• Transactions on Control, Automation and Systems Engineering
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• 제3권4호
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• pp.242-249
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• 2001

In this paper, the open-loop state response of the two-time-scale systems by unified approach using the $\delta$-operator is presented with an example of the aircraft longitudinal dynamics. First, the $\delta$-operator system unifies both the continuous system and the discrete system simultaneously, and the $\delta$-operator approach improves the finite word-length characteristics. This saves more computing time than that of the discrete system. Second, the singular perturbation method by block diagonalization reduces the sizes and orders of the systems. This also reduces the floating-point operations (flops). The advantage of those two approaches is shown by comparing our results with the earlier ones in the illustrative example of the longitudinal motion of F-8 aircraft.

• 대한수학회지
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• 제31권2호
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• pp.169-177
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• 1994

• 한국지능시스템학회논문지
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• 제19권2호
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• pp.265-272
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• 2009

Fuzzy number intuitionistic fuzzy sets (FNIFSs), each of which is characterized by a membership function and a non-membership function whose values are trigonometric fuzzy number rather than exact numbers, are a very useful means to describe the decision information in the process of decision making. Wang [10] developed some arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator. In this paper, based on the FIFHA operator and the FIFWA operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as fuzzy number intuitionistic fuzzy decision matrices where each of the elements is characterized by fuzzy number intuitionistic fuzzy numbers, and the information about attribute weights is partially known. An example is used to illustrate the applicability of the proposed approach.

• 대한수학회지
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• 제58권6호
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• pp.1385-1405
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• 2021

Let A be a positive bounded linear operator acting on a complex Hilbert space (𝓗, ⟨·,·⟩). Let ω_A(T) and ║T║_A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (𝓗, ⟨·,·⟩_A), respectively, where ⟨x, y⟩_A := ⟨Ax, y⟩ for all x, y ∈ 𝓗. In this paper, we show with different techniques from that used by Kittaneh in [24] that $$\frac{1}{4}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A{\leq}{\omega}^2_A(T){\leq}\frac{1}{2}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A.$$ Here T^#_A denotes a distinguished A-adjoint operator of T. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the 𝔸-numerical radius of the operator matrix $\(\array{I&T\\0&-I}\)$ where 𝔸 = diag(A, A). In addition, several A-numerical radius inequalities for semi-Hilbert space operators are also established.

• 대한수학회지
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• 제45권4호
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• pp.1043-1056
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• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.465-472
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• 2010

In this paper, we consider two extreme sets of zero-term rank sum of fuzzy matrix pairs: $$\cal{z}_1(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=min\{z(X),z(Y)\}\};$$ $$\cal{z}_2(\cal{F})=\{(X,Y){\in}\cal{M}_{m,n}(\cal{F})^2{\mid}z(X+Y)=0\}$$. We characterize the linear operators that preserve these two extreme sets of zero-term rank sum of fuzzy matrix pairs.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2001년도 추계학술대회 논문집
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• pp.96-100
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• 2001

A method is presented for determining the free vibration characteristics of a rotating blade having nonuniform span wise properies and cantilevers boundary condition. The equations which govern the coupled the coupled flapwise, choirwise, 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 eigenvalues problem whose solution may be determined by conventional method. Computer results are compared with experimental data.

• 대한수학회지
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• 제47권1호
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• pp.71-81
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• 2010

We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme cases with respect to maximal column rank inequalities of matrix multiplications over semirings.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.287-307
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• 2016

Using the fixed point method, we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in matrix fuzzy normed spaces.

• Bulletin of the Korean Chemical Society
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• 제6권5호
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• pp.309-311
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• 1985

When a molecule is perturbed by an external field, the perturbed moecue can be described as a doubly perturbed system. Hartree-Fock operator in the absence of the field is the zeroth order Hamiltonian, and a correlation operator and the external field operator are perturbations. The effective Hamiltonian, which is a projection of the total Hamiltonian onto a small finite subspace (usually a valence space), has been formally derived. The influence of the external field to the molecular Hamiltonian itself has been examined within an effective Hamiltonian framework. The first order effective expectation values, for instance electromagnetic transition amplitudes, between valence states are found to be easily calculated - by simply taking matrix elements of the effective external field operator. Implications of the terms in perturbation expansion are discussed.