• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.165-175
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• 2010

In the paper we consider deemed three mock theta functions introduced by Hikami. We have given their alternative expressions in double summation analogous to Hecke type expansion. In proving we also give a new Bailey pair relative to $a^2$. I presume they will be helpful in getting fundamental transformations.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.337-352
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• 2024

In this paper, first we show that all finite BCI-algebras are solvable. We then introduce the notion of a θ-pair for a maximal ideal of a BCI-algebra. Proving various properties of maximal θ-pairs, we use them to characterize solvable and nilpotent BCI-algebras.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.23 no.3
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• pp.245-249
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• 2010

Two dimensional(2D) pair-photonic crystals (pair-PCs) have been fabricated by a multiple-exposure nanosphere lithography (MENSL) method using the self-assembled nanospheres as lens-mask patterns and the collimated laser beam as a multiple-exposing source. The arrays of the 2D pair-PCs exhibited variable lattice structures and shape the control of rotating angle (${\Theta}$), tilting angle (${\gamma}$) and the exposure conditions. In addition, the base period or filling factor of pair-PCs as well as their shapes could be changed by experimental conditions and nanosphere size. A 1.18-${\mu}m$-thick resist was spincoated on Si substrate and the multiple exposure was carried out at change of ${\gamma}$ and ${\Theta}$. Images of prepared 2D pair-PCs were observed by SEM. We believe that the MENSL method is a suitable useful tool to realize the pair-periodic arrays of large area.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.377-382
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• 2001

A suboptimal control law in turbulent pipe flow is derived and tested. Two sensing variables ${\partial}p/{\partial}{\theta}\;|_w\;and\;{\partial}{\upsilon}_{\theta}/{\partial}r\;|_w$ are applied with two actuations ${\phi}_{\theta}$ and ${\phi}_r$. To test the suboptimal control law, direct numerical simulations of turbulent pipe flow at $Re_r=150$ are performed. When the control law is applied, a $13{\sim}23%$ drag reduction is achieved. The most effective drag reduction is made at the pair of ${\partial}{\upsilon}_{\theta}/{\partial}r\;|_w$ and ${\theta}_r$. An impenetrable virtual wall concept is useful for analyzing the near-wall suction and blowing. The virtual wall concept is useful for analyzing the near-wall behavior of the controlled flow. Comparison of the present suboptimal control with that of turbulent channel flow reveals that the curvature effect is insignificant.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.2
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• pp.345-352
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• 2002

A suboptimal control law in turbulent pipe flow is derived and tested. Two sensing variables ∂p/∂$\theta$│$\_$w/ and ∂v$\_$$\theta$/∂γ│$\_$w/ are applied with two actuations ø$\_$$\theta$/ and ø$\_$γ/. To test the suboptimal control law, direct numerical simulations of turbulent pipe flow at Re$\_$$\tau$/=150 are performed. When the control law is applied, a 13∼23% drag reduction is achieved. The most effective drag reduction is made at the pair of ∂v$\_$$\theta$/∂γ│$\_$w/ and ø$\_$γ/. An impenetrable virtual wall concept is useful for analyzing the near-wall suction and blowing. The virtual wall concept is useful for analyzing the near-wall behavior of the controlled flow. Comparison of the present suboptimal control with that of turbulent channel flow reveals that the curvature effect is insignificant.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.545-549
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• 1993

an alignment system in the X-and Y-directions an X-Y-.theta. stage driven by piezoelectric actuators is presented. A pair of quadruple gratings and a quadruple photo-detector are used. The difference between the two 0-th order moire signals in reflection with a relative spatial phase of 180.deg. is used in each direction to control the alignment of the X-Y-.theta. stage. The stage is aligned at the position where the difference is zero. The quadruple gratings are 10 mm * 10 mm, and of a binary square-type with a 1/2 duty cycle. Their pitches are 16 .mu.m. Alignment accuracy of .+-.20nm was obtained in this system.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.61-66
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• 2005

Natural convection flows in a cubical, air-filled cavity that has one pair of opposing faces isothermal at different temperatures, Th and Tc, the remaining faces having a linear variation from Tc to Th are numerically simulated by a new solution code(PowerCFD) using unstructured cell-centered method. Solutions are obtained for configurations with a Rayleigh number as high as 105 and three inclination angles ${\theta}$ of the isothermal faces from horizontal: namely ${\theta}=0$, 45 and $90^{\circ}$. Interesting features are presented in detail and comparisons are made with benchmark solutions and experimental results found in the literature. It is found that the code is capable of producing accurately the nature of the laminar convection in a cubical, air-filled cavity with differentially heated walls.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.649-662
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• 1999

A random vector =(X1,…, Xn) is conditionally weakly associated if and only if for every pair of partitions 1=(X$\pi$(k+1),…,X$\pi$(k)), 2=(X$\pi$(k+1),…,X$\pi$(n)) of P(1$\in$A│2$\in$B, $\theta$$\in$I) $\geq$P$\in$A│$\theta$$\in$I whenever A and B are open upper sets and $\pi$ is any permutation of {1,…,n}. In this note we develop some concepts of conditional positive dependence, which are weaker than conditional weak association but stronger than conditional positive orthant dependence, by requiring the above inequality to hold only for some upper sets and applying the arguments in Shaked (1982).