacteriological measurements were performed to analyze spoilage kinetics of oat milk samples stored at room temperature and refrigerated conditions for up to 15 days. Principal component analysis (PCA), Discriminant Factorial Analysis (DFA) and Soft Independent Modelling by Class Analogy (SIMCA) classification techniques were used to differentiate the samples of oat milk at different days. The total plate count (bacteriological method) was selected as the reference method to consistently train the electronic nose system. The e-nose was able to differentiate between the oat milk samples of varying microbial load. The results obtained by the bacteria total viable countsshowed that the shelf-life of oat milk stored at room temperature and refrigerated conditions were 20hrs and 13 days, respectively. The models built classified oat milk samples based on the total microbial population into “unspoiled” and “spoiled”.

Keywords: Electronic-nose, bacteriological, shelf-life, classification.

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Authors: Ahmed Madian, Muaz Aljarhi

Abstract:

Coordinate Rotation Digital Computer (CORDIC) is a unique digital computing unit intended for the computation of mathematical operations and functions. This paper presents A multi CORDIC processor that integrates different CORDIC architectures on a single FPGA chip and allows the user to select the CORDIC architecture to proceed with based on what he wants to calculate and his needs. Synthesis show that radix 2 CORDIC has the lowest clock delay, radix 8 CORDIC has the highest LUT usage and lowest register usage while Hybrid Radix 4 CORDIC had the highest clock delay.

Keywords: Multi, CORDIC, FPGA, Processor.

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Authors: Kedit J.

Abstract:

This paper is the tomographic images reconstruction simulation for defects detection in specimen. The specimen is the thin cylindrical steel contained with low density materials. The defects in material are simulated in three shapes.The specimen image function will be transformed to projection data. Radon transform and its inverse provide the mathematical for reconstructing tomographic images from projection data. The result of the simulation show that the reconstruction images is complete for defect detection.

Keywords: Tomography, Tomography Reconstruction, Radon Transform

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Authors: E. K.Appiah, G. M'boungui, A. A. Jimoh, J. L. Munda, A.S.O. Ogunjuyigbe

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The operational behavior of a six-phase squirrel cage induction machine with faulted stator terminals is presented in this paper. The study is carried out using the derived mathematical model of the machine in the arbitrary reference frame. Tests are conducted on a 1 kW experimental machine. Steady-state and dynamic performance are analyzed for the machine unloaded and loaded conditions. The results shows that with one of the stator phases experiencing either an open- circuit or short circuit fault the machine still produces starting torque, albeit the running performance is significantly derated.

Keywords: Performance, fault conditions, six-phase induction machine.

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Authors: Wei Dong, Guo-Ying Gu, Xiangyang Zhu, Han Ding

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This paper presents preliminary results on modeling and control of a quadrotor UAV. With aerodynamic concepts, a mathematical model is firstly proposed to describe the dynamics of the quadrotor UAV. Parameters of this model are identified by experiments with Matlab Identify Toolbox. A group of PID controllers are then designed based on the developed model. To verify the developed model and controllers, simulations and experiments for altitude control, position control and trajectory tracking are carried out. The results show that the quadrotor UAV well follows the referenced commands, which clearly demonstrates the effectiveness of the proposed approach.

Keywords: Quadrotor UAV, Modeling, Control, Aerodynamics, System Identification.

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Authors: Wah Wah Aung, Cho Cho San

Abstract:

The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.

Keywords: boundary conditions, conservation laws, finite difference Schemes, traffic flow.

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