• Journal of KSNVE
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• v.6 no.1
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• pp.65-70
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• 1996

The sensor response of a piezoelectric transducer embedded in a fluid loaded structure is modeled using a hybrid numerical approach. The structure is excited by an obliquely incident acoustic wave. Finite element modeling in the structure and fluid surrounding the transducer region, is used and a plane wave representation is exploited to match the displacement field at the mathematical boundary. On this boundary, continuity of field derivatives is enforced by using a penalty factor and to further achieve transparency at the mathematical boundary, drilling degrees of freedom (d.o.f.) are introduced to ensure continuity of all derivatives. Numerical results are presented for the sensor response and it is found that the sensor at that location is not only non-intrusive but also sensitive to the characteristic of the structure.

• Journal of Biosystems Engineering
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• v.17 no.1
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• pp.37-44
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• 1992

This study was intended to develop the design program of the working surface of moldboard-plow by use of the computer-aided design. The mathematical model of the working surfaces of moldboard-plows by use of computer graphics was developed and plotted in two dimension on three major planes. The surfaces of moldboard-plows were represented with "B-spline surface fitting" by selecting the twenty-five three-dimensional data that could well describe the working surface of moldboard-plow. The shape of moldboard-plow on three major planes was drawn for varied design parameters. The representation of the mathematical model for the working surfaces of various types of moldboard-plows was manipulated by translation, rotation and scaling about arbitrary axes in space. By using three-dimensional graphics techique to describe moldboard-plows, it was capable of plotting the three-dimensional shape of moldboard-plow easily and quickly in comparison with the existing design methods that were difficult to grasp the shape of moldboard-plow as a whole. The design theories of moldboard plow and three-dimensional computer graphic technique were applied to find out the improved reversible Jaenggi bottom. It was resulted in the newly developed shape of Jaenggi which may be used for improving the performance compared to existing ones.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.24-29
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• 1993

This paper describes a method for generating an initial hull form by using form parameters. As a mathematical representation of curves, B-spline curves are used as well as the polynomials used by Durand et al. The five basic control curves and the centerline contour are defined to give the boundary conditions for body plan by using above mentioned mathematical models. From these curves body plan is determined. Two additional curves which are concerned the position of matching point between the cylindrical form and the water line are proposed to get the preliminary faired water lines.

• Research in Mathematical Education
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• v.23 no.1
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• pp.23-45
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• 2020

Many researches proposed different models and concepts for the PCK. It is important to understand its composition. Most studies investigated the development of PCK and its influence on students' learning from the teachers' perspectives. We developed an instrument for assessing middle school students' perceptions of mathematics teachers' PCK (SPOMTPCK) to investigate the nature of PCK. Theoretical claims and empirical research in PCK were used to design questions and sub-scales for the SPOMTPCK. The face validity of the instrument was established by the expert mathematics teachers and students. A questionnaire consisting of 38 items on a five-point Likert-type scale was used for data collection from 799 middle school students. The exploratory factor analyses resulted in the development of a three-factor scale of 17 items that was proved valid and reliable, that is, pedagogical representation, understanding students and curriculum, and encouraging students' engagement. The Cronbach α coefficients of the scale was 0.935, and the Cronbach α coefficient of three factors were ranged from 0.721 to 0.912. The confirmatory factor analysis showed that the questionnaire has good construct validity and the fit indexes are good. MANOVA analysis of variance revealed that the differences in mathematics teachers' PCK identified by students of different school types and grades were statistically significant. It is a validate measurement to evaluate the perceived mathematics teachers' PCK for middle school students.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2150-2158
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• 2002

A recent research and development has the requirement for the optimization to shorten design time of modified or new product model and to obtain more precise engineering solution. General optimization problem must consider many conflicted objective functions simultaneously. Multi-objective optimization treats the multiple objective functions and constraints with design change. But, real engineering problem doesn't describe accurate constraint and objective function owing to the limit of representation. Therefore this study applies variance analysis on the basis of structure analysis and DOE to the vertical roller mill fur portland cement and proposed statistical design model to evaluate the effect of structural modification with design change by performing practical multi-objective optimization considering mass, stress and deflection.

• Structural Engineering and Mechanics
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• v.29 no.3
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• pp.289-300
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• 2008

The use of metric trial functions to represent the real stress field in what is called the unsymmetric finite element formulation is an effective way to improve predictions from distorted finite elements. This approach works surprisingly well because the use of parametric functions for the test functions satisfies the continuity conditions while the use of metric (Cartesian) shape functions for the trial functions attempts to ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, the issue of how to handle situations where there is locking along with mesh distortion has never been addressed. In this paper, we show that the use of a consistent definition of the constrained strain field in the metric space can ensure a lock-free solution even when there is mesh distortion. The three-noded Timoshenko beam element is used to illustrate the principles. Some significant conclusions are drawn regarding the optimal strategy for finite element modelling where distortion effects and field-consistency requirements have to be reconciled simultaneously.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.265-284
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• 2019

The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.

• Research in Mathematical Education
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• v.22 no.1
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• pp.19-33
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• 2019

While the field of mathematics education strives to promote equitable mathematics learning and identifies it as a core instructional practice, less is known about its effective enactment. As teachers' teaching practices are dependent on their views and beliefs, this study investigated 133 elementary pre-service teachers' (PSTs') interpretations of diverse learners' learning experiences and proposed accommodations for them as reflected in their lesson planning process. Findings showed that PSTs came up with some strategies that are often suggested in teacher education literature, such as using multiple modes of representation and various grouping strategies. However, their responses were generic in nature rather than specific to diverse learners. Also, it was noted that many PSTs' interchangeably referred to the English Language Learners (ELLs), struggling learners, and culturally diverse learners, inferring that they thought that culturally diverse students must have been ELLs and that ELLs or culturally diverse students must have been weaker students in math. We found that the PSTs used their own frames while filtering and discarding information about diverse student populations to develop instructional plans, rather than based on the results of assessments of learning. We suggest that it is the critical first step to unwrap PSTs' unproven assumptions to better equip them for working with all of their future students.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.917-928
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• 2022

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the finiteness of generalized local cohomology modules. Let M be a finitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension r^I(M, N) and artinianness dimension a^I(M, N) of M, N with respect to I by r^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not representable} and a^I(M, N) = inf{i ∈ ℕ₀ : H^I_i(M, N) is not artinian} and we show that a^I(M, N) = r^I(M, N) = inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)} ≥ inf{a^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)}. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N/∩_t>0I^tN is artinian we prove that inf{i : H^I_i(M, N) is not minimax}=inf{r^IR_𝔭 (M_𝔭,𝔭N) : 𝔭 ∈ Spec(R)＼Max(R)}.