• Bulletin of the Korean Mathematical Society
• /
• v.31 no.2
• /
• pp.173-180
• /
• 1994

Let H be a separable, infinite dimensional, compled Hilbert space and let L(H) be the algebra of all bounded linear operators on H. A dual algebra is a subalgebra of L(H) that contains the identity operator $I_{H}$ and is closed in the ultraweak topology on L(H). Note that the ultraweak operator topology coincides with the wea $k^{*}$ topology on L(H)(see [3]). Bercovici-Foias-Pearcy [3] studied the problem of solving systems of simultaneous equations in the predual of a dual algebra. The theory of dual algebras has been applied to the topics of invariant subspaces, dilation theory and reflexibity (see [1],[2],[3],[5],[6]), and is deeply related with properties ( $A_{m,n}$). Jung-Lee-Lee [7] introduced n-separating sets for subalgebras and proved the relationship between n-separating sets and properties ( $A_{m,n}$). In this paper we will study the relationship between direct sum and properties ( $A_{m,n}$). In particular, using some results of [7] we obtain relationship between n-separating sets and direct sum of von Neumann algebras.ras.s.ras.

• Nuclear Engineering and Technology
• /
• v.40 no.7
• /
• pp.551-560
• /
• 2008

Radiation has stochastic aspects in its generation, its choice of interaction mode during traveling in media, and its impact on living bodies. In certain circumstances, like in high dose environments resulting from low-LET radiation, the variance in its impact on a target volume is negligible. On the contrary, in low dose environments, especially when they are attributed to high-LET radiation, the impact on the target carries with it a large variance. This variation is more significant for smaller target volumes. Microdosimetric techniques, which have been developed to estimate the distribution of radiation energy deposited to cellular and subcellular-sized targets, contrast with macrodosimetric techniques which count only the average value. Since cells and DNA compounds are the critical targets in human bodies, microdosimetry, or dose estimation by microscopic approach, helps one better analyze the biological effects of radiation on the human body. By utilizing microbeam systems designed for individual cell irradiation, scientists have discovered that human cells exhibit radiosensitive reactions without being hit themselves (bystander effect). During the past 10 or more years, a new therapeutic protocol using discontinuous multiple micro-slit beams has been investigated for its clinical application. It has been suggested that the beneficial bystander effect is the essence of this protocol.

• The Pure and Applied Mathematics
• /
• v.7 no.1
• /
• pp.7-18
• /
• 2000

Let M be an n-dimensional CR submanifold CR dimension n - l of a complex projective space M. We characterize M of $\bar{M}$ in terms of an estimations of the length of the derivative of Ricci tensor of the length of Ricci tensor.

• Journal of Integrative Natural Science
• /
• v.7 no.2
• /
• pp.145-147
• /
• 2014

Let $T_n(x)$ be the Chebyshev polynomials of first kind of degree n. In this paper, we show that for a > 1, the polynomial with integer coefficients $\frac{T_n(z)-T_n(a)}{z-a}$ has all its roots in $|z|{\leq}a$.

• Journal of Radiation Protection and Research
• /
• v.32 no.4
• /
• pp.178-183
• /
• 2007

Neutrons are high LET (linear energy transfer) radiation and cause more damage to the target cells than x-rays or gamma rays. The damage from neutrons is generally considered fatal to a cell and neutrons have a greater tendency to cause cell death through direct interaction on DNA. We performed experiments to measure growth delay ratio and oxygen enhancement ratio (OER) in mouse model system. We inoculated EMT-6 cells to the right hind leg of BALB-c mouse and X-rays and neutron beams were given when the average volume of tumors reached $200-300mm^3$. We irradiated 0, 11, 15.4 Gy of X-ray and 0, 5, 7 Gy of fast neutron beam at normoxic and hypoxic condition. The volume of tumors was measured 3 times per week. In x-ray experiment, growth delay ratio was 1.34 with 11 Gy and 1.33 with 15.4 Gy in normoxic condition compared to in hypoxic condition, respectively. In neutron experiment, growth delay ratio was 0.94 with 5 Gy and 0.98 with 7 Gy, respectively. The OER of neutron beam was 0.97. The neutron beam was more effective than X-ray in the control of hypoxic tumors.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.187-191
• /
• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• Journal of Agricultural Extension & Community Development
• /
• v.19 no.2
• /
• pp.273-299
• /
• 2012

This study examined importance and performance of urban agriculture education program of the trainees who attended urban agriculture education, and suggested reformation of urban agriculture instructor course of Gyeonggi Provincial Agricultural Research & Extension Services by IPA models. The investigation was done on October 7, 2011. The subject was 40 trainees of urban agriculture instructor course of Gyeonggi Provincial Agricultural Research & Extension Services. The study suggested reformation of urban agriculture education program based on the findings as follow: Firstly, the instructors should teach trainees not theoretically but practically to let the trainees make use of learning at urban agriculture. Secondly, teaching material that is not theoretically but practical enough to apply it to actual urban agriculture should be supplied. Thirdly, urban agriculture education should be done not theoretically but practically considering its characteristics. Theoretical contents have been already included in teaching material, and practice oriented education should be done to let trainees put theory into practice on-the-spot. Practice oriented education should be supported in the planning future education. In addition future urban agriculture education program should consider importance as well as practice of educational contents, lecturers, operations and facilities.

• Kyungpook Mathematical Journal
• /
• v.49 no.3
• /
• pp.473-481
• /
• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• Korean Journal of Mathematics
• /
• v.7 no.2
• /
• pp.227-233
• /
• 1999

Let $k$ be a real abelian field and $k_{\infty}={\bigcup}_{n{\geq}0}k_n$ be its $\mathbb{Z}_p$-extension for an odd prime $p$. For each $n{\geq}0$, we denote the class number of $k_n$ by $h_n$. The following is a well known theorem: Theorem. Suppose $p$ remains inert in $k$ and the prime ideal of $k$ above $p$ totally ramifies in $k_{\infty}$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$. The aim of this paper is to generalize above theorem: Theorem 1. Suppose $H^1(G_n,E_n){\simeq}(\mathbb{Z}/p^n\mathbb{Z})^l$, where $l$ is the number of prime ideals of $k$ above $p$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$. Theorem 2. Let $k$ be a real quadratic field. Suppose that $H^1(G_1,E_1){\simeq}(\mathbb{Z}/p\mathbb{Z})^l$. Then $p{\nmid}h_0$ if and only if $p{\nmid}h_n$ for all $n{\geq}0$.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.761-790
• /
• 2021

For given spaces X and Y, let map(X, Y) and map_*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map_*(X, Y ; g) be the path component of map(X, Y) containing f and map_*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane π^n+m(ΣⁿℂP²) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣⁿℂP², S^m) up to homotopy equivalence. We also determine the generalized Gottlieb groups G_n(ℂP², S^m). Finally, we compute homotopy groups of mapping spaces map(ΣⁿℂP², S^m; f) for all generators [f] of [ΣⁿℂP², S^m], and Gottlieb groups of mapping components containing constant map map(ΣⁿℂP², S^m; *).