Search results for: approximate arithmetic

Authors: Soumitr Sanjay Dubey, Shubhajit Roy Chowdhury, Rahul Shrestha

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In this paper, we have presented a novel approach of calculating eigenvalues of any matrix for the first time on Field Programmable Gate Array (FPGA) using Triangular Systolic Arra (TSA) architecture. Conventionally, additional computation unit is required in the architecture which is compliant to the algorithm for determining the eigenvalues and this in return enhances the delay and power consumption. However, recently reported works are only dedicated for symmetric matrices or some specific case of matrix. This works presents an architecture to calculate eigenvalues of any matrix based on QR algorithm which is fully implementable on FPGA. For the implementation of QR algorithm we have used TSA architecture, which is further utilising CORDIC (CO-ordinate Rotation DIgital Computer) algorithm, to calculate various trigonometric and arithmetic functions involved in the procedure. The proposed architecture gives an error in the range of 10−4. Power consumption by the design is 0.598W. It can work at the frequency of 900 MHz.

Keywords: coordinate rotation digital computer, three angle complex rotation, triangular systolic array, QR algorithm

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Authors: Hudson Akewe

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In this study, we introduce a modified Jungck (Dual Jungck) iterative scheme and use the scheme to approximate the unique common fixed point of a pair of generalized contractive-like operators in a Banach space. The iterative scheme is also shown to be stable with respect to the maps (S,T). An example is taken to justify the convergence of the scheme. Our result is a generalization and improvement of several results in the literature on single map T.

Keywords: generalized contractive-like operators, modified Jungck iterative scheme, stability results, weakly compatible maps, unique common fixed point

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Authors: Almas Mukhametov, Dina Dautkanova, Moldir Yerbulekova, Gulim Tuyakova, Raziya Zhakudaeva, Makpal Seisenaly, Asemay Kazhymurat

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The composition of samples of mixtures of vegetable oils of Kazakhstan origin, consisting of sunflower, safflower and linseed oils, has been experimentally substantiated. With an approximate optimal ratio of w-6:w-3 fatty acids in 80:15:05 triacylglycerols, providing its therapeutic and prophylactic properties. The resulting mixture can be used in the development of functional products. The result was also identified and evaluated by physical and chemical quality indicators, the content of vitamin E, and the concentration of ions of copper (Cu), iron (Fe), cadmium (Cd), lead (Pb), arsenic (As), nickel (Ni), as well as mercury (Hg).

Keywords: vegetable oil, sunflower, safflower, linseed, mixture, fatty acid composition, heavy metals

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

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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, two delays

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Authors: Shih-Wen Hsiao, Chu-Hsuan Lee, Rong-Qi Chen

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When it comes to last, it is regarded as the critical foundation of shoe design and development. Not only the last relates to the comfort of shoes wearing but also it aids the production of shoe styling and manufacturing. In order to enhance the efficiency and application of last development, a computer aided methodology for customized last form designs is proposed in this study. The reverse engineering is mainly applied to the process of scanning for the last form. Then the minimum energy is used for the revision of surface continuity, the surface of the last is reconstructed with the feature curves of the scanned last. When the surface of a last is reconstructed, based on the foundation of the proposed last form reconstruction module, the weighted arithmetic mean method is applied to the calculation on the shape morphing which differs from the grading for the control mesh of last, and the algorithm of subdivision is used to create the surface of last mesh, thus the feet-fitting 3D last form of different sizes is generated from its original form feature with functions remained. Finally, the practicability of the proposed methodology is verified through later case studies.

Keywords: 3D last design, customization, reverse engineering, weighted morphing, shape blending

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Authors: Ibrahim Ilker Ozyigit, Ertugrul Filiz, Seda Birbilener, Semsettin Kulac, Zeki Severoglu

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In this study, we have performed genetic diversity analysis of Tilia tomentosa genotypes by using randomly amplified polymorphic DNA (RAPD) primers. A total of 28 genotypes, including 25 members from the urban ecosystem and 3 genotypes from forest ecosystem as outgroup were used. 8 RAPD primers produced a total of 53 bands, of which 48 (90.6 %) were polymorphic. Percentage of polymorphic loci (P), observed number of alleles (Na), effective number of alleles (Ne), Nei's (1973) gene diversity (h), and Shannon's information index (I) were found as 94.29 %, 1.94, 1.60, 0.34, and 0.50, respectively. The unweighted pair-group method with arithmetic average (UPGMA) cluster analysis revealed that two major groups were observed. The genotypes of urban and forest ecosystems showed a high genetic similarity between 28% and 92% and these genotypes did not separate from each other in UPGMA tree. Also, urban and forest genotypes clustered together in principal component analysis (PCA).

Keywords: Tilia tomentosa, genetic diversity, urban ecosystem, RAPD, UPGMA

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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: Manana Chumburidze

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We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Danny Manuel Calvo Velasco, Robert Sanchez Cano

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By using the transference matrix formalism, in this work, it is presented the study of the optical properties of the 1D graded structure, constructed by multiple bi-layers of dielectric and air, considering a redistribution of the material lengths following an arithmetic progression as a function of two parameters. It is presented a factorization for the transference matrices for the graded structure, which allows the interpretation of their optical properties in terms of the properties of simpler structures. It is shown that the graded structure presents new transmission peaks, which can be controlled by the parameter values located in frequencies for which a periodic system has a photonic bandgap. This result is extended to the case of a photonic crystal for which the unitary cell is the proposed graded structure, showing new transmission bands which are due to the multiple new sub-structures present in the system. Also, for the TE polarization, it is observed transmission bands' low frequencies which present low variation of its width and position with the incidence angle. It is expected that these results could guide a route in the design of new photonic devices.

Keywords: graded, material redistribution, photonic system, transference matrix

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Hamdi Belgacem, Fradi Aymen

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In this paper we present a low power, low cost differential logic unit (LU). The proposed LU receives dual-rail inputs and generates dual-rail outputs. The proposed circuit can be used in Arithmetic and Logic Units (ALU) of processor. It can be also dedicated for self-checking applications based on dual duplication code. Four logic functions as well as their inverses are implemented within a single Logic Unit. The hardware overhead for the implementation of the proposed LU is lower than the hardware overhead required for standard LU implemented with standard CMOS logic style. This new implementation is attractive as fewer transistors are required to implement important logic functions. The proposed differential logic unit can perform 8 Boolean logical operations by using only 16 transistors. Spice simulations using a 32 nm technology was utilized to evaluate the performance of the proposed circuit and to prove its acceptable electrical behaviour.

Keywords: differential logic unit, double pass transistor logic, low power CMOS design, low cost CMOS design

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Djamila Aboutaleb, Brahim Safi

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In this paper, sodium borosilicates glasses were prepared by melting in air. These heat-resistant transparent glasses have subjected subsequently isothermal treatments at different times, which have transformed them at opaque glass (milky white color). Such changes indicate that these glasses showed clearly phase separation (immiscibility). The immiscibility region in a sodium borosilicate ternary system was investigated in this work, i.e. to determine the regions from which some compositions can show phase separation. For this we went through the conditions of thermodynamic equilibrium, which were translated later by mathematical equations to find an approximate solution. The latter has been translated in a simulation which was established thereafter to find the immiscibility regions in this type of special glasses.

Keywords: sodium borosilicate, heat-resistant, isothermal treatments, immiscibility, thermodynamics

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Authors: Alireza Lavaei, Alireza Lohrasbi, Mohammadali M. Shahlaei

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To reduce the overall time of structural optimization for earthquake loads two strategies are adopted. In the first strategy, a neural system consisting self-organizing map and radial basis function neural networks, is utilized to predict the time history responses. In this case, the input space is classified by employing a self-organizing map neural network. Then a distinct RBF neural network is trained in each class. In the second strategy, an improved genetic algorithm is employed to find the optimum design. A 72-bar space truss is designed for optimal weight using exact and approximate analysis for the El Centro (S-E 1940) earthquake loading. The numerical results demonstrate the computational advantages and effectiveness of the proposed method.

Keywords: optimization, genetic algorithm, neural networks, self-organizing map

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Authors: Shiksha Jain, Ramesh Mishra

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One of the most widely used complex signals processing operation is filtering. The most important FIR digital filter are widely used in DSP for filtering to alter the spectrum according to some given specifications. Power consumption and Area complexity in the algorithm of Finite Impulse Response (FIR) filter is mainly caused by multipliers. So we present a multiplier less technique (DA technique). In this technique, precomputed value of inner product is stored in LUT. Which are further added and shifted with number of iterations equal to the precision of input sample. But the exponential growth of LUT with the order of FIR filter, in this basic structure, makes it prohibitive for many applications. The significant area and power reduction over traditional Distributed Arithmetic (DA) structure is presented in this paper, by the use of slicing of LUT to the desired length. An architecture of 16 tap FIR filter is presented, with different length of slice of LUT. The result of FIR Filter implementation on Xilinx ISE synthesis tool (XST) vertex-4 FPGA Tool by using proposed method shows the increase of the maximum frequency, the decrease of the resources as usage saving in area with more number of slices and the reduction dynamic power.

Keywords: multiplier less technique, linear phase symmetric FIR filter, FPGA tool, look up table

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Authors: S. Phanyaem

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This paper presents the confidence intervals for the effect size base on bootstrap resampling method. The meta-analytic confidence interval for effect size is proposed that are easy to compute. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. The best confidence interval method will have a coverage probability close to 0.95. Simulation results have shown that our proposed confidence intervals perform well in terms of coverage probability and expected length.

Keywords: effect size, confidence interval, bootstrap method, resampling

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Authors: Sajeda Elbashabsheh, Kamel Al-Khaled

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This paper applies a modified Laplace Adomian decomposition method to solve the time-fractional JaulentMiodek system. The method produce convergent series solutions with easily compatible components. This paper considers the Caputo fractional derivative. The effectiveness and applicability of the method are demonstrated by comparing its results with those of prior studies. Results are presented in tables and figures. These solutions might be imperative and significant for the explanation of some practical physical phenomena. All computations and figures in the work are done using MATHEMATICA. The numerical results demonstrate that the current methods are effective, reliable, and simple to i implement for nonlinear fractional partial differential equations.

Keywords: approximate solutions, Jaulent-Miodek system, Adomian decomposition method, solitons

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Authors: Ercan Yilmaz, Ali Murat Sünbül

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The aim of the study is to investigate teachers’ self-efficacy with regards to their emotional intelligence. The relational model was used in the study. The participant of the study included 194 teachers from secondary schools in Konya, Turkey. In order to assess teachers’ emotional intelligence, “Trait Emotional Intelligence Questionnaire-short Form was implemented. For teachers’ self-efficacy, “Teachers’ Sense of Self-Efficacy Scale” was used. As a result of the study, a significant relationship is available between teachers’ sense of self-efficacy and their emotional intelligence. Teachers’ emotional intelligence enucleates approximate eighteen percent of the variable in dimension named teachers’ self-efficacy for the students’ involvement. About nineteen percent of the variable in dimension “self-efficacy for teaching strategies is represented through emotional intelligence. Teachers’ emotional intelligence demonstrates about seventeen percent of variable aimed at classroom management.

Keywords: teachers, self-efficacy, emotional intelligence, education

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Authors: Fayyaz Rasool, Naureen Aziz Qureshi, Shakeela Parveen

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Labeo rohita populations from five geographical locations from the hatchery and riverine system of Punjab-Pakistan were studied for the clustering on the basis of similarities and differences based on morphometric parameters within the species. Agglomerative Hierarchical Clustering (AHC) was done by using Pearson Correlation Coefficient and Unweighted Pair Group Method with Arithmetic Mean (UPGMA) as Agglomeration method by XLSTAT 2012 version 1.02. A dendrogram with the data on the morphometrics of the representative samples of each site divided the populations of Labeo rohita in to five major clusters or classes. The variance decomposition for the optimal classification values remained as 19.24% for within class variation, while 80.76% for the between class differences. The representative central objects of the each class, the distances between the class centroids and also the distance between the central objects of the classes were generated by the analysis. A measurable distinction between the classes of the populations of the Labeo rohita was indicated in this study which determined the impacts of changing environment and other possible factors influencing the variation level among the populations of the same species.

Keywords: AHC, Labeo rohita, hatchery, riverine, morphometric

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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Authors: Man-Yu Wong, Siyu Zhou, Zhiqiang Cao

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In quality of life, health service utilization is an important determinant of medical resource expenditures on Colorectal cancer (CRC) care, a better understanding of the increased utilization of health services is essential for optimizing the allocation of healthcare resources to services and thus for enhancing the service quality, especially for high expenditure on CRC care like Hong Kong region. In assessing the association between the health-related quality of life (HRQOL) and health service utilization in patients with colorectal neoplasm, count data models can be used, which account for over dispersion or extra zero counts. In our data, the HRQOL evaluation is a self-reported measure obtained from a questionnaire completed by the patients, misreports and variations in the data are inevitable. Besides, there are more zero counts from the observed number of clinical consultations (observed frequency of zero counts = 206) than those from a Poisson distribution with mean equal to 1.33 (expected frequency of zero counts = 156). This suggests that excess of zero counts may exist. Therefore, we study tests for detecting zero-inflation in models with measurement error in covariates. Method: Under classical measurement error model, the approximate likelihood function for zero-inflation Poisson regression model can be obtained, then Approximate Maximum Likelihood Estimation(AMLE) can be derived accordingly, which is consistent and asymptotically normally distributed. By calculating score function and Fisher information based on AMLE, a score test is proposed to detect zero-inflation effect in ZIP model with measurement error. The proposed test follows asymptotically standard normal distribution under H0, and it is consistent with the test proposed for zero-inflation effect when there is no measurement error. Results: Simulation results show that empirical power of our proposed test is the highest among existing tests for zero-inflation in ZIP model with measurement error. In real data analysis, with or without considering measurement error in covariates, existing tests, and our proposed test all imply H0 should be rejected with P-value less than 0.001, i.e., zero-inflation effect is very significant, ZIP model is superior to Poisson model for analyzing this data. However, if measurement error in covariates is not considered, only one covariate is significant; if measurement error in covariates is considered, only another covariate is significant. Moreover, the direction of coefficient estimations for these two covariates is different in ZIP regression model with or without considering measurement error. Conclusion: In our study, compared to Poisson model, ZIP model should be chosen when assessing the association between condition-specific HRQOL and health service utilization in patients with colorectal neoplasm. and models taking measurement error into account will result in statistically more reliable and precise information.

Keywords: count data, measurement error, score test, zero inflation

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Authors: R. Bouhennache, T. Bouden, A. A. Taleb, A. Chaddad

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In this paper we propose a method to map the urban areas. The method uses an arithmetic calculation processed from the land features indexes and Tasseled cap transformation TC of multi spectral Thematic Mapper Landsat TM image. For this purpose the derived indexes image from the original image such SAVI the soil adjusted vegetation index, UI the urban Index, and EBBI the enhanced built up and bareness index were staked to form a new image and the bands were uncorrelated, also the Spectral Angle Mapper (SAM) and Spectral Information Divergence (SID) supervised classification approaches were first applied on the new image TM data using the reference spectra of the spectral library and subsequently the four urban, vegetation, water and soil land cover categories were extracted with their accuracy assessment.The urban features were represented using a logic calculation applied to the brightness, UI-SAVI, NDBI-greenness and EBBI- brightness data sets. The study applied to Blida and mentioned that the urban features can be mapped with an accuracy ranging from 92 % to 95%.

Keywords: EBBI, SAVI, Tasseled Cap Transformation, UI

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Authors: Andrew Kurochkin, Kostiantyn Bokhan

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In this study, a new meme dataset of ~650K meme instances was created, a technology of meme generation based on the state of the art deep learning technique - GPT-2 model was researched, a comparative analysis of machine-generated memes and human-created was conducted. We justified that Amazon Mechanical Turk workers can be used for the approximate estimating of users' behavior in a social network, more precisely to measure engagement. It was shown that generated memes cause the same engagement as human memes that produced low engagement in the social network (historically). Thus, generated memes are less engaging than random memes created by humans.

Keywords: content generation, computational social science, memes generation, Reddit, social networks, social media interaction

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Authors: Dongkyu Lee, Thanh Banh Thien, Soomi Shin

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In the present study, the isogeometric topology optimization is proposed for cracked structures through using Solid Isotropic Material with Penalization (SIMP) as a design model. Design density variables defined in the variable space are used to approximate the element analysis density by the bivariate B-spline basis functions. The mathematical formulation of topology optimization problem solving minimum structural compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to strain energy of cracked structure are proposed in terms of design density variables. Numerical examples demonstrate interactions of topology optimization to structures design with cracks.

Keywords: topology optimization, isogeometric, NURBS, design

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Authors: Cüneyit Akar, Mustafa Başaran, Ufuk Uluçınar

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The purpose of this research is to examine the critical thinking dispositions of pre-service teachers in terms of several variables. In the line of this aim, we have investigated what their levels of critical thinking dispositions and whether there is any significant different in their critical thinking dispositions. Also, we have examined the relations between their critical thinking dispositions and their parents’ education statues, the number of their siblings, family income levels, and their religiosity level. 202 pre-service teachers who are studying at different departments at faculty of education at Uşak University participated in this research. In study, critical thinking dispositions scale by one of researchers was utilized and its validity and reliability was performed. The findings indicate that the level of their critical thinking dispositions was found to be .376 (arithmetic mean). On the other hand, we found that there is no significant difference in terms of their gender and the department at which they are studying. Furthermore, although there aren’t significant relationships between critical thinking dispositions and their mother education statues, their income levels, their religiosity levels and the number of their siblings; there is any significant positively at low level the relation between thinking dispositions and father educational statues. The findings obtained will be discussed together with literature and other research’ results.

Keywords: preservice teachers, critical thinking dispositions, pedagogy, education

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Authors: S. S. Bendib, L. W. Mouss, S. Kalla

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This paper proposes a self-organization-based approach for real-time systems design. The addressed issue is the mapping of an application onto an architecture of heterogeneous processors while optimizing both makespan and reliability. Since this problem is NP-hard, a heuristic algorithm is used to obtain efficiently approximate solutions. The proposed approach takes into consideration the quality as well as the diversity of solutions. Indeed, an alternate treatment of the two objectives allows to produce solutions of good quality while a self-organization approach based on the neighborhood structure is used to reorganize solutions and consequently to enhance their diversity. Produced solutions make different compromises between the makespan and the reliability giving the user the possibility to select the solution suited to his (her) needs.

Keywords: embedded real-time systems design, makespan, reliability, self-organization, compromises

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Authors: Satien Janpla, Radasa Pojard

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The objective of this study is to study bachelor's degree students’ satisfaction towards the course of Science Project based on education quality assurance. It is a case study of the Faculty of Science and Technology, Suan Sunandha Rajabhat University. The findings can be used as a guideline for analysis and revision of the content and the teaching/learning process of the subject. Moreover, other interesting factors such as teaching method can be developed based on education quality assurance. Population in this study included 267 students in year 3 and year 4 of the Faculty of Science and Technology, Suan Sunandha Rajabhat University who registered in the subject of Science Project in semester 1/2556. The research tool was a questionnaire and the research statistics included arithmetic mean and SD. The results showed that the study of bachelor degree students’ satisfaction towards the subject of Science Project based on education quality assurance reported high satisfaction with the average of 3.51. Students from different departments showed no difference in their satisfaction.

Keywords: satisfaction, science project subject, education quality assurance, students

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Authors: Weera Chotithammaporn, Bannasorn Santhan

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The purpose of this study was to investigate the students’ satisfaction towards the counseling services of the Faculty of Industrial Technology, Suan Sunandha Rajabhat University. The sample group consisted of 311 students coming for counseling services during September to October 2012 BE to complete the questionnaires developed by the researcher. The data were analyzed to find percentage, arithmetic mean, and SD, from which it can be concluded that: 1) Personal information including gender, GPA, department, year of the study, and hometown revealed that most of the students in the Faculty of Industrial Technology, Suan Sunandha Rajabhat University were female with the GPA between 2.01 and 2.50 and studied in the Department of Interior and Exhibition Design and Graphic and Multimedia Design. Most of them were in the first year of the study and came from the southern part of Thailand. 2) The level of students’ satisfaction towards the counseling services of the Faculty of Industrial Technology, Suan Sunandha Rajabhat University was in overall at high level with the highest aspect on IT services followed by follow-up and evaluation service, counseling service, individual personal data collecting service, and personal placement service respectively.

Keywords: satisfaction, students, counseling service, Faculty of Industrial Technology

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Authors: S. Aizikovich, L. Krenev, Y. Tokovyy, Y. C. Wang

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An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical indentation of a flat cylindrical punch into an arbitrarily non-homogeneous elastic half-space is constructed by making use of the bilateral asymptotic method. The key point of this method lies in evaluation of the ker¬nels in the obtained integral equations by making use of a numerical technique. Once the structure of the kernel is defined, it then is approximated by an analytical expression of special kind so that the solution of the integral equation can be achieved analytically. This fact allows for construction of the solution in an analytical form, which is convenient for analysis of the mechanical effects concerned with arbitrarily presumed non-homogeneity of the material.

Keywords: contact problem, circular punch, arbitrarily-nonhomogeneous halfspace

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Authors: Alexiou Dimitra, Fragkaki Maria

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The objective of the paper is the study of geographic, economic and educational variables and their contribution to determine the position of each member-state among the EU-28 countries based on the values of seven variables as given by Eurostat. The Data Analysis methods of Multiple Factorial Correspondence Analysis (MFCA) Principal Component Analysis and Factor Analysis have been used. The cross tabulation tables of data consist of the values of seven variables for the 28 countries for 2014. The data are manipulated using the CHIC Analysis V 1.1 software package. The results of this program using MFCA and Ascending Hierarchical Classification are given in arithmetic and graphical form. For comparison reasons with the same data the Factor procedure of Statistical package IBM SPSS 20 has been used. The numerical and graphical results presented with tables and graphs, demonstrate the agreement between the two methods. The most important result is the study of the relation between the 28 countries and the position of each country in groups or clouds, which are formed according to the values of the corresponding variables.

Keywords: Multiple Factorial Correspondence Analysis, Principal Component Analysis, Factor Analysis, E.U.-28 countries, Statistical package IBM SPSS 20, CHIC Analysis V 1.1 Software, Eurostat.eu Statistics

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