• 대한전기학회:학술대회논문집
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• 대한전기학회 2008년도 춘계학술대회 논문집 전기기기 및 에너지변환시스템부문
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• pp.9-12
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• 2008

Mathematical singularities of circuit equations with three-phase ideal transformer connections are studied. Three-wired wye-wye connections, delta-delta connections, and primary four-wired wye-delta connections are singular. The matrices of their circuit equations have zeros in their eigenvalues. Three-wired wye-delta connections, wye-wye-delta connections, and primary four-wired wye-wye connections are not singular. The physical meaning of their singularities is that they are sensitive and prone to be ill-conditioned. Equivalent shunt admittances representing ion losses and magnetizing inductances make the singular matrices non-singular in wye-connected circuits. And, equivalent series impedances representing copper losses and leakage inductances make the singular matrices non-singular in delta-connected circuits. The tableau analysis is used for the study.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.281-292
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• 2009

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.

• 대한수학회보
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• 제48권2호
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• pp.261-275
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• 2011

We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) singulr function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than 0 and the packing dimension of the infinite derivative points of the RNT singular function is less than 1. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the ($\tau$, $\tau$ - 1)-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.

• 호남수학학술지
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• 제29권4호
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• pp.701-721
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• 2007

Recently, a new singular function(NSF) method was posed to get accurate numerical solution on quasi-uniform grids for two-dimensional Poisson and interface problems with domain singularities by the first author and his coworkers. Using the singular function representation of the solution, dual singular functions, and an extraction formula for stress intensity factors, the method poses a weak problem whose solution is in $H^2({\Omega})$ or $H^2({\Omega}_i)$. In this paper, we show that the singular functions, which are not in $H^2({\Omega})$, also satisfy the integration by parts and note that this fact suggests the possibility of different choice of the weak formulations. We show that the original choice of weak formulation of NSF method is critical.

• 한국소음진동공학회논문집
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• 제11권9호
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• pp.431-438
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• 2001

This paper present experimental results of source identification for non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method can\`t be applied for a non-minimum phase system, the reason is that the system has ill-conditioning. Therefore, in this study to execute an effective inversion, SVD inverse technique is introduced. In a Non-minimum phase system, its system matrix may be singular or near-singular and has one more very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property we could solve the ill-conditioned problem of the system and then verified it for the practical system(cantilever beam). The experimental results show that SVD inverse technique works well for non-minimum phase system.

• 제어로봇시스템학회논문지
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• 제6권1호
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• pp.1-7
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• 2000

This paper studies the delay-characteristics using the singular values and vectors of Hankel operators for input delay systems. First, the computational method of Hankel singular values and their corresponding singular vectors are introduced, and then it is analytically provea that all the Hankel singular vlues have a monotone increasing properties as the length of delay time increases. Furthermore, through a simple numerical example, it is shown that the Hankel singular values are dependent only on the ratio of the time constant of a lumped parameter system to the length of delay , and in case that the time constant is relatively larger than the delay time, the lumped parameter characteristic has a great influence on the input delay systems.

• 대한전자공학회논문지
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• 제25권12호
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• pp.1625-1632
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• 1988

This paper aims not only to introduce the concept of linear singular systems, geometric structure, and feedback but also to provide applications of the multivariable linear singular system theories to electric circuits which may appear in some electronic equipments. The impulsive or discontinuous behavior which is not desirable can be removed by the set of admissible initial conditions. The output-nulling supremal (A,E,B) invariant subspace and the singular system structure algorithm are applied to this double-input double-output electric circuit. The Weierstrass form of the pencil (s E-A) is related to the output-nulling supremal (A,E,B) invariant subspace from which the time domain solutions of the finite and the infinite subsystems are found. The generalized Lyapunov equation for this application with feedback is studied and finally, the use of orthogonal functions in singular systems is discussed.

• East Asian mathematical journal
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• 제38권5호
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• pp.603-610
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• 2022

In [6, 7] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L²(Ω). In this paper we consider a PDE with the input function f ∈ H¹(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.

• 충청수학회지
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• 제21권2호
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• pp.183-188
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• 2008

We will derive recursion formulas satisfied by the traces of singular moduli for the higher level modular function.

• 한국음향학회지
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• 제20권8호
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• pp.3-11
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• 2001

본 연구에서는 SVD (Singular Value Decomposition)를 이용하여 다중입력과 다중출력을 가지는 시스템에서의 입력을 알아내기 위해 역변환 필터를 구현하였다. SISO (Single-Input and Single-Output)시스템의 입력과 출력의 관계에 대한 행렬공식화 작업을 확장하여 MIMO (Multi-Input and Multi-Output)시스템에 적용하였다. 그리고 시간영역과 주파수영역에서 최소위상 (Minimum phase)시스템과 비최소위상 (Non-minimum phase)시스템에 대한 그 역벽환에 대해 알아보았으며 비최소 위상요소에 대한 효과적인 역변환을 위해 SVD를 도입하였다. 먼저 전체시스템 행렬의 특이값 (singular value)을 계산하고 시스템의 위상에 대해 알아본다. 전체시스템이 비최소 위상인 경우 하나 이상의 매우 작은 특이값을 가지며 이는 시스템의 최소 위상/비최소 위상에 대한 정보를 가짐을 알 수 있다. 이를 이용하여 전체시스템에 대한 근사적인 역변환 필터를 구할 수 있으며 보다 근사적인 역변환 필터를 얻기 위하여 특이벡터를 이용하여 근사적인 역변환 필터를 얻었다. 수치적 예는 이러한 역변환 필터 행렬의 이용에 대한 잠재성을 보여준다.