Search results for: Direct method.

Authors: Huaiyu Zhang

Abstract:

The method of modeling is the key technology for digital mockup (DMU). Based upon the developing for mechanical product DMU, the theory, method and approach for virtual environment (VE) and virtual object (VO) were studied. This paper has expounded the design goal and architecture of DMU system, analyzed the method of DMU application, and researched the general process of physics modeling and behavior modeling.

Keywords: DMU, VR, virtual environment, virtual object, physics modeling, behavior modeling

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Authors: M. Akhlaque Ahmed, Sidra A. Shaikh, Maliha A. Siddiqui

Abstract:

Global and diffuse solar radiation on horizontal surface of Lower Sindh, namely Karachi, Hyderabad, Nawabshah were carried out using sunshine hour data of the area to assess the feasibility of solar energy utilization for power generation in Sindh province. The results obtained show a large variation in the direct and diffuse component of solar radiation in summer and winter months in Lower Sindh (50% direct and 50% diffuse for Karachi and Hyderabad). In Nawabshah area, the contribution of diffuse solar radiation is low during the monsoon months, July and August. The K_T value of Nawabshah indicates a clear sky throughout almost the entire year. The percentage of diffuse radiation does not exceed more than 20%. In Nawabshah, the appearance of cloud is rare even during the monsoon months. The estimated values indicate that Nawabshah has high solar potential, whereas Karachi and Hyderabad have low solar potential. During the monsoon months the Lower part of Sindh can utilize the hybrid system with wind power. Near Karachi and Hyderabad, the wind speed ranges between 6.2 m/sec to 6.9 m/sec. A wind corridor exists near Karachi, Hyderabad, Gharo, Keti Bander and Shah Bander. The short fall of solar can be compensated by wind because in the monsoon months of July and August, wind speeds are higher in the Lower region of Sindh.

Keywords: Hybrid power system, power generation, solar and wind energy potential, Lower Sindh.

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Authors: Wen-Yen Wu, Wen-Bin Yu

Abstract:

In this paper, we propose a method for detecting circular shapes with subpixel accuracy. First, the geometric properties of circles have been used to find the diameters as well as the circumference pixels. The center and radius are then estimated by the circumference pixels. Both synthetic and real images have been tested by the proposed method. The experimental results show that the new method is efficient.

Keywords: Subpixel, least squares estimation, circle detection, Hough transformation.

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Authors: Sarun Phibanchon, Michael A. Allen

Abstract:

A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr¨odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.

Keywords: Soliton, instability, variational method, spectral method.

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Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

Abstract:

Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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Authors: A. Hossein Sahoolizadeh, B. Zargham Heidari, C. Hamid Dehghani

Abstract:

In this paper, a new face recognition method based on PCA (principal Component Analysis), LDA (Linear Discriminant Analysis) and neural networks is proposed. This method consists of four steps: i) Preprocessing, ii) Dimension reduction using PCA, iii) feature extraction using LDA and iv) classification using neural network. Combination of PCA and LDA is used for improving the capability of LDA when a few samples of images are available and neural classifier is used to reduce number misclassification caused by not-linearly separable classes. The proposed method was tested on Yale face database. Experimental results on this database demonstrated the effectiveness of the proposed method for face recognition with less misclassification in comparison with previous methods.

Keywords: Face recognition Principal component analysis, Linear discriminant analysis, Neural networks.

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Authors: Meei-Hoan Ho, Chee-Ming Chan

Abstract:

Soft clays are defined as cohesive soil whose water content is higher than its liquid limits. Thus, soil-cement mixing is adopted to improve the ground conditions by enhancing the strength and deformation characteristics of the soft clays. For the above mentioned reasons, a series of laboratory tests were carried out to study some fundamental mechanical properties of cement stabilized soft clay. The test specimens were prepared by varying the portion of ordinary Portland cement to the soft clay sample retrieved from the test site of RECESS (Research Centre for Soft Soil). Comparisons were made for both homogeneous and columnar system specimens by relating the effects of cement stabilized clay of for 0, 5 and 10 % cement and curing for 3, 28 and 56 days. The mechanical properties examined included one-dimensional compressibility and undrained shear strength. For the mechanical properties, both homogeneous and columnar system specimens were prepared to examine the effect of different cement contents and curing periods on the stabilized soil. The one-dimensional compressibility test was conducted using an oedometer, while a direct shear box was used for measuring the undrained shear strength. The higher the value of cement content, the greater is the enhancement of the yield stress and the decrease of compression index. The value of cement content in a specimen is a more active parameter than the curing period.

Keywords: Soft soil, Oedometer, Direct shear box, Cementstabilisedcolumn.

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Authors: Hadi Farhadian, Homayoon Katibeh

Abstract:

In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occured in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m.

Keywords: Water Seepage, Amirkabir Tunnel, Analytical Method, DEM, SGR.

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Authors: Liping Yang, Curran Crawford, Jr. Ren, Zhengyi Ren

Abstract:

Considering the cost evaluation and the stress analysis, a fuzzy satisfactory optimization (FSO) method has been developed for a hybrid composite flywheel. To evaluate the cost, the cost coefficients of the flywheel components are obtained through calculating the weighted sum of the scores of the material manufacturability, the structure character, and the material price. To express the satisfactory degree of the energy, the cost, and the mass, the satisfactory functions are proposed by using the decline function and introducing a satisfactory coefficient. To imply the different significance of the objectives, the object weight coefficients are defined. Based on the stress analysis of composite material, the circumferential and radial stresses are considered into the optimization formulation. The simulations of the FSO method with different weight coefficients and storage energy density optimization (SEDO) method of a flywheel are contrasted. The analysis results show that the FSO method can satisfy different requirements of the designer and the FSO method with suitable weight coefficients can replace the SEDO method.

Keywords: Flywheel energy storage, fuzzy, optimization, stress analysis.

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Authors: A. Tagar, F. A. Chandio, I. A. Mari, B. Wagan

Abstract:

An experiment was conducted on the comparative study of drip and furrow irrigation methods at the farmer-s field in Umar Kot. The total area under experiment about 4000m2 was divided into two equal portions. One portion about 40m X 50m was occupied by drip and the other portion about 40m X 50m by furrow irrigation method. Soil at the experimental site was clay loam in texture for 0-60cm depth; average dry bulk density and field capacity was 1.16g/cm3 and 28.5% respectively. The results reveal that the drip irrigation method saved 56.4% water and gave 22% more yield as compared to that of furrow irrigation method. Higher water use efficiency about 4.87 was obtained in drip irrigation method; whereas lower water used efficiency about 1.66 was obtained in furrow irrigation method. The present study suggests farming community to adopt drip irrigation method instead of old traditional flooding methods.

Keywords: Drip and furrow irrigations methods, water saving, yield of tomato crop.

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Authors: Jun Hee Lee, Young Kyu Kim, Seong Jae Hong, Chamroeun Chhorn, Seung Woo Lee

Abstract:

Roller-compacted concrete pavement (RCCP), an environmental friendly pavement of which load carry capacity benefitted from both hydration and aggregate interlock from roller compacting, demonstrated a superb structural performance for a relatively small amount of water and cement content. Even though an excellent structural performance can be secured, it is required to investigate roller-compacted concrete (RCC) under environmental loading and its long-term durability under critical conditions. In order to secure long-term durability, an appropriate internal air-void structure is required for this concrete. In this study, a method for improving the long-term durability of RCCP is suggested by analyzing the internal air-void structure and corresponding durability of RCC. The method of improving the long-term durability involves measurements of air content, air voids, and air-spacing factors in RCC that experiences changes in terms of type of air-entraining agent and its usage amount. This test is conducted according to the testing criteria in ASTM C 457, 672, and KS F 2456. It was found that the freezing-thawing and scaling resistances of RCC without any chemical admixture was quite low. Interestingly, an improvement of freezing-thawing and scaling resistances was observed for RCC with appropriate the air entraining (AE) agent content; Relative dynamic elastic modulus was found to be more than 80% for those mixtures. In RCC with AE agent mixtures, large amount of air was distributed within a range of 2% to 3%, and an air void spacing factor ranging between 200 and 300 μm (close to 250 μm, recommended by PCA) was secured. The long-term durability of RCC has a direct relationship with air-void spacing factor, and thus it can only be secured by ensuring the air void spacing factor through the inclusion of the AE in the mixture.

Keywords: RCCP, durability, air spacing factor, surface scaling resistance test, freezing and thawing resistance test.

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Authors: Yuki Kondo, Takanori Nagano, Yuki Takeda, Young-Bok Choi, Hiromi Okada

Abstract:

Optical burst switching(OBS) is considered as one of preferable network technologies for the next generation Internet. The Internet has two traffic classes, i.e. real-time bursts and reliable bursts. It is an important subject for OBS to achieve cooperated operation of real-time bursts and reliable bursts. In this paper, we proposes a new effective traffic control method named Separate TB+LB (Token Bucket + Leaky Bucket : TB+LB) method. The proposed method presents a new Token Bucket scheme for real-time bursts called as RBO-TB (Real-time Bursts Oriented Token Bucket). The method also applies the LB method to reliable bursts for obtaining better performance. This paper verifies the effectiveness of the Separate TB+LB method through the performance evaluation.

Keywords: leaky bucket, OBS, traffic control, token bucket.

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Authors: H. Dujmic, V. Papic, H. Turic

Abstract:

The article presents a new method for detection of artificial objects and materials from images of the environmental (non-urban) terrain. Our approach uses the hue and saturation (or Cb and Cr) components of the image as the input to the segmentation module that uses the mean shift method. The clusters obtained as the output of this stage have been processed by the decision-making module in order to find the regions of the image with the significant possibility of representing human. Although this method will detect various non-natural objects, it is primarily intended and optimized for detection of humans; i.e. for search and rescue purposes in non-urban terrain where, in normal circumstances, non-natural objects shouldn-t be present. Real world images are used for the evaluation of the method.

Keywords: Landscape surveillance, mean shift algorithm, image segmentation, target detection.

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Authors: V.Ashok, A.Nirmalkumar, N.Jeyashanthi

Abstract:

A method and apparatus for noninvasive measurement of blood glucose concentration based on transilluminated laser beam via the Index Finger has been reported in this paper. This method depends on atomic gas (He-Ne) laser operating at 632.8nm wavelength. During measurement, the index finger is inserted into the glucose sensing unit, the transilluminated optical signal is converted into an electrical signal, compared with the reference electrical signal, and the obtained difference signal is processed by signal processing unit which presents the results in the form of blood glucose concentration. This method would enable the monitoring blood glucose level of the diabetic patient continuously, safely and noninvasively.

Keywords: Anisotropy factor, Blood glucose, Diabetes Mellitus, Noninvasive method, Photo detectors.

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Authors: A. M. Sagir

Abstract:

In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: Azali Saudi, Jumat Sulaiman

Abstract:

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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Authors: Junji Kaneko, Shigeyuki Haruyama, Ken Kaminishi, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

Abstract:

This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physic fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: System Model, Physical Models, Empirical Models, Conservation Law, Differential Algebraic Equation, Object-Oriented.

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Authors: B. J. C. Horsten, L. L. M. Veldhuis

Abstract:

Because support interference corrections are not properly understood, engineers mostly rely on expensive dummy measurements or CFD calculations. This paper presents a method based on uncorrected wind tunnel measurements and fast calculation techniques (it is a hybrid method) to calculate wall interference, support interference and residual interference (when e.g. a support member closely approaches the wind tunnel walls) for any type of wind tunnel and support configuration. The method provides with a simple formula for the calculation of the interference gradient. This gradient is based on the uncorrected measurements and a successive calculation of the slopes of the interference-free aerodynamic coefficients. For the latter purpose a new vortex-lattice routine is developed that corrects the slopes for viscous effects. A test case of a measurement on a wing proves the value of this hybrid method as trends and orders of magnitudes of the interference are correctly determined.

Keywords: Hybrid method, support interference, wall interference, wind tunnel corrections.

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Authors: Jaedo Kim, Youngjoon Han, Hernsoo Hahn

Abstract:

This paper propose the robust character segmentation method for license plate with topological transform such as twist,rotation. The first step of the proposed method is to find a candidate region for character and license plate. The character or license plate must be appeared as closed loop in the edge image. In the case of detecting candidate for character region, the evaluation of detected region is using topological relationship between each character. When this method decides license plate candidate region, character features in the region with binarization are used. After binarization for the detected candidate region, each character region is decided again. In this step, each character region is fitted more than previous step. In the next step, the method checks other character regions with different scale near the detected character regions, because most license plates have license numbers with some meaningful characters around them. The method uses perspective projection for geometrical normalization. If there is topological distortion in the character region, the method projects the region on a template which is defined as standard license plate using perspective projection. In this step, the method is able to separate each number region and small meaningful characters. The evaluation results are tested with a number of test images.

Keywords: License Plate Detection, Character Segmentation, Perspective Projection, Topological Transform.

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

Abstract:

This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: Expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon.

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Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

Abstract:

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

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Authors: M. Zelinkova, M. Ondova

Abstract:

Fly ash (FA) thanks to the significant presence of SiO2 and Al2O3 as the main components is a potential raw material for geopolymers production. Mechanical activation is a method for improving FA reactivity and also the porosity of final mixture; those parameters can be analysed through sorption properties. They have direct impact on the durability of fly ash based geopolymer mortars. In the paper, effect of FA fineness on sorption properties of geopolymers based on sodium silicate, as well as relationship between fly ash fineness and apparent density, compressive and flexural strength of geopolymers are presented. The best results in the evaluated area reached the sample H1, which contents the highest portion of particle under 20μm (100% of GFA). The interdependence of individual tested properties was confirmed for geopolymer mixtures corresponding to those in the cement based mixtures: higher is portion of fine particles < 20μm, higher is strength, density and lower are sorption properties. The compressive strength as well as sorption parameters of the geopolymer can be reasonably controlled by grinding process and also ensured by the higher share of fine particle (to 20μm) in total mass of the material.

Keywords: Alkali activation, geopolymers, fly ash, particle fineness.

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Authors: Mohammad Taghi Darvishi, Samad Kheybari

Abstract:

In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.

Keywords: Parameter-expansion method, classical Van der Pol oscillator.

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Authors: M. Khosravy-el-Hossani, Q. Dorosti

Abstract:

One of the important applications of gas turbines is their utilization for heat recovery steam generator in combine-cycle technology. Exhaust flow and energy are two key parameters for determining heat recovery steam generator performance which are mainly determined by the main gas turbine components performance data. For this reason a method was developed for determining the exhaust energy in the new edition of ASME PTC22. The result of this investigation shows that the method of standard has considerable error. Therefore in this paper a new method is presented for modifying of the performance calculation. The modified method is based on exhaust gas constituent analysis and combustion calculations. The case study presented here by two kind of General Electric gas turbine design data for validation of methodologies. The result shows that the modified method is more precise than the ASME PTC22 method. The exhaust flow calculation deviation from design data is 1.5-2 % by ASME PTC22 method so that the deviation regarding with modified method is 0.3-0.5%. Based on precision of analyzer instruments, the method can be suitable alternative for gas turbine standard performance test. In advance two methods are proposed based on known and unknown fuel in modified method procedure. The result of this paper shows that the difference between the two methods is below than %0.02. In according to reasonable esult of the second procedure (unknown fuel composition), the method can be applied to performance evaluation of gas turbine, so that the measuring cost and data gathering should be reduced.

Keywords: Gas turbine, Performance test code, Combined cycle.

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

Abstract:

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given.

Keywords: Integro-differential equations, initial value problem, hybrid methods, predictor-corrector method

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Authors: Sambit Prasad Kar, P.Palanisamy

Abstract:

In this paper a novel method for multiple one dimensional real valued sinusoidal signal frequency estimation in the presence of additive Gaussian noise is postulated. A computationally simple frequency estimation method with efficient statistical performance is attractive in many array signal processing applications. The prime focus of this paper is to combine the subspace-based technique and a simple peak search approach. This paper presents a variant of the Propagator Method (PM), where a collaborative approach of SUMWE and Propagator method is applied in order to estimate the multiple real valued sine wave frequencies. A new data model is proposed, which gives the dimension of the signal subspace is equal to the number of frequencies present in the observation. But, the signal subspace dimension is twice the number of frequencies in the conventional MUSIC method for estimating frequencies of real-valued sinusoidal signal. The statistical analysis of the proposed method is studied, and the explicit expression of asymptotic (large-sample) mean-squared-error (MSE) or variance of the estimation error is derived. The performance of the method is demonstrated, and the theoretical analysis is substantiated through numerical examples. The proposed method can achieve sustainable high estimation accuracy and frequency resolution at a lower SNR, which is verified by simulation by comparing with conventional MUSIC, ESPRIT and Propagator Method.

Keywords: Frequency estimation, peak search, subspace-based method without eigen decomposition, quadratic convex function.

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Authors: P. W. C. Prasad, A. Assi, M. Raseen, A. Harb

Abstract:

The goal of this work is to describe a new algorithm for finding the optimal variable order, number of nodes for any order and other ROBDD parameters, based on a tabular method. The tabular method makes use of a pre-built backend database table that stores the ROBDD size for selected combinations of min-terms. The user uses the backend table and the proposed algorithm to find the necessary ROBDD parameters, such as best variable order, number of nodes etc. Experimental results on benchmarks are given for this technique.

Keywords: Tabular Method, Binary Decision Diagram, BDD Manipulation, Boolean Function.

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Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat

Abstract:

Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.

Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.

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Authors: Nemat Abazari, Reza Abazari

Abstract:

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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