• 대한수학회지
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• 제54권5호
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• pp.1379-1410
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• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2011년도 추계학술대회 논문집
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• pp.124-129
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• 2011

An improved NDIF method is introduced to efficiently extract eigenvalues of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, membranes, and plates, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods (FEM and BEM). However, the NDIF method has the weak point that the system matrix of the NDIF method depends on the frequency parameter and, as a result, a final system equation doesn't take the form of an algebra eigenvalue problem. The system matrix of the improved NDIF method developed in the paper is independent of the frequency parameter and eigenvalues can be efficiently obtained by solving a typical algebraic eigenvalue problem. Finally, the validity and accuracy of the proposed method is verified in two case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to the exact method, the NDIF method or FEM(ANSYS).

• 한국소음진동공학회논문집
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• 제21권10호
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• pp.960-966
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• 2011

An improved NDIF method is introduced to efficiently extract eigenvalues and eigenmodes of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, membranes, and plates, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that the system matrix of the NDIF method depends on the frequency parameter and, as a result, a final system equation doesn's take the form of an algebra eigenvalue problem. The system matrix of the improved NDIF method developed in the paper is independent of the frequency parameter and eigenvalues and mode shapes can be efficiently obtained by solving a typical algebraic eigenvalue problem. Finally, the validity and accuracy of the proposed method is verified in two case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to the exact method, the NDIF method or FEM(ANSYS).

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 1999년도 추계종합학술대회
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• pp.248-251
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• 1999

We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-1, we may compute the updated estimate of this vector at i(oration n upon the arrival of new data. The RLS algorithm may be viewed as a special case of the Kalman filter. Indeed this special relationship between the RLS algorithm and the Kalman filter is considered. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. The resulting rate of convergence is therefore typically an order of magnitude faster than the simple LMS algorithm. This improvement in performance, however, Is achieved at the expensive of a large increase in computational complexity.

• Tribology and Lubricants
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• 제14권2호
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• pp.26-34
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• 1998

This paper presents a high-speed performance analysis of ball bearings with ceramic balls under thrust loads. The sliding velocity profiles between a ball and raceways were obtained by the 3-D quasi-dynamic equations of motion including both centrifugal force and gyroscopic moment derived by vector matrix algebra. The friction at the contact areas was obtained by the Bair-Winer's non-Newtonian rheological model and the Hamrock-Dowson's central film thickness in EHL analysis. The nonlinear equations were solved by the Newton-Raphson method and the underrelaxation iterative method. The friction torques and ball behaviors with various loads, ball materials, and contact angles were predicted by this model. It was shown that the friction torque was sensitive to thrust load and contact angle, and that the friction torque and the pitch angle of the bearing with ceramic balls are smaller than those of the bearing with steel balls.

• 한국지능정보시스템학회:학술대회논문집
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• 한국지능정보시스템학회 1999년도 추계학술대회-지능형 정보기술과 미래조직 Information Technology and Future Organization
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• pp.281-289
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• 1999

The objective of this paper is to propose a brand new interface mechanism to provide more intelligent decision making support for EC problems. Its main virtue is based on a numerical process mechanism by using an Extended AND-OR Graph (EAOG)-based logic algebra. Using this mechanism, decision makers engaged in electronic commerce (EC) can effectively deal with complicated decision making problems. In the field of traditional expert systems research, AND-OR Graph approach has been suggested as a useful tool for representing the logic flowchart of the forward and/or backward chaining inference methods. However, the AND-OR Graph approach cannot be effectively used in the EC problems in which real-time problem-solving property should be highly required. In this sense, we propose the EAOG inference mechanism for EC problem-solving in which heurisric knowledge necessary for intelligent EC problem-solving can be represented in a form of matrix. Finally, we have proved the validity of our approach with several propositions and an illustrative EC example

• 대한전자공학회논문지TC
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• 제42권8호
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• pp.1-10
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• 2005

본 논문에서는 대수 이론과 관련된 일반화된 치환 행렬로부터 저밀도 부호의 명시적 구성을 고찰하였으며, 순환공식과 치환행렬에 관한 재킷 역 블록 행렬을 설계하였다. 설계 결과로부터 제안 기법은 저밀도 부호를 얻기 위한 간단하며, 고속화된 기법임을 알 수 있다. 또한, $\pi$-회전 LDPC(low density parity check) 부호와 같은 구조화 LDPC 부호 역시 저밀도 재킷 역 블록 행렬임을 증명하였다.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.886-889
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• 2004

A simple macro triangle with drilling d.o.f.'s is proposed for plane stress problems based on IET(Individual element test) and finite element template. Three-node triangular element has geometrical advantages in preprocessing but suffers from bad performance comparing to other shapes of elements -especially quadrilateral. Main purpose of this study is to construct a high-performance linear triangular element with limited supplementary d.o.f.'s. A triangle is divided by three sub-triangles with drilling d.o.f.'s. The sub-triangle stiffness come from IET passing force-lumping matrix, so this assures the consistency of the element. The macro element strategy takes care of the element‘s stability and accuracy like higher-order stiffness in the F.E. template. The resulting element fits on the uses of conventional three-node. Benchmark examples show proposed element in closed form stiffness from CAS (Computer algebra system) gives the improved results without more computational efforts than others.

• 대한수학회지
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• 제31권4호
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• pp.645-657
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• 1994

If S is a semiring of nonnegative reals, which linear operators T on the space of $m \times n$ matrices over S preserve the column rank of each matrix\ulcorner Evidently if P and Q are invertible matrices whose inverses have entries in S, then $T : X \longrightarrow PXQ$ is a column rank preserving, linear operator. Beasley and Song obtained some characterizations of column rank preserving linear operators on the space of $m \times n$ matrices over $Z_+$, the semiring of nonnegative integers in [1] and over the binary Boolean algebra in [7] and [8]. In [4], Beasley, Gregory and Pullman obtained characterizations of semiring rank-1 matrices and semiring rank preserving operators over certain semirings of the nonnegative reals. We considers over certain semirings of the nonnegative reals. We consider some results in [4] in view of a certain column rank instead of semiring rank.