• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.3
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• pp.1106-1113
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• 1996

The phase criterion of the feedback cycle of low-speed edgetones has been obtained using the jet-edge interaction model which is based on the substitution of an array of dipoles for the reaction of the wedge to the impinging jet. The edgetone is produced by the feedback loop between the downstream-convected sinuous disturbance and upstream-propagating waves generated by the impingement of the disturbance on the wedge. By estimation of the phase difference between the downstream and the upstream disturbances, the relationship between the edge distance and the wavelength is obtained according to the phase-locking condition at the nozzle lip. With a little variation depending on the characteristics of jet-edge interaction, the criterion can be approximated as follows: h/.LAMBDA. + h/.lambda. = n - 1/4, where h is the stand-off distance between the nozzle lip and the edge tip, .LAMBDA. is the wavelength of downstream-convected wave, .lambda. is the wavelength of the upstream-propagating acoustic wave and n is the stage number for the ladder-like characteristics of frequency. The present criterion has been confirmed by estimating wavelengths from available experimental data and investigating their appropriateness. The above criterion has been found to be effective up to 90.deg. of wedge angle corresponding to the cavitytones.

• BMB Reports
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• v.38 no.1
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• pp.89-96
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• 2005

Earlier, we reported that the bacteriophage $\lambda$ P gene product is lethal to Escherichia coli, and the E. coli rpl mutants are resistant to this $\lambda$ P gene-mediated lethality. In this paper, we show that under the $\lambda$ P gene-mediated lethal condition, the host DNA synthesis is inhibited at the initiation step. The rpl8 mutation maps around the 83 min position in the E. coli chromosome and is 94% linked with the dnaA gene. The rpl8 mutant gene has been cloned in a plasmid. This plasmid clone can protect the wild-type E. coli from $\lambda$ P gene-mediated killing and complements E. coli dnaAts46 at $42^{\circ}C$. Also, starting with the wild-type dnaA gene in a plasmid, the rpl-like mutations have been isolated by in vitro mutagenesis. DNA sequencing data show that each of the rpl8, rpl12 and rpl14 mutations has changed a single base in the dnaA gene, which translates into the amino acid changes N313T, Y200N, and S246T respectively within the DnaA protein. These results have led us to conclude that the rpl mutations, which make E. coli resistant to $\lambda$ P gene-mediated host lethality, are located within the DNA initiator gene dnaA of the host.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.127-145
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• 2009

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1937-1943
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• 2015

For $1{\leq}{\alpha}<2$, let $\mathcal{F}({\alpha})$ denote the class of locally univalent normalized analytic functions $f(z)=z+{\Sigma}_{n=2}^{\infty}{a_nz^n}$ in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\left|z\right|}<1\}$ satisfying the condition $Re\(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\)>{\frac{{\alpha}}{2}}-1$. In the present paper, we shall obtain the sharp upper bound for Fekete-$Szeg{\ddot{o}}$ functional $|a_3-{\lambda}a_2^2|$ for the complex parameter ${\lambda}$.

• Korean Journal of Optics and Photonics
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• v.2 no.4
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• pp.186-192
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• 1991

For the micro-lithography using a excimer laser beam $(\lambda\leq0.248$\mu\textrm{m})$. a mirror system consisting of four spherical surfaces with reductlon magnification 5X is designed. Initially the aplanat, flat field and the distortion free condition of the system are analytically investigated within Seidel 3rd order aberrations. And the computer-aided optimization technique has been employed for the further improved performance of the system. The final system has N.A. of 0.15 and image field diameter 3.3 mm, and has the diffraction-limited performance for KrF eximer laser beam.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.127-135
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• 2017

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 5-dimensional $^*g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.