Search results for: weight method

Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, Step method, delay differential equation, simulation.

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Authors: Pakorn Traiprasertpong, Apichit Svang-Ariyaskul

Abstract:

The production of ethyl tert-butyl ether (ETBE) was simulated through Aspen Plus. The objective of this work was to use the simulation results to be an alternative platform for ETBE production from naphtha cracking wastes for the industry to develop. ETBE is produced from isobutylene which is one of the wastes in naphtha cracking process. The content of isobutylene in the waste is less than 30% weight. The main part of this work was to propose a process to save the environment and to increase the product value by converting a great majority of the wastes into ETBE. Various processes were considered to determine the optimal production of ETBE. The proposed process increased ETBE production yield by 100% from conventional process with the purity of 96% weight. The results showed a great promise for developing this proposed process in an industrial scale.

Keywords: ETBE, process simulation, naphtha cracking, Aspen Plus

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: A. P. Singh

Abstract:

The results reported in this paper are the part of an extensive laboratory investigation undertaken to study the effects of fibre parameters on the permeability and strength characteristics of steel fibre reinforced concrete (SFRC). The effect of varying fibre content and curing age on the water permeability, compressive and split tensile strengths of SFRC was investigated using straight steel fibres having an aspect ratio of 65. Samples containing three different weight fractions of 1.0%, 2.0% and 4.0% were cast and tested for permeability and strength after 7, 14, 28 and 60 days of curing. Plain concrete samples were also cast and tested for reference purposes.

Permeability was observed to decrease significantly with the addition of steel fibres and continued to decrease with increasing fibre content and increasing curing age. An exponential relationship was observed between permeability and compressive and split tensile strengths for SFRC as well as PCC. To evaluate the effect of fibre content on the permeability and strength characteristics, the Analysis of Variance (ANOVA) statistical method was used. An a level (probability of error) of 0.05 was used for ANOVA test. Regression analysis was carried out to develop relationship between permeability, compressive strength and curing age.

Keywords: Permeability, grade of concrete, fibre shape, fibre content, curing age, steady state, Darcy’s law, method of penetration.

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Authors: B. S. Raghavendra, D. Narayana Dutt

Abstract:

In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signal. The loglog plot of total number of boxes required to cover the curve versus size of the box used appears to be a straight line, whose slope is taken as an estimate of FD of the signal. The results are provided to demonstrate the performance of the proposed method using parametric fractal signals. The estimation accuracy of the method is compared with that of Katz, Sevcik, and Higuchi methods. In addition, some properties of the FD are discussed.

Keywords: Box-counting, Fractal dimension, Higuchi method, Katz method, Parametric fractal signals, Sevcik method.

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Authors: Sperisa Distantina, Rieke Ulfha Noviyanti, Sri Sutriyani, Fadilah Fadilah, Mujtahid Kaavessina

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In this research, carrageenan extracted from seaweed Eucheuma cottonii was mixed with polyvinyl alcohol (PVA) and then crosslinked using glutaraldehyde (GA). The obtained hydrogel films were applied to control the drug release rate of paracetamol. The aim of this research was to develop a mathematical model that can be used to describe the mass transfer rate of paracetamol from the hydrogel film into buffer solution. The effect of weight ratio carrageenan-PVA (5: 0, 1: 0.5, 1: 1, 1: 2, 0: 5) on the parameters of the mathematical model was investigated also. Based on the experimental data, the proposed mathematical model could describe the mass transfer rate of paracetamol. The weight ratio of carrageenan-PVA greatly affected the amount of paracetamol absorbed in the hydrogel film and the mass transfer rate of paracetamol.

Keywords: Carrageenan-PVA, crosslinking, hydrogel, glutaraldehyde, paracetamol, mass transfer.

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Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

Abstract:

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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Authors: S. J. Hosseini Ghoncheh, M. Paripour

Abstract:

In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

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Authors: Amir Ghasemlouei, Alireza Khalaj

Abstract:

Breast cancer is in the top rate of cancer. We analyzed the prevalence of obesity and its association with breast cancer and finally we reviewed 25 article that 320 patient and 320 control which enrolled to our study. The distribution of breast cancer patients and controls with respect to their anthropometric indices in patients with higher weight, which was statistically significant (60.2 ± 10.2 kg) compared with control group (56.1 ± 11.3 kg). The body mass index of patients was (26.06+/-3.42) and significantly higher than the control group (24.1+/-1.7). Obesity leads to increased levels of adipose tissue in the body that can be stored toxins and carcinogens to produce a continuous supply. Due to the high level of fat and the role of estrogen in a woman which is endogenous estrogen of the tumor and regulates the activities of growth steroids, obesity has confirmed as a risk factor for breast cancer. Our study and other studies have shown that obesity is a risk factor for breast cancer. And it can be prevented with a weight loss intervention for breast cancer in the future.

Keywords: Breast cancer, review study, obesity, overweight.

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Authors: Yeanchon H. Dulanlebit, Nikmans Hattu, Gloria Bora

Abstract:

Seaweed is a type of macro algae which are good source of iodine and have been widely used as food and nutrition supplement. One of iodine species that found in ocean plant is iodate. Analysis of iodate in seaweed (Eucheuma cottonii) from coastal area of Maluku has been done. The determination is done by using spectrophotometric method. Iodate in sample is reduced in excess of potassium iodide in the presence of acid solution, and then is reacted with starch to form blue complex. The study found out that the highest wavelength on determination of iodate species using spectrophotometer analysis method is 570 nm. Optimum value to yield maximum absorption is used in this research. Contents of iodate in seawater from coastal area of Ambon Island, Western Seram and Southeast Maluku are 0.2655, 0.2719 and 0.1760 mg/L, respectively. While in seaweeds from Ambon Island, Western Seram, Southeast Maluku-Taar, Ohoidertawun and Wab are 6.3122, 6.3293, 6.2333, 3.7406 and 4.4207 mg/kg in dry weight. Bioconcentration (enrichment) factor of iodate in seaweed (Eucheuma cottonii) from the three samples (cluster) is different; in Coastal area of Ambon Island, Western Seram and Southeast Maluku respectively are 23.78, 23.28 and 27.26.

Keywords: Bioconcentration, Eucheuma cottonii, iodate, iodine, seaweed.

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Authors: A. G. Silva Sobrinho, L. G. A. Cirne, V. T. Santana

Abstract:

The aim of this trial was to evaluate fatty acid profile of meat from lambs fed on diets containing 0, 12.5 and 25.0% mulberry hay as a substitute for the concentrate. Twenty-four feedlot Ile de France lambs (average weight of 15kg and average age of 60 days) were randomized to receive the different diets and slaughtered at 32kg body weight. Increases were observed in the concentrations of the saturated pentadecanoic, heptadecanoic and arachidic fatty acids; of the monounsaturated nervonic fatty acid and of the polyunsaturated α-linolenic, ɣ-linolenic and eicosapentaenoic fatty acids. Increased conjugated linoleic acid (CLA) was also found in the meat of lambs fed on 12.5% mulberry hay. In addition, the omega-3 composition was augmented, while the omega-3/omega-6 ratio was decreased in mulberry hay-fed animals. In conclusion, a more desirable fatty acid profile was observed in lamb meat following the substitution of mulberry hay in the concentrate of fed, resulting in improved nutritional characteristics of the meat.

Keywords: Alternative food, fatty acids, feedlot, sheep meat.

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: S. Sutin, M. Pollar, M. Jaroensutasinee, K. Jaroensutasinee

Abstract:

This study investigated morphology of the Spanner Barb (Puntius lateristriga Valenciennes, 1842) and water quality at Thepchana waterfall. This study was conducted at Thepchana Waterfall, Khao Nan National Park from March to May 2007. There were 40 Spanner Barb collected with 20 males and 20 females. Males had an average of 5.57 cm in standard length, 6.62 cm in total length and 5.18 g in total body weight. Females had an average of 7.25 cm in standard length, 8.24 cm in total length and 10.96 g in total body weight. The length (L) – weight (W) relationships for combining sexes, males and females were LogW = -2.137 + 3.355logL, log W = -0.068 + 3.297logL, and log W = -2.068 + 3.297logL, respectively. The Spanner Barb were smaller size fish with a compressed form; terminal mouth; villiform teeth; ctenoid scale; concave tail; general body color yellowish olive, with slight reddish tint to fins; vertical band beginning below dorsal and horizontal stripe from base of tail almost to vertical band. They also had a vertical band midway between the eye and first vertical band. There was a black spot above anal fin. The bladder looked like J-shape. Inside of the bladder was found small insects and insect lava. The body length and the bowels length was 1:1 ratio. The water temperature ranged from 25.00 – 27.00 °C which was appropriate for their habitat characteristics. Acid - alkalinity ranged from 6.65 – 6.90 mg/l. Dissolved oxygen ranged from 4.55 – 4.70 mg/l. Water hardness ranged from 31.00 – 48.00 mg/l. The amount of ammonia was about 0.25 mg/l.

Keywords: Spanner barb, morphology, water quality.

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Authors: M. Selvaggi, F. Pinto, A. R. Pesce Delfino, A. Vicenti, C. Dario

Abstract:

Data from 1731 Gentile di Puglia lambs, sired by 65 rams over a 5-year period were analyzed by a mixed model to estimate the variance components for heritability. The considered growth traits were: birth weight (BW), weight at 30 days of age (W30) and average daily gain from birth to 30 days of age (DG). Year of birth, sex of lamb, type of birth (single or twin), dam age at lambing and farm were significant sources of variation for all the considered growth traits. The average lamb weights were 3.85±0.16 kg at birth, 9.57±0.91 kg at 30 days of age and the average daily gain was 191±14 g. Estimates of heritability were 0.33±0.05, 0.41±0.06 and 0.16±0.05 respectively for the same traits. These values suggest there is a good opportunity to improve Gentile di Puglia lambs by selecting animals for growth traits.

Keywords: heritability estimate, growth traits, lambs, Gentile diPuglia.

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

Abstract:

The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: the Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: Apportionment, Bias, Divisor, Fair, Simulation

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Authors: B.-A. Behrens, H. J. Maier, A. Neumann, J. Moritz, S. Hübner, T. Gretzki, F. Nürnberger, A. Spiekermeier

Abstract:

Press-hardened profiles are used e.g. for automotive applications in order to improve light weight construction due to the high reachable strength. The application of interior water-air spray cooling contributes to significantly reducing the cycle time in the production of heat-treated tubes. This paper describes a new manufacturing method for producing press-hardened hollow profiles by means of an additional interior cooling based on a water-air spray. Furthermore, this paper provides the results of thorough investigations on the properties of press-hardened tubes in dependence of varying spray parameters.

Keywords: 22MnB5, hollow profiles, press hardening, tubes, water-air spray cooling.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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Authors: Nikola Karanovic, Aleksandar Djuric

Abstract:

This paper introduces a method of calculating the quantities of construction materials and construction waste on site in city of Novi Sad. In buildings is about 40% of the total weight of materials that are in circulation in the world economic space. The best solution for this waste is to be stored at source, at the point of generation. There are several treatment options for this type of waste, reduction at source, reuse, recycling. Beside its negative effects on the environment, construction waste can be and resource. Novi Sad is divided in 16 single family resident zones and 10 multi family resident zones. For every zone of the city, quantities of used construction materials and construction waste were obtained. Rational use of natural resources is an essential factor in applying the principles of development with savings.

Keywords: Construction materials, Construction waste, Novi Sad, Recycling

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

Abstract:

An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: Toan Vu Duc, Son Ha Viet

Abstract:

An evaluation of the PCBs residues in the surface soils from Bacninh, Vietnam was carried out. Sixty representative soil samples were collected from the centre of Bacninh and three surrounding districts. The analyzed results indicated the wide extent of contamination of total PCBs in Bacninh. In industrial and urban zones, total PCBs concentrations ranged from ranged from <0.02 to 32.68ng g-1 (mean 19.89 ±15.64ng g-1) dry weight, while those in agricultural zones ranged from <0.02 to 13.26ng g-1 (mean 8.14 ± 4.89ng g-1) dry weight. The mean percentages of PCB28, PCB52, PCB101, PCB138, PCB153 and PCB180 compared with Σ6PCBs in the analyzed soil samples are 3.1%, 13.9%, 21.7%, 30.7%, 25.8% and 4.8%, respectively. These values can be explained by the chemical properties as well as the compositions of PCBs mixture which probably escaped from dielectric oil. An increasing trend and the long-time release of PCBs are observed.

Keywords: Contamination, PCBs, soil, temporal trend.

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Authors: Wehash, F. E., Ismail I. Abo-Ghanema, Rasha Mohamed Saleh

Abstract:

This study was conducted to evaluate the anti-diabetic properties of ethanolic extract of two plants commonly used in folk medicine, Mormodica charantia (bitter melon) and Trigonella foenum-graecum (fenugreek). The study was performed on STZinduced diabetic rats (DM type-I). Plant extracts of these two plants were given to STZ diabetic rats at the concentration of 500 mg/kg body weight ,50 mg/kg body weight respectively. Cidophage® (metformin HCl) were administered to another group to support the results at a dose of 500 mg/kg body weight, the ethanolic extracts and Cidophage administered orally once a day for four weeks using a stomach tube and; serum samples were obtained for biochemical analysis. The extracts caused significant decreases in glucose levels compared with diabetic control rats. Insulin secretions were increased after 4 weeks of treatment with Cidophage® compared with the control non-diabetic rats. Levels of AST and ALT liver enzymes were normalized by all treatments. Decreases in liver cholesterol, triglycerides, and LDL in diabetic rats were observed with all treatments. HDL levels were increased by the treatments in the following order: bitter melon, Cidophage®, and fenugreek. Creatinine levels were reduced by all treatments. Serum nitric oxide and malonaldehyde levels were reduced by all extracts. GSH levels were increased by all extracts. Extravasation as measured by the Evans Blue test increased significantly in STZ-induced diabetic animals. This effect was reversed by ethanolic extracts of bitter melon or fenugreek.

Keywords: Cidophage®, Diabetic rats, Mormodica charantia, Trigonella foenum-graecum

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Authors: Shigeaki Sakurai, Youichi Kitahata, Ryohei Orihara

Abstract:

This paper proposes a method that discovers sequential patterns corresponding to user-s interests from sequential data. This method expresses the interests as constraint patterns. The constraint patterns can define relationships among attributes of the items composing the data. The method recursively decomposes the constraint patterns into constraint subpatterns. The method evaluates the constraint subpatterns in order to efficiently discover sequential patterns satisfying the constraint patterns. Also, this paper applies the method to the sequential data composed of stock price indexes and verifies its effectiveness through comparing it with a method without using the constraint patterns.

Keywords: Sequential pattern mining, Constraint pattern, Attribute constraint, Stock price indexes

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Authors: D. P. Rahardja, A. L. Toleng, M. Yusuf

Abstract:

The objective of this study was to investigate the lifelong effect of in utero nutrition fed at different stages of pregnancy in Bali cows (n = 40): (U1) without in utero nutrition (0 – parturition, negative control); (U2) 0 – 90 d of gestation; (U3) 90 - 180 d of gestation; (U4) 180 d – parturition; and (U5) in utero nutrition along gestation period (0 d to parturition – positive control) on the growth performance of the offspring to weaning age. The results indicated that effect of maternal nutrition on male and female offspring were particularly indicated by the growth performance of both the male and female offspring from birth to weaning.

Keywords: Bali cows, birth weight, maternal nutrition, preweaning daily gain, weaning weight.

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Authors: M. Mohagheghian, A. M. Ghaedi, A. Vafaei

Abstract:

An artificial neural network (ANN) model is presented for the prediction of kinematic viscosity of binary mixtures of poly (ethylene glycol) (PEG) in water as a function of temperature, number-average molecular weight and mass fraction. Kinematic viscosities data of aqueous solutions for PEG (0.55419×10-6 – 9.875×10-6 m2/s) were obtained from the literature for a wide range of temperatures (277.15 - 338.15 K), number-average molecular weight (200 -10000), and mass fraction (0.0 – 1.0). A three layer feed-forward artificial neural network was employed. This model predicts the kinematic viscosity with a mean square error (MSE) of 0.281 and the coefficient of determination (R2) of 0.983. The results show that the kinematic viscosity of binary mixture of PEG in water could be successfully predicted using an artificial neural network model.

Keywords: Artificial neural network, kinematic viscosity, poly ethylene glycol (PEG)

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Authors: T. Matsubayashi, T. Yamada

Abstract:

In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.

Keywords: visualization, graph drawing, Internet Map

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Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

Abstract:

Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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