• Korean Journal of Computational Design and Engineering
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• v.8 no.4
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• pp.243-253
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• 2003

This paper presents a new geometric morphing algorithm for polygons based on a simple geometric structure called direction map, which is mainly composed of a circular list of direction vectors defined by two neighboring vertices of a polygon. To generate a sequence of intermediate morphing shapes, first we merge direction maps of given control shapes based on a certain ordering rule of direction vectors, and scale the length of each direction vectors using Bezier or blossom controls. We show that the proposed algorithm is an improvement of the previous methods based on Minkowski sum (or convolution) in th aspects of computational efficiency and geometric properties.

• Honam Mathematical Journal
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• v.15 no.1
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• pp.75-85
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• 1993

For A and B, $-1{\leq}B<A{\leq}1$, let P[A, B] be the class of functions p analytic in the unit disk E with P(0) = 1 and subordinate to $\frac{1+Az}{1+Bz}$. We introduce the class $T_{\alpha}[A,B]$ of functions $f:f(z)=z+\sum\limits_{n=2}^{{\infty}}a_nz^n$ which are analytic in E and for $z{\in}E$, ${\alpha}{\geq}0$, $[(1-{\alpha}){\frac{f(z)}{z}}+{\alpha}f^{\prime}(z)]{\in}P[A,B]$. It is shown that, for ${\alpha}{\geq}1$, $T_{\alpha}[A,B]$ consists entirely of univalent functions and the radius of univalence for $f{\in}T_{\alpha}[A,B]$, $0<{\alpha}<1$ is obtained. Coefficient bounds and some other properties of this class are studied. Some radii problems are also solved.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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• pp.636-642
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• 2012

Delay-and-sum (DAS) Planar Beamforming has been a widely used Noise Source Identification Technique for the last decade. It is a quick one shot measurement technique being able to map sources that are larger than the array itself. The spatial resolution is proportional to distance between array and source, and inversely proportional to wavelength, thus the resolution is only good at medium to high frequencies. Improved algorithms using iterative de-convolution techniques offers up to ten times better resolution. The principle behind these techniques is described in this paper, as well as measurement examples from the automotive industry are presented.

• Proceedings of the Korea Information Processing Society Conference
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• 2021.05a
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• pp.457-458
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• 2021

딥러닝 알고리즘 중 DCNN(DeConvolutional Neural Network)은 이미지 업스케일링과 생성·복원 등 다양한 분야에서 뛰어난 성능을 보여주고 있다. DCNN은 많은 양의 데이터를 병렬로 처리할 수 있기 때문에 하드웨어로 설계하는 것이 유용하다. 최근 DCNN의 하드웨어 구조 연구에서는 overlapping sum 문제를 해결하기 위해 deconvolution 필터를 convolution 필터로 변환하는 TDC(Transforming the Deconvolutional layer into the Convolutional layer) 알고리즘이 제안되었다. 하지만 TDC를 CPU(Central Processing Unit)로 수행하기 때문에 연산의 최적화가 어려우며, 외부 메모리를 사용하기에 추가적인 전력이 소모된다. 이에 본 논문에서는 저전력으로 구동할 수 있는 FPGA 기반 TDC 하드웨어 구조를 제안한다. 제안하는 하드웨어 구조는 자원 사용량이 적어 저전력으로 구동 가능할 뿐만 아니라, 병렬 처리 구조로 설계되어 빠른 연산 처리 속도를 보인다.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.10
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• pp.1005-1011
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• 2011

In this paper, we present a marching-on-in-degree(MOD) finite difference method(FDM) based on the Helmholtz wave equation for analyzing transient electromagnetic responses in a general dispersive media. The two issues related to the finite difference approximation of the time derivatives and the time consuming convolution operations are handled analytically using the properties of the Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity with a finite sum of orthogonal Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from finite difference time-domain(FDTD) to a finite difference formulation through a Galerkin testing. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, and Lorentz dispersive medium.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.937-942
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• 2009

In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.85-101
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• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.3
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• pp.156-162
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• 2007

The parallel beam SPECT system acquires projection data by using collimators in conjunction with photon detectors. The projection data of the parallel beam SPECT system is, however, blurred by the point response function of the collimator that is used to define the range of directions where photons can be detected. By increasing the number of parallel holes per unit area in collimator, one can reduce such blurring effect. This approach also, however, has the blurring problem if the distance between the object and the collimator becomes large. In this paper we consider correction methods for artifacts caused by non-circular orbit of parallel beam SPECT with many parallel holes per detector cell. To do so, we model the relationship between the object and its projection data as a linear system, and propose an iterative reconstruction method including artifacts correction. We compute the projector and the backprojector, which are required in iterative method, as a sum of convolutions with distance-dependent point response functions instead of matrix form, where those functions are analytically computed from a single function. By doing so, we dramatically reduce the computation time and memory required for the generation of the projector and the backprojector. We conducted several simulation studies to compare the performance of the proposed method with that of conventional Fourier method. The result shows that the proposed method outperforms Fourier methods objectively and subjectively.