• 대한수학회지
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• 제45권3호
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• pp.597-609
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• 2008

In this paper, we will consider certain amalgamated free product structure in crossed product algebras. Let M be a von Neumann algebra acting on a Hilbert space Hand G, a group and let ${\alpha}$ : G${\rightarrow}$ AutM be an action of G on M, where AutM is the group of all automorphisms on M. Then the crossed product $\mathbb{M}=M{\times}{\alpha}$ G of M and G with respect to ${\alpha}$ is a von Neumann algebra acting on $H{\bigotimes}{\iota}^2(G)$, generated by M and $(u_g)_g{\in}G$, where $u_g$ is the unitary representation of g on ${\iota}^2(G)$. We show that $M{\times}{\alpha}(G_1\;*\;G_2)=(M\;{\times}{\alpha}\;G_1)\;*_M\;(M\;{\times}{\alpha}\;G_2)$. We compute moments and cumulants of operators in $\mathbb{M}$. By doing that, we can verify that there is a close relation between Group Freeness and Amalgamated Freeness under the crossed product. As an application, we can show that if $F_N$ is the free group with N-generators, then the crossed product algebra $L_M(F_n){\equiv}M\;{\times}{\alpha}\;F_n$ satisfies that $$L_M(F_n)=L_M(F_{{\kappa}1})\;*_M\;L_M(F_{{\kappa}2})$$, whenerver $n={\kappa}_1+{\kappa}_2\;for\;n,\;{\kappa}_1,\;{\kappa}_2{\in}\mathbb{N}$.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.83-94
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• 2016

Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and $Im({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$, if and only if a module M is semi N-injective and $Ker({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$. Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Im({\alpha}{\beta}){\subseteq}^{\oplus}N$, if and only if a module M is direct N-injective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Ker({\beta}{\alpha}){\subseteq}^{\oplus}M$. The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.

• 한국대기환경학회지
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• 제3권2호
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• pp.11-17
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• 1987

Atmospheric particulate matter (A.P.M.) was collected on quartz fiber filters from March 1985 to February 1986 at Chung-Ang University according to particle size using Andersen high-volume air smapler, and benzo (a) pyrene concentration in these particulates were analyzed by high performance liquid chromatography. The annual arithmetic mean concentration of A.P.M. was 115.50$\mug/m^3$. The annual arithmetic mean concentrations of coarse particles and fine particles in A.P.M. were 52.54$\mum/m^3$ and 62.96$\mum/m^3$ respectively. THe annual arithmetic mean concentration of benzo(a)pyrene in A.P.M. was 1.44$ng/m^3$. THe annual arithmetic mean concentrations of benzo(a)pyrene in coarse particles and fine particles were 0.05 $ng/m^3$ and 1.39 $ng/m^3$ respectively. Thus, the concentration of benzo(a)pyrene showed maldistribution of 96.53% in fine particle. A.P.M. showed wide fluctuation according to the season. The concentration of A.P.M. was lowest in summer and high in spring and winter. Coarse and fine particle concentrations in A.P.M. were highest in spring and winter, respectively. The concentrations of benzo(a)pyrene was highest in winter and lowest in summer. The concentrations of benzo(a)pyrene in fine and coarse particles were highest in winter and spring, respectively.

• 대한수학회논문집
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• 제32권3호
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• pp.661-676
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• 2017

Let T be a bounded linear operator acting on a complex Hilbert space ${\mathfrak{H}}$. In this paper we introduce the class, denoted ${\mathcal{Q}}(A(k),m)$, of operators satisfying $T^{m{\ast}}(T^{\ast}{\mid}T{\mid}^{2k}T)^{1/(k+1)}T^m{\geq}T^{{\ast}m}{\mid}T{\mid}^2T^m$, where m is a positive integer and k is a positive real number and we prove basic structural properties of these operators. Using these results, we prove that if P is the Riesz idempotent for isolated point ${\lambda}$ of the spectrum of $T{\in}{\mathcal{Q}}(A(k),m)$, then P is self-adjoint, and we give a necessary and sufficient condition for $T{\otimes}S$ to be in ${\mathcal{Q}}(A(k),m)$ when T and S are both non-zero operators. Moreover, we characterize the quasinilpotent part $H_0(T-{\lambda})$ of class A(k) operator.

• 한국환경농학회지
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• 제42권4호
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• pp.389-395
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• 2023

This study evaluated the effects of gibberellic acid (GA₃) on the growth and quality of creeping bentgrass (Agrostis palustris Huds.). Experimental treatments included a No application of fertilizer and GA₃ (NFG) Control [3 N active ingredient (a.i.) g/m²], 0.3GA₃ (GA₃ 0.3 a.i. mg/m²/200 mL), 0.6GA₃ (GA₃ 0.6 a.i. mg/m²/200 mL), 1.2GA₃ (GA₃ 1.2 a.i. mg/m²/200 mL), and 2.4GA₃ (GA₃ 2.4 a.i. mg/m²/200 mL). Additionally, the study included a 1.5N+GA₃ experiment with similar GA₃ treatments combined with 1.5N a.i. g/m² : NFG, Control (3N a.i. g/m²), 1.5N+ 0.3GA₃ (1.5N a.i. g/m²+GA₃ 0.3 a.i. mg/m²/200 mL), 1.5N+0.6GA₃ (1.5N a.i. g/m²+GA₃ 0.6 a.i. mg/m²/200 mL), 1.5N+1.2GA₃ (1.5N a.i. g/m²+GA₃ 1.2 a.i. mg/m²/ 200 mL), and 1.5N+2.4GA₃ (1.5N a.i. g/m²+GA₃ 2.4 a.i. mg/m²/200 mL). Compared to the NFG, turf color index chlorophyll content was not significantly different (p< 0.05). However, shoot length in 1.2GA₃, 2.4GA₃, 1.5N+0.3GA₃, 1.5N+0.6GA₃, 1.5N+1.2GA₃, and 1.5N+2.4GA₃ treatments increased by 0.8%, 10.6%, 5.15%, 8.3%, 13.5 %, and 21.6%, respectively, compared to the control. As compared to the control, clipping yield in 1.5N+1.2GA₃ and 1.5N+2.4GA₃ treatments increased by 7.1% and 14.3 %, respectively. These results indicated that GA₃ application increased shoot length, with the 1.2GA₃ treatment showing shoot length similar to the control (3N a.i. g /m² ).

• 벤처다이제스트
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• 통권129호
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• pp.34-35
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• 2009

2009년 3월 발표된 한국은행의 M&A 자료에 따르면 우리나라의 2008넌 M&A 거래건수는 1,153건이고, 거래 금액은 419억 달러에 달한다고 한다. 거래금액은 다소 감소한 것이나, 거래건수는 2007년에 비하여 107% 증가한 수준이다. M&A 거래 건수가 증가 했다는 것은 M&A가 활성화 되지 않은 국내 상황에서 상당히 고무적인 현상으로 볼 수 있겠다. 이 같은 M&A거래에는 여러 가지 거래유형이 숨어 있다. 이번호에서는 M&A 실제사례를 살펴보면서 유형별 특징과 주의사항을 알아보자.

• 대한수학회논문집
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• 제38권4호
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• pp.993-999
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• 2023

Let A be a G-graded commutative ring with identity and M a graded A-module. Let m, n be positive integers with m > n. A proper graded submodule L of M is said to be graded (m, n)-closed if a^m_g·x_t ∈ L implies that aⁿ_g·x_t ∈ L, where a_g ∈ h(A) and x_t ∈ h(M). The aim of this paper is to explore some basic properties of these class of submodules which are a generalization of graded (m, n)-closed ideals. Also, we investigate GC^m_n - rad property for graded submodules.

• 대한수학회보
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• 제51권3호
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• pp.613-619
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• 2014

It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if $M=M_1{\oplus}M_2$, where $M_1$ and $M_2$ are CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is $M_2$-ejective), then M is a CLS-module and some known results are generalized.

• 대한수학회지
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• 제56권5호
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• pp.1285-1307
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• 2019

For a multiplication R-module M we consider the Zariski topology in the set Spec (M) of prime submodules of M. We investigate the relationship between the algebraic properties of the submodules of M and the topological properties of some subspaces of Spec (M). We also consider some topological aspects of certain frames. We prove that if R is a commutative ring and M is a multiplication R-module, then the lattice Semp (M/N) of semiprime submodules of M/N is a spatial frame for every submodule N of M. When M is a quasi projective module, we obtain that the interval ${\uparrow}(N)^{Semp}(M)=\{P{\in}Semp(M){\mid}N{\subseteq}P\}$ and the lattice Semp (M/N) are isomorphic as frames. Finally, we obtain results about quantales and the classical Krull dimension of M.

• 호남수학학술지
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• 제27권2호
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• pp.301-315
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• 2005

Let $\{A_u,\;u=0,\;1,\;2,\;{\cdots}\}$ be a sequence of coefficient matrices such that ${\sum}_{u=0}^{\infty}{\parallel}A_u{\parallel}<{\infty}$ and ${\sum}_{u=0}^{\infty}\;A_u{\neq}O_{m{\times}m}$, where for any $m{\times}m(m{\geq}1)$, matrix $A=(a_{ij})$, ${\parallel}A{\parallel}={\sum}_{i=1}^m{\sum}_{j=1}^m{\mid}a_{ij}{\mid}$ and $O_{m{\times}m}$ denotes the $m{\times}m$ zero matrix. In this paper, a functional central limit theorem is derived for a stationary m-dimensional linear process ${\mathbb{X}}_t$ of the form ${\mathbb{X}_t}={\sum}_{u=0}^{\infty}A_u{\mathbb{Z}_{t-u}}$, where $\{\mathbb{Z}_t,\;t=0,\;{\pm}1,\;{\pm}2,\;{\cdots}\}$ is a stationary sequence of linearly positive quadrant dependent m-dimensional random vectors with $E({\mathbb{Z}_t})={{\mathbb{O}}$ and $E{\parallel}{\mathbb{Z}_t}{\parallel}^2<{\infty}$.