• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.57-75
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• 2004

The aim of this paper is to solve the general solution of a quadratic functional equation f(x + 2y) + 2f(x - y) = f(x - 2y) + 2f(x + y) in the class of functions between real vector spaces and to obtain the generalized Hyers-Ulam stability problem for the equation.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.377-392
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• 2004

In the present paper, we obtain the Hyers-Ulam-Rassias stability in the sense of Gavruta for the general quadratic functional equation f(χ + y + z) + f(χ - y) + f(χ - z) = f(χ - y - z) + f(χ + y) + f(χ + z).

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.133-144
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• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.403-412
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• 2022

In this paper, we introduce the following cubic-quartic functional equation of the form $$f(x+4y)+f(x-4y)=16[f(x+y)+f(x-y)]{\pm}30f(-x)+\frac{5}{2}[f(4y)-64f(y)]$$. Further, we investigate the general solution and the Ulam stability for the above functional equation in non-Archimedean spaces by using the direct method.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.8
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• pp.3583-3587
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• 2012

SUMOylation has emerged as an important post-translational modification that modulates the localization, stability and activity of a broad spectrum of proteins. A dynamic process, it can be reversed by a family of SUMO-specific proteases (SENPs). However, the biological roles of SENPs in mammalian development and pathogenesis remain largely elusive. Here, we demonstrated that SENP2 plays a critical role in the control of hepatocellular carcinoma cell growth. SENP2 was found to be down-regulated in hepatocellular carcinoma (HCC) tissues and over-expression suppressed the growth and colony formation of HCC cells. In contrast, silencing of SENP2 by siRNAs promoted cancer cell growth. We further found that stability of ${\beta}$-catenin was markedly decreased when SENP2 was over-expressed. Interestingly, the decrease was dependent on the de-SUMOylation activity of SENP2, because over-expression of a SENP2 catalytic mutant form had no obviously effects on ${\beta}$-catenin. Our results suggest that SENP2 might play a role in hepatocellular carcinoma cell growth control by modulating the stability of ${\beta}$-catenin.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.51-68
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• 2005

In this paper we solve a generalized Popoviciu functional equation and investigate the stability of this equation.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.597-603
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• 2010

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1748-1753
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• 2011

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.51-53
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• 2008

The vehicle aerodynamic crosswind characteristics are mainly governed by the coefficient of side force and yawing moment. These performances affect not only the driving comfort which can be felt by driver but also the safety due to the instability of vehicle. The aims of this investigation are to improve the aerodynamic crosswind performance of sedan vehicle under the crosswind conditions. In order to improve the crosswind stability, numerical analysis has been performed by modifying the rear body shape of vehicle. As the results, we observed about 20% reduction of yawing moment coefficient relative to the base vehicle.

• International Journal of Highway Engineering
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• v.18 no.3
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• pp.67-74
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• 2016

PURPOSES : This study evaluated the field applicability and laboratory performance of glass fiber-reinforced asphalt (GFRA) mixtures. METHODS : The general hot-mix asphalt (HMA) and GFRA mixtures were paved in five sites, including three national highways, one express highway, and an arterial road, to evaluate field applicability and durability. The plant mixing and construction method for the GFRA were similar to those for the general HMA. The lab performances of the field samples were relatively compared through the mechanical measures from the Marshall stability, indirect tensile strength, and dynamic stability. The field performance was surveyed after a year. RESULTS : The lab tests verified the superior lab performances of the GFRA compared to the general HMA. The Marshall stability of the GFRA increased for about 128% of the general HMA. The indirect tensile strength of the GFRA was 115% greater than that of the general HMA. The dynamic stability of the GFRA resulted in 16,180 reps/mm, which indicated that high rut resistance may be expected. No noticeable defects, such as cracks or deformation, were observed for the GFRA sections after a year. CONCLUSIONS : The lab tests and field survey for the five GFRA sites resulted in superior performances compared to the general HMA. The relatively low-cost GFRA, which required no pre-processing procedures, such as polymer modification, may be a promising alternative to the polymer-modified asphalt mixtures. The long-term performance will be verified by the superior field durability of the GFRA in the near future.