Search results for: height method.

Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: Melting furnace, inverse heat transfer, enthalpy method, Levenberg–Marquardt Method.

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Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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Authors: Ricardo Espinosa

Abstract:

The coherent Self-Averaging (CSA), is a new method proposed in this work; applied to simulated signals evoked potentials related to events (ERP) to find the wave P300, useful systems in the brain computer interface (BCI). The CSA method cleans signal in the time domain of white noise through of successive averaging of a single signal. The method is compared with the traditional method, coherent averaging or synchronized (CA), showing optimal results in the improvement of the signal to noise ratio (SNR). The method of CSA is easy to implement, robust and applicable to any physiological time series contaminated with white noise

Keywords: Evoked potentials, wave P300, Coherent Self-averaging, brain - computer interface (BCI).

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Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: Jean-Jacques Randrianarimanana, Nassim Sebaibi, Mohamed Boutouil

Abstract:

In order to solve problems associated with stormwater runoff in urban areas and their effects on natural and artificial water bodies, the integration of new technical solutions to the rainwater drainage becomes even more essential. Permeable pavement systems are one of the most widely used techniques. This paper presents a laboratory analysis of stormwater runoff hydraulic and pollutant removal performance of permeable pavement system using pervious pavements based on seashell products. The laboratory prototype is a square column of 25 cm of side and consists of the surface in pervious concrete, a bedding of 3 cm in height, a geotextile and a subbase layer of 50 cm in height. A series of constant simulated rain events using semi-synthetic runoff which varied in intensity and duration were carried out. The initial vertical saturated hydraulic conductivity of the entire pervious pavement system was 0.25 cm/s (148 L/m²/min). The hydraulic functioning was influenced by both the inlet flow rate value and the test duration. The total water losses including evaporation ranged between 9% to 20% for all hydraulic experiments. The temporal and vertical variability of the pollutant removal efficiency (PRE) of the system were studied for total suspended solids (TSS). The results showed that the PRE along the vertical profile was influenced by the size of the suspended solids, and the pervious paver has the highest capacity to trap pollutant than the other porous layers of the permeable pavement system after the geotextile. The TSS removal efficiency was about 80% for the entire system. The first-flush effect of TSS was observed, but it appeared only at the beginning (2 to 6 min) of the experiments. It has been shown that the PPS can capture first-flush. The project in which this study is integrated aims to contribute to both the valorization of shellfish waste and the sustainable management of rainwater.

Keywords: Hydraulic, pervious concrete, pollutant removal efficiency, seashell by-products, stormwater runoff.

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Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.

Keywords: classification, functional data, feature extraction, K-Lseperability, wavelet.

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Authors: Amir Abolfazl Suratgar, Mohammad Bagher Tavakoli, Abbas Hoseinabadi

Abstract:

In this paper a modification on Levenberg-Marquardt algorithm for MLP neural network learning is proposed. The proposed algorithm has good convergence. This method reduces the amount of oscillation in learning procedure. An example is given to show usefulness of this method. Finally a simulation verifies the results of proposed method.

Keywords: Levenberg-Marquardt, modification, neural network, variable learning rate.

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Authors: L. Sriphong, A. Chaidedgumjorn, K. Chaisuroj

Abstract:

A spectrophotometric method was developed for simultaneous quantification of pseudoephedrine hydrochloride (PSE) triprolidine hydrochloride (TRI) using second derivative method (zero-crossing technique). The second derivative amplitudes of PSE and TRI were measured at 271 and 321 nm, respectively. The calibration curves were linear in the range of 200 to 1,000 g/ml for PSE and 10 to 50 g/ml for TRI. The method was validated for specificity, accuracy, precision, limit of detection and limit of quantitation. The proposed method was applied to the assaying and dissolution of PSE and TRI in commercial tablets without any chemical separation. The results were compared with those obtained by the official USP31 method and statistical tests showed that there is no significant between the methods at 95% confidence level. The proposed method is simple, rapid and suitable for the routine quality control application. KeywordsTriprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

Keywords: Triprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

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Authors: Zanariah Abdul Majid, Mohamed Suleiman

Abstract:

The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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Authors: Smarajit Ghosh , Karma Sonam Sherpa

Abstract:

This paper reports a new and accurate method for load-flow solution of radial distribution networks with minimum data preparation. The node and branch numbering need not to be sequential like other available methods. The proposed method does not need sending-node, receiving-node and branch numbers if these are sequential. The proposed method uses the simple equation to compute the voltage magnitude and has the capability to handle composite load modelling. The proposed method uses the set of nodes of feeder, lateral(s) and sub lateral(s). The effectiveness of the proposed method is compared with other methods using two examples. The detailed load-flow results for different kind of load-modellings are also presented.

Keywords: Load−flow, Feeder, Lateral, Power, Voltage, Composite, Exponential

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Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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Authors: Bogusław Schreyer

Abstract:

The paper enquires on the two methods of the wheeled robot braking torque control. Those two methods are applied when the adhesion coefficient under left side wheels is different from the adhesion coefficient under the right side wheels. In case of the select-low (SL) method the braking torque on both wheels is controlled by the signals originating from the wheels on the side of the lower adhesion. In the select-high (SH) method the torque is controlled by the signals originating from the wheels on the side of the higher adhesion. The SL method is securing stable and secure robot behaviors during the braking process. However, the efficiency of this method is relatively low. The SH method is more efficient in terms of time and braking distance but in some situations may cause wheels blocking. It is important to monitor the velocity of all wheels and then take a decision about the braking torque distribution accordingly. In case of the SH method the braking torque slope may require significant decrease in order to avoid wheel blocking.

Keywords: Select-high method, select-low method, torque distribution, wheeled robot.

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Authors: Francisco Echarte, José Javier Astrain, Alberto Córdoba, Jesús Villadangos

Abstract:

Ontologies and tagging systems are two different ways to organize the knowledge present in the current Web. In this paper we propose a simple method to model folksonomies, as tagging systems, with ontologies. We show the scalability of the method using real data sets. The modeling method is composed of a generic ontology that represents any folksonomy and an algorithm to transform the information contained in folksonomies to the generic ontology. The method allows representing folksonomies at any instant of time.

Keywords: Folksonomies, ontologies, OWL, semantic web.

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Authors: Harun Sumbul, Orhan Ozyurt

Abstract:

The accelerations generated by the shoes in the body should be known in order to prevent balance problems, degradation of body shape and to spend less energy. In this study, it is aimed to investigate the effects of the shoe heel height on the human body. The working group has been created as five women (range 27-32 years) with different characteristics and five shoes with different heel heights (1, 3.5, 5, 7 and 9 cm). Individuals in the study group wore shoes and walked along a 20-meter racecourse. The accelerations created by the shoes are measured in three axes (30.270 accelerometric data) and analyzed. Results show us that; while walking with high-heeled shoes, the foot is lifted more; in this case, more effort has been spent. So, more weight has occurred at ankles and joints. Since high-heeled shoes cause greater acceleration, women wearing high-heeled shoes tend to pay more attention when taking a step. As a result, for foot and body health, shoe heel must be designed to absorb the reaction from the ground. High heels disrupt the structure of the foot and it is damaging the body shape. In this respect, this study is considered to be a remarkable method to find of effect of high-heeled shoes on gait by using accelerometer in the literature.

Keywords: Acceleration, sensor, gait analysis, high shoe heel, micro-electro-mechanical-systems.

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Authors: M. Zamani, O. Kahar

Abstract:

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: Manfred Hartmann, Andreas Graef, Hannes Perko, Christoph Baumgartner, Tilmann Kluge

Abstract:

In this paper we introduce a novel method for the characterization of synchronziation and coupling effects in multivariate time series that can be used for the analysis of EEG or ECoG signals recorded during epileptic seizures. The method allows to visualize the spatio-temporal evolution of synchronization and coupling effects that are characteristic for epileptic seizures. Similar to other methods proposed for this purpose our method is based on a regression analysis. However, a more general definition of the regression together with an effective channel selection procedure allows to use the method even for time series that are highly correlated, which is commonly the case in EEG/ECoG recordings with large numbers of electrodes. The method was experimentally tested on ECoG recordings of epileptic seizures from patients with temporal lobe epilepsies. A comparision with the results from a independent visual inspection by clinical experts showed an excellent agreement with the patterns obtained with the proposed method.

Keywords: EEG, epilepsy, regression analysis, seizurepropagation.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Matheus Müller, Delma Vidal

Abstract:

The present paper aims to expose two techniques of dewatering for sludge, analyzing its operations and dewatering processes, aiming at improving the conditions of disposal of residues with high liquid content. It describes the field tests performed on two geotextile systems, a closed geotextile tube and an open geotextile drying bed, both of which are submitted to two filling cycles. The sludge used in the filling cycles for the field trials is from the water treatment plant of the Technological Center of Aeronautics – CTA, in São José dos Campos, Brazil. Data about volume and height abatement due to the dewatering and consolidation were collected per time, until it was observed constancy. With the laboratory analysis of the sludge allied to the data collected in the field, it was possible to perform a critical comparative study between the observed and the scientific literature, in this way, this paper expresses the data obtained and compares them with the bibliography. The tests were carried out on three fronts: field tests, including the filling cycles of the systems with the sludge from CTA, taking measurements of filling time per cycle and maximum filling height per cycle, heights against the abatement by dewatering of the systems over time; tests carried out in the laboratory, including the characterization of the sludge and removal of material samples from the systems to ascertain the solids content within the systems per time and; comparing the data obtained in the field and laboratory tests with the scientific literature. Through the study, it was possible to perceive that the process of densification of the material inside a closed system, such as the geotextile tube, occurs faster than the observed in the drying bed system. This process of accelerated densification can be brought about by the pumping pressure of the sludge in its filling and by the confinement of the residue through the permeable geotextile membrane (allowing water to pass through), accelerating the process of densification and dewatering by its own weight after the filling with sludge.

Keywords: Consolidation, dewatering, geotextile drying bed, geotextile tube.

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Authors: Ali Shojaee Bakhtiari, Ali Asghar Beheshti Shirazi, Amir Sepasi Zahmati

Abstract:

An efficient iris segmentation method based on analyzing the local entropy characteristic of the iris image, is proposed in this paper and the strength and weaknesses of the method are analyzed for practical purposes. The method shows special strength in providing designers with an adequate degree of freedom in choosing the proper sections of the iris for their application purposes.

Keywords: Iris segmentation, entropy, biocryptosystem, biometric identification.

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Authors: A. F. Agboola, B. R. O. Omidiwura, A. Oyeyemi, E. A. Iyayi, A. S. Adelani

Abstract:

Dietary cholesterol has elicited the most public interest as it relates with coronary heart disease. Thus, humans have been paying more attention to health, thereby reducing consumption of cholesterol enriched food. Egg is considered as one of the major sources of human dietary cholesterol. However, an alternative way to reduce the potential cholesterolemic effect of eggs is to modify the fatty acid composition of the yolk. The effect of palm oil (PO), soybean oil (SO), sesame seed oil (SSO) and fish oil (FO) supplementation in the diets of layers on egg yolk fatty acid, cholesterol, egg production and egg quality parameters were evaluated in a 42-day feeding trial. One hundred and five Isa Brown laying hens of 34 weeks of age were randomly distributed into seven groups of five replicates and three birds per replicate in a completely randomized design. Seven corn-soybean basal diets (BD) were formulated: BD+No oil (T1), BD+1.5% PO (T2), BD+1.5% SO (T3), BD+1.5% SSO (T4), BD+1.5% FO (T5), BD+0.75% SO+0.75% FO (T6) and BD+0.75% SSO+0.75% FO (T7). Five eggs were randomly sampled at day 42 from each replicate to assay for the cholesterol, fatty acid profile of egg yolk and egg quality assessment. Results showed that there were no significant (P>0.05) differences observed in production performance, egg cholesterol and egg quality parameters except for yolk height, albumen height, yolk index, egg shape index, haugh unit, and yolk colour. There were no significant differences (P>0.05) observed in total cholesterol, high density lipoprotein and low density lipoprotein levels of egg yolk across the treatments. However, diets had effect (P<0.05) on TAG (triacylglycerol) and VLDL (very low density lipoprotein) of the egg yolk. The highest TAG (603.78 mg/dl) and VLDL values (120.76 mg/dl) were recorded in eggs of hens on T4 (1.5% sesame seed oil) and was similar to those on T3 (1.5% soybean oil), T5 (1.5% fish oil) and T6 (0.75% soybean oil + 0.75% fish oil). However, results revealed a significant (P<0.05) variations on eggs’ summation of polyunsaturated fatty acid (PUFA). In conclusion, it is suggested that dietary oils could be included in layers’ diets to produce designer eggs low in cholesterol and high in PUFA especially omega-3 fatty acids.

Keywords: Dietary oils, Egg cholesterol, Egg fatty acid profile, Egg quality parameters.

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Authors: Jaka Suyana, Komariah, Masateru Senge

Abstract:

This research was aimed at determining the impact of conservation techniques including bench terrace, stone terrace, mulching, grass strip and intercropping on soil erosion at tobacco-based farming system at Progo Hulu subwatershed, Central Java, Indonesia. Research was conducted from September 2007 to September 2009, located at Progo Hulu subwatershed, Central Java, Indonesia. Research site divided into 27 land units, and experimental fields were grouped based on the soil type and slope, ie: 30%, 45% and 70%, with the following treatments: 1) ST0= stone terrace (control); 2) ST1= stone terrace + Setaria spacelata grass strip on a 5 cm height dike at terrace lips + tobacco stem mulch with dose of 50% (7 ton/ ha); 3) ST2= stone terrace + Setaria spacelata grass strip on a 5 cm height dike at terrace lips + tobacco stem mulch with dose of 100% (14 ton/ ha); 4) ST3= stone terrace + tobacco and red bean intercropping + tobacco stem mulch with dose of 50% (7 ton/ ha). 5) BT0= bench terrace (control); 6) BT1= bench terrace + Setaria spacelata grass strip at terrace lips + tobacco stem mulch with dose of 50% (7 ton/ ha); 7) BT2= bench terrace + Setaria spacelata grass strip at terrace lips + tobacco stem mulch with dose of 100% (14 ton/ ha); 8) BT3= bench terrace + tobacco and red bean intercropping + tobacco stem mulch with dose of 50% (7 ton/ ha). The results showed that the actual erosion rates of research site were higher than that of tolerance erosion with mean value 89.08 ton/ha/year and 33.40 ton/ha/year, respectively. These resulted in 69% of total research site (5,119.15 ha) highly degraded. Conservation technique of ST2 was the most effective in suppressing soil erosion, by 42.87%, following with BT2 as much 30.63%. Others suppressed erosion only less than 21%.

Keywords: Steep land, subwatershed, conservation terrace, tolerance erosion.

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Authors: C. C. Lv, Y. L. Sun, D. W. Zuo

Abstract:

Cemented carbide balls are usually implemented in industry under the environment of high speed, high temperature, corrosiveness and strong collisions. However, its application is limited due to high fabrication cost, processing efficiency and quality. A novel eccentric lapping method with two rotatable lapping plates was proposed in this paper. A mathematical model was constructed to analyze the influence of each design parameter on this lapping method. To validate this new lapping method, an orthogonal experiment was conducted with cemented carbide balls (YG6). The simulation model was verified and the optimal lapping parameters were derived. The results show that the surface roundness of the balls reaches to 0.65um from 2um in 1 hour using this lapping method. So, using this novel lapping method, it can effectively improve the machining precision and efficiency of cemented carbide balls.

Keywords: Cemented carbide balls, eccentric lapping, high precision, lapping tracks, V-groove.

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Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

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The radiation effect within the solid anode, electrolyte, and cathode SOFC layers problem has been investigated in this paper. Energy equation is solved by the Lattice Boltzmann method (LBM). The Rosseland method is used to model the radiative transfer in the electrodes. The Schuster-Schwarzschild method is used to model the radiative transfer in the electrolyte. Without radiative effect, the found results are in good agreement with those published. The obtained results show that the radiative effect can be neglected.

Keywords: SOFC, lattice Boltzmann method, conduction, radiation.

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Authors: Kejun Zhuang, Hailong Zhu

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In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.

Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.

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Authors: U. Rubins, Z. Marcinkevics, K.Volceka

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The cardiovascular system has become the most important subject of clinical research, particularly measurement of arterial blood flow. Therefore correct determination of arterial diameter is crucial. We propose a novel, semi-automatic method for artery lumen detection. The method is based on Gaussian probability function. Usability of our proposed method was assessed by analyzing ultrasound B-mode CFA video sequences acquired from eleven healthy volunteers. The correlation coefficient between the manual and semi-automatic measurement of arterial diameter was 0.996. Our proposed method for detecting artery boundary is novel and accurate enough for the measurement of artery diameter.

Keywords: Ultrasound, boundary detection, artery diameter, curve fitting.

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Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

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In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

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Authors: Chiharu Okuma, Naoki Yamamoto, Jun Murakami

Abstract:

As a method of expanding a higher-order tensor data to tensor products of vectors we have proposed the Third-order Orthogonal Tensor Product Expansion (3OTPE) that did similar expansion as Higher-Order Singular Value Decomposition (HOSVD). In this paper we provide a computation algorithm to improve our previous method, in which SVD is applied to the matrix that constituted by the contraction of original tensor data and one of the expansion vector obtained. The residual of the improved method is smaller than the previous method, truncating the expanding tensor products to the same number of terms. Moreover, the residual is smaller than HOSVD when applying to color image data. It is able to be confirmed that the computing time of improved method is the same as the previous method and considerably better than HOSVD.

Keywords: Singular value decomposition (SVD), higher-orderSVD (HOSVD), outer product expansion, power method.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

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In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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