• Journal of the Korean Chemical Society
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• v.24 no.3
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• pp.250-258
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• 1980

Various radicals may add to isonitriles to give imidoyl radcals RN=CR'. This may be also generated via abstraction of imidoyl hydrogen from imine in the following manner: RN=CR' ＋ R"${\cdot}{\rightarrow}$ RN=CR' ＋ R"-H Imidoyl radicals would be stabilized via two pathways, ${\beta}$-cleavage and atom transfer reactions. ${\beta}$-Cleavage may occur in two directions depending upon structure of the radicals. Cyanide transfer and the "so-called" normal ${\beta}$-cleavage are the two modes of ${\beta}$-cleavage. Addition of t-butoxy radical to t-butyl isocyanide 7 generates an imidoyl radical t-Bu-N=C-O-Bu-t, which undergoes ${\beta}$-cleavage to give t-butyl isocyanate and t-butyl radical. Addition of phenyl radical to 7 forms the intermediate radical t-Bu-N=$C-C_6H_5$, which decomposes to give benzonitrile and t-butyl radical. The t-butyl radical generated from the ${\beta}$-cleavage adds to 7 giving the radical t-Bu-N=C-Bu-t, which cleaves only to pivalonitrile and t-butyl radical, inducing radical chain isomerization. Trimethylsilyl radical adds to 7 to give the intermediate t-Bu-N=$C-Si(CH_3)_3$, which collapses to $(CH_3)_3$SiCN and a t-butyl radical.

• The Korean Journal of Malacology
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• v.12 no.2
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• pp.91-97
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• 1996

바윗굴의 산란유발 및 종묘생산을 위한 생물학적 기초자료를 얻고자 자극방법별 효과와 난발생 및 유생사육에 미치는 수온의 영향에 관하여 실험한 결과, 자극방법별 산란유발은 정자현탁액 첨가구에서 가장 많은 산란량과 높은 수정률을 나타냈고, 난발생 및 유생사육의 각 단계에 이르기까지의 수온(T, $^{\circ}C$)에 따른 발생속도(h, 시간)는 수온이 높을 수록 빨랐으며, 그 관계식은 다음과 같다. 담륜자기 :1/h= 0.0069T - 0.0950(r=0.9447)D형 유생 :1/h= 0.0006T - 0.0045(r=0.9288)초기 각정기 유생:1/h= 0.0002T - 0.0019(r=0.9358)후기 각정기 유생:1/h= 0.0002T - 0.0022(r=0.9868)부착기 유생:1/h= 0.0001T - 0.0013(r=0.9897)또한 바윗굴의 수온과 난발생 속도와의 관계에서 추정된 난발생의 생물학적 영도는 평균 10.96$^{\circ}C$였으며, 수온별 유생사육시 바윗굴의 생존율은 24$^{\circ}C$에서 6.8%로 가장 좋았다.

• Journal of the Korean Society for information Management
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• v.6 no.1
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• pp.15-36
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• 1989

The r a p i d i n c r e a s e o f microcomputer technology has r e s u l t e d i n t h e broad a p p l i c a t i o n t o various f i e l d s . The purpose of t h l s paper 1s to design a computerized r e t r i e v a l system f o r nuclear information m a t e r i a l s using a microcomputer.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.179-200
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.275-285
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• 1997

Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

• The Korean Nurse
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• v.23 no.4 s.127
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• pp.49-51
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• 1984

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1297-1314
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• 2019

In this work, we investigate the following fractional boundary value problems $$\{_tD^{\alpha}_T({\mid}_0D^{\alpha}_t(u(t)){\mid}^{p-2}_0D^{\alpha}_tu(t))\\={\nabla}W(t,u(t))+{\lambda}g(t){\mid}u(t){\mid}^{q-2}u(t),\;t{\in}(0,T),\\u(0)=u(T)=0,$$ where ${\nabla}W(t,u)$ is the gradient of W(t, u) at u and $W{\in}C([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ is homogeneous of degree r, ${\lambda}$ is a positive parameter, $g{\in}C([0,T])$, 1 < r < p < q and ${\frac{1}{p}}<{\alpha}<1$. Using the Fibering map and Nehari manifold, for some positive constant ${\lambda}_0$ such that $0<{\lambda}<{\lambda}_0$, we prove the existence of at least two non-trivial solutions

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.753-765
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• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.