• Advances in materials Research
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• v.9 no.2
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• pp.155-170
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• 2020

In this paper, using the recently introduced analytical approach for the analysis of mass and heat transfer during film growth in reactors for epitaxy from the gas phase, these processes are analyzed taking into account natural convection and the possibility of changing the rate of chemical interaction between reagents. As a result of the analysis, the conditions under which the homogeneity of the grown epitaxial layers increases with a change in the values of the parameters of the growth process are formulated.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.271-280
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• 2022

In this study, We have applied the right operator k-Riemann-Liouville is involving two orders α and β with a positive parameter p > 0, further, the left operator k-Riemann-Liouville is used with the negative parameter p < 0 to introduce a new version related to Hardy-type inequalities. These inequalities are given and reversed for the cases 0 < p < 1 and p < 0. We then improved and generalized various consequences in the framework of Hardy-type fractional integral inequalities.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.467-472
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• 2021

In this paper, we give some new Copson-type integral inequality with a sharp constant.

• The Mathematical Education
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• v.49 no.1
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• pp.15-37
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• 2010

In this study, we investigated the application of oriental history of mathematics in school mathematics teaching. We set up three study problems to achieve this purpose. First, we analyze the middle and high school mathematics textbooks and auxiliary books. Second, we survey the mathematics teacher's knowledge and degree of application on history of mathematics. Third, we develop the teaching and learning materials on oriental history of mathematics. We performed three study-methods to settle above study problem. First, we analyzed 24 textbooks and auxiliary books for study problem 1. There were 6 middle school mathematics textbooks and 6 auxiliary books and also 6 high school mathematics textbooks and 6 auxiliary books. We categorized the contents into "anecdote", "systematization", "application of problem", "expansibility of thought", and "comparative of the contents". Second, we surveyed the 78 mathematics teachers's knowledge and degree of application using questionnaire about knowledge and application on history of mathematics. The questionnaire was made up of four types of question; the effect of material about history of mathematics, the understanding of western history of mathematics, the understanding of oriental history of mathematics; the direction of development of teaching material. Third, we exemplified the teaching and learning materials about three categories: "anecdote", "comparative of the contents".

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.131-148
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• 2000

Above all, the ability to solve problems must be emphasized as a basic skill of mathematics, but it is neglected when we teach. In this study, learning task means ［same meaning］ ［same form］ ［same technique］, so I tried to extend mathematical scholastic ability of the students as an extensional problem solving that is a basic element of mathematics. The purpose of this study is the investigation of level type learning, using the basic learning elements to extend thinking ability. From the constructed hypothesis as follows and then implement it. I selected basic learning elements from an analyzed textbook and then task learning material was created for each level type learning. The problem solving ability will be extended through the level type learning of the small group, using the level type learning task material. The conclusions this study are as follows. The level type learning in small group learning, using and making level type learning material, having basic learning elements in analysed text are. Basic learning content is understood clearly and deeply, so, fundamentally, it is effective in achieving the problem solving in mathematics. It is an effective method to achieve the meta-cognitive faculty because achieved the expected method of solving problems and resulted in the true learning of content.

• Structural Engineering and Mechanics
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• v.61 no.4
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• pp.519-526
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• 2017

In the present paper, the effects of cutting parameters and coating material on the performances of cutting tools in turning of AISI 52100 steel are discussed experimentally. A comparative study was carried out between uncoated and coated (with TiCN-TiN coating layer) cermet tools. The substrate composition and the geometry of the inserts compared were the same. A mathematical model was developed based on the Response Surface Methodology (RSM). ANOVA method was used to quantify the effect of cutting parameters on the machining surface quality and the cutting forces. The results show that feed rate has the most effect on surface quality. However, cutting depth has the significant effect on the cutting force components. The effect of coating layers on the surface quality was also studied. A lower surface roughness was observed when using PVD (TiCN-TiN) coated insert. A second order regression model was developed and a good accuracy was obtained with correlation coefficients in the range of 95% to 97%.

• Advances in nano research
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• v.4 no.2
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• pp.85-111
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• 2016

In this paper, the classical and non-classical boundary conditions effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams are investigated by presenting a semi analytical differential transform method (DTM) for the first time. Three kinds of mathematical models, namely; power law (P-FGM), sigmoid (S-FGM) and Mori-Tanaka (MT-FGM) distribution are considered to describe the material properties in the thickness direction. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle and they are solved applying semi analytical differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as small scale effects, spring constant factors, various material compositions and mode number on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

• Advances in nano research
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• v.13 no.1
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• pp.1-12
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• 2022

The existence of active material in the environment causes the small-scale systems to be sensitive to the actual environment. Carbon dioxide is one of the active materials that exists a lot in the air conditions of the living environment. However, in some applications, the carbon dioxide-coated is used to improve the performance of systems against the destructive factors such as the corrosion; nevertheless, in the current research, the stability analysis of a carbon dioxide capture mechanism-coated beam is investigated according to the mathematical simulation of a rectangular composite beam utilizing the modified couple stress theory. The composite mechanism of carbon dioxide trapping is made of a polyacrylonitrile substrate that supports a cross-link polydimethylsiloxane gutter layer as the carbon dioxide mechanism trapping. Three novel types of carbon dioxide trapping mechanism involving methacrylate, poly (ethylene glycol) methyl ether methacrylate, and three pedant methacrylates are considered, which were introduced by Fu et al. (2016). Finally, according to introducing the methodology of carbon dioxide (CO₂) trapping, the impact of various effective parameters on the stability of composite beams will be analyzed in detail.

• Education of Primary School Mathematics
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• v.18 no.2
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• pp.61-75
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• 2015

This study analyzed the characteristics of mathematical tasks including the level of cognitive demands set up by pre-service elementary school teachers. 50 pre-service teachers in G university of education who participated in their 4 weeks teaching practicum were selected as subjects. They planned and implemented mathematics lesson with their lesson plans. Lesson plans, video of their lessons, transcript of video were gathered and analyzed the characteristics of mathematical tasks used in their lesson. Through the analysis, several conclusions were drawn as follow. First, 78% of the subjects modified tasks in mathematics textbooks. Since modification or construction of mathematical tasks gives good chance for constructing mathematical task knowledge for teaching, more chance should be given to pre-service teachers to construct new tasks or modify tasks in mathematics textbooks. Second, types of modification done by pre-service teachers were categorized as number change(15.6%), situation change(78.1%) and material change(6.3%). As Chapman(2013) emphasized the importance of MtKT, pre-service teachers must have more MtKT by understanding the characteristics of mathematical tasks. Third, the level of cognitive demands required by mathematical tasks were relatively low. 74% of mathematical tasks was lower cognitive demands and only 26% was higher cognitive demands. The level of cognitive demands of tasks in mathematics textbooks tended to be lowered by the directions given right after the tasks were given. In this respect, the structure of mathematics textbooks need to be changed.

• Computers and Concrete
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• v.8 no.6
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• pp.647-675
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• 2011

Our ability to predict hydration behavior is becoming increasingly relevant to the concrete community as modelers begin to link material performance to the dynamics of material properties and chemistry. At early ages, the properties of concrete are changing rapidly due to chemical transformations that affect mechanical, thermal and transport responses of the composite. At later ages, the resulting, nano-, micro-, meso- and macroscopic structure generated by hydration will control the life-cycle performance of the material in the field. Ultimately, creep, shrinkage, chemical and physical durability, and all manner of mechanical response are linked to hydration. As a way to enable the modeling community to better understand hydration, a review of hydration models is presented offering insights into their mathematical origins and relationships one-to-the-other. The quest for a universal model begins in the 1920's and continues to the present, and is marked by a number of critical milestones. Unfortunately, the origins and physical interpretation of many of the most commonly used models have been lost in their overuse and the trail of citations that vaguely lead to the original manuscripts. To help restore some organization, models were sorted into four categories based primarily on their mathematical and theoretical basis: (1) mass continuity-based, (2) nucleation-based, (3) particle ensembles, and (4) complex multi-physical and simulation environments. This review provides a concise catalogue of models and in most cases enough detail to derive their mathematical form. Furthermore, classes of models are unified by linking them to their theoretical origins, thereby making their derivations and physical interpretations more transparent. Models are also used to fit experimental data so that their characteristics and ability to predict hydration calorimetry curves can be compared. A sort of evolutionary tree showing the progression of models is given along with some insights into the nature of future work yet needed to develop the next generation of cement hydration models.