• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.789-801
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• 2014

In this paper, we study the existence of ground state solutions for a class of non-resonant cooperative elliptic systems by a variant weak linking theorem. Here the classical Ambrosetti-Rabinowitz superquadratic condition is replaced by a general super quadratic condition.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1181-1209
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• 2021

In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schrödinger-Poisson-Kirchhoff system $$\;\{\begin{array}{lll}-(1+b{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+k(x){\phi}u={\lambda}f(x)u+{\mid}u{\mid}^4u,&&\text{in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=k(x)u^2,&&\text{in }{\mathbb{R}}^3,\end{array}$$ where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ₁ and λ₁ is the first eigenvalue of the problem -∆u + V(x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ₁. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.

• Bulletin of the Korean Chemical Society
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• v.12 no.4
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• pp.441-444
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• 1991

The intramolecular proton transfers of 2-hydroxy-4,5-naphthotropone in room temperature solutions are studied using static and time-resolved absorption and emission spectroscopy. Dual normal and tautomer fluorescence is observed in ethanol solution, while only the tautomer fluorescence is observed in cyclohexane solution. The fluorescence lifetimes and quantum yields in ethanol and cyclohexane solutions indicate that in hydrocarbon solvents, rapid intersystem crossing competes with proton transfer in the first excited singlet state. Transient absorption spectra and kinetics indicate that proton transfer also undergoes in the first triplet state with a transfer time of ∼ 3 ns. No transient absorption from the tautomer ground state indicates a rapid back proton transfer in the ground state.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1269-1284
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• 2022

This paper is concerned with the following Schrödinger-Poisson system $$\{\begin{array}{lll}-{\Delta}u+V(x)u+K(x){\phi}u=a(x){\mid}u{\mid}^{p-2}u&&\text{ in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=K(x)u^2&&\text{ in }{\mathbb{R}}^3,\end{array}$$ where 4 < p < 6. For the case that K is nonnegative, V and a are indefinite, we prove the above problem possesses one ground state sign-changing solution with exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions is larger than that of the ground state solutions. The novelty of this paper is that the potential a is indefinite and allowed to vanish at infinity. In this sense, we complement the existing results obtained by Batista and Furtado [5].

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1601-1615
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• 2019

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

• Geomechanics and Engineering
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• v.21 no.3
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• pp.279-288
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• 2020

The permeation grouting is a commonly used technique to improve the engineering geology condition of the soft ground. It is of great significance to predict the permeation range of the grout so as to ensure the effects of grouting. This paper conducts a theoretical analysis of jet-grouting effects in ground improvement and rotary grouting pile installation by utilizing deformation-permeation coupled poroelastic solutions based on Biot's theory and Laplace-Fourier integral transform technique. The exponential function and the intermittent trigonometric function are chosen to represent time-dependent grouting pressure usually encountered in ground improvement and rotary grouting pile installation process, respectively. The results, including the radial displacement, the hoop stress, the excess pore fluid pressure, the radial discharge, and the permeation radius of grout, are presented for different grouting time, radial positions and grouting lengths. Parametric study is conducted to explore the effects of variation of the exponent in the exponential grouting pressure-time relationship on grouting-induced responses. It is expected that the proposed solutions can be used to estimate the permeation range of grouting in ground improvement and rotary grouting pile installation.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1011-1016
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• 2011

In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equation on $R^N$. we obtained the results under different suitable conditions on the locally H$\"{o}$lder continuous nonlinearity f(x, u), we needn't any mono-tonicity condition about the nonlinearity.

• Journal of Photoscience
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• v.10 no.1
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• pp.149-155
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• 2003

The absorption, fluorescence and fluorescence-excitation spectra of concentrated toluene solutions of selected para substituted trans-stilbene derivatives provide strong evidence for aggregation. A red-shifted fluorescence spectrum peaking at 420 nm gains in intensity as the stilbene concentration is increased. The excitation spectrum of this new emission is well to the red of the normal stilbene absorption spectrum, consistent with the appearance of a red shifted shoulder in the UV spectrum. Formation of a fluorescent ground state dimer (or higher aggregate) is proposed to account for these observations. The presence of polar substituents is crucial to the formation of this ground state complex.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.45-61
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• 2009

We consider finite time blowup solutions of the $L^2$-critical focusing Hartree equation on $\mathbb{R}^n$, $n{\geq}3$ below $H^1$.

• Journal of The Korean Astronomical Society
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• v.49 no.3
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• pp.93-107
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• 2016

Augmenting the Wide Field Infrared Survey Telescope (WFIRST) microlensing campaigns with intensive observations from a ground-based network of wide-field survey telescopes would have several major advantages. First, it would enable full two-dimensional (2-D) vector microlens parallax measurements for a substantial fraction of low-mass lenses as well as planetary and binary events that show caustic crossing features. For a significant fraction of the free-floating planet (FFP) events and all caustic-crossing planetary/binary events, these 2-D parallax measurements directly lead to complete solutions (mass, distance, transverse velocity) of the lens object (or lens system). For even more events, the complementary ground-based observations will yield 1-D parallax measurements. Together with the 1-D parallaxes from WFIRST alone, they can probe the entire mass range M ≳ M_⊕. For luminous lenses, such 1-D parallax measurements can be promoted to complete solutions (mass, distance, transverse velocity) by high-resolution imaging. This would provide crucial information not only about the hosts of planets and other lenses, but also enable a much more precise Galactic model. Other benefits of such a survey include improved understanding of binaries (particularly with low mass primaries), and sensitivity to distant ice-giant and gas-giant companions of WFIRST lenses that cannot be detected by WFIRST itself due to its restricted observing windows. Existing ground-based microlensing surveys can be employed if WFIRST is pointed at lower-extinction fields than is currently envisaged. This would come at some cost to the event rate. Therefore the benefits of improved characterization of lenses must be weighed against these costs.