• Journal of the Korean Electrochemical Society
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• v.4 no.4
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• pp.146-151
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• 2001

The Frumkin adsorption isotherm of the over-potentially deposited hydrogen (OPD H) for the cathodic $H_2$ evolution reaction (HER) at the poly-Ni|0.05M KOH aqueous electrolyte interface has been studied using the phase-shift method. The behavior of the phase shift $(0^{\circ}\leq{\phi}\leq90^{\circ})$ for the optimum intermediate frequency corresponds well to that of the fractional surface coverage $(1\geq{\theta}\geq0)$ at the interface. The phase-shift method, i.e., the Phase-shift profile $(-{\phi}\;vs.\;E)$ for the optimum intermediate frequency, can be used as a new method to estimate the Frumkin adsorption isotherm $(\theta\;vs.\;E)$ of the OPD H for the cathodic HER at the interface. At the poly-Ni|0.05M KOH aqueous electrolyte interface, the rate (r) of change of the standard free energy of the OPD H with $\theta$, the interaction parameter (g) for the Frumkin adsorption isotherm, the equilibrium constant (K) for the OPD H with $\theta$, and the standard free energy $({\Delta}G_{\theta})$ of the OPD H with ${\theta}$ are $24.8kJ mol^{-1},\;10,\;5.9\times10^{-6}{\leq}K{\leq}0.13,\;and\;5.1\leq{\Delta}G_{\theta}\leq29.8kJ\;mol^{-1}$. The electrode kinetic parameters $(r,\;g,\;K,\;{\Delta}G_{\theta})$ depend strongly on ${\theta} (0{\leq}{\theta}{\leq}1)$.

• Solar Energy
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• v.14 no.2
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• pp.75-90
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• 1994

Thermal energy transport in a two-dimensional horizontal and vertical channel with an isothermal rectangular beam attached to one adiabatic wall is investigated from the numerical solution of Navier-Stokes and energy equations. The solutions have been obtained for dimensionless aspect equations. The solutions have been obtained for dimensionless aspect ratios of beam, H/B=$0.25{sim}4$, Reynolds numbers, Re=$50{\sim}500$ and Grashof numbers, Gr=$0{\sim}5{\times}10^4$. The mean Nusselt number, $\overline{Nu}$ for horizontal and vertical channels shows same value at Gr=0 and increases as Gr increases and decreases as H/B increases at Re=100. $\overline{Nu}$ of vertical channel shows higher in $0.25{\leq}H/B<1.1$ and lower in $1.1{\leq}H/B{\leq}4.0$ than that of horizontal channel at $Gr=10^4$, Re=100. $\overline{Nu}$ of vertical channel shows higher in $0.25{\leq}H/B<1.1$ and lower in $1.1{\leq}H/B=1.0$ than that of horizontal channel at Re=100, $0<Gr{\leq}5{\times}10^4$. A comparison between the experimental and numerical results shows good agreement.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10A
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• pp.1560-1565
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• 2000

Over an additive abelian group G of order g and for a given positive integer λ, a generalized Hadamard matrix GF(g,λ) is defined as a gλ$\times$gλ matrix [h(i,j)] where 1$\leq$i$\leq$gλ,1$\leq$j$\leq$gλ, such that every element of G appears exactly λ times in the list h(i$_1$,1)-h(i$_2$,1), h(i$_1$,2)-h(i$_2$,2),...,h(i$_1$,gλ)-h(i$_2$, gλ) for any i$\neq$j. In this paper, we propose a new method of expanding a GH(\ulcorner,λ$_1$) = B = \ulcorner over G by replacing each of its m-tuple \ulcorner with \ulcorner GH(g,λ$_2$) where m=gλ$_2$. We may use \ulcornerλ$_1$(not necessarily all distinct) GH(g,λ$_2$)'s for the substitution and the resulting matrix is defined over the group of order g.

• Journal of Korean Ophthalmic Optics Society
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• v.9 no.2
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• pp.323-332
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• 2004

This study researched the visual acuity test object and Auto-refractormeter, visual of near power. The object were composed of middle aged, the old men and women who in habit Daegu. The results were as follows : 1. The subjects consisted of 537 people, 29.98% men, 70.02% women. 2. The emmetropia was 1.12% for myopia, 2.79% for hyperopia, 96.09% for astigmatism. 3. The abnormal refraction was composition for myopic compound astigmatism(16.57%), hyperopia compound astigmatism(45.62%), Mixed astigmatism(33.89%). 4. On the Myopic Spherical Equivalent(S.E) power, the range of -0.50D ${\leq}$ M.S.E < -1.00D was 21.67%, -1.00D ${\leq}$ M.S.E < -2.00D was 48.89%, -2.00D ${\leq}$ M.S.E < -6.00D was 29.44%. 5. On the Hyperopic Spherical Equivalent(S.E) power, the range of +0.50D ${\leq}$ H.S.E < +1.00D was 28.57%, +1.00D ${\leq}$ H.S.E < +2.00D was 49.30%, +2.00D ${\leq}$ H.S.E < +6.00D was 23.13%. 6. The addition power was 1.00D(8.01%), 1.50D(8.57%), 2.00D(13.78%), 2.50D(16.57%), 3.00D(16.95%), 3.50D(17.88%), 4.00D(18.25%).

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.117-122
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• 1994

In this paper we show that if {$H_n$} is a continuous strong higher derivation of order n on an ultraprime Banach algebra with a constant c, then $c||H_1||^2{\leq}4||H_2||$ and for each $1{\leq}l$ < n $$c^2||H_1||\;||H_{n-l}{\leq}6||H_n||+\frac{3}{2}\sum_{\array{i+j+k=n\\i,j,k{\geq}1}}||H_i||\;||H_j||\;||H_k||+\frac{3}{2}\sum_{\array{i+k=n\\i{\neq}l,\;n-1}}||H_i||\;||H_k|| $$ and for a strong higher derivation {$H_n$} of order n on a prime ring A we also show that if [$H_n$(x),x]=0 for all $x{\in}A$ and for every $n{\geq}1$, then A is commutative or $H_n=0$ for every $n{\geq}1$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.35-43
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• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1341-1352
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• 2016

Let R be a commutative Noetherian ring, ${\Phi}$ a system of ideals of R and $I{\in}{\Phi}$. In this paper among other things we prove that if M is finitely generated and $t{\in}\mathbb{N}$ such that the R-module $H^i_{\Phi}(M)$ is $FD_{{\leq}1}$ (or weakly Laskerian) for all i < t, then $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all i < t and for any $FD_{{\leq}0}$ (or minimax) submodule N of $H^t_{\Phi}(M)$, the R-modules $Hom_R(R/I,H^t_{\Phi}(M)/N)$ and $Ext^1_R(R/I,H^t_{\Phi}(M)/N)$ are finitely generated. Also it is shown that if cd I = 1 or $dimM/IM{\leq}1$ (e.g., $dim\;R/I{\leq}1$) for all $I{\in}{\Phi}$, then the local cohomology module $H^i_{\Phi}(M)$ is ${\Phi}$-cofinite for all $i{\geq}0$. These generalize the main results of Aghapournahr and Bahmanpour [2], Bahmanpour and Naghipour [6, 7]. Also we study cominimaxness and weakly cofiniteness of local cohomology modules with respect to a system of ideals.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1613-1622
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• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.205-211
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• 2012

Let R be a graded Noetherian domain and A a graded Krull overring of R. We show that if h-dim $R\leq2$, then A is a graded Noetherian domain with h-dim $A\leq2$. This is a generalization of the well-know theorem that a Krull overring of a Noetherian domain with dimension $\leq2$ is also a Noetherian domain with dimension $\leq2$.