• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.155-164
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• 2007

It is the objective of this paper to study further the notion of ${\Lambda}_s$-semi-${\theta}$-closed sets which is defined as the intersection of a ${\theta}$-${\Lambda}_s$-set and a semi-${\theta}$-closed set. Moreover, introduce some low separation axioms using the above notions. Also we present and study the notions of ${\Lambda}_s$-continuous functions, ${\Lambda}_s$-compact spaces and ${\Lambda}_s$-connected spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.224-230
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• 2013

In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy ${\theta}$-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy ${\theta}$-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy ${\theta}$-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy ${\theta}$-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.

• Publications of The Korean Astronomical Society
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• v.23 no.2
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• pp.25-29
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• 2008

Scattering of incident light by the interstellar dust is usually approximated by Henyey-Greenstein scattering phase function. Recently, Draine (2003) proposed a new analytic phase function with two parameters. We describe an algorithm to generate random numbers distributed according to the Draine’s function, and compare two phase functions. It is also derived exact solutions of two parameters for given values ${\langle}cos{\theta}{\rangle}$ and ${\langle}cos^2{\theta}{\rangle}$. It is found that Henyey-Greenstein function with g = ${\langle}cos{\theta}{\rangle}$ provides a good approximation for ${\lambda}\;>\;2000{\AA}$. At shorter wavelengths, more realistic phase function may be needed for radiative transfer models.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.761-766
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• 2013

We derive several modular equations and present their proofs based on concise algebraic computations. In addition, we establish explicit relations and formulas for some parameterizations for the theta functions ${\varphi}$ and ${\psi}$ and show some applications of the modular equations to evaluations of the cubic continued fraction and the theta function ${\psi}$.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.365-376
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• 2004

The purpose of this study is to show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met. In particular, as a basis function, we are interested in using a conditionally positive definite function $\Phi$ whose generalized Fourier transform is of the form $\Phi(\theta)\;=\;F(\theta)$\mid$\theta$\mid$^{-2m}$ with a bounded function F > 0.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.85-107
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• 2007

In this paper, we develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.303-312
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• 1995

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.135-149
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• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

• 한국해양학회지
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• v.5 no.2
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• pp.41-51
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• 1970

Periodic characters of water temperature in the regions of the Mishima and the Okinoshima were derived through the analysis of the five days interval data during 1914 to 1970 mainly. In terms of ten days mean temperatures, annual variation function of the Mishima region, Korea Strait, is F($\theta_d$)=17.45-5.34 cos $\theta_d$-3.77 sin $\theta_d$+0.62 sin $2\theta_d$ -0.52 sin $3\theta_d$, where $\theta_d$=$\frac{\pi}{18}$(d-2), d is the order of ten days period 1 to 36. And in the region of Okinoshima, Tsushima Strait, we find F($\theta_d$)=18.88-5.39 cos $\theta_d$-3.60 sin $\theta_d$+0.52 sin $2\theta_d$. The annual mean temperature is 17.4$^{\circ}C$ in the Mishima region, 18.9$^{\circ}C$ in the Okinoshima region, and the amplitudes of annual variation functions are 7$^{\circ}C$ in both regions with minimum temperature in the middle ten days of February, maximum in the middle ten days of August. The long term variations of surface water temperature with 12 5 years period were observed in the annual mean temperature, monthly mean temperatures and the fixed day temperatures of every year. In addition to these, relatively short term variations were also found significant periods of 3 years, 4 years and 2 years, respectively.

• The Mathematical Education
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• v.24 no.3
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• pp.13-14
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• 1986