Search results for: Discrete boundary value problems

Authors: Tahmine. V. Moghaddam, N. Bigdeli, K. Afshar

Abstract:

To achieve the desired specifications of gain and phase margins for plants with time-delay that stabilized with FO-PID controller a lead compensator is designed. At first the range of controlled system stability based on stability boundary criteria is determined. Using stability boundary locus method in frequency domain the fractional order controller parameters are tuned and then with drawing bode diagram in frequency domain accessing to desired gain and phase margin are shown. Numerical examples are given to illustrate the shapes of the stabilizing region and to show the design procedure.

Keywords: Fractional controller, Lead compensator, Stabilityregions, Stability boundary locus

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Authors: P. Joyce Beryl Princess, Y. Harold Robinson

Abstract:

Image Processing is a structure of Signal Processing for which the input is the image and the output is also an image or parameter of the image. Image Resolution has been frequently referred as an important aspect of an image. In Image Resolution Enhancement, images are being processed in order to obtain more enhanced resolution. To generate highly resoluted image for a low resoluted input image with high PSNR value. Stationary Wavelet Transform is used for Edge Detection and minimize the loss occurs during Downsampling. Inverse Discrete Wavelet Transform is to get highly resoluted image. Highly resoluted output is generated from the Low resolution input with high quality. Noisy input will generate output with low PSNR value. So Noisy resolution enhancement technique has been used for adaptive sub-band thresholding is used. Downsampling in each of the DWT subbands causes information loss in the respective subbands. SWT is employed to minimize this loss. Inverse Discrete wavelet transform (IDWT) is to convert the object which is downsampled using DWT into a highly resoluted object. Used Image denoising and resolution enhancement techniques will generate image with high PSNR value. Our Proposed method will improve Image Resolution and reached the optimized threshold.

Keywords: Image Processing, Inverse Discrete wavelet transform, PSNR.

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Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots.

Keywords: Leslie-Gower, predator–prey model, prey refuge, allee effect.

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Authors: Chong Wang, Kellem M. Soares, Luis E. Kosteski

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The problem of toughening in brittle materials reinforced by fibers is complex, involving all of the mechanical properties of fibers, matrix and the fiber/matrix interface, as well as the geometry of the fiber. Development of new numerical methods appropriate to toughening simulation and analysis is necessary. In this work, we have performed simulations and analysis of toughening in brittle matrix reinforced by randomly distributed fibers by means of the discrete elements method. At first, we put forward a mechanical model of toughening contributed by random fibers. Then with a numerical program, we investigated the stress, damage and bridging force in the composite material when a crack appeared in the brittle matrix. From the results obtained, we conclude that: (i) fibers of high strength and low elasticity modulus are beneficial to toughening; (ii) fibers of relatively high elastic modulus compared to the matrix may result in substantial matrix damage due to spalling effect; (iii) employment of high-strength synthetic fibers is a good option for toughening. We expect that the combination of the discrete element method (DEM) with the finite element method (FEM) can increase the versatility and efficiency of the software developed. The present work can guide the design of ceramic composites of high performance through the optimization of the parameters.

Keywords: Bridging stress, discrete element method, fiber reinforced composites, toughening.

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Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

Abstract:

The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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Authors: Adam Czornik, Aleksander Nawrat

Abstract:

This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.

Keywords: Exponential stability, time-varying linear systems, periodic systems.

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Authors: Chuanyun Gu

Abstract:

By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.

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Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

Abstract:

Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points, which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem, since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: Airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design.

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Authors: Hojjat Saberinejad, Adel Hashiehbaf, Ehsan Afrasiabian

Abstract:

Among the various cooling processes in industrial applications such as: electronic devices, heat exchangers, gas turbines, etc. Gas turbine blades cooling is the most challenging one. One of the most common practices is using ribbed wall because of the boundary layer excitation and therefore making the ultimate cooling. Vortex formation between rib and channel wall will result in a complicated behavior of flow regime. At the other hand, selecting the most efficient method for capturing the best results comparing to experimental works would be a fascinating issue. In this paper 4 common methods in turbulence modeling: standard k-e, rationalized k-e with enhanced wall boundary layer treatment, k-w and RSM (Reynolds stress model) are employed to a square ribbed channel to investigate the separation and thermal behavior of the flow in the channel. Finally all results from different methods which are used in this paper will be compared with experimental data available in literature to ensure the numerical method accuracy.

Keywords: boundary layer, turbulence, numerical method, rib cooling

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Authors: Cj Gletus Matthews Cn Jacobs, Kogilah Narayanasamy

Abstract:

This article explores the sociological perspectives on social problems and the role of the media which has a delicate role to tread in balancing its duty to the public and the victim Whilst social problems have objective conditions, it is the subjective definition of such problems that ensure which social problem comes to the fore and which doesn-t. Further it explores the roles and functions of policymakers when addressing social problems and the impact of the inception of media profiling as well as the advantages and disadvantages of media profiling towards social problems. It focuses on the inception of media profiling due to its length and a follow up article will explore how current media profiling towards social problems have evolved since its inception.

Keywords: Media Profiling, Policy Response, Social Problems

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Authors: Samba Raju, Chiluveru, Manoj Tripathy

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Intelligibility is an essential characteristic of a speech signal, which is used to help in the understanding of information in speech signal. Background noise in the environment can deteriorate the intelligibility of a recorded speech. In this paper, we presented a simple variance subtracted - variable level discrete wavelet transform, which improve the intelligibility of speech. The proposed algorithm does not require an explicit estimation of noise, i.e., prior knowledge of the noise; hence, it is easy to implement, and it reduces the computational burden. The proposed algorithm decides a separate decomposition level for each frame based on signal dominant and dominant noise criteria. The performance of the proposed algorithm is evaluated with speech intelligibility measure (STOI), and results obtained are compared with Universal Discrete Wavelet Transform (DWT) thresholding and Minimum Mean Square Error (MMSE) methods. The experimental results revealed that the proposed scheme outperformed competing methods

Keywords: Discrete Wavelet Transform, speech intelligibility, STOI, standard deviation.

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Authors: Grigorios D. Dimitroulakos, N. D. Zervas, N. Sklavos, Costas E. Goutis

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In this paper, the implementation of low power, high throughput convolutional filters for the one dimensional Discrete Wavelet Transform and its inverse are presented. The analysis filters have already been used for the implementation of a high performance DWT encoder [15] with minimum memory requirements for the JPEG 2000 standard. This paper presents the design techniques and the implementation of the convolutional filters included in the JPEG2000 standard for the forward and inverse DWT for achieving low-power operation, high performance and reduced memory accesses. Moreover, they have the ability of performing progressive computations so as to minimize the buffering between the decomposition and reconstruction phases. The experimental results illustrate the filters- low power high throughput characteristics as well as their memory efficient operation.

Keywords: Discrete Wavelet Transform; JPEG2000 standard; VLSI design; Low Power-Throughput-optimized filters

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Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh

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In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.

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Authors: Zeinab Zeinalpour-Tabrizi, Faeze Asdaghi, Mahmooh Fathy, Mohammad Reza Jahed-Motlagh

Abstract:

Shot boundary detection is a fundamental step for the organization of large video data. In this paper, we propose a new method for video gradual shots detection and classification, using advantages of fractal analysis and AIS-based classifier. Proposed features are “vertical intercept" and “fractal dimension" of each frame of videos which are computed using Fourier transform coefficients. We also used a classifier based on Clonal Selection Algorithm. We have carried out our solution and assessed it according to the TRECVID2006 benchmark dataset.

Keywords: shot boundary detection, gradual shots, fractal analysis, artificial immune system, choose Clooney.

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Authors: T. Tchawe Moukam, N. Ngongang François, D. Thomas, K. Bienvenu, T. -Toko Dénis

Abstract:

Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.

Keywords: Hydroelectric dam, penstock, turbulent friction, boundary layer, CFD.

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

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Authors: Kamaldeep Joshi, Rajkumar Yadav, Ashok Kumar Yadav

Abstract:

Digital Watermarking is a procedure to prevent the unauthorized access and modification of personal data. It assures that the communication between two parties remains secure and their communication should be undetected. This paper investigates the consequence of the watermark strength of the grayscale image using a Discrete Wavelet Transformation (DWT) additive technique. In this method, the gray scale host image is divided into four sub bands: LL (Low-Low), HL (High-Low), LH (Low-High), HH (High-High) and the watermark is inserted in an LL sub band using DWT technique. As the image is divided into four sub bands, a watermark of equal size of the LL sub band has been inserted and the results are discussed. LL represents the average component of the host image which contains the maximum information of the image. Two kinds of experiments are performed. In the first, the same watermark is embedded in different images and in the later on the strength of the watermark varies by a factor of s i.e. (s=10, 20, 30, 40, 50) and it is inserted in the same image.

Keywords: Watermarking, discrete wavelet transform, scaling factor, steganography.

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Authors: R. Sabre, W. Horrigue, J. C. Simon

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This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: Spectral density, stable processes, aliasing, periodogram.

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Authors: M. Tahar Bouzaher

Abstract:

This study involves numerical simulation of the flow around a NACA2415 airfoil, with a 18° angle of attack, and flow separation control using a rod, It involves putting a cylindrical rod - upstream of the leading edge- in vertical translation movement in order to accelerate the transition of the boundary layer by interaction between the rod wake and the boundary layer. The viscous, nonstationary flow is simulated using ANSYS FLUENT 13. The rod movement is reproduced using the dynamic mesh technique and an in-house developed UDF (User Define Function). The frequency varies from 75 to 450 Hz and the considered amplitudes are 2%, and 3% of the foil chord. The frequency chosen closed to the frequency of separation. Our results showed a substantial modification in the flow behavior and a maximum drag reduction of 61%.

Keywords: CFD, Flow separation, Active control, Boundary layer, rod, NACA 2415.

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Authors: Negar Riazifar, Mehran Yazdi

Abstract:

Discrete Wavelet Transform (DWT) has demonstrated far superior to previous Discrete Cosine Transform (DCT) and standard JPEG in natural as well as medical image compression. Due to its localization properties both in special and transform domain, the quantization error introduced in DWT does not propagate globally as in DCT. Moreover, DWT is a global approach that avoids block artifacts as in the JPEG. However, recent reports on natural image compression have shown the superior performance of contourlet transform, a new extension to the wavelet transform in two dimensions using nonseparable and directional filter banks, compared to DWT. It is mostly due to the optimality of contourlet in representing the edges when they are smooth curves. In this work, we investigate this fact for medical images, especially for CT images, which has not been reported yet. To do that, we propose a compression scheme in transform domain and compare the performance of both DWT and contourlet transform in PSNR for different compression ratios (CR) using this scheme. The results obtained using different type of computed tomography images show that the DWT has still good performance at lower CR but contourlet transform performs better at higher CR.

Keywords: Computed Tomography (CT), DWT, Discrete Contourlet Transform, Image Compression.

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Authors: Hyun-Koo Kim, Sangmoon Lee, Ho-Youl Jung, Ju H. Park

Abstract:

We present a system that finds road boundaries and constructs the virtual lane based on fusion data from a laser and a monocular sensor, and detects forward vehicle position even in no lane markers or bad environmental conditions. When the road environment is dark or a lot of vehicles are parked on the both sides of the road, it is difficult to detect lane and road boundary. For this reason we use fusion of laser and vision sensor to extract road boundary to acquire three dimensional data. We use parabolic road model to calculate road boundaries which is based on vehicle and sensors state parameters and construct virtual lane. And then we distinguish vehicle position in each lane.

Keywords: Vehicle Detection, Adaboost, Haar-like Feature, Road Boundary Detection

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Authors: Ferhat Kadioglu, Ahmet Reha Gunay

Abstract:

Correct measurement of a structural damping value is an important issue for the reliable design of the components exposed to vibratory and noise conditions. As far as a vibrating beam technique is concerned, the specimens under the test somehow are interacted with measuring and exciting devices and also with boundary conditions of the test set-up. The aim of this study is to propose a vibrating beam method that offers a non-contact dynamic measurement of solid beam specimens. To evaluate possible effects of the clamped portion of the specimens with clamped-free ends on the dynamic values (damping and the elastic modulus), the same measuring devices were used, and the results were compared to those with the free-free ends. To get clear idea about the sensitivity of the boundary conditions to the damping values at low, medium and high levels, representative materials were subjected to the tests. The results show that the specimens with low damping values are especially sensitive to the boundary conditions and the most reliable structural damping values are obtained for the specimens with free-free ends. For the damping values at the low levels, a deviation of about 368% was obtained between the specimens with free-free and clamped-free ends, yet, for those having high inherent damping values, comparable results were obtained.

Keywords: Vibrating beam technique, dynamic values, damping, boundary conditions, non-contact measuring systems.

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Authors: Mohamed Ali

Abstract:

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. The surface temperature is assumed to vary inversely with the vertical direction x for n = -1. The skin friction at the surface scales as (x-1/2) at m = 0. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as the buoyancy parameter λ and the suction/injection parameter fw for air (Pr = 0.72) are studied. The choice of n and m ensures that the used similarity solutions are x independent. The results show that, assisting flow (λ > 0) enhancing the heat transfer coefficient along the surface for any constant value of fw. Furthermore, injection increases the heat transfer coefficient but suction reduces it at constant λ.

Keywords: Stretching surface, Boundary layers, Prescribed skin friction, Suction or injection, similarity solutions, buoyancy effects.

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

Abstract:

A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: Analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction.

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Authors: Ngoc Trung Ngo, Buddhima Indraratna, Cholachat Rujikiathmakjornr

Abstract:

For several hundred years, the design of railway tracks has practically remained unchanged. Traditionally, rail tracks are placed on a ballast layer due to several reasons, including economy, rapid drainage, and high load bearing capacity. The primary function of ballast is to distributing dynamic track loads to sub-ballast and subgrade layers, while also providing lateral resistance and allowing for rapid drainage. Upon repeated trainloads, the ballast becomes fouled due to ballast degradation and the intrusion of fines which adversely affects the strength and deformation behaviour of ballast. This paper presents the use of three-dimensional discrete element method (DEM) in studying the shear behaviour of the fouled ballast subjected to direct shear loading. Irregularly shaped particles of ballast were modelled by grouping many spherical balls together in appropriate sizes to simulate representative ballast aggregates. Fouled ballast was modelled by injecting a specified number of miniature spherical particles into the void spaces. The DEM simulation highlights that the peak shear stress of the ballast assembly decreases and the dilation of fouled ballast increases with an increase level of fouling. Additionally, the distributions of contact force chain and particle displacement vectors were captured during shearing progress, explaining the formation of shear band and the evolutions of volumetric change of fouled ballast.

Keywords: Railway ballast, coal fouling, discrete element modelling, discrete element method.

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Authors: N. A. Samat, D. F. Percy

Abstract:

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease. 

Keywords: Dengue disease, disease mapping, numerical analysis, SIR-SI differential equations.

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Authors: Dimitrios Zarpalas, Anastasios Zafeiropoulos, Petros Daras, Nicos Maglaveras

Abstract:

Segmentation techniques based on Active Contour Models have been strongly benefited from the use of prior information during their evolution. Shape prior information is captured from a training set and is introduced in the optimization procedure to restrict the evolution into allowable shapes. In this way, the evolution converges onto regions even with weak boundaries. Although significant effort has been devoted on different ways of capturing and analyzing prior information, very little thought has been devoted on the way of combining image information with prior information. This paper focuses on a more natural way of incorporating the prior information in the level set framework. For proof of concept the method is applied on hippocampus segmentation in T1-MR images. Hippocampus segmentation is a very challenging task, due to the multivariate surrounding region and the missing boundary with the neighboring amygdala, whose intensities are identical. The proposed method, mimics the human segmentation way and thus shows enhancements in the segmentation accuracy.

Keywords: Medical imaging & processing, Brain MRI segmentation, hippocampus segmentation, hippocampus-amygdala missingboundary, weak boundary segmentation, region based segmentation, prior information, local weighting scheme in level sets, spatialdistribution of labels, gradient distribution on boundary.

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Authors: Lei Lei, Chao Wang, Xin Liu

Abstract:

Discrete wavelet transform (DWT) has been widely adopted in biomedical signal processing for denoising, compression and so on. Choosing a suitable decomposition level (DL) in DWT is of paramount importance to its performance. In this paper, we propose to exploit sparseness of the transformed signals to determine the appropriate DL. Simulation results have shown that the sparseness of transformed signals after DWT increases with the increasing DLs. Additional Monte-Carlo simulation results have verified the effectiveness of sparseness measure in determining the DL.

Keywords: Sparseness, DWT, decomposition level, ECG.

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Authors: O. Miraliyari

Abstract:

This article attempts to analyze functionally graded beam thermal buckling along with piezoelectric layers applying based on the third order shearing deformation theory considering various boundary conditions. The beam properties are assumed to vary continuously from the lower surface to the upper surface of the beam. The equilibrium equations are derived using the total potential energy equations, Euler equations, piezoelectric material constitutive equations and third order shear deformation theory assumptions. In order to fulfill such an aim, at first functionally graded beam with piezoelectric layers applying the third order shearing deformation theory along with clamped -clamped boundary conditions are thoroughly analyzed, and then following making sure of the correctness of all the equations, the very same beam is analyzed with piezoelectric layers through simply-simply and simply-clamped boundary conditions. In this article buckling critical temperature for functionally graded beam is derived in two different ways, without piezoelectric layer and with piezoelectric layer and the results are compared together. Finally, all the conclusions obtained will be compared and contrasted with the same samples in the same and distinguished conditions through tables and charts. It would be noteworthy that in this article, the software MAPLE has been applied in order to do the numeral calculations.

Keywords: Thermal buckling, functionally graded beam, piezoelectric layer, various boundary conditions.

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Authors: Catalin Gales, Ionel Dumitrel Ghiba

Abstract:

This paper studies questions of continuous data dependence and uniqueness for solutions of initial boundary value problems in linear micropolar thermoelastic mixtures. Logarithmic convexity arguments are used to establish results with no definiteness assumptions upon the internal energy.

Keywords: Cellular materials, continuous dependence, micro polar mixtures, uniqueness.

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