• 대한수학회보
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• 제46권2호
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• pp.229-234
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• 2009

We find congruences for the t-expansion coefficients of a Drinfeld modular form for ${\Gamma}^+_0$(Q), where Q is a monic irreducible polynomial. As an application we obtain new congruence relations for the t-expansion coefficients of Drinfeld modular forms for ${GL_2}(\mathbb{F}_q[T])$.

• 비파괴검사학회지
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• 제25권3호
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• pp.163-170
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• 2005

A modular Gaussian beam model is developed to simulate some ultrasonic testing configurations where multiple interfaces are involved. A general formulation is given in a modular matrix form to represent the Gaussian beam propagation with multiple interfaces. The ultrasonic transducer fields are modeled by a multi-Gaussian beam model which is formed by superposing 10 single Gaussian beams. The proposed model, referred to as "MMGB" (modular multi-Gaussian beam) model, is then applied to a typical contact and angle beam testing configuration to predict the output signal reflected from the corner of a vertical crack. The resulting expressions given in a modular matrix form are implemented in a personal computer using the MATLAB program. Simulation results are presented and compared with available experimental results.

• 충청수학회지
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• 제25권4호
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• pp.687-689
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• 2012

We find an upper bound on the least positive exponent of a nonzero Fourier coefficient for a modular form with a nonzero constant term for ${\Gamma}_0(N)$ under certain conditions where N is a prime number $p$ or $2p$.

• 대한수학회지
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• 제34권4호
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• pp.809-824
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• 1997

With the primitive orders in quaternion algebra, theta series associated with these orders are constructed. Here, we studied the space of modular forms generated by these theta series.

• 대한수학회논문집
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• 제24권2호
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• pp.181-185
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• 2009

The Drinfeld modular function ${\mu}$ is a generator of the function field of the Drinfeld modular curve $X_0(T)$ and has an t-expansion with the integral coefficients at infinity. In this paper, we show that the coefficients of ${\mu}$ has congruence properties modulo powers of T.

• 대한수학회보
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• 제54권6호
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• pp.2155-2163
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• 2017

Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.

• Advances in concrete construction
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• 제15권6호
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• pp.377-389
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• 2023

In this study, an improved modular arch system with the lower arch space composed of a precast arch block and an outrigger was proposed as an underground culvert, and its applicability and structural behaviors were confirmed. This modular arch culvert structure with vertical walls was designed using precast blocks and by adjusting the placement spacing of concrete blocks to the upper part form an arch shape and the lower part form a vertical wall shape, based on previously researched modular arch systems. Owing to the vertical wall of the proposed modular arch system, it is possible to secure a load-carrying capacity and an arch space that can sufficiently resist the earth pressure generated from the backfill soil and loading on the arch system. To verify the structural characteristics, and applicability of the proposed modular precast arch culvert structure, a full-scale modular culvert specimen was fabricated, and a loading test was conducted. By examining its construction process and loading test results, the applicability and constructability of the proposed structure were analyzed along with its structural characteristics. In addition, its the structural predictability and safety for the applicability were evaluated by comparing the construction process and loading test results with the FE analysis results.

• 대한수학회지
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• 제49권2호
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• pp.293-314
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• 2012

We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group ${\Gamma}_1$(1, 2) to Siegel modular cusp forms over certain subgroups ${\Gamma}^{para}$(t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 봄 학술발표회 논문집
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• pp.751-756
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• 2001

Permanent-Form is one of system forms for reducing human labor, work costs, oscillation, noise, construction wastes and so on. Permanent-Form is made from precast method in facilities. and carried in construction site to assemble with no demolding. The biggest expense to produce Permanent-Form is about manufacturing mold. To satisfy various size of building member, the same number of manufacturing mold is needed. In this paper, studied about manufacturing mold module for acquiring economic merit and construction member safety. Permanent-Form is member stress and structural analyzed if temporary equipment were used. The result of this study is below. (1) Column sizes of Permanent-Form are 47 kinds of prototype that based on Modular coordination's basic module. 4 pieces or 6 pieces are composed basically. (2) For beam size modular coordination, standard height and width of beam are 150mm and 100mm. It brings 24 kinds of prototype. 4 pieces or 5 pieces are composed basically. (3) Structural analysis value of modular member is like this Column member shows 9.4 to 85kgf/$cm^{2}$ stress distribution and beam member shows 6.3 to 95kgf/$cm^{2}$ stress distribution. Constructing permanent form could have structural safety with use of temporary equipment

• 충청수학회지
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• 제20권4호
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• pp.375-386
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• 2007

Let p be a prime and $f(z)=\Sigma_{n}a(n)q^n$ be a weakly holomorphic modular function for ${\Gamma}^*_0(p)$ with a(0) = 0. We use Bruinier and Funke's work to find the generating series of modular traces of f(z) as Jacobi forms.