• Honam Mathematical Journal
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• v.26 no.4
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• pp.379-389
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• 2004

Given operators X and Y acting on a Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for $i=1,2,{\cdots},n$. In this article, we obtained the following : Let ${\mathcal{H}}$ be a Hilbert space and let ${\mathcal{L}}$ be a commutative subspace lattice on ${\mathcal{H}}$. Let X and Y be operators acting on ${\mathcal{H}}$. Then the following statements are equivalent. (1) There exists an operator A in $Alg{\mathcal{L}}$ such that AX = Y, A is positive and every E in ${\mathcal{L}}$ reduces A. (2) sup ${\frac{{\parallel}{\sum}^n_{i=1}\;E_iY\;f_i{\parallel}}{{\parallel}{\sum}^n_{i=1}\;E_iX\;f_i{\parallel}}}:n{\in}{\mathbb{N}},\;E_i{\in}{\mathcal{L}}$ and $f_i{\in}{\mathcal{H}}<{\infty}$ and <${\sum}^n_{i=1}\;E_iY\;f_i$, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$, $n{\in}{\mathbb{N}}$, $E_i{\in}{\mathcal{L}}$ and $f_i{\in}H$.

• Korean journal of applied entomology
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• v.2
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• pp.16-21
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• 1963

The present study was undertaken to investigate the effects of different nitrogen source and rate on the growth of Fusarium oxysporum f. vasinfectum which is known to be a noticeable fungus causing the wilt disease of both sesame and cotton in Korea. From the results of this study, It was known that different N source and rate markedly affect the growth of Fusarium oxyspsrum f. vasinfectum Among four N sourses were used in this study, nitrate-N and urea-N were appropriate N source for the growth of fungus. Above all, nitrate N was the best N source because it is utilized in more extensive range of concentration in comparison with the other N source by the fungus, On the other hand, ammonia-N is of little avail for the growth of the fungus because of the formation of unusual colonies with wavy margin and bead-like mycelial cells in addition to marked reduction of mycelial growth and B sporulation of the fungus irrespective of concentration. Judging from the formation of such an abnormal colony and bead-like mycelial cell which is known to be a characteristic of 'staling-type' growth of fungi, the effect of ammonia-N on the growth of Fusarium oxysporum f. vasinfectum is similar to that of phenoxy componnds on some other fungi previously investigated by some workers. Ammonium and nitrate also was not considered to be an appropriate source for the growth of the fungus because of the formation of colonies with slight wavy margin and appreciable reduction of mycelial growth and sporulation in higher concentration than 50meq. , although much or less masking of the irregularity of colony occurs. Therefore, ammonia N alone or any other N combined with ammonia N is of little avail for the growth of Fusarium oxysporum f. vasinfectum.

• Journal for History of Mathematics
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• v.10 no.2
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• pp.24-29
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• 1997

Derivation은 Lie group, Lie ring 그리고 Lie Algebra에서 정의되어 사용되며 발전하였으며 ring에서 일반화 되었다. 역시 prime ring에서 연구되어지는 derivation의 성질들은 prime near-ring에서 일반화 시키려고 하고 있다. 1957년 E. Posner는 prime ring에서 두 개의 derivation의 곱(함수합성)이 derivation이면 이들중 하나의 derivation이 0임을 밝혔다. 본 논문에서는 prime ring에서 derivation이 연구된 역사적인 배경을 소개하고 몇가지 성질을 찾는다. 즉, D. F를 prime ring R의 derivation들이라 할 때 정수 $n{\ge}1$에 대하여 $DF^n$=0이면 D=0이거나 또는 $F^{3n-1}$=0이고, $D^nF$=0이면 $D^{9n-7}$=0 이거나 또는 $F^2$=0 이다.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.227-234
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• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.395-398
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• 2006

In this note, for any given positive integer n, we determine all the continuous solutions f : R ${\rightarrow}$ R of the integral-functional equation $f^n(x)=n_{_o}{^x}f(t)dt$.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.591-603
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• 2006

For a set $X{\subset}{\mathbb{Z}}^n$ let $(X,\;T^n_X)$ be the subspace of the Khalimsky n-dimensional space $({\mathbb{Z}}^n,\;T^n)$, $n{\in}N$. Considering a k-adjacency of $(X,\;T^n_X)$, we use the notation $(X,\;k,\;T^n_X)$. In this paper for a map $$f:(X,\;k,\;T^n_X){\rightarrow}(Y,\;2\;T_Y)$$, we find the condition that weak (k, 2)-continuity of the map f implies strong (k, 2)-continuity of f.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.395-407
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.709-716
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• 1996

Nielsen coincidence theory is concerned with the determinatin of a lower bound of the minimal number MC[f,g] of coincidence points for all maps in the homotopy class of a given map (f,g) : X $\to$ Y. The Nielsen Nielsen number $N_R(f,g)$ (similar to [9]) is introduced in [3], which is a lower bound for the number of coincidence points in the relative homotopy class of (f,g) and $N_R(f,g) \geq N(f,g)$.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.235-247
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• 1996

Many numerical computations in science and engineering can only be solved approximately since the available infomation is partial. For instance, for problems defined ona space of functions, information about f is typically provided by few function values, $N(f) = [f(x_1), f(x_2), \ldots, f(x_n)]$. Knwing N(f), the solution is approximated by a numerical method. The error between the true and the approximate solutions can be reduced by acquiring more information. However, this increases the cost. Hence there is a trade-off between the error and the cost.