• Education of Primary School Mathematics
• /
• v.22 no.2
• /
• pp.129-147
• /
• 2019

Because of the various concepts and meanings of fractions and the difficulty of learning, studies to improve the teaching methods of fraction have been carried out. Particularly, because there are various methods of teaching depending on the type of fractions or the models or methods used for problem solving in fraction operations, many researches have been implemented. In this study, I analyzed the fractional operations of CCSSM-CA and its U.S. textbooks. It was CCSSM-CA revised and presented in California and the textbooks of Houghton Mifflin Harcourt Publishing Co., which reflect the content and direction of CCSSM-CA. As a result of the analysis, although the grades presented in CCSSM-CA and Korean textbooks were consistent in the addition and subtraction of fractions, there are the features of expressing fractions by the sum of fractions with the same denominator or unit fraction and the evaluation of the appropriateness of the answer. In the multiplication and division of fractions, there is a difference in the presentation according to the grades. There are the features of the comparison the results of products based on the number of factor, presenting the division including the unit fractions at first, and suggesting the solving of division problems using various ways.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.9
• /
• pp.2770-2781
• /
• 1996

Longitudinal shear modulus of continuous fiber reinforced 2-phase composites is predicted by theoretical and numerical analysis methods. In this paper, circular, hexagonal and rectangular shapes of reinforced fiber are considered using unit cell concept. And fiber array is regular rectangular and hexagonal fiber arrangement. Longitudinal shear modulus is a function of fiber distribution pattern and fiber volume change. It is found that the rectangular array has a higher longitudinal shear modulus than the hexagonal one. Also, the rectangular fiber shape in lower fiber volume fraction and the circular fiber shape in higher fiber volume fraction show the higher longitudinal shear modulus. And it has been found that the theoretical and numerical predictions of the longitudinal shear modulus give a good agreement with the experimental data at lower fiber volume fraction. Both the distance and stress transfer between the fibers are discussed as the major determing factors.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.251-274
• /
• 2020

We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the Farey map on the unit interval which generates an additive continued fraction algorithm. We explore some number theoretical properties of the Romik system. In particular, we prove an analogue of Lagrange's theorem in the case of the Romik system on the unit quarter circle, which states that a point possesses an eventually periodic digit expansion if and only if the point is defined over a real quadratic extension field of rationals.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1163-1167
• /
• 2003

Effective properties of ceramic matrix plain woven textile composites were calculated using finite element analysis. The considered geometry is a unit cell of plain weave and the analysis was performed by commercial finite element program, ANSYS. The materials for analysis are 3 types for matrix, 1 type for fiber with various volume fraction. The result indicates that the effective properties of ceramic matrix composites can be controlled by the volume fraction. The result can be used for numerical analysis using ceramic matrix composites.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.31 no.2
• /
• pp.43-50
• /
• 2008

In this paper we suggest the methods that compute the total inventory cost based on EOQ and the total inventory cost based on OMMIP. The total inventory cost consists of purchasing cost, ordering cost, inventory holding cost, stockout cost and so on. This papers also proposes the method that decides optimum order quantity as the order amount to minimize the total inventory cost with comparison of EOQ total inventory cost and OMMIP total inventory cost according to inventory holding cost as a fraction of unit cost.

• Journal of Aerospace System Engineering
• /
• v.14 no.4
• /
• pp.25-31
• /
• 2020

The development of manufacturing technology for braided composites has led to farther extension of the applications in aerospace structures. Since the mechanical characteristics of braided composites are affected by various materials and manufacturing parameters, it is important to determine the parameters required to appropriately design the braided composite structures. In this study, we proposed a geometric model of RUC (repeating unit cell) for 2D braided composites, and predicted the mechanical properties according to the change of fiber volume fraction, fiber filament size, braiding angle, and gap between adjacent yarns by the yarn slicing technique and stress averaging method. Finally, we analyze the characteristics of mechanical properties according to each manufacturing parameter of the braided composite material.

• Nuclear Engineering and Technology
• /
• v.42 no.4
• /
• pp.394-413
• /
• 2010

The object of this paper is to identify the key elements that impact a radiation dose at EAB (Exclusion Area Boundary). This study is based on the AST (Alternative Source Terms) as defined in Regulatory Guide 1.183. The LOCA (Loss of Coolant Accident) and the LRA (Locked Rotor Accident) are selected as limiting cases. A sensitivity analysis of accidental behavior with respect to various parameters during LOCA and LRA at Kori Unit 1 is also undertaken for the following objectives: to determine the limiting parameters, to find the impact trend of the radiation dose, and to find the safety margin between AST and TID (Technical Information Document) methodologies. This work confirms that key parameters are particulate removal rate, decontamination factor, iodine chemical form, gap fraction, partitioning factor, and the impact of isotopes group. Comparing TID with AST, the radiation dose of TID is about 80% greater than that of AST under a LOCA, and about 60% greater than that of AST for the case of a LRA; thus the safety margin is remarkably increased when the AST is used. In this work, the sensitivity analysis results are presented in terms of a sensitivity index called the "NDD (Normalized Dose Difference)", which compares the impact of parameters with that of a reference case. These values are derived by using a combination of the leak rate (primary to secondary), iodine chemical form, gap fraction, partitioning factor, spray removal rate, source term, and other variables.

• Journal of the military operations research society of Korea
• /
• v.9 no.1
• /
• pp.69-74
• /
• 1983

This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction ${\beta}$ of the demand is backordered and the remaining fraction $1-{\beta}$ is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes ${\beta}\;=\;1$ and ${\beta}\;=\;0$ the model presented reduces to the usual backorders and lost sales case, respectively.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.733-741
• /
• 2008

Let T be Gauss transformation on the unit interval defined by T (x) = ${\frac{1}{x}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1149-1161
• /
• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.