• East Asian mathematical journal
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• 제38권5호
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• pp.643-647
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• 2022

Let F² denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F². We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.

• 대한수학회보
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• 제52권2호
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• 대한수학회보
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• 제55권6호
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• pp.1869-1889
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• 2018

We are concerned with the following fractional p-Laplacian inclusion: $$(-{\Delta})^s_pu+V(x){\mid}u{\mid}^{p-2}u{\in}{\lambda}[{\underline{f}}(x,u(x)),\;{\bar{f}}(s,u(x))]$$ in ${\mathbb{R}}^N$, where $(-{\Delta})^s_p$ is the fractional p-Laplacian operator, 0 < s < 1 < p < $+{\infty}$, sp < N, and $f:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is measurable with respect to each variable separately. We show that our problem with the discontinuous nonlinearity f admits at least one or two nontrivial weak solutions. In order to do this, the main tool is the Berkovits-Tienari degree theory for weakly upper semicontinuous set-valued operators. In addition, our main assertions continue to hold when $(-{\Delta})^s_pu$ is replaced by any non-local integro-differential operator.

• 대한수학회보
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• 제51권1호
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• pp.237-252
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• 2014

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.

• Bulletin of the Korean Chemical Society
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• 제32권2호
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• pp.467-471
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• 2011

Spin exchange interactions of $(C_2N_2H_{10})[Fe(HPO_3)F_3]$ were examined by performing a spin dimer analysis based on extended Huckel tight binding method and a mapping analysis based on first principles density functional theory. Spin exchange interactions occur through the super-superexchange paths $J_1$ and $J_2$ in $(C_2N_2H_{10})[Fe(HPO_3)F_3]$. In the super-superexchange path $J_2$ magnetic orbital interactions between eg-block levels are much stronger than those from $t_{2g}$-block levels. Both electronic structure calculations show that the spin exchange interaction through the super-superexchange path $J_2$ is much stronger than that of $J_1$.

• 한국방사선학회논문지
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• 제2권1호
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• pp.31-34
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• 2008

The neutron capture spectrum for the light nuclide was very useful to study the nuclear structure. In the present study, the capture gamma-ray from the 27-keV resonance of $^{19}F(n,g)^{20}F$ reaction were measured with an anti-Compton NaI(Tl) spectrometer and the 3-MV Pelletron accelerator of the Research Laboratory for Nuclear Reactors at the Tokyo institute of technology. A neutron Time-of-Flight method was adopted with a 1.5 ns pulsed neutron source by the $^7Li(p,n)^7Be$ reaction. In the present experiment, a Teflon(($CF_2$)n) sample was used The sample was disk with a diameter of 90mm. The thickness of sample was determined so that reasonable counting rates could be obtained and the correction was not so large for the self-shielding and multiple scattering of neutrons in the sample, and was 5mm. The primary gamma-ray transitions were compared with previous measurement of Kenny.

• 대한산업공학회지
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• 제26권2호
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• pp.128-135
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• 2000

This paper considers a consecutive k-out-of-n:F system when the failure of a component in the system induces higher failure rate of the preceding survivor. The reliability, mean time to failure(MTTF), and average failure number of a consecutive k-out-of-n:F system are obtained, when the failure of a component increases the failure rate of the survivor which is working just before the failed component. Then the optimal number of consecutive failed components to minimize this long run average cost rate can be obtained. An example is considered to calculate the reliability, MTTF and average failure number of the system. And two procedures that find the optimal number of consecutive failed components are studied. Then, various cases of system parameters are also studied.

• Journal of Photoscience
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• 제4권1호
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• pp.1-5
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• 1997

A hitherto unknown diphenylbutadiene analog viz. 1-(p-N,N-dimethylaminophenyl)-4-phenyl-2-methyl-1E,3E-butadiene (10) has been prepared and its absorption, excitation, and fluorescent emission properties in different media including various organic solvents and aqueous bovine serum albumin (BSA) have been studied. For comparision, these properties have also been investigated for the parent diphenylbutadiene (2). Diene 10 exhibits solvent polarity/polarizability-sensitive fluorescence properties ($\lambda$$_{max}$, $\Phi$$_f$, $\tau$$_f$, K$_f$, f). It also binds to the hydrophobic domains of aqueous bovine serum albumin (BSA) with a binding constant of 3.89 x 10$^4$ M$^{-1}$. The relative fluorescence quantum yield of 10 increases, while, the fluorescence lifetime decreases with increasing concentration of-BSA. The results highlight the polar character of the singlet excited state of diphenylpolyenes and the utility of 10 as fluorescence probe for studying microenvironments of organized assemblies and biological supramolecular structures.

• Journal of Welding and Joining
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• 제28권2호
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• pp.91-95
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• 2010

Stress distribution and deformation on the CT-type(Cross Tension type) spot welded lap joint subjected to out of plane tensile load were investigated by finite element method. Using the maximum principal stresses at the nugget edge obtained by FEM analysis, evaluated the fatigue strength of the CT-type spot welded lap joints having various dimensions and materials. and also, the influence of the geometrical parameters of CT-type spot welded lap joints on stress distribution and fatigue strength must be evaluated. thus, in this paper, ${\Delta}P-N_f$ curve were obtained by fatigue tests. Using these results, ${\Delta}P-N_f$ curve were systematically rearranged in the $\Delta\sigma-N_f$ relation with the hot spot stresses at the CT-type spot welded lab joints. It was found that the proposed $\Delta\sigma-N_f$ relation could provide a more reasonable fatigue design criterion for the CT-type spot welded lap joints.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.77-85
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• 2011

In this paper, we introduce the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) analytic functions with positive real part. The radius of convexity of this integral operator when ${\beta}$ = 1 is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with Re {f(z)/z} > 0 and Re {f'(z)} > 0. Furthermore, we derive sufficient condition for the integral operator $I_{\beta}$($p_1$, ${\ldots}$, $p_n$; ${\alpha}_1$, ${\ldots}$, ${\alpha}_n$)(z) to be analytic and univalent in the open unit disc, which leads to univalency of the operators $\int\limits_0^z(f(t)/t)^{\alpha}$dt and $\int\limits_0^z(f'(t))^{\alpha}dt$.