• Journal of KSNVE
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• v.7 no.4
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• pp.637-644
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• 1997

In this paper, a method of finite element analysis is presented for efficient calculation of vibration characteristics of not only simply interconnected structure with cyclic symmetry but also multiply interconnected structure with cyclic symmetry by using discrete Fourier trandform by means of a computer with small memory in a short time. Simply interconnected structure means it is composed of substructures which are adjacent themselves in circumferential direction. First, a mathematical model of multiply interconnected structure with cyclic symmetry is defined. The multiply interconnected structure is partitioned into substructures with the same goemetric configuration and constraint eqauations to be satisfied on connecting boundaries are defined. Nodal displacements and forces are transformed into complex forms through discrete Fourier transform and then finite element analysis is performed for just only a representative substructure. In free vibration analysis, natural frequencies of a whole structure can be obtained through a series of calculation for a substructure along the number of nodal diameter. And in forced vibration analysis, forced response of whole structure can be achieved by using inverse discrete Fourier transform of results which come from analysis for a substructure.

• Bulletin of the Korean Chemical Society
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• v.16 no.11
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• pp.1015-1019
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• 1995

The electronic structures and properties of the neutral and multiply charged C60n ions (n=2+ to 6-) with spin states have been investigated by semi-empirical MNDO calculations. In the ground state, C601- has the lowest total energy and the highest binding energy. The neutral C60 ion is supposed to have a high ionization potential and a high electron affinity. The HOMO and LUMO positions are lower in the cationic C60 than in the anionic C60. The LUMO energy becomes increasingly positive from C601- to C606- and the HOMO energy becomes increasingly negative from C602+ to C60. The HOMO-LUMO gap of the neutral C60 ion is higher than that of the multiply charged C60 ions. From the HOMO-LUMO gap, it seems reasonable to expect that electrons of the multiply charged C60 ions will be more polarizable than those of the neutral C60 ion. The HOMO and LUMO energies increase as the negative charge increases.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.521-539
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• 2016

The structures of partitive and quotitive division of fractions are dealt with differently, and this led to using partitive division context for helping develop invert-multiply algorithm and quotitive division for common denominator algorithm. This approach is unlikely to provide children with an opportunity to develop an understanding of common structure involved in solving different types of division. In this study, I propose two approaches, measurement approach and isomorphism approach, to develop a unifying understanding of fraction division. From each of two approaches of solving quotitive division based on proportional reasoning, I discuss an idea of constructing a measure space, unit of which is a quantity of divisor, and another idea of constructing an isomorphic relationship between the measure spaces of dividend and divisor. These ideas support invert-multiply algorithm for quotitive as well as partitive division and bring proportional reasoning into the context of fraction division. I also discuss some curriculum issues regarding fraction division and proportion in order to promote the proposed unifying understanding of partitive and quotitive division of fractions.

• Advances in Computational Design
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• v.5 no.3
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• pp.277-289
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• 2020

This article describes the technology for constructing of a multiply-connected three-dimensional area's finite element representation. Representation of finite-element configuration of an area is described by a discrete set that consist of the number of nodes and elements of the finite-element grid, that are orderly set of nodes' coordinates and numbers of finite elements. Corresponding theorems are given, to prove the correctness of the solution method. The adequacy of multiply-connected area topology's finite element model is shown. The merging of subareas is based on the criterion of boundary nodes' coincidence by establishing a simple hierarchy of volumes, surfaces, lines and points. Renumbering nodes is carried out by the frontal method, where nodes located on the outer edges of the structure are used as the initial front.

• The Mathematical Education
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• v.50 no.3
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• pp.337-354
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• 2011

The purpose of the study was to investigate how students understand multiplication and division of fractions and how their understanding influences the solutions of fractional word problems. Thirteen students from 5th to 6th grades were involved in the study. Students' understanding of operations with fractions was categorized into "a part of the parts", "multiplicative comparison", "equal groups", "area of a rectangular", and "computational procedures of fractional multiplication (e.g., multiply the numerators and denominators separately)" for multiplications, and "sharing", "measuring", "multiplicative inverse", and "computational procedures of fractional division (e.g., multiply by the reciprocal)" for divisions. Most students understood multiplications as a situation of multiplicative comparison, and divisions as a situation of measuring. In addition, some students understood operations of fractions as computational procedures without associating these operations with the particular situations (e.g., equal groups, sharing). Most students tended to solve the word problems based on their semantic structure of these operations. Students with the same understanding of multiplication and division of fractions showed some commonalities during solving word problems. Particularly, some students who understood operations on fractions as computational procedures without assigning meanings could not solve word problems with fractions successfully compared to other students.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.385-403
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• 2018

Fraction division can be categorized as partitive division, measurement division, and the inverse of a Cartesian product. In the contexts of quotitive division and the inverse of a Cartesian product, the multiply-by-the-reciprocal algorithm is drawn well out. In this study, I analyze the potential and significance of the method of using $1{\div}$(divisor) as an alternative way of developing the multiply-by-the-reciprocal algorithm in the context of quotitive division. The method of using $1{\div}$(divisor) in quotitive division has the following advantages. First, by this method we can draw the multiply-by-the-reciprocal algorithm keeping connection with the context of quotitive division. Second, as in other contexts, this method focuses on the multiplicative relationship between the divisor and 1. Third, as in other contexts, this method investigates the multiplicative relationship between the divisor and 1 by two kinds of reasoning that use either ${\frac{1}{the\;denominator\;of\;the\;divisor}}$ or the numerator of the divisor as a stepping stone. These advantages indicates the potential of this method in understanding the multiply-by-the-reciprocal algorithm as the common structure of fraction division. This method is based on the dual meaning of a fraction as a quantity and the composition of times which the current elementary mathematics textbook does not focus on. It is necessary to pay attention to how to form this basis when developing teaching materials for fraction division.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.47 no.4
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• pp.38-45
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• 2015

Fold cracking is one of quality troubles of coated papers. In this study, the fold cracking of high grammage ($250g/m^2$) coated paper made with the different pulp composition and layer structure of base paper was investigated. The single layered, high grammage base paper was prepared by mixing of hardwood and softwood bleached kraft pulp fibers with the different ratios. The high grammage coated paper showed the higher fold cracking than low grammage coated paper because of the increase in thickness. The increase in the content of softwood pulp fibers reduced the fold cracking in the case of high grammage coated paper. When the creasing process was conducted before folding process, the fold cracking of coated paper decreased. By manufacturing the base paper with multiply structure, the fold cracking of coated paper could be reduced significantly, especially when the BCTMP and OCC were used as a middle layer and the creasing process was carried out. The delamination of layers in base paper affected the fold cracking positively.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.147-162
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• 2007

This paper reports an analysis of 19 Chinese and Korean middles school mathematics teachers' understanding of division by fractions. The study analyzes the teachers' responses to the teaching task of generating a real-world situation representing the meaning of division by fractions. The findings of this study suggests that the teachers' conceptual models of division are dominated by the partitive model of division with whole numbers as equal sharing. The dominance of partitive model of division constraints the teachers' ability to generate real-world representations of the meaning of division by fractions, such that they are able to teach only the rule-based algorithm (invert-and-multiply) for handling division by fractions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.1
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• pp.104-111
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• 1997

Accounting for the additional damages come out from non-proportional loading path effect, material damage according to crystal structure dependence was studied. Microscopic observations of damaged material by SEM(Scanning Electron Microscope) showed crystal structure dependence. Biaxial in-phase loaded specimens showed the slips of same direction, which pararell each other, but biaxial 90.deg. out-of-phase loaded specimens showed multiply crossed slips. S. H. Doong and D. F. Socie reported that wavy/planar or planar slip material showed the increase in the cyclic hardening level during non-proportional cycling. From these results, the additional hardening and non-proportional loading effects were related with slip mechanism, and the slip mechanism was related with crystal structure. In the present study, a damage mechanism which accounts for the non-proportional loading effect from crystal structure dependence was considered and applied to A17075-T651.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.12
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• pp.44-55
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• 2001

MAC(Multiply and ACcumulate) is the core operation of multimedia data processing. Because MAC units implemented on traditional DSP units or embedded processors have latency of three cycles and cannot operate on multiple data simultaneously, then, performances are seriously limited. Many high end general purpose microprocessors have SIMD MAC unit as a functional unit. But these high end MAC units must support pipeline structure for various operation modes and high clock frequency, which makes control logic complex and increases chip area. In this paper, a 64bit SIMD MAC unit for embedded processors is designed. It is implemented to have a latency of one clock cycle to remove pipeline control logics and a minimal area overhead for SIMD support is added to existing Booth multipliers.