• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1811-1822
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• 2018

In this paper, we exhibit the explicit forms of continued fraction expansions of a family of algebraic power series over a finite field and we study their asymptotic distribution of approximation exponents.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.699-709
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• 2016

Our paper is devoted to the study of certain diophantine equations on the ring of polynomials over a finite field, which are intimately related to algebraic formal power series which have partial quotients of unbounded degree in their continued fraction expansion. In particular it is shown that there are Pisot formal power series with degree greater than 2, having infinitely many large partial quotients in their simple continued fraction expansions. This generalizes an earlier result of Baum and Sweet for algebraic formal power series.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.79-83
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• 2011

In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $n^{th}$-term of the lower autocentral series of some finite abelian group.

• Structural Engineering and Mechanics
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• v.16 no.6
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• pp.655-674
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• 2003

Investigated in this study are the natural vibration characteristics of the coaxial cylindrical shells coupled with a fluid. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier series expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of the fluid-filled annulus and the boundary conditions on the modal characteristics of the coaxial shells is investigated using a finite element modeling.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.1-24
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• 2006

We study the theory of finite series in Chosun Dynasty Mathematics. We divide it into two parts by the publication of Lee Sang Hyuk(李尙爀, 1810-?)'s Ik San(翼算, 1868) and then investigate their history. The first part is examined by Gyung Sun Jing(慶善徵, 1616-?)'s Muk Sa Jib San Bub(默思集算法), Choi Suk Jung(崔錫鼎)'s Gu Su Ryak(九數略), Hong Jung Ha(洪正夏)'s Gu Il Jib(九一集), Cho Tae Gu(趙泰耉)'s Ju Su Gwan Gyun(籌書管見), Hwang Yun Suk(黃胤錫)'s San Hak Ib Mun(算學入門), Bae Sang Sul(裵相設)'s Su Gye Soe Rok and Nam Byung Gil(南秉吉), 1820-1869)'s San Hak Jung Ei(算學正義, 1867), and then conclude that the theory of finite series in the period is rather stable. Lee Sang Hyuk obtained the most creative results on the theory in his Ik San if not in whole mathematics in Chosun Dynasty. He introduced a new problem of truncated series(截積). By a new method, called the partition method(分積法), he completely solved the problem and further obtained the complete structure of finite series.

• Journal of KSNVE
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• v.6 no.3
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• pp.297-303
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• 1996

The general approach using sine series expansions was represented to evaluate the radiation loading from a vibrating surface on a simply supported cylinder. In this paper, the fluid-loading coefficients (radiation impedance) for a submerged finite cylindrical shell with an arbitrary end condition are defined and evaluated. The vibrations of cylindrical shell are expressed by using cosine series expansions to analyze the radiation impedance for a finite cylindrical shell. It is possible to represent the displacements at both ends of cylindrical shell in comparison with sine series. The direct and cross modal components of fluid-loading coefficients are shown and the validity of cosine series expansions are verified from the results of numerical computations. This approach and results are directly applicable in the analysis of sound radiation from subemerged finite cylindrical shell with arbitrary end conditions.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2005.10a
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• pp.418-422
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• 2005

In this study, the die design and die series on the surface residual stress of cold drawn eutectoid steel wire has been investigated. Test pieces were fabricated using die series with different mean and final reduction ratio. Surface residual stresses in the axial direction were measured by X-ray diffraction, Broker's 2-dimensional GADDS system. Results were compared with stress profiles which were calculated by 3D and 2D finite element simulation, Hibbitt's ABAQUS 6.4 program in Finite Element Analysis. By means of FEA method, optimal die shape considering delta-parameter were induced and applied in order to determine die sequence designs. Balance of the drawing stresses was also introduced to optimize die sequence.

• Transactions of Materials Processing
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• v.15 no.2 s.83
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• pp.153-157
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• 2006

In this study, the die design and die series on the surface residual stress of cold drawn eutectoid steel wire have been investigated. Test pieces were fabricated using die series with different mean and final reduction ratios. Surface residual stresses in the axial direction were measured by X-ray diffraction, Bruker's 2-dimensional GADDS system. The results were compared with stress profiles that were calculated by 3D and 2D finite element simulations, ABAQUS 6.4 program in finite element analysis(FEA). By means of the FEA method, optimal die shape considering delta-parameter were induced and applied in order to determine die sequence designs. Balance of the drawing stresses was also introduced to optimize die sequence.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.18-23
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• 1993

In this paper, we attempt to estimate the state of a finite state system. In such system, we can observe time series data which has some significant behaviors corresponding to its system states. The behavior is characterized by feature parameters extracted from time series. Our thought is that the system output time series data is expressed as a sequence of behavior patterns which are represented by clusters in feature parameters space. An algorithm jointing fuzzy clustering to fuzzy finite state transition model is suggested.

• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.