Search results for: Elliptic Curve Digital Signature Algorithm

Authors: Jérôme Azé, Mathieu Roche, Yves Kodratoff, Michèle Sebag

Abstract:

Term Extraction, a key data preparation step in Text Mining, extracts the terms, i.e. relevant collocation of words, attached to specific concepts (e.g. genetic-algorithms and decisiontrees are terms associated to the concept “Machine Learning" ). In this paper, the task of extracting interesting collocations is achieved through a supervised learning algorithm, exploiting a few collocations manually labelled as interesting/not interesting. From these examples, the ROGER algorithm learns a numerical function, inducing some ranking on the collocations. This ranking is optimized using genetic algorithms, maximizing the trade-off between the false positive and true positive rates (Area Under the ROC curve). This approach uses a particular representation for the word collocations, namely the vector of values corresponding to the standard statistical interestingness measures attached to this collocation. As this representation is general (over corpora and natural languages), generality tests were performed by experimenting the ranking function learned from an English corpus in Biology, onto a French corpus of Curriculum Vitae, and vice versa, showing a good robustness of the approaches compared to the state-of-the-art Support Vector Machine (SVM).

Keywords: Text-mining, Terminology Extraction, Evolutionary algorithm, ROC Curve.

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Authors: Roger L Goodwin

Abstract:

This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, ”first-glance” correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve.

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: Path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart.

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Authors: Ashutosh Kumar Singh, Anand Mohan

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This paper deals with efficient computation of probability coefficients which offers computational simplicity as compared to spectral coefficients. It eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function. The method for computation of probability coefficients using transform matrix, fast transform method and using BDD is given. Theoretical relations for achievable computational advantage in terms of required additions in computing all 2n probability coefficients of n variable function have been developed. It is shown that for n ≥ 5, only 50% additions are needed to compute all probability coefficients as compared to spectral coefficients. The fault detection techniques based on spectral signature can be used with probability signature also to offer computational advantage.

Keywords: Binary Decision Diagrams, Spectral Coefficients, Fault detection

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Authors: K. Machida, H. Yamada

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Displacement measurement was conducted on compact normal and shear specimens made of acrylic homogeneous material subjected to mixed-mode loading by digital image correlation. The intelligent hybrid method proposed by Nishioka et al. was applied to the stress-strain analysis near the crack tip. The accuracy of stress-intensity factor at the free surface was discussed from the viewpoint of both the experiment and 3-D finite element analysis. The surface images before and after deformation were taken by a CMOS camera, and we developed the system which enabled the real time stress analysis based on digital image correlation and inverse problem analysis. The great portion of processing time of this system was spent on displacement analysis. Then, we tried improvement in speed of this portion. In the case of cracked body, it is also possible to evaluate fracture mechanics parameters such as the J integral, the strain energy release rate, and the stress-intensity factor of mixed-mode. The 9-points elliptic paraboloid approximation could not analyze the displacement of submicron order with high accuracy. The analysis accuracy of displacement was improved considerably by introducing the Newton-Raphson method in consideration of deformation of a subset. The stress-intensity factor was evaluated with high accuracy of less than 1% of the error.

Keywords: Digital image correlation, mixed mode, Newton-Raphson method, stress intensity factor.

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Authors: Jamshaid ur Rehman, Shahida Wizarat

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The principal focus of this study is on the measurement and analysis of labor learnings in Pakistan. The study at the aggregate economy level focus on the labor productivity movements and at large-scale manufacturing level focus on the cost structure, with isolating the contribution of the learning curve. The analysis of S-shaped curve suggests that learnings are only below one half of aggregate learning curve and other half shows the retardation in learning, hence retardation in productivity movements. The study implies the existence of learning economies in term of cost reduction that is input cost per unit produced decreases by 0.51 percent every time the cumulative production output doubles.

Keywords: Cost, Inflection Point, Learning Curve, Minima, Maxima, and Productivity

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Authors: Tong Liu, Xuan Xu, Xiaodi Wang

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Computational techniques derived from digital image processing are playing a significant role in the security and digital copyrights of multimedia and visual arts. This technology has the effect within the domain of computers. This research presents discrete M-band wavelet transform (MWT) and cosine transform (DCT) based watermarking algorithm by incorporating the principal component analysis (PCA). The proposed algorithm is expected to achieve higher perceptual transparency. Specifically, the developed watermarking scheme can successfully resist common signal processing, such as geometric distortions, and Gaussian noise. In addition, the proposed algorithm can be parameterized, thus resulting in more security. To meet these requirements, the image is transformed by a combination of MWT & DCT. In order to improve the security further, we randomize the watermark image to create three code books. During the watermark embedding, PCA is applied to the coefficients in approximation sub-band. Finally, first few component bands represent an excellent domain for inserting the watermark.

Keywords: discrete M-band wavelet transform , discrete M-band wavelet transform, randomized watermark, principal component analysis

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Authors: Eun-Jun Yoon, Kee-Young Yoo

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Recently, Jia et al. proposed a remote user authentication scheme using bilinear pairings and an Elliptic Curve Cryptosystem (ECC). However, the scheme is vulnerable to privileged insider attack at their proposed registration phase and to forgery attack at their proposed authentication phase. In addition, the scheme can be vulnerable to server spoofing attack because it does not provide mutual authentication between the user and the remote server. Therefore, this paper points out that the Jia et al. scheme is vulnerable to the above three attacks.

Keywords: Cryptography, authentication, smart card, password, cryptanalysis, bilinear pairings.

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Authors: Federico Amato, Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini

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The aerodynamic performances of vertical axis wind turbines are highly affected by tip vortexes. In the present work, different tip devices are considered and simulated against a baseline rotor configuration, with the aim of identifying the best tip architecture. Three different configurations are tested: winglets, an elliptic termination and an aerodynamic bulkhead. A comparative analysis on the most promising architectures is conducted, focusing also on blade torque evolution during a full revolution of the rotor blade. The most promising technology is concluded to be a well designed winglet.

Keywords: Darrieus Wind Turbine, Tip Devices, Tip Vortexes, Winglet, Elliptic Termination, Aerodynamic Bulkhead

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Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu

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Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC_4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC₃ cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC_4,6 cryptosystem than LUC₃ and LUC cryptosystems. Current study concludes that LUC_4,6 cryptosystem is more secure than LUC and LUC₃ cryptosystems in sustaining against Lenstra’s attack.

Keywords: Lucas sequence, Dickson Polynomial, faulty signature, corresponding signature, congruence.

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Authors: M.H. Ahmad Fadzil, Esa Prakasa, Hurriyatul Fitriyah, Hermawan Nugroho, Azura Mohd Affandi, S.H. Hussein

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Psoriasis is a widespread skin disease affecting up to 2% population with plaque psoriasis accounting to about 80%. It can be identified as a red lesion and for the higher severity the lesion is usually covered with rough scale. Psoriasis Area Severity Index (PASI) scoring is the gold standard method for measuring psoriasis severity. Scaliness is one of PASI parameter that needs to be quantified in PASI scoring. Surface roughness of lesion can be used as a scaliness feature, since existing scale on lesion surface makes the lesion rougher. The dermatologist usually assesses the severity through their tactile sense, therefore direct contact between doctor and patient is required. The problem is the doctor may not assess the lesion objectively. In this paper, a digital image analysis technique is developed to objectively determine the scaliness of the psoriasis lesion and provide the PASI scaliness score. Psoriasis lesion is modelled by a rough surface. The rough surface is created by superimposing a smooth average (curve) surface with a triangular waveform. For roughness determination, a polynomial surface fitting is used to estimate average surface followed by a subtraction between rough and average surface to give elevation surface (surface deviations). Roughness index is calculated by using average roughness equation to the height map matrix. The roughness algorithm has been tested to 444 lesion models. From roughness validation result, only 6 models can not be accepted (percentage error is greater than 10%). These errors occur due the scanned image quality. Roughness algorithm is validated for roughness measurement on abrasive papers at flat surface. The Pearson-s correlation coefficient of grade value (G) of abrasive paper and Ra is -0.9488, its shows there is a strong relation between G and Ra. The algorithm needs to be improved by surface filtering, especially to overcome a problem with noisy data.

Keywords: psoriasis, roughness algorithm, polynomial surfacefitting.

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Authors: Ali Gholami, Ebrahim Panahpour, Amir Hossein Davami

Abstract:

In this research, a part of Aghche basin in Isfahan province with an area about 2000 hectars, was chosen to be obtain curve number coefficient runoff and W indicator in second Cook method By using aerial photos 1968 and 1995, the satellite data of the IRS in 2008. Then the process of land use changes in the period of study and its effect on the changes of curve number (CN), W indicator and surface runoff coefficient (C) of the basin was investigated. These results showed that on the track of these land use changes the weight averages curve number (CN), surface runoff coefficient (C) and W indicator of the basin were increased to 0.92, 0.02 and 0.78 unit in the first period of study and 1.18, 0.03, 0.99 Unit in the second period of study respectively.

Keywords: Aghche Watershed, Curve Numbers (CV), Land UseChanges, Surface Runoff Coefficient(C) Map, W indicator

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Authors: Yi-Pin Hsu, Shin-Yu Lin

Abstract:

An efficient parallel form in digital signal processor can improve the algorithm performance. The butterfly structure is an important role in fast Fourier transform (FFT), because its symmetry form is suitable for hardware implementation. Although it can perform a symmetric structure, the performance will be reduced under the data-dependent flow characteristic. Even though recent research which call as novel memory reference reduction methods (NMRRM) for FFT focus on reduce memory reference in twiddle factor, the data-dependent property still exists. In this paper, we propose a parallel-computing approach for FFT implementation on digital signal processor (DSP) which is based on data-independent property and still hold the property of low-memory reference. The proposed method combines final two steps in NMRRM FFT to perform a novel data-independent structure, besides it is very suitable for multi-operation-unit digital signal processor and dual-core system. We have applied the proposed method of radix-2 FFT algorithm in low memory reference on TI TMSC320C64x DSP. Experimental results show the method can reduce 33.8% clock cycles comparing with the NMRRM FFT implementation and keep the low-memory reference property.

Keywords: Parallel-computing, FFT, low-memory reference, TIDSP.

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Authors: Emin Özyılmaz

Abstract:

In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.

Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.

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Authors: Liu Xuedong , Liu Zhiyan

Abstract:

When the crisscross baffles and logarithmic spiral baffles are placed on the bottom of the stirred tank with elliptic bottom, using CFD software FLUENT simulates the velocity field of the stirred tank with elliptic bottom and bottom baffles. Compare the velocity field of stirred tank with bottom crisscross baffle to the velocity field of stirred tank without bottom baffle and analysis the flow pattern on the same axis-section and different cross-sections. The sizes of the axial and radial velocity are compared respectively when the stirred tank with bottom crisscross baffles, bottom logarithmic spiral baffles and without bottom baffle. At the same time, the numerical calculations of mixing power are compared when the stirred tank with bottom crisscross baffles and bottom logarithmic spiral baffles. Research shows that bottom crisscross baffles and logarithmic spiral baffles have a great impact on flow pattern within the reactor and improve the mixing effect better than without baffle. It also has shown that bottom logarithmic spiral baffles has lower power consumption than bottom crisscross baffles.

Keywords: Bottom baffle, Flow field, Numerical simulation, Stirred tank.

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Authors: Hailong Zhu, Zhaoxiang Li

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In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.

Keywords: positive solutions, concave-convex, sub-super solution method, pseudo arclength method.

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Authors: Said M. Easa, Shinya Kikuchi

Abstract:

When the profile information of an existing road is missing or not up-to-date and the parameters of the vertical alignment are needed for engineering analysis, the engineer has to recreate the geometric design features of the road alignment using collected profile data. The profile data may be collected using traditional surveying methods, global positioning systems, or digital imagery. This paper develops a method that estimates the parameters of the geometric features that best characterize the existing vertical alignments in terms of tangents and the expressions of the curve, that may be symmetrical, asymmetrical, reverse, and complex vertical curves. The method is implemented using an Excel-based optimization method that minimizes the differences between the observed profile and the profiles estimated from the equations of the vertical curve. The method uses a 'wireframe' representation of the profile that makes the proposed method applicable to all types of vertical curves. A secondary contribution of this paper is to introduce the properties of the equal-arc asymmetrical curve that has been recently developed in the highway geometric design field.

Keywords: Optimization, parameters, data, reverse, spreadsheet, vertical curves

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Authors: E. Golden Julie, S. Tamil Selvi, Y. Harold Robinson

Abstract:

Many Wireless Sensor Network (WSN) applications necessitate secure multicast services for the purpose of broadcasting delay sensitive data like video files and live telecast at fixed time-slot. This work provides a novel method to deal with end-to-end delay and drop rate of packets. Opportunistic Routing chooses a link based on the maximum probability of packet delivery ratio. Null Key Generation helps in authenticating packets to the receiver. Markov Decision Process based Adaptive Scheduling algorithm determines the time slot for packet transmission. Both theoretical analysis and simulation results show that the proposed protocol ensures better performance in terms of packet delivery ratio, average end-to-end delay and normalized routing overhead.

Keywords: Delay-sensitive data, Markovian Decision Process based Adaptive Scheduling, Opportunistic Routing, Digital Signature authentication.

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Authors: H. Kelkoul, Y. Zaz

Abstract:

Nowadays, the vigorous popularity of video processing techniques has resulted in an explosive growth of multimedia data illegal use. So, watermarking security has received much more attention. The purpose of this paper is to explore some watermarking techniques in order to observe their specificities and select the finest methods to apply in digital cinema domain against movie piracy by creating an invisible watermark that includes the date, time and the place where the hacking was done. We have studied three principal watermarking techniques in the frequency domain: Spread spectrum, Wavelet transform domain and finally the digital cinema watermarking transform domain. In this paper, a detailed technique is presented where embedding is performed using direct sequence spread spectrum technique in DWT transform domain. Experiment results shows that the algorithm provides high robustness and good imperceptibility.

Keywords: Digital cinema, watermarking, wavelet, spread spectrum, JPEG2000.

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Authors: Nan Chen, Baoguang Tian

Abstract:

In this paper, some relative efficiency have been discussed, including the LSE estimate with respect to BLUE in curve model. Four new kinds of relative efficiency have defined, and their upper bounds have been discussed.

Keywords: Relative efficiency, LSE estimate, BLUE estimate, Upper bound, Curve model.

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Authors: Krishnamoorthi R., Sheba Kezia Malarchelvi P. D.

Abstract:

In this paper, an image adaptive, invisible digital watermarking algorithm with Orthogonal Polynomials based Transformation (OPT) is proposed, for copyright protection of digital images. The proposed algorithm utilizes a visual model to determine the watermarking strength necessary to invisibly embed the watermark in the mid frequency AC coefficients of the cover image, chosen with a secret key. The visual model is designed to generate a Just Noticeable Distortion mask (JND) by analyzing the low level image characteristics such as textures, edges and luminance of the cover image in the orthogonal polynomials based transformation domain. Since the secret key is required for both embedding and extraction of watermark, it is not possible for an unauthorized user to extract the embedded watermark. The proposed scheme is robust to common image processing distortions like filtering, JPEG compression and additive noise. Experimental results show that the quality of OPT domain watermarked images is better than its DCT counterpart.

Keywords: Orthogonal Polynomials based Transformation, Digital Watermarking, Copyright Protection, Visual model.

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Authors: Benalia Nadia, Bensiali Nadia, Mekki Mounira

Abstract:

In this paper, we propose an easily computable proximity index for predicting voltage collapse of a load bus using only measured values of the bus voltage and power; Using these measurements a polynomial of fourth order is obtained by using LES estimation algorithms. The sum of the absolute values of the polynomial coefficient gives an idea of the critical bus. We demonstrate the applicability of our proposed method on 6 bus test system. The results obtained verify its applicability, as well as its accuracy and the simplicity. From this indicator, it is allowed to predict the voltage instability or the proximity of a collapse. Results obtained by the PV curve are compared with corresponding values by QV curves and are observed to be in close agreement.

Keywords: least square method, Voltage Collapse, Voltage Stability, PV curve

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Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos

Abstract:

This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.

Keywords: Bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution.

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Authors: E. V. Larkin, T. A. Akimenko, A. V. Bogomolov, A. N. Privalov

Abstract:

The digital control system of mobile robots (MR) control is considered. It is shown that sequential interpretation of control algorithm operators, unfolding in physical time, suggests the occurrence of time delays between inputting data from sensors and outputting data to actuators. Another destabilizing control factor is presence of backlash in the joints of an actuator with an executive unit. Complex model of control system, which takes into account the dynamics of the MR, the dynamics of the digital controller and backlash in actuators, is worked out. The digital controller model is divided into two parts: the first part describes the control law embedded in the controller in the form of a control program that realizes a polling procedure when organizing transactions to sensors and actuators. The second part of the model describes the time delays that occur in the Von Neumann-type controller when processing data. To estimate time intervals, the algorithm is represented in the form of an ergodic semi-Markov process. For an ergodic semi-Markov process of common form, a method is proposed for estimation a wandering time from one arbitrary state to another arbitrary state. Example shows how the backlash and time delays affect the quality characteristics of the MR control system functioning.

Keywords: Mobile robot, backlash, control algorithm, Von Neumann controller, semi-Markov process, time delay.

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Authors: Asfar Ali Khan

Abstract:

Analytical expression for maximum power transfer through a transmission line limited by voltage stability has been formulated using exact representation of transmission line with ABCD parameters. The expression has been used for plotting PV curve at different power factors of a radial transmission line. Limiting values of reactive power have been obtained.

Keywords: Power Transfer, PV Curve, Voltage Stability.

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Authors: V. Prapulla, A. Mitra, R. Bhattacharjee, S. Nandi

Abstract:

We present a simplified equalization technique for a π/4 differential quadrature phase shift keying ( π/4 -DQPSK) modulated signal in a multipath fading environment. The proposed equalizer is realized as a fractionally spaced adaptive decision feedback equalizer (FS-ADFE), employing exponential step-size least mean square (LMS) algorithm as the adaptation technique. The main advantage of the scheme stems from the usage of exponential step-size LMS algorithm in the equalizer, which achieves similar convergence behavior as that of a recursive least squares (RLS) algorithm with significantly reduced computational complexity. To investigate the finite-precision performance of the proposed equalizer along with the π/4 -DQPSK modem, the entire system is evaluated on a 16-bit fixed point digital signal processor (DSP) environment. The proposed scheme is found to be attractive even for those cases where equalization is to be performed within a restricted number of training samples.

Keywords: Adaptive decision feedback equalizer, Fractionally spaced equalizer, π/4 DQPSK signal, Digital signal processor.

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Authors: Mohammed Shatnawi, Qusai Abuein, Susumu Shibusawa

Abstract:

Signature amortization schemes have been introduced for authenticating multicast streams, in which, a single signature is amortized over several packets. The hash value of each packet is computed, some hash values are appended to other packets, forming what is known as hash chain. These schemes divide the stream into blocks, each block is a number of packets, the signature packet in these schemes is either the first or the last packet of the block. Amortization schemes are efficient solutions in terms of computation and communication overhead, specially in real-time environment. The main effictive factor of amortization schemes is it-s hash chain construction. Some studies show that signing the first packet of each block reduces the receiver-s delay and prevents DoS attacks, other studies show that signing the last packet reduces the sender-s delay. To our knowledge, there is no studies that show which is better, to sign the first or the last packet in terms of authentication probability and resistance to packet loss. In th is paper we will introduce another scheme for authenticating multicast streams that is robust against packet loss, reduces the overhead, and prevents the DoS attacks experienced by the receiver in the same time. Our scheme-The Multiple Connected Chain signing the First packet (MCF) is to append the hash values of specific packets to other packets,then append some hashes to the signature packet which is sent as the first packet in the block. This scheme is aspecially efficient in terms of receiver-s delay. We discuss and evaluate the performance of our proposed scheme against those that sign the last packet of the block.

Keywords: multicast stream authentication, hash chain construction, signature amortization, authentication probability.

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Authors: Peiangpob Monnuanprang

Abstract:

In this paper we study the transformation of Euler equations  1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.

Keywords: Euler equations, transformation, hyperbolic, elliptic

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Authors: Ashok Ganguly, Pranjali Arondekar

Abstract:

In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.

Keywords: Bézier, Circle Involute, NAUT B-Spline, Spur Gear.

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