• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.641-648
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• 1994

Let M be a minimally immersed closed hypersurface in $S^{n+1}$, II the second fundamental form and $S = \Vert II \Vert^2$. It is well known that if $0 \leq S \leq n$, then $S \equiv 0$ or $S \equiv n$ and totally geodesic hypersheres and Clifford tori are the only possible minimal hypersurfaces with $S \equiv 0$ or $S \equiv n$ ([6], [2]). From these results, Chern suggested some questions on the study of compact minimal hypersurfaces on the sphere with S =constant: what are the next possible values of S to n, and does in the ambient sphere\ulcorner By the way, S is defined extrinsically but, in fact, it is an intrinsic invariant for the minimal hypersurface, i.e., S = n(n-1) - R, where R is the scalar, curvature of M. Some partial answers have been obtained for dim M = 3: Assuming $M^3 \subset S^4$ is closed and minimal with S =constant, de Almeida and Brito [1] proved that if $R \geq 0$ (or equivalently $S \leq 6$), then S = 0, 3 or 6, Peng and Terng ([5]) proved that if M has 3 distint principal curvatures, then S = 6, and in [3] Chang showed that if there exists a point which has two distinct principal curvatures, then S = 3. Hence the problem for dim M = 3 is completely done. For higher dimensional cases, not much has been known and these problems seem to be very hard without imposing some more conditions on M.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1913-1925
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• 2017

Let R be a ring with identity. An ideal N of R is called ideal-symmetric (resp., ideal-reversible) if $ABC{\subseteq}N$ implies $ACB{\subseteq}N$ (resp., $AB{\subseteq}N$ implies $BA{\subseteq}N$) for any ideals A, B, C in R. A ring R is called ideal-symmetric if zero ideal of R is ideal-symmetric. Let S(R) (called the ideal-symmetric radical of R) be the intersection of all ideal-symmetric ideals of R. In this paper, the following are investigated: (1) Some equivalent conditions on an ideal-symmetric ideal of a ring are obtained; (2) Ideal-symmetric property is Morita invariant; (3) For any ring R, we have $S(M_n(R))=M_n(S(R))$ where $M_n(R)$ is the ring of all n by n matrices over R; (4) For a quasi-Baer ring R, R is semiprime if and only if R is ideal-symmetric if and only if R is ideal-reversible.

• The Korean Journal of Zoology
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• v.19 no.2
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• pp.71-78
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• 1976

Chromosome aberration induced by methyl methanesulfonate (MMS) and the effects of thymidine analogs (BUdR or IUdR) on MMS-induced chromosome aberration were studied in human lymphocyte cultures. Single treatment with MMS to lymphocytes induces both chromatid and chromosome type aberrations with high frequency of chromatid type. The combined treatment of BUdR or IUdR with MMS was found to be more effective in increasing the rate of chromosome type aberrations.

• Nuclear Engineering and Technology
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• v.6 no.2
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• pp.89-96
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• 1974

The cross-section ratios of the nuclear isomeric pairs $^{80}$ B $r^{m, g}$, sup 81/S $e^{m, g}$, $^{104}$ R $h^{m, g}$, $^{116}$ I $n^{m, g}$ and $^{134}$ C $s^{m, g}$ through the radiative thermal neutron capture process have been studied. The experimental values of these ratios obtained by the activation method have been compared with the calculated ones deduced from the modified Huizenga-Vandenbosch method. Agreement between these values within 30% could be attained by controlling the spin cut-off parameter and gamma-ray multiplicity.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.785-802
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• 2024

Given M a monoid with a neutral element e. We show that the solutions of d'Alembert's functional equation for n × n matrices Φ(pr, qs) + Φ(sp, rq) = 2Φ(r, s)Φ(p, q), p, q, r, s ∈ M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation $$\begin{cases}f(pr, qs) + f(sp, rq) = 2\phi(r, s)f(p, q),\\Φ(p, q) = \phi(q, p),{\quad}p, q, r, s {\in} M\end{cases}$$ are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.23-30
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• 2014

For two positive integers r and s, $\mathcal{G}$(n; r; ${\theta}_s$) denotes to the class of graphs on n vertices containing no r of edge disjoint ${\theta}_s$-graphs and f(n; r; ${\theta}_s$) = max{${\varepsilon}(G)$ : G ${\in}$ $\mathcal{G}$(n; r; ${\theta}_s$)}. In this paper, for integers r, $k{\geq}2$, we determine f(n; r; ${\theta}_{2k+1}$) and characterize the edge maximal members in G(n; r; ${\theta}_{2k+1}$).

• Korean Journal of Medicinal Crop Science
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• v.11 no.5
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• pp.402-407
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• 2003

Karyotype analysis and chromosomal localization of 5S and 45S rDNAs using multi-color fluorescence in situ hybridization (McFISH) technique were carried out in Bupleurum longeradiatum. Somatic metaphase chromosome number was 2n=12. Karyotype was composed of three pairs of metacentrics (No.3, 4 and 6) and three pairs of submetacentrics (No. 1, 2 and 5). The length of somatic prometaphase chromosomes ranges from 2.55 to $5.05{\mu}m$ with total length of $18.15\;{\mu}m$. In FISH experiment, one pair of 5S rDNA signals was detected on the pericentromeric region of chromosome 4 and one pair of 45S rDNA signals was detected on the telomeric region of chromosome 2.

• Journal of Microbiology and Biotechnology
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• v.14 no.5
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• pp.985-990
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• 2004

Levans produced from Microbacterium laevaniformans were isolated, characterized, and fractionated by molecular weight. TLC, HPLC, and GC-MS analyses of the exopolysaccharide showed that it was a fructan-type polymer and was composed of (2,6)- and (2,1)-glycosidic linkages. $^{13}C$-NMR analysis proved that the polysaccharide was mainly a $\beta$-(2,6)-linked levan-type polysaccharide. To investigate the cytotoxicity of the acetone-precipitated levan fractions such as M1, M2, and M3, HepG2, P388D1, U937, SNU-1, and SNUC2A cell lines were screened. Among the cell lines tested, the cytotoxicity of M1- M3 fractions were detected from only SNU-1 and HepG2 cells at the dosage level of $100-800\mu\textrm{g}ml$. The M2 fraction M_r$, 80,000) at 400 $mu{g/ml}$ had the greatest cell growth inhibition (84.6%) on SNU-1, while the M1 $(M_r$, 50,000) at $800\mu\textrm{g}ml$ showed the greatest (46.32%) on HepG2. To obtain more uniform M_r$ fractions of levan, the levan was further fractionated from S1 $(M_r$ 1,000,000) to S5 $(M_r$ 10,000) using gel permeation chromatography. Again, the S1-S5 fractions had strong cytotoxicity on SNU-1 and HepG2 cell lines. The greatest inhibition effects of S4 $(M_r$ 80,000) on SNU-1 and S5 $(M_r$ 10,000) on HepG2 were shown to be 49.5% and 73.0%, respectively. The cytotoxicity of the levan fractions was more effective on SNU-1 than on HepG2. Although the relationship between the Mw and the cytotoxicity was not clear, smaller $M_r$, fractions of levan showed greater growth inhibition effect on the cancer cell lines in general. Therefore, it was indicated that a specific Mw class of levan is responsible for the effective cytotoxicity.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.31-36
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• 1983

The indirect M.R.A.C. method using the W.L.S. algorithm is applied to the speed control of a D.C. motor on the assumption that the motor is the 1-st order, completely controllable and observable, non-minimum phase plant. By the help of M6809 microprocessor system the experiments are performed with respect to the sinusoidal and square reference input. The results show that the speed of a D.C. motor is well controlled by the indirect M.R.A.C. method using W.L.S, algorithm, and that the W.L.S. algorithm is quite suitable to the time-varying plant.

• The Korean Journal of Pharmacology
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• v.23 no.2
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• pp.101-111
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• 1987

We investigated the binding properties of $(^3H)$ QNB and $(^3H)$ NMS to mAchR to elucidate the characterstics of mAchR in rat brain by using two different preparations (homogemates & intact brain cell aggregates). The binding properties of both ligands demonstrated high affinity and saturability in both experiments, however $(^3H)$ QNB showed a significantly higher maximal binding capacity than tha ot $(^3H)$ NMS 1. In rat brain homogenates; Displacement of both lignands with several mAchR antagonists resulted in competition curves in accoradnce with the law of massaction for QNB, atropine & scopolamine in thie preparation, also a similar profile was found for the quaternary ammonium analogs of atropine & scopolamine (methyl atropine & methylscopolamine) when $(^3H)$ NMS was used to label the receptors in rat brain. But when these hydrophillic antagonists were used to displace $(^3H)$ QNB, they showed interaction with high- and low-affinity binding sites in brain homogenates. Pirenzepine, the nonclassical mAchR antagonist, was able to displace both ligands from binding sites in this preparation. 2. In intact rat brain cell aggregates; Intact bain cell aggregates were used to elucidate the binding characteristics of $(^3H)$ NMS to mAchR in rat. The magnitude of binding of this ligand was related linearly to the amount of cell protein in the binding assay with a high ratio of total to nonspecific binding. mAchR antagonists displaced specific $(^3H)$ NMS binding according to the law of mass-action, while it was possible to resolve displacement curves using mAchR agonist into high-& low-affinity component. 3. Our results indicate that more hydrophilic receptor ligand $(^3H)$ QNB, displacement experiments in both tissues demonstrated that the lipid solubility of a particulr mAchR ligand might play an important role in determining its profile of binding to the mAchR, and the concentrations of mAchR in rat brain are both on the cell surface (membrane-bound receptor) and in the intracelluar membrane (intermembrane-bound receptor). 4. The results are discussed in terms of the usefulness of dissociated intact rat brain cells in studying mAchR in central nervous system.