Search results for: Double dispersion

Authors: Chang Liu, Zishu He

Abstract:

Adaptive echo cancellers with two-path algorithm are applied to avoid the false adaptation during the double-talk situation. In the two-path algorithm, several transfer logic solutions have been proposed to control the filter update. This paper presents an improved transfer logic solution. It improves the convergence speed of the two-path algorithm, and allows the reduction of the memory elements and computational complexity. Results of simulations show the improved performance of the proposed solution.

Keywords: Acoustic echo cancellation, Echo return lossenhancement (ERLE), Two-path algorithm, Transfer logic

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Authors: Abdulatif Abdusalam, Mohamed Shaban

Abstract:

In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We then discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, Nonuniform fiber, Nonlinear pulse.

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Authors: S. Fawzia, M. A. Karim

Abstract:

The use of externally bonded Carbon Fiber Reinforced Polymer (CFRP) reinforcement has proven to be an effective technique to strengthen steel structures. An experimental study on CFRP bonded steel plate with double strap joint has been conducted and specimens are tested under tensile loadings. An empirical model has been developed using stress-based approach to predict ultimate capacity of the CFRP bonded steel structure. The results from the model are comparable with the experimental result with a reasonable accuracy.

Keywords: Carbon fibre reinforced polymer, shear stress, slip, effective bond, steel structure.

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Authors: Gianluca Cornetta, Abdellah Touhafi, David J. Santos, Jose Manuel Vazquez

Abstract:

A direct downconversion receiver implemented in 0.13 μm 1P8M process is presented. The circuit is formed by a single-end LNA, an active balun for conversion into balanced mode, a quadrature double-balanced passive switch mixer and a quadrature voltage-controlled oscillator. The receiver operates in the 2.4 GHz ISM band and complies with IEEE 802.15.4 (ZigBee) specifications. The circuit exhibits a very low noise figure of only 2.27 dB and dissipates only 14.6 mW with a 1.2 V supply voltage and is hence suitable for low-power applications.

Keywords: LNA, Active Balun, Passive Mixer, VCO, IEEE 802.15.4(ZigBee).

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Authors: A.Guntida, K. Suriye, S. Kunjara Na Ayudhya, J. Panpranot, P. Praserthdam

Abstract:

Propylene self-metathesis to ethylene and butene was studied over WOx/SiO2 catalysts at 450oC and atmospheric pressure. The WOx/SiO2 catalysts were prepared by incipient wetness impregnation of ammonium metatungstate aqueous solution. It was found that, adding nano-sized extra supports (SiO2 and TiO2) by physical mixing with the WOx/SiO2 enhanced propylene conversion. The UV-Vis and FT-Raman results revealed that WOx could migrate from the original silica support to the extra support, leading to a better dispersion of WOx. The ICP-OES results also indicate that WOx existed on the extra support. Coke formation was investigated on the catalysts after 10 h time-on-stream by TPO. However, adding nano-sized extra supports led to higher coke formation which may be related to acidity as characterized by NH3-TPD.

Keywords: Extra support, nanomaterial, propylene self-metathesis, tungsten oxide.

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Authors: M. M. Doustdar , M. Mojtahedpoor

Abstract:

This paper addresses one important aspect of combustion system analysis, the spray evaporation and dispersion modeling. In this study we assume an empty cylinder which is as a simulator for a ramjet engine and the cylinder has been studied by cold flow. Four nozzles have the duties of injection which are located in the entrance of cylinder. The air flow comes into the cylinder from one side and injection operation will be done. By changing injection velocity and entrance air flow velocity, we have studied droplet sizing and efficient mass fraction of fuel vapor near and at the exit area. We named the mass of fuel vapor inside the flammability limit as the efficient mass fraction. Further, we decreased the initial temperature of fuel droplets and we have repeated the investigating again. To fulfill the calculation we used a modified version of KIVA-3V.

Keywords: Ramjet, droplet sizing, injection velocity, air flow velocity, efficient mass fraction.

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Authors: A. Satour, F. Boubenider, R. Halimi, A. Badidibouda

Abstract:

Sandwich plates are finding an increasing range of application in the aircraft industry. The inspection of honeycomb composite structure by conventional ultrasonic technique is complex and very time consuming. The present study demonstrates a technique using guided Lamb waves at low frequencies to predict de-bond defects in aluminum skin-honeycomb core sandwich structure used in aeronautics. The numerical method was investigated for drawing the dispersion and displacement curves of ultrasonic Lamb wave propagated in Aluminum plate. An experimental study was carried out to check the theoretical prediction. The detection of unsticking between the skin and the core was tested by the two first modes for a low frequency. It was found that A0 mode is more sensitive to delamination defect compared to S0 mode.

Keywords: Damage detection, delamination, guided waves, Sandwich structure.

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Authors: Jatinderdeep Kaur

Abstract:

In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

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Authors: S. Levitsky, R. Bergman

Abstract:

Fluid rheology may have essential impact on sound propagation in a liquid-filled pipe, especially, in a low frequency range. Rheological parameters of liquid are temperature-sensitive, which ultimately results in a temperature dependence of the wave speed and attenuation in the waveguide. The study is devoted to modeling of this effect at sound propagation in an elastic pipe with polymeric liquid, described by generalized Maxwell model with non-zero high-frequency viscosity. It is assumed that relaxation spectrum is distributed according to the Spriggs law; temperature impact on the liquid rheology is described on the basis of the temperature-superposition principle and activation theory. The dispersion equation for the waveguide, considered as a thin-walled tube with polymeric solution, is obtained within a quasi-one-dimensional formulation. Results of the study illustrate the influence of temperature on sound propagation in the system.

Keywords: Elastic tube, sound propagation, temperature effect, viscoelastic liquid.

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Authors: Sukhleen Bindra Narang, Dalveer Kaur, Kunal Pubby

Abstract:

Dielectric ceramic samples in the BaO-Re2O3-TiO2 ternary system were synthesized with structural formula Ba2- xRe4+2x/3Ti8O24 where Re= rare earth metal and Re= Sm and La where x varies from 0.0 to 0.6 with step size 0.1. Polycrystalline samples were prepared by the conventional solid state reaction technique. The dielectric, electrical and impedance analysis of all the samples in the frequency range 1KHz- 1MHz at room temperature (25°C) have been done to get the understanding of electrical conduction and dielectric relaxation and their correlation. Dielectric response of the samples at lower frequencies shows dielectric dispersion while at higher frequencies it shows dielectric relaxation. The ac conductivity is well fitted by the Jonscher law. The spectroscopic data in the impedance plane confirms the existence of grain contribution to the relaxation. All the properties are found out to be function of frequency as well as the amount of substitution.

Keywords: Dielectric ceramics, Dielectric constant, Loss tangent, AC conductivity, Impedance spectroscopy.

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Authors: J. B. Seo, K. J. Kim, S. W. Nam

Abstract:

In this paper, a nonlinear acoustic echo cancellation (AEC) system is proposed, whereby 3rd order Volterra filtering is utilized along with a variable step-size Gauss-Seidel pseudo affine projection (VSSGS-PAP) algorithm. In particular, the proposed nonlinear AEC system is developed by considering a double-talk situation with near-end signal variation. Simulation results demonstrate that the proposed approach yields better nonlinear AEC performance than conventional approaches.

Keywords: Acoustic echo cancellation (AEC), Volterra filtering, variable step-size, GS-PAP.

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Authors: Hamad K. Al-Khalid, Ayman M. Alaskari, Samy E. Oraby

Abstract:

Hardness of the widely used structural steel is of vital importance since it may help in the determination of many mechanical properties of a material under loading situations. In order to obtain reliable information for design, properties homogeneity should be validated. In the current study the hardness variation over the different diameters of the same AISI 4140 bar is investigated. Measurements were taken on the two faces of the stock at equally spaced eight sectors and fifteen layers. Statistical and graphical analysis are performed to asses the distribution of hardness measurements over the specified area. Hardness measurements showed some degree of dispersion with about ± 10% of its nominal value provided by manufacturer. Hardness value is found to have a slight decrease trend as the diameter is reduced. However, an opposite behavior is noticed regarding the sequence of the sector indicating a nonuniform distribution over the same area either on the same face or considering the corresponding sector on the other face (cross section) of the same material bar.

Keywords: Hardness; Hardness variation; AISI 4140 steel; Bardiameter; Statistical Analysis.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

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Authors: Georgios C. Dogiamis, Bedrich J. Hosticka, Anton Grabmaier

Abstract:

In this work the effects of uniaxial mechanical stress on a pixel readout circuit are theoretically analyzed. It is the effects of mechanical stress on the in-pixel transistors do not arise at the output, when a correlated double sampling circuit is used. However, mechanical stress effects on the photodiode will directly appear at the readout chain output. Therefore, compensation techniques are needed to overcome this situation. Moreover simulation technique of mechanical stress is proposed and diverse layout as well as design recommendations are put forward, in order to minimize stress related effects on the output of a circuit. he shown, that wever, Moreover, a out

Keywords: mechanical uniaxial stress, pixel readout circuit

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Authors: Porag Jyoti Ligira, Gargi Khanna

Abstract:

The paper presents a simulation study of the electrical characteristic of Bulk Planar Junctionless Transistor (BPJLT) using spacer. The BPJLT is a transistor without any PN junctions in the vertical direction. It is a gate controlled variable resistor. The characteristics of BPJLT are analyzed by varying the oxide material under the gate. It can be shown from the simulation that an ideal subthreshold slope of ~60 mV/decade can be achieved by using highk dielectric. The effects of variation of spacer length and material on the electrical characteristic of BPJLT are also investigated in the paper. The ION / IOFF ratio improvement is of the order of 107 and the OFF current reduction of 10-4 is obtained by using gate dielectric of HfO2 instead of SiO2.

Keywords: BPJLT, double gate, high-k, spacer.

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Authors: M. F. V. Montezuma, E. P. Deus, M. C. Carvalho

Abstract:

Steel bridges are normally subjected to random loads with different traffic frequencies. They are structures with dynamic behavior and are subject to fatigue failure process, where the nucleation of a crack, growth and failure can occur. After locating and determining the size of an existing fault, it is important to predict the crack propagation and the convenient time for repair. Therefore, fracture mechanics and fatigue concepts are essential to the right approach to the problem. To study the fatigue crack growth, a computational code was developed by using the root mean square (RMS) and the cycle-by-cycle models. One observes the variable amplitude loading influence on the life structural prediction. Different loads histories and initial crack length were considered as input variables. Thus, it was evaluated the dispersion of results of the expected structural life choosing different initial parameters.

Keywords: Fatigue crack propagation, life prediction, variable loadings, steel bridges.

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Authors: Walid M. Saad

Abstract:

techniques are examined to overcome the performance degradation caused by the channel dispersion using slow frequency hopping (SFH) with dynamic frequency hopping (DFH) pattern adaptation. In DFH systems, the frequency slots are selected by continuous quality monitoring of all frequencies available in a system and modification of hopping patterns for each individual link based on replacing slots which its signal to interference ratio (SIR) measurement is below a required threshold. Simulation results will show the improvements in BER obtained by DFH in comparison with matched frequency hopping (MFH), random frequency hopping (RFH) and multi-carrier code division multiple access (MC-CDMA) in multipath slowly fading dispersive channels using a generalized bandpass two-path transfer function model, and will show the improvement obtained according to the threshold selection.

Keywords: code division multiple access (CDMA), dynamic channel allocation (DCA), dynamic channel assignment, frequency hopping, matched frequency hopping (MFH).

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Authors: A. Jawahar

Abstract:

In this paper, the dependence of soliton pulses with respect to phase in a 10Gbps, single channel, dispersion uncompensated telecommunication system was studied. The characteristic feature of periodic soliton interaction was noted at the Interaction point (I=6202.5Km) in one collision length of L=12405.1 Km. The interaction point is located for 10Gbps system with an initial relative spacing (qo) of soliton as 5.28 using Perturbation theory. It is shown that, when two in-phase solitons are launched, they interact at the point I=6202.5 Km, but the interaction could be restricted with introduction of different phase initially. When the phase of the input solitons increases, the deviation of soliton pulses at the ‘I’ also increases. We have successfully demonstrated this effect in a telecommunication set-up in terms of Quality factor (Q), where the Q=0 for in-phase soliton. The Q was noted to be 125.9, 38.63, 47.53, 59.60, 161.37, and 78.04 for different phases such as 10o, 20o, 30o, 45o, 60o and 90o degrees respectively at Interaction point (I).

Keywords: Soliton interaction, Initial relative spacing, phase, Perturbation theory and telecommunication system.

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Authors: A. Amar, N. Burtebayev, Kerimkulov Zhambul, Sh. Hamada, N. Amangeldi

Abstract:

the elastic scattering of protons, deuterons and 3He on 6Li at different incident energies have been analyzed in the framework of the optical model using ECIS88 as well as SPI GENOA codes. The potential parameters were extracted in the phenomenological treatment of measured by us angular distributions and literature data. A good agreement between theoretical and experimental differential cross sections was obtained in whole angular range. Parameters for real part of potential have been also calculated microscopically with singleand double-folding model for the p and d, 3He scattering, respectively, using DFPOT code. For best agreement with experiment the normalization factor N for the potential depth is obtained in the range of 0.7-0.9.

Keywords: Elastic scattering, Esis88 Code single and doublefolding model, phenomenological, DWBA.

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Authors: A. Taqaddas

Abstract:

Purpose: Planning and dosimetry of different VMAT algorithms (SmartArc, Ergo++, Autobeam) is compared with IMRT for Head and Neck Cancer patients. Modelling was performed to rule out the causes of discrepancies between planned and delivered dose. Methods: Five HNC patients previously treated with IMRT were re-planned with SmartArc (SA), Ergo++ and Autobeam. Plans were compared with each other and against IMRT and evaluated using DVHs for PTVs and OARs, delivery time, monitor units (MU) and dosimetric accuracy. Modelling of control point (CP) spacing, Leaf-end Separation and MLC/Aperture shape was performed to rule out causes of discrepancies between planned and delivered doses. Additionally estimated arc delivery times, overall plan generation times and effect of CP spacing and number of arcs on plan generation times were recorded. Results: Single arc SmartArc plans (SA4d) were generally better than IMRT and double arc plans (SA2Arcs) in terms of homogeneity and target coverage. Double arc plans seemed to have a positive role in achieving improved Conformity Index (CI) and better sparing of some Organs at Risk (OARs) compared to Step and Shoot IMRT (ss-IMRT) and SA4d. Overall Ergo++ plans achieved best CI for both PTVs. Dosimetric validation of all VMAT plans without modelling was found to be lower than ss-IMRT. Total MUs required for delivery were on average 19%, 30%, 10.6% and 6.5% lower than ss-IMRT for SA4d, SA2d (Single arc with 2⁰ Gantry Spacing), SA2Arcs and Autobeam plans respectively. Autobeam was most efficient in terms of actual treatment delivery times whereas Ergo++ plans took longest to deliver. Conclusion: Overall SA single arc plans on average achieved best target coverage and homogeneity for both PTVs. SA2Arc plans showed improved CI and some OARs sparing. Very good dosimetric results were achieved with modelling. Ergo++ plans achieved best CI. Autobeam resulted in fastest treatment delivery times.

Keywords: Dosimetry, Intensity Modulated Radiotherapy, Optimization Algorithms, Volumetric Modulated Arc Therapy.

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Authors: Ju-Na Hwang, Yong-Jun Park, Min-Hae Park, Kee-Joe Lim

Abstract:

Many studies have been conducted on DC transmission. Of power apparatus for DC transmission, high voltage direct current (HVDC) cable systems are being evaluated because of the increase in power demand and transmission distance. Therefore, dc insulation characteristics of liquid silicone rubber (LSR), which has various advantages such as short curing time and the ease of maintenance, were investigated to assess its performance as a HVDC insulation material for cable joints. The electrical performance of LSR added to nano-aluminum trihydrate (ATH) were confirmed by measurements of the breakdown strength and electrical conductivity. In addition, field emission scanning electron microscope (FE-SEM) was used as a means of confirmation of nanofiller dispersion state. The LSR nanocomposite was prepared by compounding LSR filled nano-sized ATH filler. The dc insulation properties of LSR added to nano-sized ATH fillers were found to be superior to those of the LSR without a filler. 

Keywords: Liquid silicone rubber, Nanocomposite, Nano-ATH, HVDC insulation, Cable joints.

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Authors: Hala A. Hassan, Vasiliki K. Tsiouri, Konstantinos E. Konstantinos

Abstract:

Fugitive particulate matter (PM) is a major source of airborne pollution in the Middle East countries. The meteorological conditions and topography of the area makes it highly susceptible to wind-blown particles which raise many air quality concerns. Air quality tools such as field monitoring, emission factors and dispersion modeling have been used in previous research studies to analyze the release and impacts of fugitive PM in the region. However, these tools have been originally developed based on experiments made for European and North American regions. In this work, an experimental campaign was conducted on April-May 2014 in a construction site in Doha city, Qatar. The ultimate goal is to evaluate the applicability of the existing emission factors for construction sites in dry and arid areas like the Middle East.

Keywords: Air pollution, construction, emissions, middle east, fugitive particulate matter.

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Authors: Bruno Henriques, Rafaela Santos, Mihaela Buciumeanu, Júlio Matias de Souza, Filipe Silva, Rubens Nascimento, Márcio Fredel

Abstract:

Dental porcelain composites reinforced and toughened by 20 wt.% tetragonal zirconia (3Y-TZP) were processed by hot pressing at 1000°C. Two types of particles were tested: yttriastabilized zirconia (ZrO2–3%Y2O3) agglomerates and pre-sintered yttria-stabilized zirconia (ZrO2–3%Y2O3) particles. The composites as well as the reinforcing particles were analyzed by the means of optical and Scanning Electron Microscopy (SEM), Energy Dispersion Spectroscopy (EDS) and X-Ray Diffraction (XRD). The mechanical properties were obtained by the transverse rupture strength test. Wear tests were also performed on the composites and monolithic porcelain. The best mechanical results were displayed by the porcelain reinforced with the pre-sintered ZrO2–3%Y2O3 agglomerates.

Keywords: Composite, dental restoration, porcelain, strengthening, toughening, wear, zirconia.

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Authors: Y. Bentoutou, A.M. Si Mohammed

Abstract:

This paper presents a review of an 8-year study on radiation effects in commercial memory devices operating within the main on-board computer system OBC386 of the Algerian microsatellite Alsat-1. A statistical analysis of single-event upset (SEU) and multiple-bit upset (MBU) activity in these commercial memories shows that the typical SEU rate at alsat-1's orbit is 4.04 × 10-7 SEU/bit/day, where 98.6% of these SEUs cause single-bit errors, 1.22% cause double-byte errors, and the remaining SEUs result in multiple-bit and severe errors.

Keywords: Radiation effects, error detection and correction, satellite computer, small satellite mission.

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Authors: R. Santos Jiménez, A. San-Antonio-González, M. Del Río Merino, M. González Cortina, C. Viñas Arrebola

Abstract:

In this study, the feasibility of incorporating ceramic waste from bricks (perforated brick and double hollow brick) and extruded polystyrene (XPS) waste, is analysed. Results show that it is possible to incorporate up to 25% of ceramic waste and 4% of XPS waste over the weight of gypsum in a gypsum matrix. Furthermore, with the addition of ceramic waste an 8% of surface hardness increase and a 25% of capillary water absorption reduction can be obtained. On the other hand, with the addition of XPS, a 26% reduction of density and a 37% improvement of thermal conductivity can be obtained. The obtained results are favorable to use these materials in order to produce prefabricated gypsum and also as material for interior cladding walls.

Keywords: CDW, waste materials, ceramic waste, XPS, construction materials, gypsum.

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Authors: Habib Shaban

Abstract:

Nanocomposites of isotactic polypropylene (iPP) and date wood fiber were prepared after modification of the host matrix by reactive extrusion grafting of maleic anhydride. Chemical and mechanical treatment of date wood flour (WF) was conducted to obtain nanocrystalline cellulose. Layered silicates (clay) were partially intercalated with date wood fiber, and the modified layered silicate was used as filler in the PP matrix via a melt-blending process. The tensile strength of composites prepared from wood fiber modified clay was greater than that of the iPP-clay and iPP-WF composites at a 6% filler concentration, whereas deterioration of mechanical properties was observed when clay and WF were used alone for reinforcement. The dispersion of the filler in the matrix significantly decreased after clay modification with cellulose at higher concentrations, as shown by X-ray diffraction (XRD) data.

Keywords: Nanocomposites, isotactic polypropylene, date wood flour, intercalated, melt-blending.

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Authors: Y. Bentoutou

Abstract:

Memory Errors Detection and Correction aim to secure the transaction of data between the central processing unit of a satellite onboard computer and its local memory. In this paper, the application of a double-bit error detection and correction method is described and implemented in Field Programmable Gate Array (FPGA) technology. The performance of the proposed EDAC method is measured and compared with two different EDAC devices, using the same FPGA technology. Statistical analysis of single-event upset (SEU) and multiple-bit upset (MBU) activity in commercial memories onboard the first Algerian microsatellite Alsat-1 is given.

Keywords: Error Detection and Correction, On-board computer, small satellite missions.

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Authors: Chien-Hung Chen, Yan-Chun Hsing, Yung-Chun Chang

Abstract:

The Internet has grown into a powerful medium for information dispersion and social interaction that leads to a rapid growth of social media which allows users to easily post their emotions and perspectives regarding certain topics online. Our research aims at using natural language processing and text mining techniques to explore the public emotions expressed on Twitter by analyzing the sentiment behind tweets. In this paper, we propose a composite kernel method that integrates tree kernel with the linear kernel to simultaneously exploit both the tree representation and the distributed emotion keyword representation to analyze the syntactic and content information in tweets. The experiment results demonstrate that our method can effectively detect public emotion of tweets while outperforming the other compared methods.

Keywords: Public emotion recognition, natural language processing, composite kernel, sentiment analysis, text mining.

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

Abstract:

A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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