• 한국지능시스템학회논문지
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• 제20권3호
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• pp.434-440
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• 2010

In this paper, we define generalized induced linguistic aggregation operator called generalized induced linguistic ordered weighted harmonic mean(GILOWHM) operator. Each object processed by this operator consists of three components, where the first component represents the importance degree or character of the second component, and the second component isused to induce an ordering, through the first component, over the third components which are linguistic variables and then aggregated. It is shown that the induced linguistic ordered weighted harmonic mean(ILOWHM) operator and linguistic ordered weighted harmonic mean(LOWHM) operator are the special cases of the GILOWHM operator. Based on the GILOWHM and LWHM operators, we develop an approach to group decision making with linguistic preference relations. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

• 대한수학회논문집
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• 제34권3호
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• pp.863-879
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• 2019

In this paper we study the Myers' theorem for orientable Riemannian hypersurfaces under some restrictions on the mean curvature, the second-order mean curvature, or the divergence of the shape operator and give some estimates for the diameter of such hypersurfaces.

• 대한수학회보
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• 제41권2호
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• 대한수학회논문집
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• 제29권1호
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• pp.205-212
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• 2014

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The L-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small ${\varepsilon}$ > 0. An example is presented to illustrate the efficiency of the obtained results.

• 대한수학회지
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• 제44권3호
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.497-506
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• 2024

In this paper, some integral mean estimates for the polar derivative of a polynomial with complex coefficients are proved. We will see that these type of estimates are new in this direction and discuss their importance with respect to existing results comparatively. In addition, the obtained results provide valuable insights into the behavior of integrals involving operator preserving inequalities.

• 한국정보처리학회논문지
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• 제3권6호
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• pp.1607-1615
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• 1996

본 논문에서는 계산이 간단하면서 효과적으로 스케치 특징을 추출할수 있는 새로운 연산자 DBAH(differ-ence between arithmetic mean and harmonic mean) 를 제안하고,임계치를 자동으로 결정하는 퍼지 임계치 추론기를 제안한다. 제안한 연산자는 국부 밝기를 고려하며,매우 어두운 영역에서의 밝기변화에서는 낮은 출력을 나타내는 장점을 가진다. 또한 제안된 퍼지 임계치 추론기는 조작자의 개입 없이도 스케치 특징점을 매우 잘 검출한다.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.751-767
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• 2022

This paper deals with the Paneitz-Branson operator in compact Riemannian manifolds with negative Yamabe invariant. We start off by providing a new criterion for the positivity of the Paneitz-Branson operator when the Yamabe invariant of the manifold is negative. Another result stated in this paper is about the existence of a metric on a manifold of dimension 5 such that the Paneitz-Branson operator has multiple negative eigenvalues. Finally, we provide new inequalities related to the upper bound of the mean value of the Q-curvature.

• 대한수학회보
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• 제54권6호
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• pp.1981-1990
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• 2017

Let R be a root system in $\mathbb{R}^d$ with Coxeter-Weyl group W and let k be a nonnegative multiplicity function on R. The generalized volume mean of a function $f{\in}L^1_{loc}(\mathbb{R}^d,m_k)$, with $m_k$ the measure given by $dmk(x):={\omega}_k(x)dx:=\prod_{{\alpha}{\in}R}{\mid}{\langle}{\alpha},x{\rangle}{\mid}^{k({\alpha})}dx$, is defined by: ${\forall}x{\in}\mathbb{R}^d$, ${\forall}r$ > 0, $M^r_B(f)(x):=\frac{1}{m_k[B(0,r)]}\int_{\mathbb{R}^d}f(y)h_k(r,x,y){\omega}_k(y)dy$, where $h_k(r,x,{\cdot})$ is a compactly supported nonnegative explicit measurable function depending on R and k. In this paper, we prove that for almost every $x{\in}\mathbb{R}^d$, $lim_{r{\rightarrow}0}M^r_B(f)(x)= f(x)$.

• 대한수학회지
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• 제41권5호
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• pp.795-808
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• 2004

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.