• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.391-399
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• 1992

The analysis of the evaporative heat transfer in the inclined porous layer (0.deg.<.theta.<90.deg.) is made by using capillary model. The length of the evaporation zone is obtained numerically by integrating the differential equation using a Runge-Kutta algorithm. As a result, the length of the evaporation zone is inverse proportional to the dimensionless number, E(=Re*.phi./cos.theta.) representing the evaporation intensity, and the relationship of these parameters shows linear in the log graph.

• Proceedings of the Korean Society for Cognitive Science Conference
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• 2010.05a
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• pp.55-59
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• 2010

To examine iterocular interactions in normal subjects, we recorded EEG activity from channel O1 and O2 on 14 healthy subjects while checkerboard pattern reversals were presented to each eye with different interstimulus intervals (ISIs) ranging from 0 to 218 ms. When pattern reversals were presented asynchronously to each eye, P-1 activity evoked by each reversal was significantly suppressed compared to the activation evoked by synchronous reversals. Furthermore, when there was time delay between pattern reversals to each eye, theta (4-10 Hz) band power was also significantly decreased, whereas beta (10-30 Hz) band power was relatively preserved. Our results suggest that neural activity evoked by sustained but not yet reversed checkerboard from one eye might inhibit upcoming neural response evoked by reversed checkerboard from the other eye. Decreased P-1 activity might reflect such inhibitory interaction between two eyes. Also, decreased theta and preserved beta band power might reflect engagement of different neural circuit for binocular / monocular vision.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.655-669
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• 2010

In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(\kappa)$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}$, $q\;{\geq}\;1$. If a strictly feasible starting point is available and the parameter $q\;=\;\log\;\(1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}\)$, where $a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})$ iteration complexity.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.293-314
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• 2012

We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group ${\Gamma}_1$(1, 2) to Siegel modular cusp forms over certain subgroups ${\Gamma}^{para}$(t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.471-487
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• 2020

We find congruences modulo 32, 64 and 128 for the partition function ${\overline{PP}_o}(n)$, the number of overpartition pairs of n into odd parts, with the aid of Ramamnujan's theta function identities and some known identities of t_k(n), for k = 6, 7, where t_k(n) denotes the number of representations of n as a sum of k triangular numbers. We also find two Ramanujan-like congruences for ${\overline{PP}_o}(n)$ modulo 128.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1269-1281
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• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.

• 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).

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1379-1391
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• 2008

Let k be an imaginary quadratic field, ${\eta}$ the complex upper half plane, and let ${\tau}{\in}{\eta}{\cap}k,\;q=e^{{\pi}{i}{\tau}}$. For n, t ${\in}{\mathbb{Z}}^+$ with $1{\leq}t{\leq}n-1$, set n=${\delta}{\cdot}2^{\iota}$(${\delta}$=2, 3, 5, 7, 9, 13, 15) with ${\iota}{\geq}0$ integer. Then we show that $q{\frac}{n}{12}-{\frac}{t}{2}+{\frac}{t^2}{2n}{\prod}_{m=1}^{\infty}(1-q^{nm-t})(1-q^{{nm}-(n-t)})$ are algebraic numbers.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.313-321
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• 2003

In this Paper we show the following: Let R be a prime ring (with characteristic different two) and a $\in$ R. Let Θ, $\phi$ : R longrightarrow R be automorphisms and let d : R longrightarrow R be a nonzero Θ-derivation. (i) if［d($\chi$), a］Θo$\phi$ = 0 (or d(［$\chi$, a］$\phi$ = 0) for all $\chi$ $\in$ R, then a+$\phi$(a) $\in$ Z, the conte. of R, (ii) if〈d($\chi$), a〉 = 0 for all $\chi$$\in$R, then d(a) =0. (iii) if [ad($\chi$), $\chi$］$\phi$= 0 for all $\chi$$\in$R, then either a = 0 or R is commutative.