• 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.

• International conference on construction engineering and project management
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• 2022.06a
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• pp.484-491
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• 2022

A paradigm shift in teaching modular construction in higher education and K-12 is proposed as a means to increase the future adoption of the modular construction technique. To this effect, a new education module is presented to STEM educators. This education module is based on LEGOs and directed towards educators in the architecture, engineering, and construction (AEC) industry. The main objectives of the education module are to increase interest and knowledge of modular construction, acknowledge the benefits of using 3D design with 4D scheduling, and create a simulating hands-on educational opportunity. The education module is designed to allow participants to experience a hands-on simulation of modular construction and stick-built construction through building a LEGO project. Participants are challenged to find the advantages and disadvantages in both construction systems first-hand and record their findings. Results are presented from the preliminary testing of this education model on a group of construction management students at the University of Nevada, Las Vegas. Overall, the survey results showed that the LEGO education module was successful at achieving the project's three main objectives: 1) increasing the participants' interest and knowledge of modular construction through an interactive project; 2) increasing the participants' understanding of the benefits of 3D design with 4D scheduling over the use of 2D drawings; and 3) creating a simulating hands-on educational opportunity to help participants compare modular construction to stick-built construction. In the end, this proposed a new LEGO education module addressing the problems identified from this study with more participants.

• Journal of KIISE
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• v.44 no.11
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• pp.1149-1155
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• 2017

Recently, with the development of communication technology, it has become possible to collect various sensor data that indicate the environmental stimuli within a space. In this paper, we propose a group emotion prediction system using a modular Bayesian network that was designed considering the psychological impact of environmental stimuli. A Bayesian network can compensate for the uncertain and incomplete characteristics of the sensor data by the probabilistic consideration of the evidence for reasoning. Also, modularizing the Bayesian network has enabled flexible response and efficient reasoning of environmental stimulus fluctuations within the space. To verify the performance of the system, we predict public emotion based on the brightness, volume, temperature, humidity, color temperature, sound, smell, and group emotion data collected in a kindergarten. Experimental results show that the accuracy of the proposed method is 85% greater than that of other classification methods. Using quantitative and qualitative analyses, we explore the possibilities and limitations of probabilistic methodology for predicting group emotion.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.31-44
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• 2006

We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We prove that a special class of intuitionitic fuzzy normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1997.10a
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• pp.121-124
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• 1997

This paper is concerned with the generation and use of modular BOM, which is typically utilized in representing product configurations for two-level master production schedule. A method called VCM (Value Clustering Method) is proposed to build modular BOMS. We adopted a where-used matrix to represent part-product relationships. VCM is a method that can identify modules of components based on the where-used matrix. The method uses product family group value, product value, and component value. This can facilitate retrieving information about modules, finding out alternative usage pattern of components, and recognizing modules used in a particular product.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.269-277
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• 2007

Let L := L(G) denote the classical modular Lie algebra of $E_6$-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for $E_8$-type in [4], we shall search for irreducible (=simple) L-modules in this paper.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• ETRI Journal
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• v.45 no.2
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• pp.203-212
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• 2023

In this study, we developed a co-located and space-shared multiple-input multiple-output (MIMO) antenna module with a modular design and high integration level. The proposed antenna pair includes a half-wavelength loop antenna and a dipole-type antenna printed on the front and back sides of a compact modular board. Owing to their modal orthogonality, these two independent antenna elements are highly self-isolated and free of additional decoupling components, even though they are assembled at the same location and within the same space. Thus, the proposed antenna is attractive in 5G MIMO systems. Furthermore, the proposed co-located and space-shared MIMO antenna module was employed in a 5G smartphone to verify their radiation and diversity performances. A 12 × 12 MIMO antenna system was simulated and fabricated using the proposed module. Based on the results, the proposed module can be employed in large-scale MIMO antenna systems for current and future terminal devices owing to its high integration, compactness, simple implementation, and inherent isolation.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Journal of Korean Association for Spatial Structures
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• v.20 no.3
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• pp.27-34
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• 2020

This paper examines the seismic performance and structural design of the ceiling bracket-type modular connection. The bracket-type system reduces the cross-sectional area loss of members and combines units using fitting steel plate, and it has been developed to be fit for medium-story and higher-story buildings. In particular, this study conducted the cyclic loading test for the performance of the C-type and L-type brackets, and compared the results. The test results were also compared with the commercial FEA program. In addition, the structural design process for the bracket-type modular connection was presented. The two connections, proposed as a result of the test results, were all found to secure the seismic performance level of the special moment steel frame. In the case of initial stiffness, the L-type bracket connection was found to be great, but in the case of the maximum moment or fully plastic moment, it was different depending on the loading direction.