• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.173-178
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• 1996

In this paper, we discuss quasi-fuzzy H-closed space and introduce ${\theta}$-convergence of prefilter in fuzzy topological space. And we define ${\theta}$-closed fuzzy set using by ${\theta}$-convergence.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.51-57
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• 2010

In this paper we introduce and study the lacunary strong Zweier sequence spaces $N_{\theta}^O[Z]$, $N_{\theta}[Z]$ consisting of all sequences x = $(x_k)$ such that (Zx) in the space $N_{\theta}$ and $N_{\theta}^O$ respectively, which is normed. Also, prove that $N_{\theta}^O[Z}$, $N_{\theta}[Z}$, are linearly isomorphic to the space $N_{\theta}^O$ and $N_{\theta}$, respectively. And we study some connections between lacunary strong Zweier sequence and lacunary statistical Zweier convergence sequence.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.403-414
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• 2019

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin's result on bosonic operators, and the author's previous result on fermionic operators.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.815-828
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• 2006

Let {$V_{nk},\;k\;{\geq}\;1,\;{\geq}\;1$} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with $E\|X\|^{\frac{\alpha}{\gamma}+{\theta}}log^{\rho}(\|X\|)\;<\;{\infty}$ for some ${\rho}\;>\;0,\;{\alpha}\;>\;0,\;{\gamma}\;>\;0,\;{\theta}\;>\;0$ such that ${\theta}+{\alpha}/{\gamma}<2$. Let {$a_{nk},k{\geq}1,n{\geq}1$) be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.153-165
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• 2007

This paper deals with the empirical Bayes two-action problem of testing $H_0\;:\;{\theta}{\leq}{\theta}_0$: versus $H_1\;:\;{\theta}>{\theta}_0$ using a linear error loss for some discrete nonexponential families having probability function either $$f_1(x{\mid}{\theta})=(x{\alpha}+1-{\theta}){\theta}^x\prod\limits_{j=0}^x\;(j{\alpha}+1)$$ or $$f_2(x{\mid}{\theta})=[{\theta}\prod\limits_{j=0}^{x-1}(j{\alpha}+1-{\theta})]/[\prod\limits_{j=0}^x\;(j{\alpha}+1)]$$. Two empirical Bayes tests ${\delta}_n^*\;and\;{\delta}_n^{**}$ are constructed. We have shown that both ${\delta}_n^*\;and\;{\delta}_n^{**}$ are asymptotically optimal, and their regrets converge to zero at an exponential decay rate O(exp(-cn)) for some c>0, where n is the number of historical data available when the present decision problem is considered.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.111-118
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• 2006

The present paper investigates the weighted $L^1$-convergence of Gr$\ddot{u}$nwald interpolatory operators based on the zeros of the second Chebyshev polynomials $U_n(x)=\frac{sin(n+1)\theta}{sin\theta}$. The approximation rate is sharp.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.5
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• pp.1-7
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• 2020

This study examines the processing and performance of an f-theta lens, one of the main components used in laser printer and laser scanning systems. To design an f-theta lens, the optical path of the components of the laser scanning unit f-theta lens, cylinder lens, and collimator lens must be identified. The goal after machining the master f-theta lens is to understand the optical properties, root mean square, and peak to valley.

• 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.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.