• Honam Mathematical Journal
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• v.26 no.2
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• pp.155-161
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• 2004

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1113-1122
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• 2016

Let (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Yamabe flow. In the paper we derive the evolution for the first eigenvalue of geometric operator $-{\Delta}_{\phi}+{\frac{R}{2}}$ under the Yamabe flow, where ${\Delta}_{\phi}$ is the Witten-Laplacian operator, ${\phi}{\in}C^2(M)$, and R is the scalar curvature with respect to the metric g(t). As a consequence, we construct some monotonic quantities under the Yamabe flow.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1315-1327
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• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1289-1304
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• 2022

In this note, we show that a strongly 𝜙-ring R is a 𝜙-PvMR if and only if any 𝜙-torsion-free R-module is 𝜙-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely w-pure, if and only if any GV-torsion-free h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.8 no.2
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• pp.47-60
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• 1975

For the calculation of population parameter and estimation of recruitment of a fish population, an application of multiple regression method was used with some statistical inferences. Then, the differences between the calculated values and the true parameters were discussed. In addition, this method criticized by applying it to the statistical data of a population of bigeye tuna, Thunnus obesus of the Indian Ocean. The method was also applied to the available data of a population of Pacific saury, Cololabis saira, to estimate its recuitments. A stock at t year and t+1 year is, $N_{0,\;t+1}=N_{0,\;t}(1-m_t)-C_t+R_{t+1}$ where $N_0$ is the initial number of fish in a given year; C, number o: fish caught; R, number of recruitment; and M, rate of natural mortality. The foregoing equation is $$\phi_{t+1}=\frac{(1-\varrho^{-z}{t+1})Z_t}{(1-\varrho^{-z}t)Z_{t+1}}-\frac{1-\varrho^{-z}t+1}{Z_{t+1}}\phi_t-a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}C_t+a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}R_{t+1}......(1)$$ where $\phi$ is CPUE; a', CPUE $(\phi)$ to average stock $(\bar{N})$ in number; Z, total mortality coefficient; and M, natural mortality coefficient. In the equation (1) , the term $(1-\varrho^{-z}t+1)/Z_{t+1}$s almost constant to the variation of effort (X) there fore coefficients $\phi$ and $C_t$, can be calculated, when R is a constant, by applying the method of multiple regression, where $\phi_{t+1}$ is a dependent variable; $\phi_t$ and $C_t$ are independent variables. The values of Mand a' are calculated from the coefficients of $\phi_t$ and $C_t$; and total mortality coefficient (Z), where Z is a'X+M. By substituting M, a', $Z_t$, and $Z_{t+1}$ to the equation (1) recruitment $(R_{t+1})$ can be calculated. In this precess $\phi$ can be substituted by index of stock in number (N'). This operational procedures of the method of multiple regression can be applicable to the data which satisfy the above assumptions, even though the data were collected from any chosen year with similar recruitments, though it were not collected from the consecutive years. Under the condition of varying effort the data with such variation can be treated effectively by this method. The calculated values of M and a' include some deviation from the population parameters. Therefore, the estimated recruitment (R) is a relative value instead of all absolute one. This method of multiple regression is also applicable to the stock density and yield in weight instead of in number. For the data of the bigeye tuna of the Indian Ocean, the values of estimated recruitment (R) calculated from the parameter which is obtained by the present multiple regression method is proportional with an identical fluctuation pattern to the values of those derived from the parameters M and a', which were calculated by Suda (1970) for the same data. Estimated recruitments of Pacific saury of the eastern coast of Korea were calculated by the present multiple regression method. Not only spring recruitment $(1965\~1974)$ but also fall recruitment $(1964\~1973)$ was found to fluctuate in accordance with the fluctuations of stock densities (CPUE) of the same spring and fall, respectively.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.4
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• pp.681-693
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• 1995

A new set of capillary tube selection charts for R-22 is proposed. The set of charts takes into account of the roughness effect on the mass flow rate. For this purpose, a set of numerical model is developed and a series of experiments is conducted to verify the numerical model. A numerical model is used to calculated the mass flow rate for several sets of tube diameter, length, inlet pressures and degree of subcooling. The outlet of the tube is controlled to be at critical condition. The experimental flow rate is compared with calculated values. The calculated values are consistently less than the experimental ones except for the flow rate range below 40kg/hr. The deviation is within 10---. Based on the nunmerical model and results of experiments, the set of capillary tube selection charts for R-22 is constructed. The set of charts consists of standard capillary tube chart(L=2030mm, d=1.63mm, ${\varepsilon}=2.5{\mu}m$), non -standard flow factor(${\phi}_1$) chart, and non-standard roughness factor(${\phi}_2$) chart. The mass flow rate, flow factor, and the roughness factor are defined respectively as; $\dot{m}={\phi}_1{\phi}_2\dot{m}_{standard}\\{\phi}_1=\frac{\dot{m}(L,\;d,\;\varepsilon_{standard})}{\dot{m}_{standard}(L_{standard},\;d_{standard},\;{\varepsilon}_{standard})}\\{\phi}_2=\frac{\dot{m}(L_{standard},\;d_{standard},\;{\varepsilon})}{\dot{m}_{standard}(L_{standard},\;d_{standard},\;{\varepsilon}_{standard})}$.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.61-74
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• 2018

Let $\mathcal{A}$ and $\mathcal{B}$ be two prime ${\ast}$-algebras. Let ${\Phi}:\mathcal{A}{\rightarrow}\mathcal{B}$ be a bijective and satisfies $${\Phi}(A{\bullet}B{\bullet}A)={\Phi}(A){\bullet}{\Phi}(B){\bullet}{\Phi}(A)$$, for all $A,B{\in}{\mathcal{A}}$ where $A{\bullet}B=A^{\ast}B+BA^{\ast}$. Then, ${\Phi}$ is additive. Moreover, if ${\Phi}(I)$ is idempotent then we show that ${\Phi}$ is ${\mathbb{R}}$-linear ${\ast}$-isomorphism.

• BMB Reports
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• v.40 no.5
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• pp.740-748
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• 2007

To gain insight into the structure and function of repressor proteins of bacteriophages of gram-positive bacteria, repressor of temperate Staphylococcus aureus phage ${\phi}11$ was undertaken as a model system here and purified as an N-terminal histidine-tagged variant (His-CI) by affinity chromatography. A ~19 kDa protein copurified with intact His-CI (~ 30 kDa) at low level was resulted most possibly due to partial cleavage at its Ala-Gly site. At ~10 nM and higher concentrations, His-CI forms significant amount of dimers in solution. There are two repressor binding sites in ${\phi}11$ cI-cro intergenic region and binding to two sites occurs possibly by a cooperative manner. Two sites dissected by HincII digestion were designated operators $O_L$ and $O_R$, respectively. Equilibrium binding studies indicate that His-CI binds to $O_R$ with a little more strongly than $O_L$ and binding species is probably dimeric in nature. Interestingly His-CI binding affinity reduces drastically at elevated temperatures ($32-42^{\circ}C$). Both $O_L$ and $O_R$ harbor a nearly identical inverted repeat and studies show that ${\phi}11$ repressor binds to each repeat efficiently. Additional analyses indicate that ${\phi}11$ repressor, like $\lambda$ repressor, harbors an N-terminal domain and a C-terminal domain which are separated by a hinge region. Secondary structure of ${\phi}11$ CI even nearly resembles to that of $\lambda$ phage repressor though they differ at sequence level. The putative N-terminal HTH (helix-turn-helix) motif of ${\phi}11$ repressor belongs to the HTH -XRE-family of proteins and shows significant identity to the HTH motifs of some proteins of evolutionary distant organisms but not to HTH motifs of most S. aureus phage repressors.

• Journal of Korean Tunnelling and Underground Space Association
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• v.3 no.3
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• pp.15-29
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• 2001

For the pertinent use of NMT method, both characteristics of joints (JRC, JCS and ${\phi}_r$) and characteristics of rock mass (Q-Value) must be investigated carefully. The main objective of the study presented is to investigate how sensitive the predicted behaviour of an underground excavation is to various realistic assumptions about some input parameter for the jointed rock mass. Joint pattern in the tunnel is predicted by statistical approach (chi-square test). In this paper, sensitivity studies involving in joint characteristics were carried out. The parametric studies involving change in Barton-Bandis joint model have shown that JCS is relatively insensitive to JRC and ${\phi}_r$. An increase in JRC value may not, according to the Barton-Bandis model, necessarily lead to a decrease in displacement. The importance of dilation in predicting the behaviour of a rock mass around an excavation is emphasized from a comparison of the Barton-Bandis joint behaviour model with the Mohr-Coulomb model. The Barton-Bandis model predicted higher stress, which allow for the build-up of stress caused by dilatant behaviour.