• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• Journal of The Korea Institute of Healthcare Architecture
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• v.29 no.2
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• pp.49-60
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• 2023

Purpose: This study aims to establish detailed spatial planning by identifying the needs for a seclusion module for emergency psychiatric patients. Methods: The necessity of medical space with seclusion function was analyzed from spatial, medical, and social perspectives. The needs for a space capable of performing three medical functions: protection, isolation, and treatment, was analyzed. Among various types of mobile medical facilities, seclusion space was considered suitable for utilizing modular construction methods, as it is the most rational method that can satisfy the environmental level of fixed healthcare facilities' space. Therefore, seclusion modules based on modular construction were planned, consisting of two protective units for stabilizing patients with psychiatric illness, one for treatment unit that can accommodate both internal and external treatment, and another one for an infectious disease isolation unit equipped with negative pressure equipment. Implications: This study analyzed the necessary medical functions of the interior space of the mobile stabilization module based on the spatial analysis of existing medical facilities, and proposed alternative spatial configurations according to treatment, seclusion, isolation functions.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.183-200
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• 2017

Zagier lift gives a relation between weakly holomorphic modular functions and weakly holomorphic modular forms of weight 3/2. Duke and Jenkins extended Zagier-lifts for weakly holomorphic modular forms of negative-integral weights and recently Bringmann, Guerzhoy and Kane extended them further to certain harmonic weak Maass forms of negative-integral weights. New Zagier-lifts for harmonic weak Maass forms and their relation with Bringmann-Guerzhoy-Kane's lifts were discussed earlier. In this paper, we give explicit relations between the two different lifts via direct computation.

• The Research Journal of the Costume Culture
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• v.20 no.2
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• pp.222-237
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• 2012

Air-containing fashion, which can offer diverse functions through the inflow and outflow of air, is highly relevant in today's mobile society, where people are experiencing a wider range of environments. This study attempts to suggest the possibility of air-containing multi-functional fashion that could continuously be utilized by developing a design for an air-containing jacket using modular systems. In this research, the modular systems in architecture and furniture design were referenced through a review of the literature for the purpose of establishing modular systems in fashion. Functions relevant to the mobility of today's society are derived from the results of advanced research and applied to the design of modules of the jacket. The modules are integrated through the modular systems. The folding and unfolding structure in architecture and furniture is applied as a folding system in fashion, the vertical accumulation structure as a layering system, and the horizontal integration structure as a combining system, and in addition, the containing system has emerged in fashion. Each module is designed to fulfill certain functions, such as cushioning, heat insulation, and portability. The folding system is utilized in designing the cushion module to support the neck and back of a wearer by making its hood and hem fold in the back. The application of a layering system was suggested by making the vest, combined with the neck cushion and back cushion via the combining system, layered with its insulation module. By applying the combining system, the hood that includes the neck cushion, the skirt that includes the back cushion, the body that includes the insulation module, and the sleeves can be connected and separated by a zipper. The applicability of this concept was proven by applying a developed design to an actual item.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.04a
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• pp.301-305
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• 1992

A mold plant is characterized by complex processes, frequent schedule changes, and lots of troubles. In order to control the production in mold plant efficiently, huge amount of informations are to be managed in the appropriate way. In this paper, a modular software system for production control is described, which is located between a higher level production planning system and a process control system. It contains the functions such as order processing, operations scheduling and control, tool managemant, NC program managememt including DNC functions, production data acquisition and progress control and statistics.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.465-480
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• 2011

B. C. Berndt established many identities about infinite series. In this paper, continuing his work, we find new identities about infinite series containing hyperbolic functions and trigonometric functions.

• Journal of the Korea Safety Management & Science
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• v.4 no.4
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• pp.73-85
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• 2002

The supply chain not only includes the manufacturer and suppliers, but also transporters, warehouses, retailers, and customers themselves. Within each organization, such as manufacturer, the supply chain includes all functions involved in filling a customer request. these functions include, but are not limited to, new product development, marketing, operation, distribution, finance, and customer service. Lean Supply chain coordination improves if all supplier of chain take actions that together increase total supply chain profits. To design of Modularity by the grouping supplier, the proposed method is to develop the most appropriate production system models in the Supply Chain Management which is necessity of the times and its importance. The objects of this study is development of model and cost analysis to the modular production system in Lean SCM. Introduction of modular production system in Lean SCM is effective in reducing the cost in processing, manufacturing, inventory holding, ordering, etc.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.223-236
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• 2016

We show how to evaluate the cubic continued fraction $G(e^{-{\pi}\sqrt{n}})$ and $G(-e^{-{\pi}\sqrt{n}})$ for n = 4^m, 4^−m, 2 · 4^m, and 2⁻¹ · 4^−m for some nonnegative integer m by using modular equations of degree 9. We then find some explicit values of them.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.919-920
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• 2011

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that ${\theta}_A(\tau)/{\theta}_B(\tau)$ is a rational function of J, satisfying a certain condition. Where ${\theta}_A(\tau)$ and ${\theta}_B(\tau)$ are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].