• Communications of the Korean Mathematical Society
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• 제10권1호
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• Journal of the Korean Mathematical Society
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• 제40권6호
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• pp.977-998
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• 2003

Let k be an imaginary quadratic field, η the complex upper half plane, and let $\tau$ $\in$ η $textsc{k}$, p = $e^{{\pi}i{\tau}}$. In this article, using the infinite product formulas for g2 and g3, we prove that values of certain infinite products are transcendental whenever $\tau$ are imaginary quadratic. And we derive analogous results of Berndt-Chan-Zhang ([4]). Also we find the values of (equation omitted) when we know j($\tau$). And we construct an elliptic curve E : $y^2$ = $x^3$ ＋ 3 $x^2$ ＋ {3-(j/256)}x ＋ 1 with j = j($\tau$) $\neq$ 0 and P = (equation omitted) $\in$ E.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.595-606
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• 2014

In this paper three more right Jacobson-type radicals, $J^r_{g{\nu}}$, are introduced for near-rings which generalize the Jacobson radical of rings, ${\nu}{\in}\{0,1,2\}$. It is proved that $J^r_{g{\nu}}$ is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a $J^r_{g{\nu}}$-semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-$g_{\nu}$, ${\nu}{\in}\{0,1,2\}$. Moreover, a finite right $g_2$-primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-field (which is isomorphic to eRe), where e is a right $g_2$-primitive idempotent in R.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 한국해양공학회 2001년도 춘계학술대회 논문집
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• pp.350-356
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• 2001

SG-50 steel is an important material and used for manufacturing a pressure vessel which the gas piping. In this investigation, the elastic plastic fracture toughness of this material is evaluated by the an unloading compliance method according to the ASTM E813-97 and E1152-97 method on the smooth and side groove 1CT specimens. The effect of smooth and side groove is studied on the elastic plastic fracture toughness. The side grooved specimen is very useful in estimation of the J$_{IC}$. Because it is much easier than the smooth specimen to the onset of the ductile tearing by the R curve method. Besides, it improves the accuracy of toughness values, decreases the scattering of them and tunneling and shear lip by the side groove.e.

• Journal of the Korean Mathematical Society
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• 제48권1호
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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.

• Journal of Ocean Engineering and Technology
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• 제15권2호
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• pp.99-104
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• 2001

Elastic-plastic fracture toughness $J_{lc}$ can be used as an effective design criterion in elastic plastic fracture mechanics. Most of these systems are$J_{lc}$ $J_{lc}$ value at high temperature must be determined for use of integrity evaluation and designing of such systems. Elastic-plastic fracture toughness $J_{lc}$ tests were performed on SA516/70 carbon steel plate and test results were analyzed according to ASTM E 813-87, ASTM E 813-89 and ASTM E 1152-87.safety and integrity are required for reactor pressure vessels because, they are operated in high temperature. There are single specimen method, which used as evaluation of safety and integrity for reactor pressure vessels. In this study, elastic-plastic fracture toughness($J_{lc}$) and J-$\Delta$a of SA 516/70 steel used as reactor pressure vessel steel are measured and evaluated at room temperature, 150$^{\circ}C $, 250$^{\circ}C $ and 370$^{\circ}C $ according to unloading compliance method.

• Journal of the Korean Vacuum Society
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• 제7권s1호
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• pp.44-49
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• 1998

The antimicrobial effects of HAp and Ag-HAp was observed using periprosthetic infection bacteria such as Pseudomonas Aeruginosa, Staphylococcus Epidermidis, Escherichia coli (DH5$\alpha$). Ag-HAp showed good antimicrobial effects. TEM study of E. coli with and without Ag treatment in HAp was experimented in order to find the mechanism of Ag in antimicrobial effects. It was observed that the shape of Ag-treated E. coli was changed, the cells walls became inhomogeneous. The vaculoes at cytoplasm formed into E. coli and finally it was discovered by EDAX that there were many dark granules which contain the Ag element inside the cells.

• Proceedings of the KIEE Conference
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• 대한전기학회 2007년도 제38회 하계학술대회
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• pp.750-751
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• 2007

본 논문에서는 고압 모터의 절연열화 상태를 감시하기 위해 소선단락, 도체표면 공극, 주절연재료 내부공극, 반도전체 제거, 정상권선으로 모델권선을 제작하고 이 모델 권선에 고전압을 인가하여 shering bridge를 이용하여 교류전류의 변화분 및 정전용량, 유전정접 시험을 하였다. 이를 통해 얻어진 결과는 고압 모터의 고정자 권선의 절연상태를 판단하는 중요한 기초자료가 될것으로 판단한다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
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• pp.337-340
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• 2001

In this paper, we consider the observability conditions for the following nonlinear fuzzy neutral functional differential equations : (equation omitted), where x(t) is state function on E$\_$N/$\^$2/, u(t) is control function on E$\_$N/$\^$2/ and nonlinear continuous functions f:J C$\_$0/ E$\_$N/$\^$2/, k:J C$\_$0/ E$\_$N/$\^$2/ are satisfies global Lipschitz conditions.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.