• Research in Mathematical Education
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• v.18 no.1
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• pp.31-40
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• 2014

Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.

• Journal of Korean Society of Transportation
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• v.12 no.3
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• pp.5-13
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• 1994

In the fields of rail and road design, most vertical alignment design have been thus far heavily dependent upon trial-and-errors of experienced engineers. However, it has long been inefficient in productivity of designing process. In order to overcome this inefficiency, this paper presents the optimal vertical alignment design method using mathematical optimization techniques. For optimization, mathematical model to minimize the construction cost is formulated and the separable programming technique and the Zoutendijk method are introduced to solve it. As result, it is shown that this optimization technique can give efficient solutions to all vertical alignment design fields with properly-estimated cost function.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.10
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• pp.947-954
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• 2013

This article focuses on a hemispherical resonator gyro driven by the Coriolis effect. The operational principle of resonator gyros and mathematical models are introduced. These models are useful to explain the behavior of a resonator and to design controllers. Several control tests of a resonator have been done. A resonator has been excited by electromagnets controlled by a computer. Its amplitude has been adjusted by a PI control. The transient response is matched with a simulation result based on a mathematical model. A vibrating pattern may drift due to non-uniform factors of a resonator. The drift of the vibrating pattern is controlled and aligned to a reference direction by a PI control. These results are very useful to understand the behavior of resonator gyros and to design advanced control algorithm for better performance.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.109-124
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• 2009

Based on the observed data for Clarithromycin released, three commonly used inflow models: the power, the exponential, and the logarithmic models are considered. Among them, the power model is used most in practice for simplicity. Using the numerical parameter estimation techniques, the parameters appeared in the model equations are estimated. Through the numerical estimation results using the several experimental data sets, the exponential model turns out to be best among the three models. More specifically, the sum of squares of absolute errors and the sum of squares of relative errors for the exponential model are reduced by 80-95 % for the experimental data sets and 60-90 % for the noise added data sets compared with those for the power and logarithmic models. A typical experimental data set is used in this paper to show the estimation method and its numerical results. The proposed numerical method and its algorithm are designed for estimating the parameters appeared in the model differential equations for which the exact form of the solution is unknown in general. The methodology developed can be applied to more general cases such as the nonlinear ordinary differential equations or the partial differential equations.

• Computers and Concrete
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• v.27 no.3
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• pp.225-239
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• 2021

Carbon fiber reinforced polymer (CFRP) has extensive use in strengthening reinforced concrete structures due to its high strength and elastic modulus, low weight, fast and easy application, and excellent durability performance. Many studies have been carried out to determine the performance of the CFRP confined concrete cylinder. Although studies about the prediction of confined compressive strength using ANN are in the literature, the insufficiency of the studies to predict the strain of confined concrete cylinder using ANN, which is the most appropriate analysis method for nonlinear and complex problems, draws attention. Therefore, to predict both strengths and also strain values, two different ANNs were created using an extensive experimental database. The strength and strain networks were evaluated with the statistical parameters of correlation coefficients (R2), root mean square error (RMSE), and mean absolute error (MAE). The estimated values were found to be close to the experimental results. Mathematical equations to predict the strength and strain values were derived using networks prepared for convenience in engineering applications. The sensitivity analysis of mathematical models was performed by considering the inputs with the highest importance factors. Considering the limit values obtained from the sensitivity analysis of the parameters, the performances of the proposed models were evaluated by using the test data determined from the experimental database. Model performances were evaluated comparatively with other analytical models most commonly used in the literature, and it was found that the closest results to experimental data were obtained from the proposed strength and strain models.

• Coupled systems mechanics
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• v.11 no.1
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• pp.79-91
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• 2022

Models for water treatment processes include simulation, i.e., modelling of water quality, flow hydraulics, process controls and design. Water treatment processes are inherently dynamic because of the large variations in the influent water flow rate, concentration and composition. Moreover, these variations are to a large extent not possible to control. Mathematical models and computer simulations are essential to describe, predict and control the complicated interactions of the water treatment processes. An accurate description of such systems can therefore result in highly complex models, which may not be very useful from a practical, operational point of view. The main objective is to combine knowledge of the process dynamics with mathematical methods for processes estimation and identification. Good modelling practice is way to obtain this objective and to improve water treatment processes(its understanding, design, control and performance- efficiency). By synthesize of existing knowledge and experience on good modelling practices and principles the aim is to help address the critical strategic gaps and weaknessesin water treatment models application.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.529-552
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• 2014

As we know, some indices and data are strong influence to the price movement of some assets now, but not to another assets and in future. Thus we define some asset models for several time intervals; intraday, weekly, monthly, and yearly asset models. We define these asset models by using Brownian motion with volatility and Poisson process, and several deterministic functions(index function, twitter data function and big-jump simple function etc). In our asset models, these deterministic functions are the positive or negative levels of auxiliary indices, of analyzed data, and for imminent and extreme state(for example, financial shock or the highest popularity in the market). These functions determined by indices, twitter data and shocking news are a kind of one of speciality of our asset models. For reasonableness of our asset models, we introduce several real data, figurers and tables, and simulations. Perhaps from our asset models, for short-term or long-term investment, we can classify and reference many kinds of usual auxiliary indices, information and data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.1-21
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• 2024

This review comprehensively explores the evolution, theoretical underpinnings, variations, and applications of diffusion models. Originating as a generative framework, diffusion models have rapidly ascended to the forefront of machine learning research, owing to their exceptional capability, stability, and versatility. We dissect the core principles driving diffusion processes, elucidating their mathematical foundations and the mechanisms by which they iteratively refine noise into structured data. We highlight pivotal advancements and the integration of auxiliary techniques that have significantly enhanced their efficiency and stability. Variants such as bridges that broaden the applicability of diffusion models to wider domains are introduced. We put special emphasis on the ability of diffusion models as a crucial foundation model, with modalities ranging from image, 3D assets, and video. The role of diffusion models as a general foundation model leads to its versatility in many of the downstream tasks such as solving inverse problems and image editing. Through this review, we aim to provide a thorough and accessible compendium for both newcomers and seasoned researchers in the field.

• Journal of Soil and Groundwater Environment
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• v.13 no.6
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• pp.40-49
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• 2008

Matrix diffusion from planar fractures was studied mathematically and through physical model experiments. Mathematical models were developed to simulate diffusion from 2D and 3D instantaneous disk sources and a 3D continuous disk source. The models were based on analytical solutions previously developed by Carslaw and Jaeger (1959). The mathematical simulations indicated that the 2D scenario produces significantly different results from the 3D scenario, the time for mass disappearance is significantly larger for continuous sources than for instantaneous sources, the normalized concentration generally decreased over time for instantaneous sources while it increased over time for continuous sources, diffusion rates decrease significantly over time and space, and the normalized mass loss from the source zone never reaches 1 for continuous sources due to the semi-infinite integral. The simulations also showed that disappearance times increase exponentially with increasing source radii and matrix porosity, and decrease with increasing aqueous-phase NAPL solubilities.

• Research in Mathematical Education
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• v.20 no.1
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• pp.11-19
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• 2016

Investigating students' lived mathematical experiences presents dual challenges for the researcher. On the one hand, we must respect that students' experiences are not directly accessible to us and are likely very different from our own experiences. On the other hand, we might not want to rely upon the students' own characterizations of what constitutes mathematics because these characterizations could be limited to the formal products students learn in school. I suggest a characterization of mathematics as objectified action, which would lead the researcher to focus on students' operations-mental actions organized as objects within structures so that they can be acted upon. Teachers' and researchers' models of these operations and structures can be used as a launching point for understanding students' experiences of mathematics. Teaching experiments and clinical interviews provide a means for the teacher-researcher to infer students' available operations and structures on the basis of their physical activity (including verbalizations) and to begin harmonizing with their mathematical experience.