• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Applied Chemistry for Engineering
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• v.18 no.5
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• pp.483-489
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• 2007

Polyaniline (PANI)/Polyimide (PI) membranes were prepared and the effects of PANI contents and doping on the structural properties and gas separation properties were studied. The polyamic acid (PAA) solution was prepared by the polycondensation reaction of 4,4'-(hexafluoroisopropylidene) diphthalic anhydride (6FDA) and 4,4'-oxydianiline (ODA) in 1-methyl-2-pyrrolydinone (NMP) solvent. The PANI/PI blends were obtained by mixing PAA solution and PANI solution, and were doped with 1 M aqueous HCl solution for 24 h. The structural characterizations of the as-cast and doped membranes were examined by FT-IR, XRD, and TGA. The gas permeation experiments with $H_2$, $CO_2$, $O_2$, $N_2$, and $CH_4$ were carried out by variable pressure method at $30^{\circ}C$ and 5 atm. For all gases tested, the permeability coefficients of the blends decreased with increasing PANI content and the magnitude of permeability was in the order of $H_2$ > $CO_2$ > $O_2$ > $N_2$ > $CH_4$. The permeability for PANI/PI membranes decreased after the doping process while the permselectivity increased. For $H_2/CH_4$ separation, the doped PANI/PI (75/25) membrane has a permselectivity of 991.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.709-715
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• 1997

For a fibration (E,B,p) with fiber F and a fiber map f, we show that if the inclusion $i : F \to E$ has a left homotopy inverse, then $G^f_n(E,F)$ is isomorphic to $G^f_n(F,E) \oplus \pi_n(B)$. In particular, by taking f as the identity map on E we have $G_n(E,F)$ is isomorphic to $G_n(F) \oplus \pi_n(B)$.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.1-6
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• 2001

We investigate the relationships between the Gottlieb groups and the generalized Gottlieb groups, and study some properties of the generalized Gottlieb groups. Lee and Woo [5] proved that $G_n(X,i_1,X{\times}Y){\simeq_-}G_n(X){\oplus}{\pi}_n(Y)$. We can easily re-prove the above main theorem of [5] using some properties of the generalized Gottlieb groups, and obtain a more powerful result as follows; if $F{\rightarrow}^iE{\rightarrow}^pB$ is a homotopically trivial fibration, then $G_n(F,i,E){\simeq_-}{\pi}_n(B){\oplus}G_n(F)$.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.377-386
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• 2021

In this paper, we use theta-function identities involving parameters 𝑙_5,n, 𝑙'_5,n, and 𝑙'_5,4n to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2{\pi}{\sqrt{n/20}}})$ and $S(e^{-{\pi}{\sqrt{n/5}}})$ for some positive rational numbers n.

• Korean Journal of Optics and Photonics
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• v.10 no.3
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• pp.188-194
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• 1999

We synthesized the nonlinear optical (NLO) PI-SOT(polyimide system, 4-[N,N-bis(hydroxyethyl)amino-4,-($\beta$-cyano-$\beta$-methylsulfonyl)vinyl]azobenzene) polymer with high electro-optic coefficients as well as good thermal and temporal stabilities of the elector-optic coefficient ${\gamma}_33$ by the simple Mitsunobu reaction. By using the simple reflection method of C. C. Teng, we measured the thermal and temporal stabilities of the electro-optic coefficient ${\gamma}_33$ of corona-poled PI-SOT polymer at the wavelength of 632.8 nm and 852 nm, respectively. At the temperature of $20^{\circ}C$, the electro-optic coefficient ${\gamma}_33$ of corona-poled PI-SOT polymer were 25.12 pm/V at the wavelength of 632.8 nm and 5.40 pm/V at the wavelength of 852 nm. These values were highly stabilized for more than 60 days at 2$0^{\circ}C$ and stabilized within 6% for more than 10 hours at $100^{\circ}C$.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.29-36
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• 2014

The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. and showed the martingale property on this operator and measure. Let $P_{\rho}$ be the unique solution of the martingale problem for $\mathcal{L}_0$ starting at ${\rho}$ and ${\pi}_1,{\pi}_2,{\cdots},{\pi}_n$ the projection of $E^n$ on $x_1,x_2,{\cdots},x_n$. In this note we define $$dQ_{\rho}=S_tdP_{\rho}$$ and show that $Q_{\rho}$ solves the martingale problem for $\mathcal{L}_{\pi}$ starting at ${\rho}$.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.119-126
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• 1989

Throughout this paper, X will always denote a Banach space over the complex numbers C, and L(X) will denote the Banach algebra of all continuous linear operators on X. Operator will always mean continuous linear operator. An n-tuple of operators T$_{1}$,..,T$_{n}$ on X will be denoted by over ^ T=(T$_{1}$,..,T$_{n}$ ). Let L$^{n}$ (X) be the set of all n-tuples of operators on X. X' will denote the dual space of X, S(X) its unit sphere and .PI.(X) the subset of X*X' defined by .PI.(X)={(x,f).mem.X*X': ∥x∥=∥f∥=f(x)=1}.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.683-689
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• 2000

The convergence rate of the expectation of the logarithm of the first return time R(sub)n with block length n has been investigated for Bernoulli processes. This idea is applied to check the randomness of the digits of the decimal expansion of $\pi$, e and √2.