• 대한수학회보
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• 제58권6호
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.459-465
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• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.40.6-40
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• 2001

Fuzzy controls are widely used in industrial fields using experts knowledge base for its high degree of performance. Genetic Algorithm(GA) is one of the numerical method that has an advantage of optimization. In this paper, we present an acquisition method of fuzzy rules using genetic algorithm. Knowledge of the system is the key to generating the control rules. As these rules, a system can be more stable and it reaches the control goal the faster. To get the optimal fuzzy control rules and the membership functions, we use the GA instead of the experts knowledge base. Information of the system is coded the chromosome with suitable phenotype. Then, it is operated by genetic operator, and evaluated by evaluation function. Passing by the decoding process with the fittest chromosome, the genetic algorithm can tune the fuzzy rules and the membership functions automatically ...

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.855-867
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• 2022

This study finds three different solutions (3-Sol's) for the fourth order nonlinear discrete anisotropic equations (DAE) with real parameter. We use the variational method(VM) and 𝜙_p-Laplacian operator (𝜙_p-LO) to prove the main results. In the following paper, we take the parameters λ, 𝜇 such that λ > 0 and 𝜇 ≥ 0 into consideration.

• 한국정밀공학회지
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• 제12권6호
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• pp.37-44
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• 1995

Grinding is used for machining high precision parts with high additional value. However, the grinding operation needs high skill and long experience of an operator because of a lack of the scientific knowledge and engineering principles. Also, the wheel and grinding conditions affect grinding results. For these reasons, it is difficult to construct computer integrated manufacturing system(CIMA). Therefore, it is necessary for Expert System to be informed of qualitative knowledge of grinding expert's skills and experiences. In this research, the Grinding Expert System is constructed by Fuzzy Decision Making Algorithm. Using this system, unskilled workers will be able to use the knowledge and experience of an expert.

• 대한수학회보
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• 제60권1호
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• pp.123-135
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• 2023

The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of α-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.

• 대한수학회보
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• 제60권3호
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• pp.763-774
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• 2023

If a paraSasakian manifold of dimension (2n + 1) represents Bach almost solitons, then the Bach tensor is a scalar multiple of the metric tensor and the manifold is of constant scalar curvature. Additionally it is shown that the Ricci operator of the metric g has a constant norm. Next, we characterize 3-dimensional paraSasakian manifolds admitting Bach almost solitons and it is proven that if a 3-dimensional paraSasakian manifold admits Bach almost solitons, then the manifold is of constant scalar curvature. Moreover, in dimension 3 the Bach almost solitons are steady if r = -6; shrinking if r > -6; expanding if r < -6.

• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.399-415
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• 2024

We looked at nonlocal controllability for Hilfer fractional differential equations with almost sectorial operator in this manuscript. We show certain necessary criteria for nonlocal controllability using the measure of noncompactness and the Mönch fixed point theorem. Finally, we provided theoretical and practical applications are given to demonstrate how the abstract results might be applied.

• Korean Journal of Mathematics
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• 제32권2호
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• pp.213-218
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• 2024

Assume that at a certain locus there are three genotypes and that for every one progeny produced by an I^AI^A homozygote, the heterozygote I^AI^B produces. W. Choi found the adapted partial differential equations for the density and operator of the frequency for one gene and applied this adapted partial differential equations to several diploid model. Also, he found adapted partial differential equations for the diploid model against recessive homozygotes and in case that the alley frequency occurs after one generation of selection when there is no dominance. (see. [1, 2]). In this paper, we find the adapted partial equations for the model of selection against heterozygotes and in case that the allele frequency changes after one generation of selection when there is overdominance. Finally, we shall find the partial differential equation of general type of selection at diploid model and it also shall apply to actual examples. This is a very meaningful result in that it can be applied in any model.

• 대한수학회지
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• 제61권5호
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• pp.1035-1050
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• 2024

The Cameron-Martin translation theorem describes how Wiener measure changes under translation by elements of the Cameron-Martin space in an abstract Wiener space (AWS). Translation theorems for the analytic Feynman integrals also have been established in the literature. In this article, we derive a more general translation theorem for the analytic Feynman integral associated with bounded linear operators (B.L.OP.) on AWSs. To do this, we use a certain behavior which exists between the analytic Fourier-Feynman transform (FFT) and the convolution product (CP) of functionals on AWS. As an interesting application, we apply this translation theorem to evaluate the analytic Feynman integral of the functional $$F(x)={\exp}\left(-iq\int_{0}^{T}x(t)y(t)dt\right),\,y{\in}C_0[0,\,T],\;q{\in}{\mathbb{R}}\,{\backslash}\,\{0\}$$ defined on the classical Wiener space C₀[0, T].