• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.115-122
• /
• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.

• 대한수학회지
• /
• 제51권4호
• /
• pp.773-789
• /
• 2014

We consider linear operators on square matrices over antinegative semirings. Let ${\varepsilon}_k$ denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set ${\varepsilon}_1$ and the set ${\varepsilon}_2$, and those that preserve the set ${\varepsilon}_{n^2-2n+2}$ and the set ${\varepsilon}_{n^2-2n+1}$. We also characterize those linear operators that strongly preserve ${\varepsilon}_2$, ${\varepsilon}_{n^2-2n+2}$ or ${\varepsilon}_{n^2-2n+1}$.

• 한국정밀공학회지
• /
• 제11권1호
• /
• pp.97-107
• /
• 1994

The method is presented for determining the free vibration characteristics of a rotating blade having nonuniform spanwise properties and cantilever boundary condition. The equations which govern the coupled flapwise, chordwise and torsional motion of such a blade are solved using an integrating matrix method. By expressing the equation of motion in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary condition, the equations are formulated into an eigenvalue problem whose solution may be determined by conventional method. Computed results are compared with experimental data.

• Journal of Biosystems Engineering
• /
• 제26권1호
• /
• pp.21-28
• /
• 2001

Major deficiencies of current automation scheme including various robots for bioproduction include the lack of task adaptability and real time processing, low job performance for diverse tasks, and the lack of robustness of take results, high system cost, failure of the credit from the operator, and so on. This paper proposed a scheme that could solve the current limitation of task abilities of conventional computer controlled automatic system. The proposed scheme is the man-machine hybrid automation via tele-operation which can handle various bioproduction processes. And it was classified into two categories. One category was the efficient task sharing between operator and CCM(computer controlled machine). The other was the efficient interface between operator and CCM. To realize the proposed concept, task of the object identification and extraction of 3D coordinate of an object was selected. 3D coordinate information was obtained from camera calibration using camera as a measurement device. Two stereo images were obtained by moving a camera certain distance in horizontal direction normal to focal axis and by acquiring two images at different locations. Transformation matrix for camera calibration was obtained via least square error approach using specified 6 known pairs of data points in 2D image and 3D world space. 3D world coordinate was obtained from two sets of image pixel coordinates of both camera images with calibrated transformation matrix. As an interface system between operator and CCM, a touch pad screen mounted on the monitor and remotely captured imaging system were used. Object indication was done by the operator’s finger touch to the captured image using the touch pad screen. A certain size of local image processing area was specified after the touch was made. And image processing was performed with the specified local area to extract desired features of the object. An MS Windows based interface software was developed using Visual C++6.0. The software was developed with four modules such as remote image acquisiton module, task command module, local image processing module and 3D coordinate extraction module. Proposed scheme shoed the feasibility of real time processing, robust and precise object identification, and adaptability of various job and environments though selected sample tasks.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제5권4호
• /
• pp.286-290
• /
• 2005

We consider the poisson equation where the functions involved are periodic including the solution function. Let $R=[0,1]{\times}[0,l]{\times}[0,1]$ be the region of interest and let $\phi$(x,y,z) be an arbitrary periodic function defined in the region R such that $\phi$(x,y,z) satisfies $\phi$(x+1, y, z)=$\phi$(x, y+1, z)=$\phi$(x, y, z+1)=$\phi$(x,y,z) for all x,y,z. We describe a very simple method for solving the equation ${\nabla}^2u(x, y, z)$ = $\phi$(x, y, z) based on the cubic spline interpolation of u(x, y, z); using the requirement that each interval [0,1] is a multiple of the period in the corresponding coordinates, the Laplacian operator applied to the cubic spline interpolation of u(x, y, z) can be replaced by a square matrix. The solution can then be computed simply by multiplying $\phi$(x, y, z) by the inverse of this matrix. A description on how the storage of nearly a Giga byte for $20{\times}20{\times}20$ nodes, equivalent to a $8000{\times}8000$ matrix is handled by using the fuzzy rule table method and a description on how the shape preserving property of the Laplacian operator will be affected by this approximation are included.

• 한국음향학회지
• /
• 제36권1호
• /
• pp.1-11
• /
• 2017

본 연구에서는 두 변수 유리함수 근사법에 기반한 3차원 음향 포물선 방정식의 제곱근 연산자의 새로운 근사식을 제안한다. 이 근사식은 기존의 제곱근 연산자에 대한 근사 연구와 비교해서 두 가지의 장점을 가진다. 첫 번째는 광대역 각도 능력이다. 제안된 식은 방위각 $45^{\circ}$에서 3차원 음향 포물선 방정식의 거리 축으로부터 $62^{\circ}$까지 넓은 각도에 대해 정확도를 가지는데, 이 값은 기존에 연구된 3차원 음향 포물선 방정식 알고리즘의 각도 한계의 약 세 배이다. 두 번째로는 본 근사식의 분모는 수심과 횡 거리에 대한 연산자의 곱으로 표현된다는 점이다. 이러한 분할 형태는 3차원 포물선 방정식을 손쉽게 삼중대각행렬 방정식으로 변환할 수 있다는 점에서 수치해석에서 선호된다. 제안된 식의 성능을 검증하기 위해 위상 오차분석을 통해 타 근사법과의 비교 연구가 수행되었고, 제안된 방법은 가장 우수한 성능을 보였다.

• 대한수학회지
• /
• 제34권4호
• /
• pp.1029-1036
• /
• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Korean Journal of Mathematics
• /
• 제15권2호
• /
• pp.101-114
• /
• 2007

For an $m$ by $n$ nonnegative real matrix A, the maximal column rank of A is the maximal number of the columns of A which are linearly independent. In this paper, we analyze relationships between ranks and maximal column ranks of matrices over nonnegative reals. We also characterize the linear operators which preserve the maximal column rank of matrices over nonnegative reals.

• 대한수학회지
• /
• 제31권4호
• /
• pp.645-657
• /
• 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.

• 대한수학회지
• /
• 제45권3호
• /
• pp.771-780
• /
• 2008

Let $M_C=\(\array{A&C\\0&B}\)$ be a $2{\times}2$ upper triangular operator matrix acting on the Hilbert space $H{\bigoplus}K\;and\;let\;{\sigma}_w(\cdot)$ denote the Weyl spectrum. We give the necessary and sufficient conditions for operators A and B which ${\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w\(\array{A&C\\0&B}\)\;or\;{\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w(A){\cup}{\sigma}_w(B)$ holds for every $C{\in}B(K,\;H)$. We also study the Weyl's theorem for operator matrices.