• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.229-257
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• 2022

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c), c ≠ 0. We denote by A and R_𝜉 the shape operator in the direction of distinguished normal vector field and the structure Jacobi operator with respect to the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(< 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉A = AR_𝜉 and at the same time ∇_𝜉R_𝜉 = 0 on M, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Electrical & Electronic Materials
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• v.7 no.5
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• pp.383-388
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• 1994

Deep levels in semi-insulating GaAs were observed by thermally stimulated current(TSC) measurement In the temperature ranges of 100-300K Tl(E$\_$c/-0.18eV), T2(E$\_$c/-0.20eV), T3(E$\_$c/-0.31eV), T4(E$\_$c/-0.40eV), and T5(E$\_$c/-O.43eV) traps have been observed. The TI, T2, and T5 traps seem to be related to the V$\_$As/, V$\_$Ga/-complex, and As$\_$Ga/$\^$++/ respectively. T4 trap is considered with respect to V$\_$Ga/-V$\_$As/ complex.

• East Asian mathematical journal
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• v.37 no.1
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• pp.41-77
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• 2021

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (��, ξ, η, g) in a complex space form Mn+1(c), c ≠ 0. We denote by Rξ = R(·, ξ)ξ and A(i) be Jacobi operator with respect to the structure vector field ξ and be the second fundamental form in the direction of the unit normal C(i), respectively. Suppose that the third fundamental form t satisfies dt(X, Y ) = 2��g(��X, Y ) for certain scalar ��(≠ 2c)and any vector fields X and Y and at the same time Rξ is ��∇ξξ-parallel, then M is a Hopf hypersurface in Mn(c) provided that it satisfies RξA(1) = A(1)Rξ, RξA(2) = A(2)Rξ and ${\bar{r}}-2(n-1)c{\leq}0$, where ${\bar{r}}$ denotes the scalar curvature of M.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.189-198
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• 2004

In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• Preventive Nutrition and Food Science
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• v.9 no.4
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• pp.336-341
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• 2004

Leptin, resisitn and PAI-1 (plasminogen activator inhibitor-1) are synthesized and secreted by rodent fat cells and recently postulated to be an important link to obesity. This study was conducted to characterize the hormonal regulation of leptin, resistin, and PAI-1 gene expression in the 3T3-L1 adipocytes. The cells were treated with 0.5 $\mu$M insulin, 1 $\mu$M dexamethasone (Dex), or 0.05 $\mu$M triiodothyronine (T3) for 72 hours. The mRNA levels of each peptide were measured by semi-quantitative RT-PCR. The mRNA level of the leptin-producing ob gene was significantly increased by insulin, Dex, and T3 by 3.2-, 3.1- and 2.7-fold, respectively, compared to the control (p < 0.05). The level of resistin mRNA was increased by insulin, Dex, and T3 by 2.7-, 2.5- and 2-fold, respectively, compared to the control (p < 0.05). Likewise, the level of PAI-1 mRNA was significantly increased by insulin, Dex, and T3 compared to the control (p < 0.05). Taken together, our results suggest that insulin, Dex, and T3 may regulate the gene expression of leptin, resistin, and PAI-1 in 3T3-L1 adipocytes.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.133-166
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉𝜙 = 𝜙R_𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.173-188
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• 2014

In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

• East Asian mathematical journal
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• v.40 no.1
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• pp.1-23
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• 2024

Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (𝜙, 𝜉, 𝜂, g) in a complex space form M_n+1(c). We denote by A, K and L the second fundamental forms with respect to the unit normal vector C, D and E respectively, where C is the distinguished normal vector, and by R_𝜉 = R(𝜉, ·)𝜉 the structure Jacobi operator. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a scalar 𝜃(≠ 2c) and any vector fields X and Y , and at the same time R_𝜉K = KR_𝜉 and ∇_{𝜙∇𝜉𝜉}R_𝜉 = 0. In this paper, we prove that if it satisfies ∇_𝜉R_𝜉 = 0 on M, then M is a real hypersurface of type (A) in M_n(c) provided that the scalar curvature $\bar{r}$ of M holds $\bar{r}-2(n-1)c{\leq}0$.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.64.1-64.1
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• 2019

The first high-resolution spectroscopic and new multiband photometric observations of the semi-detached Algol type binary XZ CMi were performed at the Bohyunsan Optical Astronomy Observatory (BOAO) and the Sobaeksan Optical Astronomy Observatory (SOAO), respectively. A total of 34 spectra were obtained using the 1.8 m reflector of the BOAO equipped with the Bohyunsan Optical Echelle Spectrograph to construct the radial velocity (RV) curves of the eclipsing pair. New BVRI photometric light curves were also covered by using the SOAO 61cm reflector and a CCD camera. A detailed analysis of all eclipse timings shows that the orbital period of XZ CMi has varied in an upward parabolic variation superposed on a sinusoidal oscillation with a period of 38.0 yr and a semi-amplitude of 0.0071 days. From the spectral analysis, the effective temperature and the projected rotational velocity of the primary component were determined to be T_eff,1 = 7387±161 K and v₁sini = 122±6 km s^-1, respectively. Our simultaneous synthesis of the double-lined RV and BVRI light curves gives the reliable system parameters of XZ CMi with a mass ratio (q) of 0.314, an orbital inclination (i) of 81.9 deg and a large temperature difference (∆T) of 2481 K. The individual masses and radii of both components are M₁ = 1.91±0.08M_⊙, M₂ = 0.60±0.02M_⊙, R₁ = 1.60±0.02R_⊙, R₂ = 1.13±0.02R_⊙, respectively. Although the primary component is located inside the δ Sct and γ Dor instability strips, no evidence of pulsation in the system was detected. The possible evolutionary status of XZ CMi is discussed.