Search results for: power method.

Authors: Mohsen Zand, Ahmadreza Naghsh Nilchi, S. Amirhassan Monadjemi

Abstract:

Optical character recognition of cursive scripts presents a number of challenging problems in both segmentation and recognition processes in different languages, including Persian. In order to overcome these problems, we use a newly developed Persian word segmentation method and a recognition-based segmentation technique to overcome its segmentation problems. This method is robust as well as flexible. It also increases the system-s tolerances to font variations. The implementation results of this method on a comprehensive database show a high degree of accuracy which meets the requirements for commercial use. Extended with a suitable pre and post-processing, the method offers a simple and fast framework to develop a full OCR system.

Keywords: OCR, Persian, Recognition, Segmentation.

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Authors: Maziar Sadeghi, Amir Moradi

Abstract:

This paper proposes a robot able to climb Columns. This robot is not dependent on the diameter and material of the columns. Some climbing robots have been designed up to now but Koala robot was designed and fabricated for climbing columns exclusively. Simple kinematics of climbing in the nature inspired us to design this robot. We used two linear mechanisms to grip the column. The gripper consists of a DC motor and a power screw mechanism with a linear bushing as a guide. This mechanism provides enough force to grip the column. In addition we needed an actuator for climbing the column; hence, two pneumatic jacks were used. All the mechanical parts were designed according to the exerted forces and operational condition. The prototype can be simply installed and controlled on the column by an inexperienced operator. This robot is intended for inspection and surveillance of pipes in oil industries and power poles in electric industries.

Keywords: Robot, Column-climber, Gripping mechanism, Koala.

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Authors: S. S. Deswal, Ratna Dahiya, D. K. Jain

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Process control and energy conservation are the two primary reasons for using an adjustable speed drive. However, voltage sags are the most important power quality problems facing many commercial and industrial customers. The development of boost converters has raised much excitement and speculation throughout the electric industry. Now utilities are looking to these devices for performance improvement and reliability in a variety of areas. Examples of these include sags, spikes, or transients in supply voltage as well as unbalanced voltages, poor electrical system grounding, and harmonics. In this paper, simulations results are presented for the verification of the proposed boost converter topology. Boost converter provides ride through capability during sag and swell. Further, input currents are near sinusoidal. This eliminates the need of braking resistor also.

Keywords: Adjustable speed drive, power quality, boost converter, ride through capabilities.

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Authors: Y. Zheng, W. Sun

Abstract:

This paper describes a new approach which can be used to interpret the experimental creep deformation data obtained from miniaturized thin plate bending specimen test to the corresponding uniaxial data based on an inversed application of the reference stress method. The geometry of the thin plate is fully defined by the span of the support, l, the width, b, and the thickness, d. Firstly, analytical solutions for the steady-state, load-line creep deformation rate of the thin plates for a Norton’s power law under plane stress (b→0) and plane strain (b→∞) conditions were obtained, from which it can be seen that the load-line deformation rate of the thin plate under plane-stress conditions is much higher than that under the plane-strain conditions. Since analytical solution is not available for the plates with random b-values, finite element (FE) analyses are used to obtain the solutions. Based on the FE results obtained for various b/l ratios and creep exponent, n, as well as the analytical solutions under plane stress and plane strain conditions, an approximate, numerical solutions for the deformation rate are obtained by curve fitting. Using these solutions, a reference stress method is utilised to establish the conversion relationships between the applied load and the equivalent uniaxial stress and between the creep deformations of thin plate and the equivalent uniaxial creep strains. Finally, the accuracy of the empirical solution was assessed by using a set of “theoretical” experimental data.

Keywords: Bending, Creep, Miniature Specimen, Thin Plate.

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Authors: S. Khademi, A. Darudi, Z. Abbasi

Abstract:

One of the main limitations for the resolution of optical instruments is the size of the sensor-s pixels. In this paper we introduce a new sub pixel resolution algorithm to enhance the resolution of images. This method is based on the analysis of multiimages which are fast recorded during the fine relative motion of image and pixel arrays of CCDs. It is shown that by applying this method for a sample noise free image one will enhance the resolution with 10-14 order of error.

Keywords: Sub Pixel Resolution, Moving Pixels, CCD, Image, Optical Instrument.

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Authors: Livinus A. Obasi, Augustine N. Ajah

Abstract:

Biotechnology in recent times has tried to develop a mechanism whereby sustainable electricity can be generated by the activity of microorganisms on waste and renewable biomass (often regarded as “negative value”) in a device called microbial fuel cell, MFC. In this paper, we established how the biocatalytic activities of bacteria on organic matter (substrates) produced some electrons with the associated removal of some water pollution parameters; Biochemical oxygen demand (BOD), chemical oxygen demand (COD) to the tune of 77.2% and 88.3% respectively from a petrochemical sanitary wastewater. The electricity generation was possible by conditioning the bacteria to operate anaerobically in one chamber referred to as the anode while the electrons are transferred to the fully aerated counter chamber containing the cathode. Power densities ranging from 12.83 mW/m² to 966.66 mW/m² were achieved using a dual-chamber starch membrane MFC experimental set-up. The maximum power density obtained in this research shows an improvement in the use of low cost MFC set up to achieve power production. Also, the level of organic matter removal from the sanitary waste water by the operation of this device clearly demonstrates its potential benefit in achieving an improved benign environment. The beauty of the MFCs is their potential utility in areas lacking electrical infrastructures like in most developing countries.

Keywords: Bioelectricity, chemical oxygen demand, microbial fuel cell, sanitary wastewater, wheat starch.

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Authors: I. Razmi, N. Choupani

Abstract:

The incidence of mechanical fracture of an automobile piston rings prompted development of fracture analysis method on this case. The three rings (two compression rings and one oil ring) were smashed into several parts during the power-test (after manufacturing the engine) causing piston and liner to be damaged. The radial and oblique cracking happened on the failed piston rings. The aim of the fracture mechanics simulations presented in this paper was the calculation of particular effective fracture mechanics parameters, such as J-integrals and stress intensity factors. Crack propagation angles were calculated as well. Two-dimensional fracture analysis of the first compression ring has been developed in this paper using ABAQUS CAE6.5-1 software. Moreover, SEM fractography was developed on fracture surfaces and is discussed in this paper. Results of numerical calculations constitute the basis for further research on real object.

Keywords: Compression piston ring, Crack, Fracture mechanics, SEM fractography.

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Authors: Leena Korpinen, Rauno Pääkkönen, Fabriziomaria Gobba, Vesa Virtanen

Abstract:

The number of persons with implanted cardiac pacemakers (PM) has increased in Western countries. The aim of this paper is to investigate the possible situations where persons with a PM may be exposed to extremely low frequency (ELF) electric (EF) and magnetic fields (MF) that may disturb their PM. Based on our earlier studies, it is possible to find such high public exposure to EFs only in some places near 400 kV power lines, where an EF may disturb a PM in unipolar mode. Such EFs cannot be found near 110 kV power lines. Disturbing MFs can be found near welding machines. However, we do not have measurement data from welding. Based on literature and earlier studies at Tampere University of Technology, it is difficult to find public EF or MF exposure that is high enough to interfere with PMs.

Keywords: Cardiac Pacemaker, Electric Field, Magnetic Field.

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Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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Authors: T. Kerdchuen

Abstract:

This paper proposes the stochastic tabu search (STS) for improving the measurement scheme for power system state estimation. If the original measured scheme is not observable, the additional measurements with minimum number of measurements are added into the system by STS so that there is no critical measurement pair. The random bit flipping and bit exchanging perturbations are used for generating the neighborhood solutions in STS. The Pδ observable concept is used to determine the network observability. Test results of 10 bus, IEEE 14 and 30 bus systems are shown that STS can improve the original measured scheme to be observable without critical measurement pair. Moreover, the results of STS are superior to deterministic tabu search (DTS) in terms of the best solution hit.

Keywords: Measurement Scheme, Power System StateEstimation, Network Observability, Stochastic Tabu Search (STS).

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Authors: Jinseon Song, Yongwan Park

Abstract:

In this paper, propose method that can user’s position that based on database is built from single camera. Previous positioning calculate distance by arrival-time of signal like GPS (Global Positioning System), RF(Radio Frequency). However, these previous method have weakness because these have large error range according to signal interference. Method for solution estimate position by camera sensor. But, signal camera is difficult to obtain relative position data and stereo camera is difficult to provide real-time position data because of a lot of image data, too. First of all, in this research we build image database at space that able to provide positioning service with single camera. Next, we judge similarity through image matching of database image and transmission image from user. Finally, we decide position of user through position of most similar database image. For verification of propose method, we experiment at real-environment like indoor and outdoor. Propose method is wide positioning range and this method can verify not only position of user but also direction.

Keywords: Positioning, Distance, Camera, Features, SURF (Speed-Up Robust Features), Database, Estimation.

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Authors: Hiromitsu Ogawa, Manato Ono, Naohiro Ban, Yoshihisa Ishida

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This paper describes the two stage control using a disturbance observer and a Kalman filter. The system feedback uses the estimated state when it controls the speed. After the change-over point, its feedback uses the controlled plant output when it controls the position. To change the system continually, a change-over point has to be determined pertinently, and the controlled plant input has to be adjusted by the addition of the appropriate value. The proposed method has noise-reduction effect. It changes the system continually, even if the controlled plant identification has the error. Although the conventional method needs a speed sensor, the proposed method does not need it. The proposed method has a superior robustness compared with the conventional two stage control.

Keywords: Disturbance observer, kalman filter, optimal control, two stage control.

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Authors: Thang Manh Hoang

Abstract:

Recent research result has shown that two multidelay feedback systems can synchronize each other under different schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating synchronization. There, the driving signal is significantly complex due that it is constituted by multiple nonlinear transformations of delayed state variable. In this paper, a secure communication model is proposed based on synchronization of coupled multidelay feedback systems, in which the plain signal is mixed with a complex signal at the transmitter side and it is precisely retrieved at the receiver side. The effectiveness of the proposed model is demonstrated and verified in the specific example, where the message signal is masked directly by the complex signal and security is examined under the breaking method of power spectrum analysis.

Keywords: chaos synchronization, time-delayed system, chaosbasedsecure communications

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: Rahmatollah Hooshmand, Mahdi Banejad

Abstract:

One of the problems in fault diagnosis of transformer based on dissolved gas, is lack of matching the result of fault diagnosis of different standards with the real world. In this paper, the result of the different standards is analyzed using fuzzy and the result is compared with the empirical test. The comparison between the suggested method and existing methods indicate the capability of the suggested method in on-line fault diagnosis of the transformers. In addition, in some cases the existing standards are not able to diagnose the fault. In theses cases, the presented method has the potential of diagnosing the fault. The information of three transformers is used to the show the capability of the suggested method in diagnosing the fault. The results validate the capability of the presented method in fault diagnosis of the transformer.

Keywords: Fault Diagnosis of Transformer, Dissolved Gas, Fuzzy Logic.

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Authors: P. Paengkoum, T. Phonmun, S. Paengkoum

Abstract:

Twenty four male Thai native × Anglo-Nubian crossbred goats were randomly allocated to receive four treatments. The experiment was conducted for four months and slaughtered that the Longissimus dorsi muscle was collected for fatty acid analysis. The results conclude that either castrated method or ages had no significantly different on monounsaturated fatty acid (MUFA) (P>0.05) except erucic acid (C22:1n9). Interaction between castrated method and ages had significantly different in MUFA (P<0.01). Although the effect of castration method and age are not difference on fatty acid composition, it contributed to known that difference castration method and age (surgical and budizzo) no effect on accumulation fatty acid in meat goats.

Keywords: Castration, goat, CLA, meat.

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Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

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The objective of positioning the fixture elements in the fixture is to make the workpiece stiff, so that geometric errors in the manufacturing process can be reduced. Most of the work for optimal fixture layout used the minimization of the sum of the nodal deflection normal to the surface as objective function. All deflections in other direction have been neglected. We propose a new method for fixture layout optimization in this paper, which uses the element strain energy. The deformations in all the directions have been considered in this way. The objective function in this method is to minimize the sum of square of element strain energy. Strain energy and stiffness are inversely proportional to each other. The optimization problem is solved by the sequential quadratic programming method. Three different kinds of case studies are presented, and results are compared with the method using nodal deflections as objective function to verify the propose method.

Keywords: Fixture layout, optimization, strain energy, quadratic programming.

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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Authors: Ahmed Hossam_ ElDin, Ahmed Farag, Ibrahim Madi., Hanaa Karawia

Abstract:

In our modern society electricity is vital to our health, safety, comfort and well-being. While our daily use of electricity is often taken for granted, public concern has arisen about potential adverse health effects from electric and magnetic – electromagnetic – fields (EMFs) produced by our use of electricity. This paper aims to compare between the measured magnetic field values and the simulated models for the indoor medium to low voltage (MV/LV) distribution substations. To calculate the magnetic flux density in the substations, interactive software SUBCALC is used which is based on closed form solution of the Biot-Savart law with 3D conductor model. The comparison between the measured values and the simulated models was acceptable. However there were some discrepancies, as expected, may be due to the current variation during measurements.

Keywords: Distribution substation, magnetic field, measurement, simulation.

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Authors: Lukumba Phiri, Simon Tembo, Kumbuso Joshua Nyoni

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In Zambia, recent initiatives by various power operators like ZESCO, CEC, and consumers like the mines, to upgrade power systems into smart grids, target an even tighter integration with information technologies to enable the integration of renewable energy sources, local and bulk generation, and demand response. Thus, for the reliable operation of smart grids, its information infrastructure must be secure and reliable in the face of both failures and cyberattacks. Due to the nature of the systems, ICS/SCADA cybersecurity and governance face additional challenges compared to the corporate networks, and critical systems may be left exposed. There exist control frameworks internationally such as the NIST framework, however, they are generic and do not meet the domain-specific needs of the SCADA systems. Zambia is also lagging in cybersecurity awareness and adoption, and therefore there is a concern about securing ICS controlling key infrastructure critical to the Zambian economy as there are few known facts about the true posture. In this paper, we present a stochastic Edged-based Anomaly Detection for SCADA systems (SEADS) framework for threat modeling and risk assessment. SEADS enables the calculation of steady-steady probabilities that are further applied to establish metrics like system availability, maintainability, and reliability.

Keywords: Anomaly detection, SmartGrid, edge, maintainability, reliability, stochastic process.

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Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, element-free Galerkin, moving least squares, meshless methods.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

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This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: M. S. Anton Merkulov

Abstract:

This article discusses the questions concerning of creating small packet networks for energy companies with application of high voltage power line carrier equipment (PLC) with functionality of IP traffic transmission. The main idea is to create converged PLC links between substations and dispatching centers where packet data and voice are transmitted in one data flow. The article contents description of basic conception of the network, evaluation of voice traffic transmission parameters, and discussion of header compression techniques in relation to PLC links. The results of exploration show us, that convergent packet PLC links can be very useful in the construction of small packet networks between substations in remote locations, such as deposits or low populated areas.

Keywords: packet PLC, VoIP, time delay, packet traffic, overhead compression

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Authors: G. Shojatalab

Abstract:

In this paper, all variables are supposed to be integer and positive. In this modern method, objective function is assumed to be maximized or minimized but constraints are always explained like less or equal to. In this method, choosing a dual combination of ideal nonequivalent and omitting one of variables. With continuing this act, finally, having one nonequivalent with (n-m+1) unknown quantities in which final nonequivalent, m is counter for constraints, n is counter for variables of decision.

Keywords: Integer, Programming, Operation Research, Variables of decision.

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Authors: M. Gomaa Abdoelatef, Robert M. Field, Lee, Yong-Kwan

Abstract:

Growing human population has placed increased demands on water supplies and spurred a heightened interest in desalination infrastructure. Key elements of the economics of desalination projects are thermal and electrical inputs. With growing concerns over use of fossil fuels to (indirectly) supply these inputs, coupling of desalination with nuclear power production represents a significant opportunity. Individually, nuclear and desalination technologies have a long history and are relatively mature. For desalination, Reverse Osmosis (RO) has the lowest energy inputs. However, the economically driven output quality of the water produced using RO, which uses only electrical inputs, is lower than the output water quality from thermal desalination plants. Therefore, modern desalination projects consider that RO should be coupled with thermal desalination technologies (MSF, MED, or MED-TVC) with attendant steam inputs to permit blending to produce various qualities of water. A large nuclear facility is well positioned to dispatch large quantities of both electrical and thermal power. This paper considers the supply of thermal energy to a large desalination facility to examine heat balance impact on the nuclear steam cycle. The APR1400 nuclear plant is selected as prototypical from both a capacity and turbine cycle heat balance perspective to examine steam supply and the impact on electrical output. Extraction points and quantities of steam are considered parametrically along with various types of thermal desalination technologies to form the basis for further evaluations of economically optimal approaches to the interface of nuclear power production with desalination projects. In our study, the thermodynamic evaluation will be executed by DE-TOP, an IAEA sponsored program. DE-TOP has capabilities to analyze power generation systems coupled to desalination plants through various steam extraction positions, taking into consideration the isolation loop between the nuclear and the thermal desalination facilities (i.e., for radiological isolation).

Keywords: APR1400, Cogeneration, Desalination, DE-TOP, IAEA, MED, MED-TVC, MSF, RO.

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Authors: Reza Faghih Mirzaee, Mohammad Hossein Moaiyeri, Keivan Navi

Abstract:

In this paper we present two novel 1-bit full adder cells in dynamic logic style. NP-CMOS (Zipper) and Multi-Output structures are used to design the adder blocks. Characteristic of dynamic logic leads to higher speeds than the other standard static full adder cells. Using HSpice and 0.18┬Ám CMOS technology exhibits a significant decrease in the cell delay which can result in a considerable reduction in the power-delay product (PDP). The PDP of Multi-Output design at 1.8v power supply is around 0.15 femto joule that is 5% lower than conventional dynamic full adder cell and at least 21% lower than other static full adders.

Keywords: Bridge Style, Dynamic Logic, Full Adder, HighSpeed, Multi Output, NP-CMOS, Zipper.

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Authors: Abdolvahab Ehsani Rad, Mohd Shafry Mohd Rahim, Alireza Norouzi

Abstract:

Medical image analysis is one of the great effects of computer image processing. There are several processes to analysis the medical images which the segmentation process is one of the challenging and most important step. In this paper the segmentation method proposed in order to segment the dental radiograph images. Thresholding method has been applied to simplify the images and to morphologically open binary image technique performed to eliminate the unnecessary regions on images. Furthermore, horizontal and vertical integral projection techniques used to extract the each individual tooth from radiograph images. Segmentation process has been done by applying the level set method on each extracted images. Nevertheless, the experiments results by 90% accuracy demonstrate that proposed method achieves high accuracy and promising result.

Keywords: Integral production, level set method, morphological operation, segmentation.

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Authors: S.B. Thakre, L.B. Bhuyar, S.J. Deshmukh

Abstract:

This paper examines the use of mechanical aerator for oxidation-ditch process. The rotor, which controls the aeration, is the main component of the aeration process. Therefore, the objective of this study is to find out the variations in overall oxygen transfer coefficient (KLa) and aeration efficiency (AE) for different configurations of aerator by varying the parameters viz. speed of aerator, depth of immersion, blade tip angles so as to yield higher values of KLa and AE. Six different configurations of aerator were developed and fabricated in the laboratory and were tested for abovementioned parameters. The curved blade rotor (CBR) emerged as a potential aerator with blade tip angle of 47°. The mathematical models are developed for predicting the behaviour of CBR w.r.t kLa and power. In laboratory studies, the optimum value of KLa and AE were observed to be 10.33 h-1 and 2.269 kg O2/ kWh.

Keywords: Aerator, Aeration efficiency, Dissolve Oxygen, Overall oxygen transfer coefficient, Oxidation ditch.

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Authors: Li Qiang, Yang Ze-Ming, Liu Bao-Xu, Jiang Zheng-Wei

Abstract:

With the increasing complexity of cyberspace security, the cyber-attack attribution has become an important challenge of the security protection systems. The difficult points of cyber-attack attribution were forced on the problems of huge data handling and key data missing. According to this situation, this paper presented a reasoning method of cyber-attack attribution based on threat intelligence. The method utilizes the intrusion kill chain model and Bayesian network to build attack chain and evidence chain of cyber-attack on threat intelligence platform through data calculation, analysis and reasoning. Then, we used a number of cyber-attack events which we have observed and analyzed to test the reasoning method and demo system, the result of testing indicates that the reasoning method can provide certain help in cyber-attack attribution.

Keywords: Reasoning, Bayesian networks, cyber-attack attribution, kill chain, threat intelligence.

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Authors: Mohamed K. El Daou

Abstract:

We construct an exponentially weighted Legendre- Gauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to Sturm-Liouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented.

Keywords: Oscillatory functions, Sturm-Liouville problems, legendre polynomial, gauss points.

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