• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.1-3
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• 1998

Let f : X longrightarrow Y be quasi-open. We show that: (1) If A $\subset$ X is open, f│A is quasi-open, (2) f : X longrightarrow f(X) is quasi-open. (3) And let $f_{\alpha}/,:X_{\alpha}$, longrightarrow $Y_{\alpha}$ be quasi-open. Then $\Pi f_{\alpha}, : \Pi X_{\alpha}$ longrightarrow $\Pi Y_{\alpha}$/ defined by {$x_{\alpha}$} longrightarrow {$f_{\alpha},({\chi}_{\alpha}$)}, is quasi-open. (4) Lastly, if $f_{i}: X_{i}$ longrightarrow Y are quasi-open, i = 1,2, then F: $X_1 \bigoplus X_2$ longrightarrow Y, defined by $F({\chi})=f_i({\chi})$, ${\chi} \in X_i$, is also quasi-open.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.393-400
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• 2008

In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||${\leq}$||f(x+y)+f(z+w)|| in normed modules over a $C^*$-algebra. This is applied to understand homomor-phisms in $C^*$-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||${\leq}$||f(x+y+z+w)||+${\theta}||x||^p||y||^p||z||^p||w||^p$ in real Banach spaces, where ${\theta}$, p are positive real numbers with $4p{\neq}1$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Journal of the Korean Ceramic Society
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• v.21 no.3
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• pp.231-238
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• 1984

Heavy metal fluoride glasses exhibit considerable promise as high transparency materials from the UV to the IR. These glasses are prepared by fusion of the mixture of metal fulorides($ZrF_4$, $BaF_2$, $LaF_3$ etc) at 800-1, 00$0^{\circ}C$ under the inert$(N_2)$ or reactive ($CCl_4$, $Cl_2$) atmosphere following the casting into glass on cooling. Infrared absorption at the 3, 400 cm-1 -OH peak has been measured as a function of thickness for several ZrF-$BaF_2$-LaF and $HfF_4$-$BaF_2$-$LaF_3$ glasses to separate contributions from bulk and surface -OH. For glasses melted under $CCl_4$ reactive atmosphere the peak is due almost entirely to surface-OH. and melting in a closed reactor was best for removing -OH. In ambient atmosphere the -OH peak exhibited no time dependence over a 30 d period indicating a very small rate of surface attack by atmospheric H2O. Removal of -OH absorption processing was generally easier and more complete for the $BaF_2$/ThF4-glasses than for the $ZrF_4$-or $HfF_4$-based glasses.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.12
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• pp.441-449
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• 1983

Recently, various kinds of computers with architecture different from the usual type of Neumann and Data flow machine have been studied for inproving computational speed. Among them, Feed Forward Computer(F.F.C.) has been remarkably developed. F.F.C. is a computer different from usual digital one in operating system. The usual computer executes operation and operand Fetch after executing instruction fetch and instruction decode. But conceptually, F.F.C. excutes instruction fetch, instruction decode operand fetch and combinational execution simultaneously. Accordingly, a suitable software is needed to operate high reliability and efficiency of this F.F.C. system. In this study, I aim at developing characteristics on highly reliable computer system which should be a blueprint of F.F.C. system in the future.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.173-183
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• 2015

A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).

• Korean Journal of Optics and Photonics
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• v.6 no.3
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• pp.214-221
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• 1995

When the broad pressure region (0.5-3.5 atm) of laser media is pumped by 70 ns [FWHM] electronbeam accelerator (800 kV, 21 kA), the correlation between free-runnuing XeF$(C\rightarrowA$ excimer laser output and Xe concentration are studied. The resonator consisted of dichroic output coupler, and the laser output is optimized with laser media $(Xe/F_2/Ar)$ as functions of total pressure and gas mixing ratio. Under the condition of F2 0.46% fixed, the laser intrinsic efficiencies of 0.38%, 1.03%, and 0.29% are obtained at 1. 2, and 3 atm, respectively. So then the peaks of laser intrinsic efficiency occured to the higher Xe concentration with decreasing total gas pressure. By analyzing the kinetics for the $XeF^*(C)$ formation efficiency and XeF$(C\rightarrowA$ laser extraction efficiency the dependence of Xe concentration on their correlation is explained. As the results we propose efficient operation of an atmosphericpressure XeF$(C\rightarrowA$ laser. laser.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• The Journal of the Korea Contents Association
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• v.18 no.11
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• pp.562-570
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• 2018

This study is a descriptive research to understand the degree and relevance of profession value, self - esteem, and sociality of nursing college students according to voluntary service activities. The results showed that the formation of profession values according to the general characteristics was related to religion (F = 4.79, p = .003) and major (F = 3.75, p = .011) and self esteem was related to grade (F = 4.84, p = .002). The profession values according to the characteristics of voluntary service activities showed a significant difference in volunteer time (F=18.70, p<.001), volunteer duration (F=18.87, p<.001), volunteer organization(F=3.41, p=.001), volunteer motivation(F=8.08, p<.001), participation path(F=3.63, p=.002), participation field(F = 2.13, p = .031). The profession value was positively correlated with self-esteem(r = .327, p <.01) and sociality(r= .248, p <.01). Self-esteem showed a statistically significant positive correlation with sociality(r= .327, p <.01).

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.127-144
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• 2009

Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.