• 대한조선학회논문집
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• 제44권5호
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• pp.534-541
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• 2007

This paper suggests the mathematical method for the estimation of the required engine output for WIG crafts. The engine size of a WIG craft Is a key parameter in the design stage, because WIGs should overcome the hump drag during the take-off. Therefore, it is very important for a WIG designer to estimate required power and state change during take-off. The mathematical method was developed based on the steady planing state model of a planing boat. Through numerical calculations on various take-off states, it was found that the suggested method could give reasonable estimation of required power and state change during take-off.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권3호
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• pp.419-423
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• 2003

The main purpose of this paper is to investigate effects of skewness and kurtosis on the one-sample test. We have found that type I error brought about a little bit change which is ignorable in relation to kurtosis. Also the change of type I error was completely based on skewness under the same size of the sample. We conclude that using t-test is more similar to robust than using z-test. In introductory statistics classes where data analysis includes techniques for detecting skewness, we recommend the t-test when skewness is smaller than the value 1 to the one-sample test for a mean when the variances is unknown using the probability of a type I error as the criterion of interest.

• 대한수학회지
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• 제58권3호
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• pp.723-740
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• 2021

Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.

• 대한수학회논문집
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• 제39권2호
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• 대한수학회지
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• 제44권4호
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• 대한수학회지
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• 제35권3호
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• pp.637-658
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• 1998

One-dimensional diffusion processes are characterized by Feller's data of canonical scales and speed measures and, if we apply the theory of spectral functions of strings developed by M. G. Krein, Feller's data are determined by paris of spectral characteristic functions so that theses pairs may be considered as invariants of diffusions under the homeomorphic change of state spaces. We show by examples how these invariants are useful in the study of one-dimensional diffusion processes.

• 대한수학회논문집
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• 제12권3호
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• pp.645-653
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• 1997

We study centrally symmetric orthogonal polynomials satisfying an admissible partial differential equation of the form $$ Au_{xx} + 2Bu_{xy} + Cu_{yy} + Du_x + Eu_y = \lambda_n y, $$ where $A, B, \cdots, E$ are polynomials independent of n and $\lambda_n$ is the eignevalue parameter depending on n. We show that they are either the product of Hermite polymials or the circle polynomials up to a complex linear change of variables. Also we give some properties of them.

• 호남수학학술지
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• 제32권1호
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• pp.101-112
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• 2010

Using some interesting convolution, we find kernels recovering the given function f. By a slight change of this convolution, we obtain an identity filter related to the Fourier series in the discrete time domain. We also introduce some techniques to decompose an impulse into several dilated pieces in the discrete domain. The detail examples deal with specific constructions of those decompositions. Also we obtain localized moving averages from a decomposition of an impulse to make hybrid Bollinger bands, that might give various strategies for stock traders.

• 대한수학회보
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• 제57권5호
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• pp.1251-1258
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• 2020

This paper establishes a formula changing the ring from a Noetherian local ring A of dimension d > 0 containing the residue field k to the polynomial ring in d variables k[X₁, X₂, …, X_d] for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of A by highest dimensional associated prime ideals of A.

• 대한수학회보
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• 제41권2호
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• pp.283-297
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• 2004

We have obtained a simplified model for the mush under the assumption of the temperature, the solid fraction and the vertical component of the velocity, depend on upward coordinate z only. We have found solutions in the asymptotical limit and solved numerically for the model.