Search results for: solution of situation

Authors: A. Abdedou, K. Bouhadef

Abstract:

The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: Forced convection, oriented confined jet, porous media.

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Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

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Authors: N. R. N. Idris, S. Baharom

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A meta-analysis may be performed using aggregate data (AD) or an individual patient data (IPD). In practice, studies may be available at both IPD and AD level. In this situation, both the IPD and AD should be utilised in order to maximize the available information. Statistical advantages of combining the studies from different level have not been fully explored. This study aims to quantify the statistical benefits of including available IPD when conducting a conventional summary-level meta-analysis. Simulated meta-analysis were used to assess the influence of the levels of data on overall meta-analysis estimates based on IPD-only, AD-only and the combination of IPD and AD (mixed data, MD), under different study scenario. The percentage relative bias (PRB), root mean-square-error (RMSE) and coverage probability were used to assess the efficiency of the overall estimates. The results demonstrate that available IPD should always be included in a conventional meta-analysis using summary level data as they would significantly increased the accuracy of the estimates.On the other hand, if more than 80% of the available data are at IPD level, including the AD does not provide significant differences in terms of accuracy of the estimates. Additionally, combining the IPD and AD has moderating effects on the biasness of the estimates of the treatment effects as the IPD tends to overestimate the treatment effects, while the AD has the tendency to produce underestimated effect estimates. These results may provide some guide in deciding if significant benefit is gained by pooling the two levels of data when conducting meta-analysis.

Keywords: Aggregate data, combined-level data, Individual patient data, meta analysis.

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Authors: Wen-Bao Qiao, Jean-Charles Créput

Abstract:

To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: Doubly linked list, parallel 2-opt, tour division, GPU.

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Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: variational inequality problems, alternating direction method, global convergence

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Authors: Tomáš Bakalár, Milan Búgel, Henrieta Pavolová

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This study deals with evaluation of influence of salinity (NaCl) onto equilibrium of Cu and Ni removal from aqueous solutions by natural sorbent – zeolite. Equilibrium data were obtained by batch experiments. The salinity of the aqueous solution was influenced by dissolving NaCl in distilled water. It was studied in the range of NaCl concentrations from 1 g.l-1 to 100g.l-1. For Cu sorption there is a significant influence of salinity. The maximum capacity of zeolite for Cu was decreasing with growing concentration of NaCl. For Ni sorption there is not so significant influence of salinity as for Cu. The maximum capacity of zeolite for Ni was slightly decreasing with growing concentration of NaCl.

Keywords: Cu, Ni, sorption, zeolite.

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Authors: Aicha Rima Cheniti, Hatem Besbes, Joseph Haggege, Christophe Sintes

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In this paper, we consider a drift flux mixture model of the blood flow. The mixture consists of gas phase which is carbon dioxide and liquid phase which is an aqueous carbon dioxide solution. This model was used to determine the distributions of the mixture velocity, the mixture pressure, and the carbon dioxide pressure. These theoretical data are used to determine a measurement method of mean gas pressure through the determination of radial velocity distribution. This method can be applicable in experimental domain.

Keywords: Mean carbon dioxide pressure, mean mixture pressure, mixture velocity, radial velocity.

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Authors: N. B. Fedosenko, A.A Iatcenko, S.A. Levanov

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The paper shows some ability to manage two-phase flows arising from the use of unsteady effects. In one case, we consider the condition of fragmentation of the interface between the two components leads to the intensification of mixing. The problem is solved when the temporal and linear scale are small for the appearance of the developed mixing layer. Showing that exist such conditions for unsteady flow velocity at the surface of the channel, which will lead to the creation and fragmentation of vortices at Re numbers of order unity. Also showing that the Re is not a criterion of similarity for this type of flows, but we can introduce a criterion that depends on both the Re, and the frequency splitting of the vortices. It turned out that feature of this situation is that streamlines behave stable, and if we analyze the behavior of the interface between the components it satisfies all the properties of unstable flows. The other problem we consider the behavior of solid impurities in the extensive system of channels. Simulated unsteady periodic flow modeled breaths. Consider the behavior of the particles along the trajectories. It is shown that, depending on the mass and diameter of the particles, they can be collected in a caustic on the channel walls, stop in a certain place or fly back. Of interest is the distribution of particle velocity in frequency. It turned out that by choosing a behavior of the velocity field of the carrier gas can affect the trajectory of individual particles including force them to fly back.

Keywords: Two-phase, mixing, separating, flow control

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Authors: G. B. Hong, H. W. Chen

Abstract:

Liquid-Liquid Equilibrium (LLE) data are measured for the ternary mixtures of water + 1-butanol + butyl acetate and quaternary mixtures of water + 1-butanol + butyl acetate + glycerol at atmospheric pressure at 313.15 K. In addition, isothermal vapor–liquid–liquid equilibrium (VLLE) data are determined experimentally at 333.15 K. The region of heterogeneity is found to increase as the hydrophilic agent (glycerol) is introduced into the aqueous mixtures. The experimental data are correlated with the NRTL model. The predicted results from the solution model with the model parameters determined from the constituent binaries are also compared with the experimental values.

Keywords: LLE, VLLE, hydrophilic agent, NRTL.

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Authors: Dhurgham Al-Karawi, Nisreen Polus, Shakir Al-Zaidi, Sabah Jassim

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The management of COVID-19 patients based on chest imaging is emerging as an essential tool for evaluating the spread of the pandemic which has gripped the global community. It has already been used to monitor the situation of COVID-19 patients who have issues in respiratory status. There has been increase to use chest imaging for medical triage of patients who are showing moderate-severe clinical COVID-19 features, this is due to the fast dispersal of the pandemic to all continents and communities. This article demonstrates the development of machine learning techniques for the test of COVID-19 patients using Chest X-Ray (CXR) images in nearly real-time, to distinguish the COVID-19 infection with a significantly high level of accuracy. The testing performance has covered a combination of different datasets of CXR images of positive COVID-19 patients, patients with viral and bacterial infections, also, people with a clear chest. The proposed AI scheme successfully distinguishes CXR scans of COVID-19 infected patients from CXR scans of viral and bacterial based pneumonia as well as normal cases with an average accuracy of 94.43%, sensitivity 95%, and specificity 93.86%. Predicted decisions would be supported by visual evidence to help clinicians speed up the initial assessment process of new suspected cases, especially in a resource-constrained environment.

Keywords: COVID-19, chest x-ray scan, artificial intelligence, texture analysis, local binary pattern transform, Gabor filter.

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

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In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: A. Rouili

Abstract:

Cantilever L-shaped walls are known to be relatively economical as retaining solution. The design starts by proportioning the wall dimensions for which the stability is checked for. A ratio between the lengths of the base and the stem, falling between 0.5 to 0.7 ensure in most case the stability requirements, however, the displacement pattern of the wall in terms of rotations and translations, and the lateral pressure profile, do not have the same figure for all wall’s proportioning, as it is usually assumed. In the present work the results of a numerical analysis are presented, different wall geometries were considered. The results show that the proportioning governs the equilibrium between the instantaneous rotation and the translation of the wall-toe, also, the lateral pressure estimation based on the average value between the at-rest and the active pressure, recommended by most design standards, is found to be not applicable for all walls.

Keywords: Cantilever wall, proportioning, numerical analysis.

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Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

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Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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Authors: I. Benning

Abstract:

Using technology to expand the learning space is critical for a productive mathematical discourse. This is a case study of two teachers who developed and enacted GeoGebra-based mathematics lessons following their engagement in a two-year professional development. The didactical and semiotic affordance of GeoGebra in widening the learning space for a productive mathematical discourse was explored. The approach of thematic analysis was used for lesson artefact, lesson observation, and interview data. The results indicated that constructing tools in GeoGebra provided a didactical milieu where students used them to explore mathematical concepts with little or no support from their teacher. The prompt feedback from the GeoGebra motivated students to practice mathematical concepts repeatedly in which they privately rethink their solutions before comparing their answers with that of their colleagues. The constructing tools enhanced self-discovery, team spirit, and dialogue among students. With regards to the semiotic construct, the tools widened the physical and psychological atmosphere of the classroom by providing animations that served as virtual concrete to enhance the recording, manipulation, testing of a mathematical idea, construction, and interpretation of geometric objects. These findings advance the discussion of widening the classroom for a productive mathematical discourse within the context of the mathematics curriculum of Ghana and similar sub-Saharan African countries.

Keywords: GeoGebra, theory of didactical situation, semiotic mediation, mathematics laboratory, mathematical discussion.

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Authors: Yun-Tao Zhang, Jong-Yeop Bae, Whoi-Yul Kim

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Background modeling and subtraction in video analysis has been widely used as an effective method for moving objects detection in many computer vision applications. Recently, a large number of approaches have been developed to tackle different types of challenges in this field. However, the dynamic background and illumination variations are the most frequently occurred problems in the practical situation. This paper presents a favorable two-layer model based on codebook algorithm incorporated with local binary pattern (LBP) texture measure, targeted for handling dynamic background and illumination variation problems. More specifically, the first layer is designed by block-based codebook combining with LBP histogram and mean value of each RGB color channel. Because of the invariance of the LBP features with respect to monotonic gray-scale changes, this layer can produce block wise detection results with considerable tolerance of illumination variations. The pixel-based codebook is employed to reinforce the precision from the output of the first layer which is to eliminate false positives further. As a result, the proposed approach can greatly promote the accuracy under the circumstances of dynamic background and illumination changes. Experimental results on several popular background subtraction datasets demonstrate very competitive performance compared to previous models.

Keywords: Background subtraction, codebook model, local binary pattern, dynamic background, illumination changes.

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Authors: Nikola Karanovic, Aleksandar Djuric

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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: Jaimala Gambhir, Tilak Thakur, Puneet Chawla

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As per the statistical data, the Doubly-fed Induction Generator (DFIG) based wind turbine with variable speed and variable pitch control is the most common wind turbine in the growing wind market. This machine is usually used on the grid connected wind energy conversion system to satisfy grid code requirements such as grid stability, Fault Ride Through (FRT), power quality improvement, grid synchronization and power control etc. Though the requirements are not fulfilled directly by the machine, the control strategy is used in both the stator as well as rotor side along with power electronic converters to fulfil the requirements stated above. To satisfy the grid code requirements of wind turbine, usually grid side converter is playing a major role. So in order to improve the operation capacity of wind turbine under critical situation, the intensive study of both machine side converter control and grid side converter control is necessary In this paper DFIG is modeled using power components as variables and the performance of the DFIG system is analysed under grid voltage fluctuations. The voltage fluctuations are made by lowering and raising the voltage values in the utility grid intentionally for the purpose of simulation keeping in view of different grid disturbances.

Keywords: DFIG, dynamic modeling, DPC, sag, swell, voltage fluctuations, FRT.

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Authors: Young Mun Lee, Seon Ho Kim, Seok Min Choi, JeongJu Kim, Seungyeong Choi, Hyung Hee Cho

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To decrease sulfur oxide in the flue gas from coal power plant, a flue gas de-sulfurization facility is operated. In the reactor, a chemical reaction occurs with a temperature change of the gas so that sulfur oxide is removed and cleaned air is emitted. In this process, temperature change induces a serious problem which is a cold erosion of stack. To solve this problem, the rotary heat exchanger is managed before the stack. In the heat exchanger, a heating element is equipped to increase a heat transfer area. Heat transfer and pressure loss is a big issue to improve a performance. In this research, thermal-fluid characteristics of the heating element are analyzed by computational fluid dynamics. Fouling simulation is also conducted to calculate a performance of heating element. Numerical analysis is performed on the situation where plugging phenomenon has already occurred and existed in the inlet region of the heating element. As the pressure of the rear part of the plugging decreases suddenly and the flow velocity becomes slower, it is found that the flow is gathered from both sides as it develops in the flow direction, and it is confirmed that the pressure difference due to plugging is increased.

Keywords: Heating element, plugging, rotary heat exchanger, thermal fluid characteristics.

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Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.

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Authors: Wen Po Cheng, Chi Hua Fu, Ping Hung Chen, Ruey Fang Yu

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Recovering resources from water purification sludge (WPS) have been gradually stipulated in environmental protection laws and regulations in many nations. Hence, reusing the WPS is becoming an important topic, and recovering alum from WPS is one of the many practical alternatives. Most previous research efforts have been conducted on studying the amphoteric characteristic of aluminum hydroxide for investigating the optimum pH range to dissolve the Al(III) species from WPS, but it has been lack of reaction kinetics or mechanisms related discussion. Therefore, in this investigation, water purification sludge (WPS) solution was broken by ultrasound to make particle size of reactants smaller, specific surface area larger. According to the reaction kinetics, these phenomena let the dissolved aluminum salt quantity increased and the reaction rate go faster.

Keywords: Aluminum, Acidification, Sludge, Recovery.

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Authors: Juyi Park, Jung-Min Kim, Hee-Hwan Park, Jin-Wook Kim, Gye-Hyung Kang, Soo-Ho Kim

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This paper presents an iterative algorithm to find a inverse kinematic solution of 5-DOF robot. The algorithm is to minimize the iteration number. Since the 5-DOF robot cannot give full orientation of tool. Only z-direction of tool is satisfied while rotation of tool is determined by kinematic constraint. This work therefore described how to specify the tool direction and let the tool rotation free. The simulation results show that this algorithm effectively worked. Using the proposed iteration algorithm, error due to inverse kinematics converged to zero rapidly in 5 iterations. This algorithm was applied in real welding robot and verified through various practical works.

Keywords: 5-DOF manipulator, Inverse kinematics, Iterative algorithm, Wrist offset.

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Authors: Mehran Yazdi, Mehdi Seyfi, Amirhossein Rafati, Meghdad Asadi

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Detection and tracking of the lip contour is an important issue in speechreading. While there are solutions for lip tracking once a good contour initialization in the first frame is available, the problem of finding such a good initialization is not yet solved automatically, but done manually. We have developed a new tracking solution for lip contour detection using only few landmarks (15 to 25) and applying the well known Active Shape Models (ASM). The proposed method is a new LMS-like adaptive scheme based on an Auto regressive (AR) model that has been fit on the landmark variations in successive video frames. Moreover, we propose an extra motion compensation model to address more general cases in lip tracking. Computer simulations demonstrate a fair match between the true and the estimated spatial pixels. Significant improvements related to the well known LMS approach has been obtained via a defined Frobenius norm index.

Keywords: Lip contour, Tracking, LMS-Like

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Authors: R. Kozik, A. Leśniak A., E. Plebankiewicz

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Contracting authorities in the public sector are obligated to apply the principles provided for in the Polish law for the evaluation and selection of contractors. In order to analyse the methods of contractors selecting applied in practice by public clients, the notices of contract award results for construction works were analysed. The analysis shows that the procedure selected more and more often is open competitive bidding, where the assessment of the competence of contractors is not very precise, as well as noncompetitive bidding, i.e. single source procurement. The share of procurement procedures, where the only criterion is price, is increasing. The solution to the problems existing here might be the introduction of one of the forms of pre-selection of contractors. The article also briefly discusses verification systems for companies applying for public contracts used in EU countries.

Keywords: Certification, contractors selection, open tendering, public investors.

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Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

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A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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Authors: Pariwat Somnuek

Abstract:

This study focused on tourism logistic services in the border areas of Thailand by an analysis and comparison of the opinions of tourists, villagers, and entrepreneurs of these services. Sample representatives of this study were a total of 600 villagers and 15 entrepreneurs in the three border areas consisting of Chong Anma, Chong Sa-Ngam, and Chong Jom checkpoints. For methodology, survey questionnaires, situation analysis, TOWS matrix, and focus group discussions were used for data collection, as well as descriptive analysis and statistics such as arithmetic means and standard deviations, were employed for data analysis. The findings revealed that business potential was at the medium level and entrepreneurs were satisfied with their turnovers. However, perspectives of transportation and tourism services provided for tourists need to be immediately improved. Recommendations for the potential development included promotion of border tourism destinations and foreign investments into accommodation, restaurants, and transport, as well as the establishment of business networks between Thailand and Cambodia, along with the introduction of new tourism destinations by co-operation between entrepreneurs in both countries. These initiatives may lead to increased visitors, collaboration of security offices, and an improved image of tourism security.

Keywords: Business potential, potential development, tourism logistics, services.

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Authors: Daesung Moon, Woo-Yong Choi, Kiyoung Moon

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Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

Keywords: Fuzzy vault, fingerprint recognition multiple polynomials.

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Authors: Yayun Hsu, Henry Horng-Shing Lu

Abstract:

This paper proposes a data-driven, biology-inspired neural segmentation method of 3D drosophila Brainbow images. We use Bayesian Sequential Partitioning algorithm for probabilistic modeling, which can be used to detect somas and to eliminate crosstalk effects. This work attempts to develop an automatic methodology for neuron image segmentation, which nowadays still lacks a complete solution due to the complexity of the image. The proposed method does not need any predetermined, risk-prone thresholds, since biological information is inherently included inside the image processing procedure. Therefore, it is less sensitive to variations in neuron morphology; meanwhile, its flexibility would be beneficial for tracing the intertwining structure of neurons.

Keywords: Brainbow, 3D imaging, image segmentation, neuron morphology, biological data mining, non-parametric learning.

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Authors: Bello Ali

Abstract:

The use of Information and Communication Technology (ICT) in tertiary institutions by lecturers and students has become a necessity for the enhancement of quality teaching and learning. This study examined availability, accessibility and utilization of ICT in Teaching-Learning Islamic Studies in Colleges of Education, North-East, Nigeria. The study adopted multi-stage sampling technique, in which, five out of the eleven Colleges of Education (both Federal and State owned) were purposively selected for the study. Primary data was drawn from the respondents by the use of questionnaire, interviews and observations. The results of the study, generally, indicate that the availability and accessibility to ICT facilities in Colleges of Education in North-East, Nigeria, especially in teaching/learning delivery of Islamic studies were relatively inadequate and rare to lecturers and students. The study further reveals that the respondents’ level of utilization of ICT is low and only few computer packages and internet services were involved in the ICT utilization, which is yet to reach the real expected situation of the globalization and advancement in the application of ICT if compared to other parts of the world, as far as the teaching and learning of Islamic studies is concerned. Observations and conclusion were drawn from the findings and finally, recommendations on how to improve on ICT availability, accessibility and utilization in teaching/ learning were suggested.

Keywords: Accessibility, availability, college of education, ICT, Islamic Studies, learning, North-Eastern, teaching, utilization.

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Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: Hussain Ali Bekhet, Nor Salwati Othman

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Malaysia has achieved remarkable economic growth since 1957, moving toward modernization from a predominantly agriculture base to manufacturing and—now—modern services. The development policies (i.e., New Economic Policy [1970–1990], the National Development Policy [1990–2000], and Vision 2020) have been recognized as the most important drivers of this transformation. The transformation of the economic structure has moved along with rapid gross domestic product (GDP) growth, urbanization growth, and greater demand for energy from mainly fossil fuel resources, which in turn, increase CO2 emissions. Malaysia faced a great challenge to bring down the CO2 emissions without compromising economic development. Solid policies and a strategy to reduce dependencies on fossil fuel resources and reduce CO2 emissions are needed in order to achieve sustainable development. This study provides an overview of the Malaysian economic, energy, and environmental situation, and explores the existing policies and strategies related to energy and the environment. The significance is to grasp a clear picture on what types of policies and strategies Malaysia has in hand. In the future, this examination should be extended by drawing a comparison with other developed countries and highlighting several options for sustainable development.

Keywords: Energy policies, energy efficiency, renewable energy, green building, Malaysia, sustainable development.

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