• 대한수학회논문집
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• 제31권4호
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• pp.857-868
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• 2016

Let (X, ${\mu}$) be a generalized topological space (GTS) and $\mathcal{H}$ be a hereditary class on X due to $Cs{\acute{a}}sz{\acute{a}}r$ [8]. In this paper, we define an operator $()^{\circ}:\mathcal{P}(X){\rightarrow}\mathcal{P}(X)$. By setting $c^{\circ}(A)=A{\cup}A^{\circ}$ for every subset A of X, we define the family ${\mu}^{\circ}=\{M{\subseteq}X:X-M=c^{\circ}(X-M)\}$ and show that ${\mu}^{\circ}$ is a GT on X such that ${\mu}({\theta}){\subseteq}{\mu}^{\circ}{\subseteq}{\mu}^*$, where ${\mu}^*$ is a GT in [8]. Moreover, we define and investigate ${\mu}^{\circ}$-codense and strongly ${\mu}^{\circ}$-codense hereditary classes.

• Bulletin of the Korean Chemical Society
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• 제9권2호
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• pp.101-105
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• 1988

The ab initio effective valence shell Hamiltonian method, based on quasidegenerate many-body perturbation theory, is generalized to calculate molecular properties as well as the valence state energies which have previously been determined for atoms and small molecules. The procedure requires the evaluation of effective operator for each molecular property. Effective operators are perturbatively expanded in powers of correlation and contain contributions from excitations outside of the multireference valence space. To demonstrate the validity of this method, calculations for dipole moments of several low lying valence states of OH, $OH^+$, and $OH^-$ to first order in the correlations have been performed and compared with configuration interaction calculations.

• Bulletin of the Korean Chemical Society
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• 제4권1호
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• pp.17-25
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• 1983

The hyperfine integrals for 4d orbitals have been evaluated adopting a general method which is applicable to a general vector, R, pointing arbitrary direction in space. The operator and the spherical harmonic part of 4d orbitals are expressed in terms of R and r$_{N}$ and the exponential part, r$^{2}$exp(-2${\beta}$r), of 4d orbitals is also translated as a function of R and r$_{N}$ and then integration is performed. The radial integrals for 4d orbitals are tabulated in analytical forms. The hyperfine integrals for 4d orbitals are also represented in analytical forms, using the specific formulas of radial series which we found.

• 충청수학회지
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• 제24권2호
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• pp.163-169
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• 2011

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• 대한수학회보
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• 제56권3호
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• pp.621-629
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• 2019

In this paper, we present a local convergence analysis of a three point method with convergence order $1.839{\ldots}$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

• Annals of Fuzzy Mathematics and Informatics
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• 제16권3호
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• pp.337-361
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• 2018

We introduce and study some basic properties of rough $I_{\lambda}$-statistical convergent of weight g (A), where $g:{\mathbb{N}}^3{\rightarrow}[0,\;{\infty})$ is a function statisying $g(m,\;n,\;k){\rightarrow}{\infty}$ and $g(m,\;n,\;k){\not{\rightarrow}}0$ as $m,\;n,\;k{\rightarrow}{\infty}$ and A represent the RH-regular matrix and also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence of weight g (A) limits of a triple sequence of Bernstein-Stancu polynomials.

• 항공우주시스템공학회지
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• 제15권2호
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• pp.36-44
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• 2021

Unmanned aerial vehicles (UAVs) are increasingly needed as they can replace manned aircrafts in dangerous military missions. However, because of their low autonomy, current UAVs can execute missions only under continuous operator control. To overcome this limitation, higher autonomy levels of UAVs based on autonomous situational awareness is required. In this paper, we propose an autonomous situational awareness software consisting of situation awareness management, threat recognition, threat identification, and threat space analysis to detect dynamic situational change by external threats. We implemented the proposed software in real mission computer hardware and evaluated the performance of situational awareness toward dynamic radar threats in flight simulations.

• 대한수학회보
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• 제58권1호
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• pp.205-215
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• 2021

In [1], Beznosova proved that the bound on the norm of the dyadic paraproduct with b ∈ BMO in the weighted Lebesgue space L2(w) depends linearly on the Ad2 characteristic of the weight w and extrapolated the result to the Lp(w) case. In this paper, we provide the weighted norm estimates of the dyadic paraproduct πb with b ∈ VMO and reduce the dependence of the Ad2 characteristic to 1/2 by using the property that for b ∈ VMO its mean oscillations are vanishing in certain cases. Using this result we also reduce the quadratic bound for the commutators of the Calderón-Zygmund operator [b, T] to 3/2.

• 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.