• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.139-155
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• 2021

Using a modular transformation formula for a class of functions related to generalized non-holomorphic Eisenstein series, we find a new class of infinite series about identities, some of which include generalized formulae of several Berndt's results.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.395-406
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• 2023

As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(𝜏). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

• Journal of Korean Society of Steel Construction
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• v.19 no.3
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• pp.323-333
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• 2007

This paper presents a study that attempted to improve the site applicability of profile sheets and check the effects of bending reinforcement in composite profiled beams, and consequently, to suggest an improved modular-type CB2 and two types of bending reinforcement methods. As a result of the reinforcing and reforming modular profiled beam experiment conducted, CBIIshowed an adequate deformation capacity as well as a sufficient plastic plateau at the maximum load and thereafter. For all the specimens, an insignificant modular slip occurred while linear relations were kept constant, at up to approximately 50% of the maximum load and at constant linear relations. The experimental values were very low. Probably, due to the small-scale experiment, the area of the concrete for the concrete filling and covering might have been insufficient, which might have led to the failure to improve the strength. Comparing the results with the standard design stress, all the specimens-except for T16 and B16-indicated more than 0.9. Based on the standard design stress, the reinforced modular profiled beam was consideredto have positive applicability.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.837-858
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• 2015

In this paper, we realize the algebra of ${\mathbb{Z}}_2$ relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of [2]. Using the results of Graham and Lehrer in [1], we give the modular representations of the algebra of ${\mathbb{Z}}_2$-relations, signed partition algebras and partition algebras.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.761-766
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• 2013

We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function ${\psi}$.

• Journal of KIBIM
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• v.2 no.2
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• pp.37-45
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• 2012

Modular bridge construction enabling better productivity of design and construction by standardized members and robotic construction becomes an important issue in construction industry. Modular structures needs accurate information delivery between design, fabrication and construction processes. BIM (Building Information Modeling) based parametric modeling was proposed for the modular bridge substructure. Considering ranges of parameters of the modular bridge, fixed value, variables and relations were defined and these parametric models were applied to design, analysis and fabrication. Experience from development of new structures can be embedded in the 3D models, and the models provide efficient and precise knowledge delivery.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.561-568
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• 2017

Hurwitz zeta function occurs in various parts of mathematics. In particular, it plays an important role in some area of number theory. In this paper, using a certain transformation formula, we find some identities of relations between ${\zeta}(2n+1)$ and ${\zeta}(2n+1,{\alpha})$ for special values of ${\alpha}$.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.451-461
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• 2012

B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.647-707
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• 2023

In this article, we discuss and survey the recent progress towards the Schottky problem, and make some comments on the relations between the André-Oort conjecture, Okounkov convex bodies, Coleman's conjecture, stable modular forms, Siegel-Jacobi spaces, stable Jacobi forms and the Schottky problem.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.7
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• pp.263-272
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• 2016

Modular product design has contributed to flexible product modification and development, production lead time reduction, and increasing product diversity. Modular product design aims to develop a product architecture that is composed of detachable modules. These modules are constructed by maximizing the similarity of components based on physical and functional interaction analysis among components. Accordingly, a systematic procedure for clustering the components, which is a main activity in modular product design, is proposed in this paper. The first phase in this procedure is to build a component-to-component correlation matrix by analyzing physical and functional interaction relations among the components. In the second phase, network flow modeling is applied to find clusters of components, maximizing their correlations. In the last phase, a network flow model formulated with linear programming is solved to find the clusters and to make them modular. Finally, the proposed procedure in this research and its application are illustrated with an example of modularization for a vacuum cleaner.