Search results for: drawing method

Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Amy Hodges, Deanna Rasmussen, Sherry Ward

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This paper examines the use of ePortfolios in a two-course sequence for ESL (English as a Second Language) students at an international branch campus in Doha, Qatar. ePortfolios support the transfer of language learning, but few have examined the sustainability of that transfer across an ESL program. Drawing upon surveys and interviews with students, we analyze three case studies that complicate previous research on metacognition, language learning, and ePortfolios. Our findings have implications for those involved in ESL programs and assessment of student writing.

Keywords: TESOL, electronic portfolios, assessment, technology

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Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.

Keywords: cable ampacity, finite element method, underground cable, thermal rating

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: drape, drape shape, automated drapemeter, fabric

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Authors: Haixu Yu, Wenhui Cao

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Tailoring Large Language Models (LLMs) to perform legal reasoning has been a popular trend in the study of AI and law. Researchers have mainly employed two methods to unlock the potential of LLMs, namely by finetuning the LLMs to expand their knowledge of law and by restructuring the prompts (In-Context Learning) to optimize the LLMs’ understanding of the legal questions. Although claiming the finetuning and renovated prompting can make LLMs more competent in legal reasoning, most state-of-the-art studies show quite limited improvements of practicability. In this paper, drawing on the study of the complexity and low interpretability of legal texts, we propose a prompting strategy based on the Chain of Thought (CoT) method. Instead of merely instructing the LLM to reason “step by step”, the prompting strategy requires the tested LLM to identify the ambiguity in the questions as the first step and then allows the LLM to generate corresponding answers in line with different understandings of the identified terms as the following step. The proposed prompting strategy attempts to encourage LLMs to "interpret" the given text from various aspects. Experiments that require the LLMs to answer “case analysis” questions of bar examination with general LLMs such as GPT 4 and legal LLMs such as LawGPT show that the prompting strategy can improve LLMs’ ability to better understand complex legal texts.

Keywords: ambiguity-identification, prompt, large language model, legal text understanding

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Chui Ka Shing

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This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.

Keywords: bar model method, curriculum development, mathematics education, problem solving

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Azizakhanim Maharramli

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The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

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Authors: Mahacine Amrani

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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Jiankang Wang, Hongyang Yu

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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Y. Gholipour, E. Rezazadeh

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Delay is one of the most serious and common problems of construction project that can affect project delivery unfavorably. This research presents the most important causes of delay in large dam projects based on a survey on some executed dam construction in Iran. In this survey a randomly selected samples of owners, consultants and contractors have been involved. The outcome of this survey revealed that scheduled payments, site management, shop drawing review process, unforeseen ground conditions and contractor experience as the most important factors affecting on delay in dam construction projects.

Keywords: delay, dam construction, project management, Iran

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Authors: Diana Pombo, Maria Loaiza, Mauricio Quijano, Alberto Cadena, Juan Pablo Tello

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In this paper, we present a semi-automatic tool for calculating ejection fraction from an echocardiographic video signal which is derived from a database in DICOM format, of Clinica de la Costa - Barranquilla. Described in this paper are each of the steps and methods used to find the respective calculation that includes acquisition and formation of the test samples, processing and finally the calculation of the parameters to obtain the ejection fraction. Two imaging segmentation methods were compared following a methodological framework that is similar only in the initial stages of processing (process of filtering and image enhancement) and differ in the end when algorithms are implemented (Active Contour and Region Growing Algorithms). The results were compared with the measurements obtained by two different medical specialists in cardiology who calculated the ejection fraction of the study samples using the traditional method, which consists of drawing the region of interest directly from the computer using echocardiography equipment and a simple equation to calculate the desired value. The results showed that if the quality of video samples are good (i.e., after the pre-processing there is evidence of an improvement in the contrast), the values provided by the tool are substantially close to those reported by physicians; also the correlation between physicians does not vary significantly.

Keywords: echocardiography, DICOM, processing, segmentation, EDV, ESV, ejection fraction

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: Katharina Fellnhofer, Kaisu Puumalainen

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Despite the current worldwide increasing interest in entrepreneurship education (EE), little attention has been paid to innovative web-based ways such as the narrative approach by telling individual stories of entrepreneurs via multimedia for demonstrating the impact on individuals towards entrepreneurship. In addition, this research discipline is faced with no consensus regarding its effective content of teaching materials and tools. Therefore, a qualitative hypothesis-generating research contribution is required to aim at drawing new insights from published works in the EE field of research to serve for future research related to multimedia entrepreneurial narratives. Based on this background, our effort will focus on finding support regarding following introductory statement: Multimedia success and failure stories of real entrepreneurs show potential to change perceptions towards entrepreneurship in a positive way. The proposed qualitative conceptual paper will introduce the underlying background for this research framework. Therefore, as a qualitative hypothesis-generating research contribution it aims at drawing new insights from published works in the EE field of research related to entrepreneurial narratives to serve for future research. With the means of the triangulation of multiple theories, we will utilize the foundation for multimedia-based entrepreneurial narratives applying a learning-through-multimedia-real-entrepreneurial-narratives pedagogical tool to facilitate entrepreneurship. Our effort will help to demystify how value-oriented entrepreneurs telling their stories multimedia can simultaneously enhance EE. Therefore, the paper will build new-fangled bridges between well-cited theoretical constructs to build a robust research framework. Overall, the intended contribution seeks to emphasize future research of currently under-researched issues in the EE sphere, which are considered to be essential not only to academia, as well as to business and society having future jobs-providing growth-oriented entrepreneurs in mind. The Authors would like to thank the Austrian Science Fund FWF: [J3740 – G27].

Keywords: entrepreneurship education, entrepreneurial attitudes and perceptions, entrepreneurial intention, entrepreneurial narratives

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Authors: Yude Wu

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Mongolia, grappling with significant socio-economic challenges, faces pressing issues of inequality and poverty, as evidenced by a high Gini coefficient and the highest poverty rate among the top 20 largest Asian countries. Despite government efforts, Mongolia's poverty rate experienced only a slight reduction from 29.6 percent in 2016 to 27.8 percent in 2020. PEER countries, such as South Africa, Botswana, Kazakhstan, and Peru, share characteristics with Mongolia, including reliance on the mining industry and classification as lower middle-income countries. Successful transitions of these countries to upper middle-income status between 1994 and the 2010s provide valuable insights. Drawing on secondary analyses of existing research and PEER country profiles, the study evaluates past policies, identifies gaps in current approaches, and proposes recommendations to combat poverty sustainably. The hypothesis includes a reliance on the mining industry and a transition from lower to upper middle-income status. Policies from these countries, such as the GEAR policy in South Africa and economic diversification in Botswana, offer insights into Mongolia's development. This essay aims to illuminate the multidimensional nature of underdevelopment in Mongolia through a secondary analysis of existing research and PEER country profiles, evaluating past policies, identifying gaps in current approaches, and providing recommendations for sustainable progress. Drawing inspiration from PEER countries, Mongolia can implement policies such as economic diversification to reduce vulnerability and create stable job opportunities. Emphasis on infrastructure, human capital, and strategic partnerships for Foreign Direct Investment (FDI) aligns with successful strategies implemented by PEER countries, providing a roadmap for Mongolia's development objectives.

Keywords: inequality, PEER countries, comparative analysis, nomadic animal husbandry, sustainable growth

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Authors: Rahou Mohamed , Sebaa Fethi, Cheikh Abdelmadjid

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Manufacturing tolerancing is intended to determine the intermediate geometrical and dimensional states of the part during its manufacturing process. These manufacturing dimensions also serve to satisfy not only the functional requirements given in the definition drawing but also the manufacturing constraints, for example geometrical defects of the machine, vibration, and the wear of the cutting tool. The choice of positioning has an important influence on the cost and quality of manufacture. To avoid this problem, a two-step approach have been developed. The first step is dedicated to the determination of the optimum position. As for the second step, a study was carried out for the tightening effect on the tolerance interval.

Keywords: dispersion, tolerance, manufacturing, position

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Authors: Young Nam Chun, Soo Hyuk Yun, Byeo Ri Jeong

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The recent gradual increase in the energy demand is mostly met by fossil fuel, but the research on and development of new alternative energy sources is drawing much attention due to the limited fossil fuel supply and the greenhouse gas problem. Biomass is an eco-friendly renewable energy that can achieve carbon neutrality. The conversion of the biomass sludge wastes discharged from a wastewater treatment plant to clean energy is an important green energy technology in an eco-friendly way. In this NRF study, a new type of microwave thermal treatment was developed to apply the biomass-CCS technology to sludge wastes. For this, the microwave dielectric heating characteristics were examined to investigate the energy conversion mechanism for the combined drying-pyrolysis/gasification of the dewatered wet sludge. The carbon dioxide gasification was tested using the CO2 captured from the pre-combustion capture process. In addition, the results of the pyrolysis and gasification test with the wet sludge were analyzed to compare the microwave energy conversion results with the results of the use of the conventional heating method. Gas was the largest component of the product of both pyrolysis and gasification, followed by sludge char and tar. In pyrolysis, the main components of the producer gas were hydrogen and carbon monoxide, and there were some methane and hydrocarbons. In gasification, however, the amount of carbon monoxide was greater than that of hydrogen. In microwave gasification, a large amount of heavy tar was produced. The largest amount of benzene among light tar was produced in both pyrolysis and gasification. NH3 and HCN which are the precursors of NOx, generated as well. In microwave heating, the sludge char had a smooth surface, like that of glass, and in the conventional heating method with an electric furnace, deep cracks were observed in the sludge char. This indicates that the gas obtained from the microwave pyrolysis and gasification of wet sewage sludge can be used as fuel, but the heavy tar and NOx precursors in the gas must be treated. Sludge char can be used as solid fuel or as a tar reduction adsorbent in the process if necessary. This work supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1R1A2A2A03003044).

Keywords: microwave heating, pyrolysis gasification, precombustion CCS, sewage sludge, biomass energy

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Authors: P. Fernández-Morales, D. Peláez, C. Isaza, J. M. Meza, E. Mendoza

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Mg AZ31B alloy sheets were processed through equal-channel angular sheet drawing (ECASD) process, following the route A and C at room temperature and varying the processing speed. SEM was used to analyze the microstructure. The grain size was refined and presence of twins was observed. Vickers microhardness and tensile testing were carried out to evaluate the mechanical properties, showing in general; a remarkable increase in the first pass and slight increases during subsequent passes and, that the route C produces better uniform properties distribution through the thickness of the samples.

Keywords: ECASD, Mg Alloy, mechanical properties, microstructure

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Authors: Natalie Frandsen

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Pursuing post-secondary education is a milestone for many Canadian youths. This transition involves many changes and opportunities for growth. However, this may also be a period where challenges arise. Perhaps not surprisingly, mental health challenges for post-secondary students are common. This poses difficulties for students and instructors. Common mental-health-related symptoms (e.g., low motivation, fatigue, inability to concentrate) can affect academic performance, and instructors may need to provide accommodations for these students without the necessary expertise. ‘Distance education’ has been growing and gaining momentum in Canada for three decades. As a consequence of the COVID-19 pandemic, post-secondary institutions have been required to deliver courses using ‘remote’ methods (i.e., various online delivery modalities). The learning challenges and subsequent academic performance issues experienced by students with mental-health-related disabilities studying online are not well understood. However, we can postulate potential factors drawing from learning theories, the relationship between mental-health-related symptoms and academic performance, and learning design. Identifying barriers and opportunities to academic performance is an essential step in ensuring that students with mental-health-related disabilities are able to achieve their academic goals. Completing post-secondary education provides graduates with more employment opportunities. It is imperative that our post-secondary institutions take a holistic view of learning by providing learning and mental health support while reducing structural barriers. Health-promoting universities and colleges infuse health into their daily operations and academic mandates. Acknowledged in this Charter is the notion that all sectors must take an active role in favour of health, social justice, and equity for all. Drawing from mental health promotion and Universal Design for Learning (UDL) frameworks, relevant adult learning concepts, and critical digital pedagogy, considerations for mental-health-promoting, online learning community development will be summarized. The education sector has the opportunity to create and foster equitable and mental health-promoting learning environments. This is of particular importance during a global pandemic when the mental health of students is being disproportionately impacted.

Keywords: academic performance, community, mental health promotion, online learning

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: Rima A. Ajlouni

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The discovery of quasi-periodic structures in material science is revealing an exciting new class of symmetries, which has never been explored before. Due to their unique structural and visual properties, these symmetries are drawing interest from many scientific and design disciplines. Especially, in art and architecture, these symmetries can provide a rich source of geometry for exploring new patterns, forms, systems, and structures. However, the structural systems of these complicated symmetries are still posing a perplexing challenge. While much of their local order has been explored, the global governing system is still unresolved. Understanding their unique global long-range order is essential to their generation and application. The recent discovery of dodecagonal quasi-periodic patterns in historical Islamic architecture is generating a renewed interest into understanding the mathematical principles of traditional Islamic geometry. Astonishingly, many centuries before its description in the modern science, ancient artists, by using the most primitive tools (a compass and a straight edge), were able to construct patterns with quasi-periodic formations. These ancient patterns can be found all over the ancient Islamic world, many of which exhibit formations with 5, 8, 10 and 12 quasi-periodic symmetries. Based on the examination of these historical patterns and derived from the generating principles of Islamic geometry, a global multi-level structural model is presented that is able to describe the global long-range order of dodecagonal quasi-periodic formations in Islamic Architecture. Furthermore, this method is used to construct new quasi-periodic tiling systems as well as generating their deflation and inflation rules. This method can be used as a general guiding principle for constructing infinite patches of dodecagon-based quasi-periodic formations, without the need for local strategies (tiling, matching, grid, substitution, etc.) or complicated mathematics; providing an easy tool for scientists, mathematicians, teachers, designers and artists, to generate and study a wide range of dodecagonal quasi-periodic formations.

Keywords: dodecagonal, Islamic architecture, long-range order, quasi-periodi

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