• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.853-871
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• 2011

In this paper, we prove the Hyers-Ulam-Rassias stability of the following additive functional inequality: ${\parallel}f(2x)+f(2y)+2f(z){\parallel}\;{\leq}\;{\parallel}2f(x+y+z){\parallel}$ We investigate homomorphisms in proper $CQ^*$-algebras and derivations on proper $CQ^*$-algebras associated with the additive functional inequality (0.1).

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.161-170
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• 2018

In this paper, we introduce and solve the following additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) $${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with ${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$ < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) in complex Banach spaces.

• East Asian mathematical journal
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• v.18 no.1
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• pp.51-58
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• 2002

• Proceedings of the Korean Society of Sericultural Science Conference
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• 2002.04a
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• pp.40-40
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• 2002

• KSBB Journal
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• v.27 no.5
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• pp.319-323
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• 2012

Vitamin C or L-ascorbic acid, an essential nutrient for humans with antioxidative property, was coated with natural wax to be used as functional additives for cosmetics. Coating of vitamin C was performed using carnauba wax and olive wax in self-designed reaction chamber for 60 min. The yield of coated vitamin C with carnawuba wax and olive wax were up to $94.6{\pm}1.2%$ and $82.5{\pm}1.4%$, respectively. The stability of the carnauba wax-coated vitamin C in the lotion was improved 17.8% than that of uncoated vitamin C during 30 day storage at $25^{\circ}C$. Color and the layer separation of the lotion added with the coated vitamin C showed better property than with the uncoated vitamin C. The coated vitamin C can be applied to cosmetic ingredients as a stable additive.

• Journal of Electrochemical Science and Technology
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• v.12 no.2
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• pp.279-284
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• 2021

The high theoretical specific capacity of lithium-sulfur (Li-S) batteries makes them a more promising energy storage system than conventional lithium-ion batteries (LIBs). However, the slow kinetics of the electrochemical conversion reaction seriously hinders the utilization of Li-S as an active battery material and has prevented the successful application of Li-S cells. Therefore, exploration of alternatives that can overcome the sluggish electrochemical reaction is necessary to increase the performance of Li-S batteries. In this work, an ionic liquid (IL) is proposed as a functional additive to promote the electrochemical reactivity of the Li-S cell. The sluggish electrochemical reaction is mainly caused by precipitation of low-order polysulfide (l-PS) onto the positive electrode, so the IL is adopted as a solubilizer to remove the precipitated l-PS from the positive electrode to promote additional electron transfer reactions. The ILs effectively dissolve l-PS and greatly improve the electrochemical performance by allowing greater utilization of l-PS, which results in a higher initial specific capacity, together with a moderate retention rate. The results presented here confirmed that the use of an IL as an additive is quite effective at enhancing the overall performance of the Li-S cell and this understanding will enable the construction of highly efficient Li-S batteries.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.1
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• pp.92-100
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• 2000

The model gas reaction tests were carried out to investigate the purification characteristics of methane on the exclusive catalyst for NGV. The experiment was conducted with the factors which affect the conversion efficiency of methane, such as Redox ratio, coexistence components of CO, MO, $H_2$O, precious metals and additives. The catalyst loaded with larger amount of pd and with additive La showed lower light-off temperature. In the presence of CO and NO, the conversion efficiency of methane was varied according to the kind of additive loaded. The conversion efficiency of methane was dropped for the catalyst loaded with La under lean air-fuel ratio, while it increased for the one loaded with Ti+Zr for the same condition. It was shown that the water vapor inhibited methane from oxidation by its poisoning on the surface of catalyst.

• YAKHAK HOEJI
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• v.54 no.4
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• pp.240-243
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• 2010

High-performance liquid chromatography (HPLC) screening method revealed that a propolis product marketed as a functional food contained an undeclared substance similar to tadalafil, the active ingredient of the prescription drug Cialis$^{(R)}$ approved for the treatment of male erectile dysfunction. In order to identify the illegal additive, the propolis product was extracted with methylene chloride, and the extract was purified further using semipreparative HPLC. The chemical structure of the isolated substance was elucidated based on IR, LC/MS-ESI, and $^1H$- and $^{13}C$-NMR spectroscopy, which showed the characteristics similar to tadalafil. The only difference was the substitution of the methyl group at the piperazinedione ring of tadalafil to the amino group of the identified illegal additive.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.1-21
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• 2013

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{\bot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.537-549
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• 1995

In this article, we propose a class of weighted estimators for the excess risk in additive risk model with a binary covariate. The proposed estimator is consistent and asymptotically normal. When the assumed model is inappropriate, however, the estimators with different weights converge to nonidentical constants. This fact enables us to develop a goodness-of-fit test for the excess assumption by comparing estimators with diffrent weights. It is shown that the proposed test converges in distribution to normal with mean zero and is consistent under the model misspecifications. Furthermore, the finite-sample properties of the proposed test procedure are investigated and two examples using real data are presented.