Search results for: variational iteration method

Authors: Muhammad Farooq Baig

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Objective: The purpose of this study was to compare results obtained using a single fecal specimen for O&P examination, direct immunofluorescence assay (DFA), and two conventional staining methods. Design: Hundred and fifty children fecal specimens were collected and examined by each method. The O&P and the DFA were used as the reference method. Setting: The study was performed at the laboratory in the Basic Medical Science Institute JPMC Karachi. Patients or Other Participants: The fecal specimens were collected from children with a suspected Giardia lamblia infection. Main Outcome Measures: The amount of agreement and disagreement between methods.1) Presence of giardiasis in our population. 2) The sensitivity and specificity of each method. Results: There was 45(30%) positive 105 (70%) negative on DFA, 41 (27.4%) positive 109 (72.6%) negative on iodine and 34 (22.6%) positive 116(77.4%) on saline method. The sensitivity and specificity of DFA in comparision to iodine were 92.2%, 92.7% respectively. The sensitivity and specificity of DFA in comparisoin to saline method were 91.2%, 87.9% respectively. The sensitivity of iodine method and saline method in compariosn to DFA were 82.2%, 68.8% respectively. There is mark diffrence in sensitivity of DFA to conventional method. Conclusion: The study supported findings of other investigators who concluded that DFA method have the greater sensitivity. The immunologic methods were more efficient and quicker than the conventional O&P method.

Keywords: direct immunofluorescence assay (DFA), ova and parasite (O&P), Giardia lamblia, children, medical science

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

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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: Young Hee Geum

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In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding, order of convergent

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Authors: Abdullah Bal, Sevdenur Bal

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This paper purposes a new type of hardware application for training of cellular neural networks (CNN) using optical joint transform correlation (JTC) architecture for image feature extraction. CNNs require much more computation during the training stage compare to test process. Since optoelectronic hardware applications offer possibility of parallel high speed processing capability for 2D data processing applications, CNN training algorithm can be realized using Fourier optics technique. JTC employs lens and CCD cameras with laser beam that realize 2D matrix multiplication and summation in the light speed. Therefore, in the each iteration of training, JTC carries more computation burden inherently and the rest of mathematical computation realized digitally. The bipolar data is encoded by phase and summation of correlation operations is realized using multi-object input joint images. Overlapping properties of JTC are then utilized for summation of two cross-correlations which provide less computation possibility for training stage. Phase-only JTC does not require data rearrangement, electronic pre-calculation and strict system alignment. The proposed system can be incorporated simultaneously with various optical image processing or optical pattern recognition techniques just in the same optical system.

Keywords: CNN training, image processing, joint transform correlation, optoelectronic hardware

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Authors: Hee-Jae Suh, Kyung-Su Kim, Min-Ji Kim, Yeon-Seong Jeong, Ok-Hwan Lee, Jae-Wook Shin, Hyang-Sook Chun, Chan Lee

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Canthaxanthin is keto-carotenoid produced from beta-carotene and it has been approved to be used in many countries as a food coloring agent. Canthaxanthin has been analyzed using High Performance Liquid Chromatography (HPLC) system with various ways of pretreatment methods. Four official methods for verification of canthaxanthin at FSA (UK), AOAC (US), EFSA (EU) and MHLW (Japan) were compared to improve its analytical and the pretreatment method. The Linearity, the limit of detection (LOD), the limit of quantification (LOQ), the accuracy, the precision and the recovery ratio were determined from each method with modification in pretreatment method. All HPLC methods exhibited correlation coefficients of calibration curves for canthaxanthin as 0.9999. The analysis methods from FSA, AOAC, and MLHW showed the LOD of 0.395 ppm, 0.105 ppm, and 0.084 ppm, and the LOQ of 1.196 ppm, 0.318 ppm, 0.254 ppm, respectively. Among tested methods, HPLC method of MHLW with modification in pretreatments was finally selected for the analysis of canthaxanthin in lab, because it exhibited the resolution factor of 4.0 and the selectivity of 1.30. This analysis method showed a correlation coefficients value of 0.9999 and the lowest LOD and LOQ. Furthermore, the precision ratio was lower than 1 and the accuracy was almost 100%. The method presented the recovery ratio of 90-110% with modification in pretreatment method. The cross-validation of coefficient variation was 5 or less among tested three institutions in Korea.

Keywords: analytic method, canthaxanthin, food colorants, pretreatment method

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Authors: Yukinori Fuse, Masato Kawaguchi

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A quantitative risk assessment method was developed for fiber emissions from sprayed asbestos-containing materials (ACMs). In Japan, instead of being quantitative, these risk assessments have relied on the subjective judgment of skilled engineers, which may vary from one person to another. Therefore, this closed sampling method aims at avoiding any potential variability between assessments. This method was used to assess emissions from ACM sprayed in eleven buildings and the obtained results were compared with the subjective judgments of a skilled engineer. An approximate correlation tendency was found between both approaches. In spite of existing uncertainties, the closed sampling method is useful for public health protection. We firmly believe that this method may find application in the management and renovation decisions of buildings using friable and sprayed ACM.

Keywords: asbestos, renovation, risk assessment, maintenance

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Puneet Kumar, Jonnalagadda Srinivas

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The authors report here vibration and buckling analysis of functionally graded carbon nanotube-polymer composite (FG-CNTPC) beams under hygro-thermo-mechanical environments using higher order shear deformation theory. The material properties of CNT and polymer matrix are often affected by temperature and moisture content. A micromechanical model with agglomeration effect is employed to compute the elastic, thermal and moisture properties of the composite beam. The governing differential equation of FG-CNTRPC beam is developed using higher-order shear deformation theory to account shear deformation effects. The elastic, thermal and hygroscopic strain terms are derived from variational principles. Moreover, thermal and hygroscopic loads are determined by considering uniform, linear and sinusoidal variation of temperature and moisture content through the thickness. Differential equations of motion are formulated as an eigenvalue problem using appropriate displacement fields and solved by using finite element modeling. The obtained results of natural frequencies and critical buckling loads show a good agreement with published data. The numerical illustrations elaborate the dynamic as well as buckling behavior under uniaxial load for different environmental conditions, boundary conditions and volume fraction distribution profile, beam slenderness ratio. Further, comparisons are shown at different boundary conditions, temperatures, degree of moisture content, volume fraction as well as agglomeration of CNTs, slenderness ratio of beam for different shear deformation theories.

Keywords: hygrothermal effect, free vibration, buckling load, agglomeration

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Authors: Nakache Radouane, M. Boukelloul, M. Fredj

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Method room and pillar sizes are key factors for safe mining and their recovery in open-stop mining. This method is advantageous due to its simplicity and requirement of little information to be used. It is probably the most representative method among the total load approach methods although it also remains a safe design method. Using a finite element software (PLAXIS 3D), analyses were carried out with an elasto-plastic model and comparisons were made with methods based on the total load approach. The results were presented as the optimization for improving the ore recovery rate while maintaining a safe working environment.

Keywords: room and pillar, mining, total load approach, elasto-plastic

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Authors: Kamlesh Vishwakarma, Bipul Behari Saha, Sunilkumar Sing, Abhishek Mishra, Sreenivas Rao

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A rapid, sensitive and inexpensive method has been developed for complete analysis of Clodinafop Propargyl. Clodinafop Propargyl enantiomers were separated on chiral column, Chiral Pak AS-H (250 mm. 4.6mm x 5µm) with mobile phase n-hexane: IPA (96:4) at flow rate 1.5 ml/min. The effluent was monitored by UV detector at 230 nm. Clodinafop Propagyl content and impurity quantification was done with reverse phase HPLC. The present study describes a HPLC method using simple mobile phase for the quantification of Clodinafop Propargyl and its impurities. The method was validated and found to be accurate, precise, convenient and effective. Moreover, the lower solvent consumption along with short analytical run time led to a cost effective analytical method.

Keywords: Clodinafop Propargyl, method, validation, HPLC-UV

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: V. Villa-Cruz, H. Pérez-Ladron de Guevara, J. E. Diaz-Díaz

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Static Light Scattering (SLS) was used as a method to analyse cow's milk raw, coming from the town of Lagos de Moreno, Jalisco, Mexico. This method is based on the analysis of the dispersion of light laser produced by a set of particles in solution. Based on the above, raw milk, which contains particles of fat globules, with a diameter of 2000 nm and particles of micelles of protein with 300 nm in diameter were analyzed. For this, dilutions of commercial milk were made (1.0%, 2.0% and 3.3%) to obtain a pattern of laser light scattering and also made measurements of raw cow's milk. Readings were taken in a sweep initial angle 10° to 170°, results were analyzed with the program OriginPro 7. The SLS method gives us an estimate of the percentage of fat content in milk samples. It can be concluded that the SLS method, is a quick method of analysis to detect adulteration in raw cow's milk.

Keywords: light scattering, milk analysis, adulteration in milk, micelles, OriginPro

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Authors: Felix Baumann, Aleksandar Milutinovic, Dieter Roller

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Up to this point business process management projects in general and business process modelling projects in particular could not rely on a practical and scientifically validated method to estimate cost and effort. Especially the model development phase is not covered by a cost estimation method or model. Further phases of business process modelling starting with implementation are covered by initial solutions which are discussed in the literature. This article proposes a method of filling this gap by deriving a cost estimation method from available methods in similar domains namely software development or software engineering. Software development is regarded as closely similar to process modelling as we show. After the proposition of this method different ideas for further analysis and validation of the method are proposed. We derive this method from COCOMO II and Function Point which are established methods of effort estimation in the domain of software development. For this we lay out similarities of the software development rocess and the process of process modelling which is a phase of the Business Process Management life-cycle.

Keywords: COCOMO II, busines process modeling, cost estimation method, BPM COCOMO

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Authors: Marjan Heidarzadeh

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High quality and purity of DNA isolated from canned tuna is essential for species identification. In this study, the efficiency of five different methods for DNA extraction was compared. Method of national standard in Iran, the CTAB precipitation method, Wizard DNA Clean Up system, Nucleospin and GenomicPrep were employed. DNA was extracted from two different canned tuna in brine and oil of the same tuna species. Three samples of each type of product were analyzed with the different methods. The quantity and quality of DNA extracted was evaluated using the 260 nm absorbance and ratio A260/A280 by spectrophotometer picodrop. Results showed that the DNA extraction from canned tuna preserved in different liquid media could be optimized by employing a specific DNA extraction method in each case. Best results were obtained with CTAB method for canned tuna in oil and with Wizard method for canned tuna in brine.

Keywords: canned tuna PCR, DNA, DNA extraction methods, species identification

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Authors: Hossein Kabir, Mojtaba Sadeghi

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Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: single-degree-of-freedom system (SDOF), linear acceleration method, nonlinear excited system, equivalent displacement method, equivalent energy method

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Authors: Elisabeth Unterfrauner, Christian Voigt

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Since the foundation of the first Fab Lab by the Massachusetts Institute of Technology about 17 years ago, the Maker movement has spread globally with the foundation of maker spaces and Fab Labs worldwide. In these workshops, citizens have access to digital fabrication technologies such as 3D printers and laser cutters to develop and test their own ideas and prototypes, which makes it an attractive place for start-up companies. Know-How is shared not only in the physical space but also online in diverse communities. According to the Horizon report, the Maker movement, however, will also have an impact on educational settings in the following years. The European project ‘DOIT - Entrepreneurial skills for young social innovators in an open digital world’ has incorporated key elements of making to develop an early entrepreneurial education program for children between the age of six and 16. The Maker pedagogy builds on constructive learning approaches, learning by doing principles, learning in collaborative and interdisciplinary teams and learning through trial and error where mistakes are acknowledged as learning opportunities. The DOIT program consists of seven consecutive elements. It starts with a motivation phase where students get motivated by envisioning the scope of their possibilities. The second step is about Co-design: Students are asked to collect and select potential ideas for innovations. In the Co-creation phase students gather in teams and develop first prototypes of their ideas. In the iteration phase, the prototype is continuously improved and in the next step, in the reflection phase, feedback on the prototypes is exchanged between the teams. In the last two steps, scaling and reaching out, the robustness of the prototype is tested with a bigger group of users outside of the educational setting and finally students will share their projects with a wider public. The DOIT program involves 1,000 children in two pilot phases at 11 pilot sites in ten different European countries. The comprehensive evaluation design is based on a mixed method approach with a theoretical backbone on Lackeus’ model of entrepreneurship education, which distinguishes between entrepreneurial attitudes, entrepreneurial skills and entrepreneurial knowledge. A pre-post-test with quantitative measures as well as qualitative data from interviews with facilitators, students and workshop protocols will reveal the effectiveness of the program. The evaluation results will be presented at the conference.

Keywords: early entrepreneurial education, Fab Lab, maker education, Maker movement

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

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Authors: Hwang Ho Kim, Do Gyun Kim, Jin Young Choi, Sang Chul Park

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Since tire production process is very complicated, company-wide management of it is very difficult, necessitating considerable amounts of capital and labors. Thus, productivity should be enhanced and maintained competitive by developing and applying effective production plans. Among major processes for tire manufacturing, consisting of mixing component preparation, building and curing, the mixing process is an essential and important step because the main component of tire, called compound, is formed at this step. Compound as a rubber synthesis with various characteristics plays its own role required for a tire as a finished product. Meanwhile, scheduling tire mixing process is similar to flexible job shop scheduling problem (FJSSP) because various kinds of compounds have their unique orders of operations, and a set of alternative machines can be used to process each operation. In addition, setup time required for different operations may differ due to alteration of additives. In other words, each operation of mixing processes requires different setup time depending on the previous one, and this kind of feature, called sequence dependent setup time (SDST), is a very important issue in traditional scheduling problems such as flexible job shop scheduling problems. However, despite of its importance, there exist few research works dealing with the tire mixing process. Thus, in this paper, we consider the scheduling problem for tire mixing process and suggest an efficient particle swarm optimization (PSO) algorithm to minimize the makespan for completing all the required jobs belonging to the process. Specifically, we design a particle encoding scheme for the considered scheduling problem, including a processing sequence for compounds and machine allocation information for each job operation, and a method for generating a tire mixing schedule from a given particle. At each iteration, the coordination and velocity of particles are updated, and the current solution is compared with new solution. This procedure is repeated until a stopping condition is satisfied. The performance of the proposed algorithm is validated through a numerical experiment by using some small-sized problem instances expressing the tire mixing process. Furthermore, we compare the solution of the proposed algorithm with it obtained by solving a mixed integer linear programming (MILP) model developed in previous research work. As for performance measure, we define an error rate which can evaluate the difference between two solutions. As a result, we show that PSO algorithm proposed in this paper outperforms MILP model with respect to the effectiveness and efficiency. As the direction for future work, we plan to consider scheduling problems in other processes such as building, curing. We can also extend our current work by considering other performance measures such as weighted makespan or processing times affected by aging or learning effects.

Keywords: compound, error rate, flexible job shop scheduling problem, makespan, particle encoding scheme, particle swarm optimization, sequence dependent setup time, tire mixing process

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Authors: Ka Lei Au

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The Dalcroze method has been emerging in music classrooms, and music teachers are encouraged to integrate music and movement in their teaching. Music programs in colleges in Hong Kong have been introducing method courses such as Orff and Dalcroze method in music teaching as teacher’s education program. Since the targeted students of the course are music teachers who are making the decision of what approach to use in their classroom, their perception is significantly valued to identify how this approach is applicable in their teaching in regards to the teaching and learning culture and environment. This qualitative study aims to explore how the Dalcroze method as a teacher’s education course is perceived by music teachers from three aspects: 1) application in music teaching, 2) self-enhancement, 3) expectation. Through the lens of music teachers, data were collected from 30 music teachers who are taking the Dalcroze method course in music teaching in Hong Kong by the survey. The findings reveal the value and their intention of the Dalcroze method in Hong Kong. It also provides a significant reference for better development of such courses in the future in adaption to the culture, teaching and learning environment and teacher’s, student’s and parent’s perception of this approach.

Keywords: Dalcroze method, music teaching, perception, self-enhancement, teacher’s education

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Authors: Mahmoudi Noureddine, Bouregba Rachid

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In this paper the stress intensity factors of a slant-cracked plate of AISI 304 stainless steel, have been calculated using extended finite element method and finite element method (FEM) in ABAQUS software, the results were compared with theoretical values.

Keywords: stress intensity factors, extended finite element method, stainless steel, abaqus

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Authors: Nesrine T. Lamie

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Four, accurate, precise, and sensitive spectrophotometric methods are developed for the simultaneous determination of a binary mixture containing amlodipine besylate (AM) and atenolol (AT) where AM is determined at its λmax 360 nm (0D), while atenolol can be determined by different methods. Method (A) is absorpotion factor (AFM). Method (B) is the new Ratio Difference method(RD) which measures the difference in amplitudes between 210 and 226 nm of ratio spectrum., Method (C) is novel constant center spectrophotometric method (CC) Method (D) is mean centering of the ratio spectra (MCR) at 284 nm. The calibration curve is linear over the concentration range of 10–80 and 4–40 μg/ml for AM and AT, respectively. These methods are tested by analyzing synthetic mixtures of the cited drugs and they are applied to their commercial pharmaceutical preparation. The validity of results was assessed by applying standard addition technique. The results obtained were found to agree statistically with those obtained by a reported method, showing no significant difference with respect to accuracy and precision.

Keywords: amlodipine, atenolol, absorption factor, constant center, mean centering, ratio difference

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: C. Bunsanit

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This paper presents the refinement method for two beams formation of wideband smart antenna. The refinement method for weighting coefficients is based on Fully Spatial Signal Processing by taking Inverse Discrete Fourier Transform (IDFT), and its simulation results are presented using MATLAB. The radiation pattern is created by multiplying the incoming signal with real weights and then summing them together. These real weighting coefficients are computed by IDFT method; however, the range of weight values is relatively wide. Therefore, for reducing this range, the refinement method is used. The radiation pattern concerns with five input parameters to control. These parameters are maximum weighting coefficient, wideband signal, direction of mainbeam, beamwidth, and maximum of minor lobe level. Comparison of the obtained simulation results between using refinement method and taking only IDFT shows that the refinement method works well for wideband two beams formation.

Keywords: fully spatial signal processing, beam forming, refinement method, smart antenna, weighting coefficient, wideband

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Abderrahim Elmoataz

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More and more contemporary applications involve data in the form of functions defined on irregular and topologically complicated domains (images, meshs, points clouds, networks, etc). Such data are not organized as familiar digital signals and images sampled on regular lattices. However, they can be conveniently represented as graphs where each vertex represents measured data and each edge represents a relationship (connectivity or certain affinities or interaction) between two vertices. Processing and analyzing these types of data is a major challenge for both image and machine learning communities. Hence, it is very important to transfer to graphs and networks many of the mathematical tools which were initially developed on usual Euclidean spaces and proven to be efficient for many inverse problems and applications dealing with usual image and signal domains. Historically, the main tools for the study of graphs or networks come from combinatorial and graph theory. In recent years there has been an increasing interest in the investigation of one of the major mathematical tools for signal and image analysis, which are Partial Differential Equations (PDEs) variational methods on graphs. The normalized p-laplacian operator has been recently introduced to model a stochastic game called tug-of-war-game with noise. Part interest of this class of operators arises from the fact that it includes, as particular case, the infinity Laplacian, the mean curvature operator and the traditionnal Laplacian operators which was extensiveley used to models and to solve problems in image processing. The purpose of this paper is to introduce and to study a new class of normalized p-Laplacian on graphs. The introduction is based on the extension of p-harmonious function introduced in as discrete approximation for both infinity Laplacian and p-Laplacian equations. Finally, we propose to use these operators as a framework for solving many inverse problems in image processing.

Keywords: normalized p-laplacian, image processing, stochastic game, inverse problems

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Authors: Muhammad Fajar Suardi, Fathimatufzzahra, Dela Isnaini Sendra

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Learning is an activity that has been used to do, especially for a student or academics. But a handful of people have not been using and maximizing their brains work and some also do not know a good brain work time in capturing the lessons, so that knowledge is absorbed is also less than the maximum. Indonesia Memory Sports Council (IMSC) is an institution which is engaged in the performance of the brain and the development of effective learning methods by using several techniques that can be used in considering the lessons and knowledge to grasp well, including: loci method, substitution method, and chain method. This study aims to determine the techniques and benefits of using the method given in learning and memorization by applying memory techniques taught by Indonesia Memory Sports Council (IMSC) to students and the difference if not using this method. This research uses quantitative research with survey method addressed to students of Indonesian Memory Sports Council (IMSC). The results of this study indicate that learn, understand and remember the lesson using the techniques of memory which is taught in Indonesia Memory Sport Council is very effective and faster to absorb the lesson than learning without using the techniques of memory, and this affects the academic achievement of students in each educational institution.

Keywords: chain method, Indonesia memory sports council, loci method, substitution method

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