• Elastomers and Composites
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• v.55 no.4
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• pp.306-313
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• 2020

To investigate the reinforcing effects of functional fillers in nitrile rubber (NBR) materials, high-structure carbon black (HS45), coated calcium carbonate (C-CaCO3), silica (200MP), and multi-walled carbon nanotubes (MWCNTs) were used as functional filler, and carbon black (SRF) as a common filler were used for oil-resistant rubber. The curing and mechanical properties of HS45-, 200MP-, and MWCNT-filled NBR compounds were improved compared to those of the SRF-filled NBR compound. The reinforcing effect also increased with a decrease in the particle size of the fillers. The C-CaCO3-filled NBR compound exhibited no reinforcing effect with increasing filler concentration because of their large primary particle size (2 ㎛). The reinforcing behavior based on 100% modulus of the functional filler based NBR compounds was compared by using several predictive equation models. The reinforcing behavior of the C-CaCO3-filled NBR compound was in accordance with the Smallwood-Einstein equation whereas the 200MP- and MWCNT-filled NBR compounds fitted well with the modified Guth-Gold (m-Guth-Gold) equation. The SRF- and HS45-filled NBR compounds exhibited reinforcing behavior in accordance with the Guth-Gold and m-Guth-Gold equations, respectively, at a low filler content. However, the values of reinforcement parameter (100Mf/100Mu) of the SRF- and HS45-filled NBR compounds were higher than those determined by the predictive equation model at a high filler content. Because the chains of SRF composed of spherical filler particles are similarly changed to rod-like filler particles embedded in a rubber matrix and the reinforcement parameter rapidly increased with a high content of HS45, the higher-structured filler. The reinforcing effectiveness of the functional fillers was numerically evaluated on the basis of the effectiveness index (��SRF/��f) determined by the ratio of the volume fraction of the functional filler (��f) to that of the SRF filler (��SRF) at three unit of reinforcing parameter (100Mf/100Mu). On the basis of their effectiveness index, MWCNT-, 200MP-, and HS45-filled compounds showed higher reinforcing effectiveness of 420%, 70%, and 20% than that of SRF-filled compound, respectively whereas C-CaCO3-filled compound exhibited lower reinforcing effectiveness of -50% than that of SRF-filled compound.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.815-830
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• 2009

In this paper we establish the general solution of the following functional equation with mixed type of quadratic and additive mappings f(mx+y)+f(mx-y)+2f(x)=f(x+y)+f(x-y)+2f(mx), where $m{\geq}2$ is a positive integer, and then investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.561-570
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• 2003

We propose a nonparametric test procedure for checking the proportionality assumption between hazard functions using a functional equation. Because of the involvement of censoring distribution function, we consider the large sample case only and obtain the asymptotic normality of the proposeed test statistic. Then we discuss the rationale of the use of the functional equation, give some examples and compare the performances with Andersen's procedure by computing powers through simulations.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.49-58
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• 2016

We study the existence of S-asymptotically ${\omega}$-periodic mild solutions of partial functional integrodifferential equation by the method of Caicedo et al. [2].

• East Asian mathematical journal
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• v.30 no.3
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• pp.271-281
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• 2014

In this paper, we consider the following cubic functional equation f(3x + y) + f(3x - y) = f(x + 2y) + 2f(x - y) + 2f(3x) - 3f(x) - 6f(y) and prove the generalized Hyers-Ulam stability for it in fuzzy normed spaces.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.157-164
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• 2021

Recently we investigated a type of Hyers-Ulam stability of the Schrödinger equation with the symmetric parabolic wall potential that efficiently describes the quantum harmonic oscillations. In this paper we study a type of Hyers-Ulam stability of the Schrödinger equation when the potential barrier is a quartic wall in the solid crystal models.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.503-514
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• 2007

In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.

• Nuclear Engineering and Technology
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• v.3 no.4
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• pp.203-208
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• 1971

Noether's theorem is applied to the one dimensional neutron transport equation. It is obtained the transformation rendering the functional of the one dimensional Boltzmann equation invariant. It is derived the law conserving the product of the directional flux and its adjoint flux. The possible types of the solution of the Boltzmann equation are discussed. The results are compared with the well-known solution.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.199-214
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• 2017

We consider fixed-point iterations constructed by simple transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.113-128
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• 2011

Let f : ${\mathbb{R}}{\rightarrow}{\mathbb{C}}$. We consider the Hyers-Ulam stability of Jensen type functional inequality $$|f(px+qy)-Pf(x)-Qf(y)|{\leq}{\epsilon}$$ in the half planes {(x, y) : $kx+sy{\geq}d$} for fixed d, k, $s{\in}{\mathbb{R}}$ with $k{\neq}0$ or $s{\neq}0$. As consequences of the results we obtain the asymptotic behaviors of f satisfying $$|f(px+qy)-Pf(x)-Qf(y)|{\rightarrow}0$$ as $kx+sy{\rightarrow}{\infty}$.