• Journal of the Korean Mathematical Society
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• International Journal of Precision Engineering and Manufacturing
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• 제8권3호
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• pp.8-13
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• 2007

A hybrid fuzzy PID controller for a pneumatic chamber is proposed in this paper. First, a mathematical model of a pneumatic pressure servocontrol system was developed where separate implementations of a PID controller and a fuzzy controller were made. The experimental results using a step input signal revealed that the PID controller accurately controlled the steady-state pressure but did not robustly handle parameter variations in the system while the fuzzy controller provided a fast rise time and low overshoot of the pressure in the system. In order to attain the advantages of both the fuzzy and PID controllers, a hybrid control scheme was developed. The experimental results show that the hybrid fuzzy PID controller proposed in this study does indeed possess the advantages of both PID and fuzzy controllers. Hence, it can be concluded that the hybrid fuzzy PID controller is suited for high-precision control of pressure in a pneumatic chamber.

• Korean Journal of Cognitive Science
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• 제27권2호
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• pp.159-219
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• 2016

Mathematical ability is important for academic achievement and technological renovations in the STEM disciplines. This study concentrated on the relationship between neural basis of mathematical cognition and its mechanisms. These cognitive functions include domain specific abilities such as numerical skills and visuospatial abilities, as well as domain general abilities which include language, long term memory, and working memory capacity. Individuals can perform higher cognitive functions such as abstract thinking and reasoning based on these basic cognitive functions. The next topic covered in this study is about individual differences in mathematical abilities. Neural efficiency theory was incorporated in this study to view mathematical talent. According to the theory, a person with mathematical talent uses his or her brain more efficiently than the effortful endeavour of the average human being. Mathematically gifted students show different brain activities when compared to average students. Interhemispheric and intrahemispheric connectivities are enhanced in those students, particularly in the right brain along fronto-parietal longitudinal fasciculus. The third topic deals with growth and development in mathematical capacity. As individuals mature, practice mathematical skills, and gain knowledge, such changes are reflected in cortical activation, which include changes in the activation level, redistribution, and reorganization in the supporting cortex. Among these, reorganization can be related to neural plasticity. Neural plasticity was observed in professional mathematicians and children with mathematical learning disabilities. Last topic is about mathematical creativity viewed from Neural Darwinism. When the brain is faced with a novel problem, it needs to collect all of the necessary concepts(knowledge) from long term memory, make multitudes of connections, and test which ones have the highest probability in helping solve the unusual problem. Having followed the above brain modifying steps, once the brain finally finds the correct response to the novel problem, the final response comes as a form of inspiration. For a novice, the first step of acquisition of knowledge structure is the most important. However, as expertise increases, the latter two stages of making connections and selection become more important.

• Korean Management Science Review
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• 제17권2호
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• pp.87-95
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• 2000

This paper presents two analytical approaches to determine the vehicle fleet size for container shuttle service. The shuttle service can be defined as the repetitive travel between the designated places during working period. In the first approach, the transportation model is adopted in order to determine the number of vehicles required. Its advantages and disadvantages in practical application are also discussed. In the second approach, a logical network which is oriented on job is transformed from a physical network which is focused on demand site. Nodes on the logical network represent jobs which include loaded travel, loading and unloading and arcs represent empty travel for the next jobs which include loaded travel, loading and unloading and arcs represent empty travel for the next job. Then a mathematical formulation is constructed similar to the multiple traveling salesman problem (TSP). A solution procedure is carried out based on the well-known insertion heuristic with the real world data.

• Korean Management Science Review
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• 제17권2호
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• pp.115-124
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• 2000

Activity-Based Costing(ABC) is an accounting cost system which allocates the overhead cost to each cost object more accurately. ABC system achieves improved accuracy in estimating the cost of cost object by using multiple cost drivers to trace the cost of activities to the cost objects associated with the resources consumed by those activities. The selection and the aggregation of these cost driver candidates can pose difficult problems. This paper deals with these problems in mathematical programming approach. The first model is formulated as an integer programming model in cost driver selection and the second model is formulated as multi-objective goal programming model in reduction of cost drivers already selected.

• Journal of The Korean Society of Grassland and Forage Science
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• 제35권3호
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• pp.257-263
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• 2015

This study was conducted to assess the potential of using NIRS to accurately determine the chemical composition and fermentation parameters in fresh coarse sorghum and sudangrass silage. Near Infrared Spectroscopy (NIRS) has been increasingly used as a rapid and accurate method to analyze the quality of cereals and dried animal forage. However, silage analysis by NIRS has a limitation in analyzing dried and ground samples in farm-scale applications because the fermentative products are lost during the drying process. Fresh coarse silage samples were scanned at 1 nm intervals over the wavelength range of 680~2500 nm, and the optical data were obtained as log 1/Reflectance (log 1/R). The spectral data were regressed, using partial least squares (PLS) multivariate analysis in conjunction with first and second order derivatization, with a scatter correction procedure (standard normal variate and detrend (SNV&D)) to reduce the effect of extraneous noise. The optimum calibrations were selected on the basis of minimizing the standard error of cross validation (SECV). The results of this study showed that NIRS predicted the chemical constituents with a high degree of accuracy (i.e. the correlation coefficient of cross validation ($R^2{_{cv}}$) ranged from 0.86~0.96), except for crude ash which had an $R^2{_{cv}}$ of 0.68. Comparison of the mathematical treatments for raw spectra showed that the second-order derivatization procedure produced the best result for all the treatments, except for neutral detergent fiber (NDF). The best mathematical treatment for moisture, acid detergent fiber (ADF), crude protein (CP) and pH was 2,16,16 respectively while the best mathematical treatment for crude ash, lactic acid and total acid was 2,8,8 respectively. The calibrations of fermentation products produced poorer calibrations (RPD < 2.5) with acetic and butyric acid. The pH, lactic acid and total acids were predicted with considerable accuracy at $R^2{_{cv}}$ 0.72~0.77. This study indicated that NIRS calibrations based on fresh coarse sorghum and sudangrass silage spectra have the capability of assessing the forage quality control

• Journal for History of Mathematics
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• 제25권3호
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• pp.53-75
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• 2012

When imaginary numbers were first encountered in the 16th century, mathematicians were able to calculate the imaginary numbers the same as they are today. However, it required 200 years to mathematically acknowledge the existence of imaginary numbers. The new mathematical situation that arose with a development in mathematics required a harmony of real numbers and imaginary numbers. As a result, the concept of complex number became clear. A history behind the development of complex numbers involved a process of determining a comprehensive perspective that ties real numbers and imaginary numbers in a single category, complex numbers. This came after a resolution of conflict between real numbers and imaginary numbers. This study identified the new perspective and way of mathematical thinking emerging from resolving the conflicts. Also educational implications of the analysis were discussed.

• Journal of Drive and Control
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• 제15권1호
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• pp.38-49
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• 2018

This research describes the development model and testing of a hybrid damper which can be applicable to a vehicle suspension. The hybrid damper is devised to improve the performance of a conventional passive oil damper using a magneto-rheological (MR) accumulator which consists of a gas accumulator and a MR device. The level of damping is continuously variable by the means of control in the applied current in a MR device fitted to a floating piston which separates the gas and the oil chamber. A simple MR device is used to resist the movement of floating piston. At first a mathematical model which describes all flows within the conventional oil damper is formulated, and then a small MR device is also devised and adopted to a mathematical model to characterize the performance of the device.

• Communications of the Korean Mathematical Society
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• 제9권4호
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• The Mathematical Education
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• 제50권1호
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• pp.103-118
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• 2011

The study examined whether the relation between mathematics self-efficacy and mathematics achievement was partially mediated by the learning strategies, using latent growth model analyses. It was also examined the auto-regressive, cross-lagged (ARCL) panel model for testing the stability and change in the relation of mathematics self-efficacy and learning strategy over time. The study analyzed the first-year to the third-year data of the Korean Educational Longitudinal Survey (KELS). The result of ARCL panel model analysis showed that earlier mathematics self-efficacy could predict later learning strategy use. There were linear trends in mathematics self-efficacy, learning strategy, and mathematics achievement. Specifically, mathematics achievement was increased over the three time points, whereas mathematics self-efficacy and learning strategies were significantly decreased. In the analyses of latent growth models, the mediating effects of learning strategies were overall supported. That is, both of initial status and change rate of rehearsal strategy partially mediated the relation of mathematics self-efficacy and mathematics achievement. However, in elaboration and meta-cognitive strategies, only the initial status of each variable showed the indirect relationship.