• East Asian mathematical journal
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• 제28권3호
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• pp.265-280
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• 2012

In this paper, we introduce an iterative sequence by using a hybrid generalized $f$-projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping an the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319-329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997-4007], and many others.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회B
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• pp.2415-2418
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• 2008

Polydiacetylenes (PDAs) are very attractive chemical substances which have distinctive features of color change and fluorescence emission by thermal or chemical stress. Especially, when PDAs contact with solutions of a particular pH, such as a strong alkaline sodium hydroxide (NaOH) solution or a strong acidic hydrogen chloride (HCl) solution, PDAs change their color from non-fluorescent blue to fluorescent red. In this study, we propose a novel method to detect alkaline pH using PDAs and NaOH solutions by hydrodynamic focusing on a microfluidic chip. Preliminary results indicate that the fluorescent intensity of PDAs increases in respond to the NaOH solution concentrations. Also, the fluorescence is quenched back when the PDAs are in contact with a HCl solution. These results are useful in a microfluidic PDA sensor chip design for pH detection.

• Journal of the korean society of oceanography
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• 제31권2호
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• pp.75-88
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• 1996

The analytic and numerical solution of the 1$\frac{1}{2}$-layer and 2$\frac{1}{2}$-layer models are derived. The large coastal-sea level drop and the fast westward speed of the anticyclonic gyre due to strong offshore winds using two ocean models are investigated. The models are forced by wind stress fields similar in structure to the intense mountain-pass jets(${\sim}$20 dyne/$cm^{2}$) that appear in the Gulfs of Tehuantepec and Papagayo in the Central America for periods of 3${\sim}$7 days. Analytic and numerical solutions compare favorably with observations, the large sea-level drop (${\sim}$30 cm) at the coast and the fast westward propagation speeds (${\sim}$13 km/day) of the gyres. The coastal sea-level drop is enhanced by several factors: horizontal mixing, enhanced forcing, coastal geometry, and the existence of a second active layer in the 2$\frac{1}{2}$-layer model. Horizontal mixing enhances the sea-level drop because the coastal boundary layer is actually narrower with mixing. The forcing ${\tau}$/h is enhanced near the coast where h is thin. Especially, in analytic solutions to the 2$\frac{1}{2}$-layer model the presence of two baroclinic modes increases the sea-level drop to some degree. Of theses factors the strengthened forcing ${\tau}$/h has the largest effect on the magnitude of the drop, and when all of them are included the resulting maximum drop is -30.0 cm, close to observed values. To investigate the processes that influence the propagation speeds of anticyclonic gyre, several test wind-forced calculations were carried out. Solutions to dynamically simpler versions of the 1$\frac{1}{2}$-layer model show that the speed is increased both by ${\beta}$-induced self-advection and by larger h at the center ofthe gyres. Solutions to the 2$\frac{1}{2}$-layer model indicate that the lower-layer flow field advects the gyre westward and southward, significantly increasing their propagation speed. The Papagayo gyre propagates westward at a speed of 12.8 km/day, close to observed speeds.

• Bulletin of the Korean Chemical Society
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• 제31권7호
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• pp.1945-1950
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• 2010

Solvent extraction experiments of Pt(IV), Pd(II) and Rh(III) by Alamine336 were performed from the mixed chloride solutions. In the HCl concentration range from 1 to 5 M, most of Pt and Pd were extracted from the mixed solutions. However, the extraction percentage of Rh was much smaller than that of Pt and Pd. Lower concentration of Alamine336 in strong HCl solution led to higher separation factor of Rh from Pt and Pd. Adding $SnCl_2$ to the mixed solutions increased the extraction percentage of Rh, while the extraction percentage of Pt and Pd was little affected. Our results showed that selective separation of Rh or coextraction of the three platinum group metals from the mixed solution would be possible by adjusting the extraction conditions.

• Bulletin of the Korean Chemical Society
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• 제13권3호
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• pp.259-265
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• 1992

Cyclic voltammetric behavior of symmetric (dimethyl, diheptyl, dioctyl, dibenzyl) and asymmetric (methyloctyl, methyldodecyl, methylbenzyl) viologens was investigated in homogeneous aqueous solution and sodium dodecyl sulfate (SDS) micellar media. In SDS-free 0.1 M NaCl solutions, the reduction potential is less negative as the chain length of alkyl substituent is longer. This is due to the stabilization of the reduced cationic radical and neutral form of viologen by adsorption on electrode surface. The adsorbed species show the "aging-effect". With the exceptions of methyldodecyl viologen and methylbenzyl viologen, the viologens show strong tendency of conproportionation reaction between viologen dications and neutral forms. In cases of methyldodecyl viologen and methylbenzyl viologen, the conproportionation reaction is kinetically disfavored, though it is thermodynamically favorable. SDS micelles dissolve the adsorbed species and the viologens exhibit two reversible redox processes in SDS micellar solutions. The reduction potentials of viologens in SDS micellar solutions depend little on the length of alkyl chain. Benzyl-substituted viologens are more easily reduced than the alkyl substituted viologens, presumably due to electron-withdrawing character of benzyl group.

• 대한수학회보
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• 제61권3호
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• pp.637-669
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• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• 대한수학회지
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• 제33권4호
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• pp.1039-1046
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• 1996

In the theory of partial differential equations with given initial values and boundary values one usually investigates to examine the well-posedness, that is, the unique existence of the solution as well as its continuous dependence on the data. This theory is strong enough for us to determine the situation anywhere and anytime provided that the initial data are actually given. However, in many cases the data are not completely known for us. Then in those situations arise the new problem to determine the unknown initial data by taking other conditions for the solutions.

• 대한수학회지
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• 제52권2호
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• pp.373-388
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• 2015

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.

• East Asian mathematical journal
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• 제30권5호
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• pp.631-637
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• 2014

In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

• East Asian mathematical journal
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• 제19권1호
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• pp.91-102
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• 2003

In this paper we prove the existence of mild and strong solutions of nonlinear delay integrodifferential equations with nonlocal conditions. The results are obtained by using the Schauder fixed point theorem and resolvent operator.