Search results for: mixed-integer linear programming

Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: Yaw-Juen Wang, Po-Chun Hsu

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This paper presents an equivalent circuit model based on piecewise linear parallel branches (PLPB) to study solar cell modules which are partially shaded. The PLPB model can easily be used in circuit simulation software such as the ElectroMagnetic Transients Program (EMTP). This PLPB model allows the user to simulate several different configurations of solar cells, the influence of partial shadowing on a single or multiple cells, the influence of the number of solar cells protected by a bypass diode and the effect of the cell connection configuration on partial shadowing.

Keywords: Cell Connection Configurations, EMTP, Equivalent Circuit, Partial Shading, Photovoltaic Module

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Authors: Neelima Gupta, Seema Aggarwal

Abstract:

Most of the biclustering/projected clustering algorithms are based either on the Euclidean distance or correlation coefficient which capture only linear relationships. However, in many applications, like gene expression data and word-document data, non linear relationships may exist between the objects. Mutual Information between two variables provides a more general criterion to investigate dependencies amongst variables. In this paper, we improve upon our previous algorithm that uses mutual information for biclustering in terms of computation time and also the type of clusters identified. The algorithm is able to find biclusters with mixed relationships and is faster than the previous one. To the best of our knowledge, none of the other existing algorithms for biclustering have used mutual information as a similarity measure. We present the experimental results on synthetic data as well as on the yeast expression data. Biclusters on the yeast data were found to be biologically and statistically significant using GO Tool Box and FuncAssociate.

Keywords: Biclustering, mutual information.

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Authors: Khaled M. EL-Naggar

Abstract:

This paper presents a fast and efficient on-line technique for estimating impedance of unbalanced loads in power systems. The proposed technique is an application of a discrete timedynamic filter based on stochastic estimation theory which is suitable for estimating parameters in noisy environment. The algorithm uses sets of digital samples of the distorted voltage and current waveforms of the non-linear load to estimate the harmonic contents of these two signal. The non-linear load impedance is then calculated from these contents. The method is tested using practical data. Results are reported and compared with those obtained using the conventional least error squares technique. In addition to the very accurate results obtained, the method can detect and reject bad measurements. This can be considered as a very important advantage over the conventional static estimation methods such as the least error square method.

Keywords: Estimation, identification, Harmonics, Dynamic Filter.

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Authors: Yucai Ding, Hong Zhu, Shouming Zhong, Yuping Zhang

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This paper considers ­H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed ­H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.

Keywords: ­H∞ performance, Markovian switching, Delaydependent stability, Linear matrix inequality (LMI)

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Authors: Reeta Devi, Hitender Kumar Tyagi, Dinesh Kumar

Abstract:

In present scenario, cardiovascular problems are growing challenge for researchers and physiologists. As heart disease have no geographic, gender or socioeconomic specific reasons; detecting cardiac irregularities at early stage followed by quick and correct treatment is very important. Electrocardiogram is the finest tool for continuous monitoring of heart activity. Heart rate variability (HRV) is used to measure naturally occurring oscillations between consecutive cardiac cycles. Analysis of this variability is carried out using time domain, frequency domain and non-linear parameters. This paper presents HRV analysis of the online dataset for normal sinus rhythm (taken as healthy subject) and sudden cardiac death (SCD subject) using all three methods computing values for parameters like standard deviation of node to node intervals (SDNN), square root of mean of the sequences of difference between adjacent RR intervals (RMSSD), mean of R to R intervals (mean RR) in time domain, very low-frequency (VLF), low-frequency (LF), high frequency (HF) and ratio of low to high frequency (LF/HF ratio) in frequency domain and Poincare plot for non linear analysis. To differentiate HRV of healthy subject from subject died with SCD, k –nearest neighbor (k-NN) classifier has been used because of its high accuracy. Results show highly reduced values for all stated parameters for SCD subjects as compared to healthy ones. As the dataset used for SCD patients is recording of their ECG signal one hour prior to their death, it is therefore, verified with an accuracy of 95% that proposed algorithm can identify mortality risk of a patient one hour before its death. The identification of a patient’s mortality risk at such an early stage may prevent him/her meeting sudden death if in-time and right treatment is given by the doctor.

Keywords: Early stage prediction, heart rate variability, linear and non linear analysis, sudden cardiac death.

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Authors: Johann Barbier, Guillaume Sicot, Sebastien Houcke

Abstract:

In this paper we present a generic approach for the problem of the blind estimation of the parameters of linear and convolutional error correcting codes. In a non-cooperative context, an adversary has only access to the noised transmission he has intercepted. The intercepter has no knowledge about the parameters used by the legal users. So, before having acess to the information he has first to blindly estimate the parameters of the error correcting code of the communication. The presented approach has the main advantage that the problem of reconstruction of such codes can be expressed in a very simple way. This allows us to evaluate theorical bounds on the complexity of the reconstruction process but also bounds on the estimation rate. We show that some classical reconstruction techniques are optimal and also explain why some of them have theorical complexities greater than these experimentally observed.

Keywords: Blind estimation parameters, error correcting codes, non-cooperative context, reconstruction algorithm

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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: M. Zareiee, A. Dideban, P. Nazemzadeh

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This paper deals with the problem of constructing constraints in non safe Petri Nets and then reducing the number of the constructed constraints. In a system, assigning some linear constraints to forbidden states is possible. Enforcing these constraints on the system prevents it from entering these states. But there is no a systematic method for assigning constraints to forbidden states in non safe Petri Nets. In this paper a useful method is proposed for constructing constraints in non safe Petri Nets. But when the number of these constraints is large enforcing them on the system may complicate the Petri Net model. So, another method is proposed for reducing the number of constructed constraints.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Tan K. B., Norhashidah Hj. M. Ali

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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Tamanna Siddiqui, M. Afshar Alam

Abstract:

Automated discovery of Rule is, due to its applicability, one of the most fundamental and important method in KDD. It has been an active research area in the recent past. Hierarchical representation allows us to easily manage the complexity of knowledge, to view the knowledge at different levels of details, and to focus our attention on the interesting aspects only. One of such efficient and easy to understand systems is Hierarchical Production rule (HPRs) system. A HPR, a standard production rule augmented with generality and specificity information, is of the following form: Decision If < condition> Generality Specificity . HPRs systems are capable of handling taxonomical structures inherent in the knowledge about the real world. This paper focuses on the issue of mining Quantified rules with crisp hierarchical structure using Genetic Programming (GP) approach to knowledge discovery. The post-processing scheme presented in this work uses Quantified production rules as initial individuals of GP and discovers hierarchical structure. In proposed approach rules are quantified by using Dempster Shafer theory. Suitable genetic operators are proposed for the suggested encoding. Based on the Subsumption Matrix(SM), an appropriate fitness function is suggested. Finally, Quantified Hierarchical Production Rules (HPRs) are generated from the discovered hierarchy, using Dempster Shafer theory. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Knowledge discovery in database, quantification, dempster shafer theory, genetic programming, hierarchy, subsumption matrix.

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Authors: Pranav Ravikumar, Arunabha Bera, Vijay K. Mehra, Anand Kumar

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This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated are compared with the graphs formulated by JDS Uniphase Corporation which uses standard values of dispersion for optical fibers. The graphs generated when compared with the JDS Uniphase Corporation plots were found to be more or less similar thus verifying that the model proposed is right. MATLAB software was used for doing the modeling.

Keywords: Modulation, Non Linear Schrodinger Equation, Optical fiber, Split Step Fourier Method.

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

Abstract:

The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: Mustafa Abdalla, Khaled A. Madi, Rajab Farhat

Abstract:

An array antenna system with innovative signal processing can improve the resolution of a source direction of arrival (DoA) estimation. High resolution techniques take the advantage of array antenna structures to better process the incoming waves. They also have the capability to identify the direction of multiple targets. This paper investigates performance of the DOA estimation algorithm namely; Capon and MUSIC on the uniform linear array (ULA). The simulation results show that in Capon and MUSIC algorithm the resolution of the DOA techniques improves as number of snapshots, number of array elements, signal-to-noise ratio and separation angle between the two sources θ increases.

Keywords: Antenna array, Capon, MUSIC, Direction-of-arrival estimation, signal processing, uniform linear arrays.

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

Abstract:

Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE work parameters have fuzzy character. Hence consideration of fuzzy skewness and kurtosis coefficients is expedient. Investigation of the basic characteristics changes- dynamics of GTE work parameters allows drawing conclusion on necessity of the Fuzzy Statistical Analysis at preliminary identification of the engines' technical condition. Researches of correlation coefficients values- changes shows also on their fuzzy character. Therefore for models choice the application of the Fuzzy Correlation Analysis results is offered. At the information sufficiency is offered to use recurrent algorithm of aviation GTE technical condition identification (Hard Computing technology is used) on measurements of input and output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stageby- stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: Said Rabah Azzam, Laura Carolina Arias, Shikun Zhou

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A product goes through various processes in a production flow which is also known as assembly line in manufacturing process management. Toyota created a new concept which is known as lean concept in manufacturing industry. Today it is the leading model in manufacturing plants through the globe. The linear walking worker assembly line is a flexible assembly system where each worker travels down the line carrying out each assembly task at each station; and each worker accomplishes the assembly of a unit from start to finish. This paper attempts to combine the flexibility of the walking worker and lean in order to quantify the benefits from applying the shop floor principles of lean management.

Keywords: Toyota Production System, TPS, LeanManufacturing, Walking Worker, Lean Management, Management, Linear Assembly Lines, U-shaped Assembly Lines, Shop FloorManagement

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Authors: Yin Yin Pey, Leok Poh Chua, Wei Long Siauw

Abstract:

Linear stochastic estimation and quadratic stochastic estimation techniques were applied to estimate the entire velocity flow-field of an open cavity with a length to depth ratio of 2. The estimations were done through the use of instantaneous velocity magnitude as estimators. These measurements were obtained by Particle Image Velocimetry. The predicted flow was compared against the original flow-field in terms of the Reynolds stresses and turbulent kinetic energy. Quadratic stochastic estimation proved to be more superior than linear stochastic estimation in resolving the shear layer flow. When the velocity fluctuations were scaled up in the quadratic estimate, both the time-averaged quantities and the instantaneous cavity flow can be predicted to a rather accurate extent.

Keywords: Open cavity, Particle Image Velocimetry, Stochastic estimation, Turbulent kinetic energy.

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Authors: Sundara Subramanian Karuppasamy, Che Hua Yang

Abstract:

In this work, the laser ultrasound technique has been used for analyzing and imaging the inner defects in metal blocks. To detect the defects in blocks, traditionally the researchers used piezoelectric transducers for the generation and reception of ultrasonic signals. These transducers can be configured into the sparse and phased array. But these two configurations have their drawbacks including the requirement of many transducers, time-consuming calculations, limited bandwidth, and provide confined image resolution. Here, we focus on the non-contact method for generating and receiving the ultrasound to examine the inner defects in aluminum blocks. A Q-switched pulsed laser has been used for the generation and the reception is done by using Laser Doppler Vibrometer (LDV). Based on the Doppler effect, LDV provides a rapid and high spatial resolution way for sensing ultrasonic waves. From the LDV, a series of scanning points are selected which serves as the phased array elements. The side-drilled hole of 10 mm diameter with a depth of 25 mm has been introduced and the defect is interrogated by the linear array of scanning points obtained from the LDV. With the aid of the Synthetic Aperture Focusing Technique (SAFT) algorithm, based on the time-shifting principle the inspected images are generated from the A-scan data acquired from the 1-D linear phased array elements. Thus the defect can be precisely detected with good resolution.

Keywords: Laser ultrasonics, linear phased array, nondestructive testing, synthetic aperture focusing technique, ultrasonic imaging.

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Authors: Hyoup-Sang Yoon

Abstract:

Video-on-demand (VOD) is designed by using content delivery networks (CDN) to minimize the overall operational cost and to maximize scalability. Estimation of the viewing pattern (i.e., the relationship between the number of viewings and the ranking of VOD contents) plays an important role in minimizing the total operational cost and maximizing the performance of the VOD systems. In this paper, we have analyzed a large body of commercial VOD viewing data and found that the viewing rank distribution fits well with the parabolic fractal distribution. The weighted linear model fitting function is used to estimate the parameters (coefficients) of the parabolic fractal distribution. This paper presents an analytical basis for designing an optimal hierarchical VOD contents distribution system in terms of its cost and performance.

Keywords: VOD, CDN, parabolic fractal distribution, viewing rank, weighted linear model fitting

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops for data links operating at 10 Gb/s or faster are low phase noise devices designed to operate with a low jitter reference clock. Characterization of their jitter transfer function is difficult because the intrinsic noise of the device is comparable to the random noise level in the reference clock signal. A linear model is proposed to account for the intrinsic noise of a PLL. The intrinsic noise data of a PLL for 10 Gb/s links is presented. The jitter transfer function of a PLL in a test chip for 12.8 Gb/s data links was determined in experiments using the 400 MHz reference clock as the source of simultaneous excitations over a wide range of frequency. The result shows that the PLL jitter transfer function can be approximated by a second order linear model.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: Isti Surjandari, Riara Novita

Abstract:

Maintenance is one of the most important activities in the shipyard industry. However, sometimes it is not supported by adequate services from the shipyard, where inaccuracy in estimating the duration of the ship maintenance is still common. This makes estimation of ship maintenance duration is crucial. This study uses Data Mining approach, i.e., CART (Classification and Regression Tree) to estimate the duration of ship maintenance that is limited to dock works or which is known as dry docking. By using the volume of dock works as an input to estimate the maintenance duration, 4 classes of dry docking duration were obtained with different linear model and job criteria for each class. These linear models can then be used to estimate the duration of dry docking based on job criteria.

Keywords: Classification and regression tree (CART), data mining, dry docking, maintenance duration.

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Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman

Abstract:

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

Keywords: Complexity reduction approach, Composite trapezoidal scheme, Jacobi method, Linear Fredholm integral equations

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

Abstract:

Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: Covariation reasoning, exponential function, modeling, representations.

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Authors: Arash Parehkar, S. Jamshid Mousavi, Shoubo Bayazidi, Vahid Karami, Laleh Shahidi, Arash Azaranfar, Ali Moridi, M. Shabakhti, Tayebeh Ariyan, Mitra Tofigh, Kaveh Masoumi, Alireza Motahari

Abstract:

Water resource systems modeling has constantly been a challenge through history for human beings. As the innovative methodological development is evolving alongside computer sciences on one hand, researches are likely to confront more complex and larger water resources systems due to new challenges regarding increased water demands, climate change and human interventions, socio-economic concerns, and environment protection and sustainability. In this research, an automatic calibration scheme has been applied on the Gilan’s large-scale water resource model using mathematical programming. The water resource model’s calibration is developed in order to attune unknown water return flows from demand sites in the complex Sefidroud irrigation network and other related areas. The calibration procedure is validated by comparing several gauged river outflows from the system in the past with model results. The calibration results are pleasantly reasonable presenting a rational insight of the system. Subsequently, the unknown optimized parameters were used in a basin-scale linear optimization model with the ability to evaluate the system’s performance against a reduced inflow scenario in future. Results showed an acceptable match between predicted and observed outflows from the system at selected hydrometric stations. Moreover, an efficient operating policy was determined for Sefidroud dam leading to a minimum water shortage in the reduced inflow scenario.

Keywords: Auto-calibration, Gilan, Large-Scale Water Resources, Simulation.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: Tsunwai Gary Yip

Abstract:

Phase locked loops in 10 Gb/s and faster data links are low phase noise devices. Characterization of their phase jitter transfer functions is difficult because the intrinsic noise of the PLLs is comparable to the phase noise of the reference clock signal. The problem is solved by using a linear model to account for the intrinsic noise. This study also introduces a novel technique for measuring the transfer function. It involves the use of the reference clock as a source of wideband excitation, in contrast to the commonly used sinusoidal excitations at discrete frequencies. The data reported here include the intrinsic noise of a PLL for 10 Gb/s links and the jitter transfer function of a PLL for 12.8 Gb/s links. The measured transfer function suggests that the PLL responded like a second order linear system to a low noise reference clock.

Keywords: Intrinsic phase noise, jitter in data link, PLL jitter transfer function, high speed clocking in electronic circuit

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Authors: Sallem F., Dahhou B., Kamoun A.

Abstract:

In this work, the main problem considered is the  detection and the isolation of the actuator fault. A new formulation of  the linear system is generated to obtain the conditions of the actuator  fault diagnosis. The proposed method is based on the representation  of the actuator as a subsystem connected with the process system in  cascade manner. The designed formulation is generated to obtain the  conditions of the actuator fault detection and isolation. Detectability  conditions are expressed in terms of the invertibility notions. An  example and a comparative analysis with the classic formulation  illustrate the performances of such approach for simple actuator fault  diagnosis by using the linear model of nuclear reactor.

 

Keywords: Actuator fault, Fault detection, left invertibility, nuclear reactor, observability, parameter intervals, system inversion.

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Authors: Long Jye Sheu

Abstract:

This paper presents a linear stability analysis of natural convection in a horizontal layer of a viscoelastic nanofluid. The Oldroyd B model was utilized to describe the rheological behavior of a viscoelastic nanofluid. The model used for the nanofluid incorporated the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was derived analytically. The effects of the Deborah number, retardation parameters, concentration Rayleigh number, Prandtl number, and Lewis number on the stability of the system were investigated. Results indicated that there was competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity which caused oscillatory rather than stationary convection to occur. Oscillatory instability is possible with both bottom- and top-heavy nanoparticle distributions. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.

Keywords: instability, viscoelastic, nanofluids, oscillatory, Brownian, thermophoresis

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Alexander Kaplunovsky, Vladimir Khailenko, Alexander Bolshoy, Shara Atambayeva, AnatoliyIvashchenko

Abstract:

Eukaryotic protein-coding genes are interrupted by spliceosomal introns, which are removed from the RNA transcripts before translation into a protein. The exon-intron structures of different eukaryotic species are quite different from each other, and the evolution of such structures raises many questions. We try to address some of these questions using statistical analysis of whole genomes. We go through all the protein-coding genes in a genome and study correlations between the net length of all the exons in a gene, the number of the exons, and the average length of an exon. We also take average values of these features for each chromosome and study correlations between those averages on the chromosomal level. Our data show universal features of exon-intron structures common to animals, plants, and protists (specifically, Arabidopsis thaliana, Caenorhabditis elegans, Drosophila melanogaster, Cryptococcus neoformans, Homo sapiens, Mus musculus, Oryza sativa, and Plasmodium falciparum). We have verified linear correlation between the number of exons in a gene and the length of a protein coded by the gene, while the protein length increases in proportion to the number of exons. On the other hand, the average length of an exon always decreases with the number of exons. Finally, chromosome clustering based on average chromosome properties and parameters of linear regression between the number of exons in a gene and the net length of those exons demonstrates that these average chromosome properties are genome-specific features.

Keywords: Comparative genomics, exon-intron structure, eukaryotic clustering, linear regression.

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