• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.467-489
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• 1994

Let $\Omega$ be a closed and bounded polygonal domain in R$^2$, or a closed line segment in R$^1$ with boundary $\Gamma$, such that there exists an invertible mapping T : $\Omega$ \longrightarrow $\Omega$ with the following correspondence: x$\in$$\Omega$ ↔ x = T(x) $\in$$\Omega$, (1.1) and (1.2) t $\in$ U$\sub$p/($\Omega$) ↔ t = to T$\^$-1/ $\in$ U$\sub$p/($\Omega$), where $\Omega$ denotes the corresponding reference elements I = [-1,1] and I ${\times}$ I in R$^1$ and R$^2$ respectively, (1.3) U$\sub$p/($\Omega$) = {t : t is a polynomial of degree $\leq$ p in each variable on $\Omega$}, and (1.4) U$\sub$p/($\Omega$) = {t : t = to T $\in$ U$\sub$p/($\Omega$)}.(omitted)

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.127-135
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• 1984

In this paper, we find the Fourier series of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$ and the Parseval relation of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$. In section 2, we investigate some basic properties of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$ In section 3, we show that the mean of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$ exists and in section 4, after showing the existence of Fourier exponents and Fourier coefficients of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$. we give the Parseval relation of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$. For convenience we will denote X(t, .omega.) as X(t) in what follows.hat follows.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.709-727
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• 2018

Here we have studied the ideas of $g^*$-closed sets, $g{\bigwedge}_{{\tau}^-}$ sets and ${\lambda}^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $T_{\frac{\omega}{4}}$, $T_{\frac{3\omega}{8}}$, $T_{\omega}$ in Alexandroff spaces and also have introduced a new separation axiom namely $T_{\frac{5\omega}{8}}$ axiom in this space.

• Journal of the Korean Applied Science and Technology
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• v.18 no.3
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• pp.214-232
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• 2001

CTA ester bonds in TG molecules were not attacked by pancreatic lipase and lipases produced by microbes such as Candida cylindracea, Chromobacterium viscosum, Geotricum candidium, Pseudomonas fluorescens, Rhizophus delemar, R. arrhizus and Mucor miehei. An aliquot of total TG of all the seed oils and each TG fraction of the oils collected from HPLC runs were deuterated prior to partial hydrolysis with Grignard reagent, because CTA molecule was destroyed with treatment of Grignard reagent. Deuterated TG (dTG) was hydrolyzed partially to a mixture of deuterated diacylglycerols (dDG), which were subsequently reacted with (S)-(+)-1-(1-naphthyl)ethyl isocyanate to derivatize into dDG-NEUs. Purified dDG-NEUs were resolved into 1, 3-, 1, 2- and 2, 3-dDG-NEU on silica columns in tandem of HPLC using a solvent of 0.4% propan-1-o1 (containing 2% water)-hexane. An aliquot of each dDG-NEU fraction was hydrolyzed and (fatty acid-PFB ester). These derivatives showed a diagnostic carboxylate ion, $(M-1)^{-}$, as parent peak and a minor peak at m/z 196 $(PFB-CH_{3})^{-}$ on NICI mass spectra. In the mass spectra of the fatty acid-PFB esters of dTGs derived from the seed oils of T. kilirowii and M. charantia, peaks at m/z 285, 287, 289 and 317 were observed, which corresponded to $(M-1)^{-}$ of deuterized oleic acid ($d_{2}-C_{18:0}$), linoleic acid ($d_{4}-C_{18:0}$), punicic acid ($d_{6}-C_{18:0}$) and eicosamonoenoic acid ($d_{2}-C_{20:0}$), respectively. Fatty acid compositions of deuterized total TG of each oil measured by relative intensities of $(M-1)^-$ ion peaks were similar with those of intact TG of the oils by GLC. The composition of fatty acid-PFB esters of total dTG derived from the seed oils of T. kilirowii are as follows; $C_{16:0}$, 4.6 mole % (4.8 mole %, intact TG by GLC), $C_{18:0}$, 3.0 mole % (3.1 mole %), $d_{2}C_{18:0}$, 11.9 mole % (12.5 mole %, sum of $C_{18:1{\omega}9}$ and $C_{18:1{\omega}7}$), $d_{4}-C_{18:0}$, 39.3 mole % (38.9 mole %, sum of $C_{18:2{\omega}6}$ and its isomer), $d_{6}-C_{18:0}$, 41.1 mole % (40.5 mole %, sum of $C_{18:3\;9c,11t,13c}$, $C_{18:3\;9c,11t,13r}$ and $C_{18:3\;9t,11t,13c}$), $d_{2}-C_{20:0}$, 0.1 mole % (0.2 mole % of $C_{20:1{\omega}9}$). In total dTG derived from the seed oils of M. charantia, the fatty acid components are $C_{16:0}$, 1.5 mole % (1.8 mole %, intact TG by GLC), $C_{18:0}$, 12.0 mole % (12.3 mole %), $d_{2}-C_{18:0}$, 16.9 mole % (17.4 mole %, sum of $C_{18:1{\omega}9}$), $d_{4}-C_{18:0}$, 11.0 mole % (10.6 mole %, sum of $C_{18:2{\omega}6}$), $d_{6}-C_{18:0}$, 58.6 mole % (57.5 mole %, sum of $C_{18:3\;9c,11t,13t}$ and $C_{18:3\;9c,11t,13c}$). In the case of Aleurites fordii, $C_{16:0}$; 2.2 mole % (2.4 mole %, intact TG by GLC), $C_{18:0}$; 1.7 mole % (1.7 mole %), $d_{2}-C_{18:0}$; 5.5 mole % (5.4 mole %, sum of $C_{18:1{\omega}9}$), $d_{4}-C_{18:0}$ ; 8.3 mole % (8.5 mole %, sum of $C_{18:2{\omega}6}$), $d_{6}-C_{18:0}$; 82.0 mole % (81.2 mole %, sum of $C_{18:3\;9c,11t,13t}$ and $C_{18:3 9c,11t,13c})$. In the stereospecific analysis of fatty acid distribution in the TG species of the seed oils of T. kilirowii, $C_{18:3\;9c,11t,13r}$ and $C_{18:2{\omega}6}$ were mainly located at sn-2 and sn-3 position, while saturated acids were usually present at sn-1 position. And the major molecular species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})_{2}$ and $(C_{18:1{\omega}9})(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})$ were predominantly composed of the stereoisomer of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:3\;9c,11t,13c}$, $sn-3-C_{18:3\;9c,11t,13c}$, and $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13c}$, respectively, and the minor TG species of $(C_{18:2{\omega}6})_{2}(C_{18:3\;9c,11t,13c})$ and $ (C_{16:0})(C_{18:3\;9c,11t,13c})_{2}$ mainly comprised the stereoisomer of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13c}$ and $sn-1-C_{16:0}$, $sn-2-C_{18:3\;9c,11t,13c}$, $sn-3-C_{18:3\;9c,11t,13c}$. The TG of the seed oils of Momordica charantia showed that most of CTA, $C_{18:3\;9c,11t,13r}$, occurred at sn-3 position, and $C_{18:2{\omega}6}$ was concentrated at sn-1 and sn-2 compared to sn-3. Main TG species of $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{18:0})(C_{18:3\;9c,11t,13t})_{2}$ were consisted of the stereoisomer of $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{18:0}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$, respectively, and minor TG species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})_{2}$ and $(C_{18:1{\omega}9})(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})$ contained mostly $sn-1-C_{18:2{\omega6}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13t}$. The TG fraction of the seed oils of Aleurites fordii was mostly occupied with simple TG species of $(C_{18:3\;9c,11t,13t})_{3}$, along with minor species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13t})_{2}$, $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{16:0})(C_{18:3\;9c,11t,13t})$. The sterospecific species of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:3\;9c,11t,13t}$, sn-3-C_{18:3\;9c,11t,13t}$, $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{16;0}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ are the main stereoisomers for the species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13t})_2$, $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{16:0})(C_{18:3\;9c,11t,13t})$, respectively.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.465-490
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• 1998

In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)＋$\delta$│ $u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)＋$\delta$ │ $v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.

• Journal of electromagnetic engineering and science
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• v.10 no.3
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• pp.186-189
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• 2010

Reflection(R($\omega$)), transmission(T($\omega$)) and loss(L($\omega$)) characteristics of multi-layer metamaterials are investigated experimentally in free space with the incident EM waves perpendicular to the substrate plane. The sample is made of split-ring resonators(SRRs) and wires which are the typical model of metamaterials. The R($\omega$) and T($\omega$) of multi-layer metamaterials have been calculated from the measured S-parameters. In this paper, we got the impedance-matched result according to the curves of R($\omega$), meanwhile the T($\omega$) decreased with increasing number of layers. At last, we attained the result that the L($\omega$) gets to nearly 98% around 8 GHz, with R($\omega$)=T($\omega$)=0. The design presented in this paper achieves experimented loss near unity.

• Water for future
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• v.17 no.4
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• pp.281-291
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• 1984

In our Koreans river basins there are many of monthly rainfall data, but unfortrnately streamflow data needed are rare. Analysing monthly rainfall data of Somjin river basin, the stochastic theory model for calculation of monthly streamflow series of that region is determined. The model is composed of Box & Jenkins stansfer function plus ARIMA residual models. This linear stochastic differenced time series equation models can adapt themselves to the structure and variety of rainfall, streamflow data on the assumption of the stationary covarience. The fiexibility of Box-Jenkins method consists mainly in the iterative technique of building an AIRMA model from observations and by the use of autocorrelation functions. The best models for Somjin river basin belong to the general calss: $Y_t=($\omega$o-$\omega$_1B) C_iX_t+$\varepsilon$t$ $Y_t$ monthly streamflow, $X_t$ : monthly rainfall, $C_i$ :monthly run-off, $$\omega$o-$\omega$_1$ : transfer parameter, $$\varepsilon$_t$ : residual The streamflow series resulted from the proposed model is satisfactory comparing with the exsting streamflow data of Somjin gauging station site.