• The Korean Journal of Applied Statistics
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• v.4 no.1
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• pp.1-11
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• 1991

It is of great interest to consider the homogeniety of covariance matrices in MANOVA of discriminant analysis. If we lock at the problem of testing hypothesis, H : $\Sigma_1 = \Sigma_2$ from an invariance point of view where $\Sigma_i$ are the covariance matrix of two independent p-variate distribution, the testing problem is invariant under the group of nonsingular transformations and the hypothesis becomes H : $\delta_1 = \delta_2 = \cdots = \delta_p = 1$ where $\delta = (\delta_1, \delta_2, \cdots, \delta_p)$ is a vector of latent roots of $\Sigma$. Bias-corrected estimators of eigenvalues and sampling distribution of the test statistics proposed are obtained. Pooled-bootstrap method also considered for Bartlett's modified likelihood ratio statistics.

• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.161-167
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• 2005

In this note we consider the projective property $\sigma(Re(T))\;=\;Re\;(\sigma$(T))$ of p-hyponormal operators and log-hyponormal operators.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.1-5
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• 2006

We will introduce tensor product spectrums on the tensor product spaces. And we will show that ${\sigma}[P(T_1,T_2,{\ldots},T_n)]=P[({\sigma}(T_1),{\sigma}(T_2){\ldots},{\sigma}(T_n)]={\sigma}(T_1,T_2{\ldots},T_n)$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1131-1145
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• 2012

The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with p-Laplacian type operators $$\{({\alpha}(t,x^{\Delta}(t)))^{\Delta}-a(t){\phi}_p(x^{\sigma}(t))+f({\sigma}(t),x^{\sigma}(t))=0,\;{\Delta}-a.e.\;t{\in}I\\x^{\sigma}(0)=0,\\{\beta}_1x^{\sigma}(1)+{\beta}_2x^{\Delta}({\sigma}(1))=0,$$ where ${\beta}_1$, ${\beta}_2$ > 0, $I=[0,1]^{k^2}$, ${\alpha}({\cdot},x({\cdot}))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.

• East Asian mathematical journal
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• v.38 no.1
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• East Asian mathematical journal
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• v.17 no.1
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• pp.87-92
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• 2001

In this paper, we have the extended result of Bunce's theorem. And we show that if T is an irreducible p-hyponormal operator such that T*T-TT* is compact, then ${\sigma}_{ap}(T)={\sigma}_e(T)$ and ${\sigma}_p({\phi}(T))={\sigma}_e({\phi}(T))$.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.103-113
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• 1991

Some properties of a path space and the fundamental group ${\sigma}(X,x_0,G)$ of a topological transformation group (X, G, ${\pi}$) are described. It is shown that ${\sigma}(X,x_0,H)$ is a normal subgroup of ${\sigma}(X,x_0,G)$ if H is a normal subgroup of G ; Let (X, G, ${\pi}$) be a transformation group with the open action property. If every identification map $p:{\Sigma}(X,x,G)\;{\longrightarrow}\;{\sigma}(X,x,G)$ is open for each $x{\in}X$, then ${\lambda}$ induces a homeomorphism between the fundamental groups ${\sigma}(X,x_0,G)$ and ${\sigma}(X,y_0,G)$ where ${\lambda}$ is a path from $x_0$ to $y_0$ in X ; The space ${\sigma}(X,x_0,G)$ is an H-space if the identification map $p:{\Sigma}(X,x_0,G)\;{\longrightarrow}\;{\sigma}(X,x_0,G)$ is open in a topological transformation group (X, G, ${\pi}$).

• Journal of the Korean Chemical Society
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• v.41 no.6
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• pp.277-283
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• 1997

Platinum(II) complexes(where, $[Pt(L)_2X_2]$; L=isoxazole(isox), 3,5-dimethylisoxazole(3,5-diMeisox), 3-methyl,5-phenylisoxazole(3-Me,5-Phisox), and 4-amino-3,5-dimethylisoxazole(4-ADI); X=Cl, Br) with planar ligands are investigated on antitumor activity by MM2 and EHMO calculations. It was found that, the net atomic charges of the halogen atoms in all of cis-, trans-isomers are greater than that of the nitrogen with planar form, indicating that ionic character of Pt-X bond is greater than that of Pt-N. Also, the ${\sigma}MO$ energy level($E{\sigma}_{(Pt-X)}$) of the interaction between $d_{x2-y2}$ orbital of Pt atom and $p_x$ orbital of X found to be higher than that of between $d_{x2-y2}$ orbital of Pt atom and $p_x$ orbital of N about all the complexes. It is found that bond strength of between Pt and X atom is weaker than that of between Pt and N atom. The ${\sigma}MO$ energy level($E{\sigma}_{(Pt-X)}$) of trans- complexes found to be higher than that of cis- complexes, as a result of bond strength of Pt-X in cis- and trans-complexes, for all the complexes. The degree of dissociation of X atom in Pt-X bond for trans-complexes are related to antitumor activity and the logIA value of inhibitory activity coefficient(IA).

• Journal of Microbiology
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• v.45 no.6
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• pp.534-540
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• 2007

The Streptomyces coelicolor A3(2) genome contains six operons (rrnA to F) for ribosomal RNA synthesis. Transcription from rrnD occurs from four promoters (p1 to p4). We found that transcripts from the p1 and p3 promoters were most abundant in vivo in the early exponential phase. However, at later phases of exponential and stationary growth, transcripts from the p1 promoter decreased drastically, with the p3 and p4 transcripts constituting the major forms. Partially purified RNA polymerase supported transcription from the p3 and p4 promoters, whereas pure reconstituted RNA polymerase with core enzyme (E) and the major vegetative sigma factor ${\sigma}^{HrdB}$ ($E{\cdot}{\sigma}^{HrdB}$) did not. In order to assess any potential requirement for additional factor(s) that allow transcription from the p3 and p4 promoters, we fractionated a partially purified RNA polymerase preparation by denaturing gel filtration chromatography. We found that transcription from the p3 and p4 promoters required factor(s) of about 30-35 kDa in addition to RNAP holoenzyme ($E{\cdot}{\sigma}^{HrdB}$). Therefore, transcription from the p3 and p4 promoters, which contain a consensus -10 region but no -35 for ${\sigma}^{HrdB}$ recognition, are likely to be regulated by transcription factor(s) that modulate RNA polymerase holoenzyme activity in S. coelicolor.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.273-284
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• 2001

Let P be a spacelike (n-2)-dimensional submanifold of an n-dimensional Lorentz manifold M and let$\sigma$ be a P-normal null geodesic with Ric($\sigma',\sigma'$)$\geq$m, for the any given nonpositive constant m. We establish a sufficient condition such that there is a focal point of P along $\sigma$.