• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.493-499
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• 2008

We construct a minimizing sequence for the Sobolev trace inequality which satises compactness in the concentration compactness property.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1419-1439
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• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1143-1156
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• 2010

In this paper, we study the following p&q-Laplacian problem with critical Sobolev and Hardy exponents {$-{\Delta}_pu-{\Delta}_qu={\mu}\frac{{\mid}u{\mid}^{p^*(s)-2}u}{{\mid}x{\mid}^s}+{\lambda}f(x,\;u)$, in $\Omega$, u=0, on $\Omega$, where ${\Omega}\;{\subset}\;\mathbb{R}^{\mathbb{N}}$ is a bounded domain and ${\Delta}_ru=div({\mid}{\nabla}u{\mid}^{r-2}{\nabla}u)$ is the r-Laplacian of u. By using the variational method and concentration-compactness principle, we obtain the existence of infinitely many small solutions for above problem which are the complement of previously known results.

• Korean Journal of Organic Agriculture
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• v.14 no.1
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• pp.85-95
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• 2006

The investigation of the effect of the deep sea water in different concentration (0%, 10%, 20%, 30%, 40%) on the inhibition of growth, fresh weight, dry weight of the tomato, hot pepper, cucumber plug seedlings were conducted. As the concentration of the deep sea water was higher, the greater inhibition was noticed. The height were decreased at the rate of 8%, 25%, 32% in tomato, 9%, 26%, 27% in hot pepper, and 21%, 50%, 58% in cucumber plug seedlings as compare to local check. The fresh weights were decreased highly, as the concentration of the deep sea water increased. Tomato seedlings showed the decrease rate of 12%, 23%, 33% at above the ground part of plants, and 2%, 30%, 52% at under the ground parts. Likewise, Hot pepper seedlings showed the decrease rate of 1.1%, 5.7%, 15.4% at above the ground part of plants, and 22.1%, 25%, 47.1%, respectively at under the ground parts. The fresh weight of cucumber was decreased at the rate of 8.1%, 36%, 51% in the above the ground, and 6.2%, 11%, 65% at the under the ground parts. In tomato, hot pepper, and cucumber seedlings, the dry weight was decreased as the concentration of deep sea water was increased. Thirty percent of deep sea water treatment reduced the dry weight of the seedlings as half of the control seedlings. One of the important factors of the seedling quality is compactness. Compactness was highest at 20% deep sea water in all the three crop seedlings.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.661-677
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• 2015

In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

• Journal of the Korean Association of Geographic Information Studies
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• v.25 no.3
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• pp.29-58
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• 2022

Recently, Korea has been experiencing a problem of population decline, therefore the transition to a compact spatial structure is being urged. However, what is required is not just physical compression, but a compact city that also considers connectivity, in view of the changes in today's demographic and industrial structure. From this point of view, this study measures the compressibility of domestic cities suffering from extinction risk due to low birth rates, aging population, and population decline, and examined the spatial structure characteristics. In addition to the compressibility evaluation index used in previous studies, the compressibility of six indicators (population, land use, service accessibility, transport accessibility, connectivity, and concentration) was compared and analyzed, and a comprehensive compression index was calculated. The analysis results, based on the comprehensive compression index, classified 2.3% cities in the first grade, 4.6% in the second grade, 16.09% in the third grade, 43.68% in the fourth grade, and 33.33% in the fifth grade areas. Currently, the urban characteristics affecting the compactness index differ from region to region. Therefore, it is necessary to establish measures and policies for extinction risk considering the influence of each region's compactness index. This study is meaningful in that connectivity was considered using spatial syntax, and the compactness of cities at risk of extinction was compared and analyzed quantitatively. It is expected that this study will be used as basic data to establish the direction and action strategy for extinction risk cities.

• Journal of ILASS-Korea
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• v.9 no.4
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• pp.67-76
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• 2004

Diode laser absorption sensors are advantageous because they may provide fast, sensitive, absolute, and selective measurements of species concentration. These systems are very attractive for practical applications owing to its compactness, reasonable cost, robustness, and ease of use. In addition, diode lasers we fiber-optic compatible and thus enable simultaneous measurements of multiple species along a line-of-sight. Recent advances of room-temperature, near-IR and visible diode laser sources for telecommunication, optical data storage applications make it possible to be applied for combustion diagnostics based on diode laser absorption spectroscopy. Therefore, combined with fiber-optics and high sensitive detection strategies, compact and portable sensor systems are now appearing for variety of applications. The objectives of this research are to develop new gas sensing system and to verify feasibility of this system. Wavelength modulation spectroscopy has been demonstrated in these experiments and has a bright prospect to this diode laser system.

• Journal of Environmental Science International
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• v.1 no.1
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• pp.69-76
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• 1992

The effects of $Ca_{2+}$ ion on the formation of micelle colloid of nonionic surfactants, nonylphenol-(ethylene oxide)n [NP-(EO)n: n= 11, 40, 100) were investigated by the iodine solubilization method. The characteristics of spectra depended on the concentration of $Ca_{2+}$ ion and the number of EO unit. Above CMC(critical micelle concentration), the intensity of the CT (charge transfer) band by the addition of $Ca_{2+}$ ion for the NP-(EO)11 and NP-(EO)40 increased and when decreased and for the NP-(EO)In continuously increased. The increase in the intensity of CT band were attributed to the compactness of micelle in the presence of $Ca_{2+}$ ion. These phenomena may be explained by the fact that the linear ethylene oxide (EO) chain, relatively free to assume various configuration in aqueous solution, could form a pseudo-crown ether structures capable of forming complexes with $Ca_{2+}$ ion.

• Journal of Bio-Environment Control
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• v.15 no.2
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• pp.156-161
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• 2006

Overhead and sub-irrigation of deep sea water to tomato seedlings reduced the height as 50% and 58% than control plants. In the same treatment with surface sea water and NaCl water, the reduced rate in tomato seedlings' height were 49% and 56% in overhead irrigation, and 47% and 57% in sub-irrigation, respectively. Most effective method for the inhibition of the growth of the seedling was sub-irrigation method, which supplied water through the roots. No significant difference was observed on fresh weight of the upper part of tomato and cucumber seedlings, though the sub-irrigation reduced the fresh weight than the overhead irrigation. The reduced rate of fresh weight of seedlings by overhead irrigation was by 38% and sub-irrigation by 49% as compared to control. Similarly dry weight of upper and under soil parts of seedlings showed same trend of results thereof as fresh weight. This result can be traced to reduction of growth caused by salts in the water. In stem diameter of seedlings no significant difference was observed between two irrigation methods, even though both deep sea and NaCl water reduced stem diameter, as compared to control water. Overhead irrigation can be chosen by seedling producers because of better seedling quality by using TH ratio. Seedling compactness were not noticed in both the overhead and sub-irrigation. Sub-irrigation was found more effective method far the inhibition of height and compactness of tomato seedlings. Higher the concentration of NaCl, deep sea, and surface sea water, lesser the growth in height, fresh and dry weight, stem diameter, and leaf area was obtained. No significant difference was found, though sub-irrigation suppress the growth of seedlings.