• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1513-1521
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• 2013

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_q[u]/(u^i)$, $\mathbb{F}_q[u_1,{\ldots},u_i]/(u^2_1,u^2_2,{\ldots},u^2_i,u_1u_2-u_2u_1,{\ldots},u_ku_j-u_ju_k,{\ldots})$, and $\mathbb{F}_q[u,v]/(u^i,v^j,uv-vu)$, where $\mathbb{F}_q$ is a field with $q$ elements $q=p^r$ for some prime number $p$ and $r{\in}\mathbb{N}-\{0\}$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.643-657
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• 2022

Let R be a ring and S a multiplicative subset of R. An R-module T is called u-S-torsion (u-always abbreviates uniformly) provided that sT = 0 for some s ∈ S. The notion of u-S-exact sequences is also introduced from the viewpoint of uniformity. An R-module F is called u-S-flat provided that the induced sequence 0 → A ⊗_R F → B ⊗_R F → C ⊗_R F → 0 is u-S-exact for any u-S-exact sequence 0 → A → B → C → 0. A ring R is called u-S-von Neumann regular provided there exists an element s ∈ S satisfying that for any a ∈ R there exists r ∈ R such that sα = rα². We obtain that a ring R is a u-S-von Neumann regular ring if and only if any R-module is u-S-flat. Several properties of u-S-flat modules and u-S-von Neumann regular rings are obtained.

• Journal of the Korean Wood Science and Technology
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• v.36 no.2
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• pp.63-72
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• 2008

As a part of abating formaldehyde emission of urea-formaldehyde (UF) resin adhesive, this study was conducted to investigate chemical structures of UF resin adhesives with different formaldehyde/urea (F/U) mole ratios, using carbon-13 nuclear magnetic resonance ($^{13}C$-NMR) spectroscopy. UF resin adhesives were synthesized at four different F/U mole ratios such as 1.6, 1.4, 1.2, and 1.0 for the analysis. The analysis $^{13}C$-NMR spectroscopy showed that UF resin adhesives with higher F/U mole ratios (i.e., 1.6 and 1.4) had two distinctive peaks, indicating the presence of dimethylene ether linkages and methylene glycols, a dissolved form of free formaldehyde. But, these peaks were not detected at the UF resins with lower F/U mole ratios (i.e., 1.2 and 1.0). These chemical structures present at the UF resins with higher F/U mole ratios indicated that UF resin adhesive with higher F/U mole ratio had a greater contribution to the formaldehyde emission than that of lower F/U mole ratio. Uronic species were detected for all UF resins regardless of F/U mole ratios.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.83-93
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• 2019

Let R be a noncommutative prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R and f($x_1,{\ldots},x_n$) a noncentral multilinear polynomial over C in n noncommuting variables. Denote by f(R) the set of all the evaluations of f($x_1,{\ldots},x_n$) on R. If d is a nonzero derivation of R and G a nonzero generalized derivation of R such that $$d(G(u)u){\in}Z(R)$$ for all $u{\in}f(R)$, then $f(x_1,{\ldots},x_n)^2$ is central-valued on R and there exists $b{\in}U$ such that G(x) = bx for all $x{\in}R$ with $d(b){\in}C$. As an application of this result, we investigate the commutator $[F(u)u,G(v)v]{\in}Z(R)$ for all $u,v{\in}f(R)$, where F and G are two nonzero generalized derivations of R.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.381-386
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• 1996

We consider the behavior of positive radial solutions (or, briefly, pp.r.s.) of the equation $$ (1.1) ^\Delta u + \lambda f(u) = 0 in\Omega, _u = 0 on \partial\Omega, $$ where $\Omega = {x \in R^n$\mid$A < $\mid$x$\mid$ < B}$ is an annulus in $R^n, n \geq 2, \lambda > 0 and f \geq 0$ is superlinear in u and satisfies f(0) = 0.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.369-374
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• 2016

In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+{\bar{f_x(z)}}$ under the integral operator $I_f(z)={\int_{o}^{z}}{\frac{f_1(u)}{u}}du+{\bar{{\int_{o}^{z}}{\frac{f_x(u)}{u}}}}$ and obtain the sharp constant ${\frac{{\sqrt[4]{6}}-{\sqrt[]{15}}}{9}}$, which generalized the result corresponding to the class of analytic functions given by Nash.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.915-923
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• 2022

The purpose of the present paper is to obtain commutativity of prime Γ-near-ring N with generalized derivations F and G with associated derivations d and h respectively satisfying one of the following conditions:(i) G([x, y]α = ±f(y)α(xoy)βγg(y), (ii) F(x)βG(y) = G(y)βF(x), for all x, y ∈ N, β ∈ Γ (iii) F(u)βG(v) = G(v)βF(u), for all u ∈ U, v ∈ V, β ∈ Γ,(iv) if 0 ≠ F(a) ∈ Z(N) for some a ∈ V such that F(x)αG(y) = G(y)αF(x) for all x ∈ V and y ∈ U, α ∈ Γ.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.157-163
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• 2020

Conley introduced attracting sets and repelling sets for a flow on a topological space and showed that if f is a flow on a compact metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}. In this paper we introduce chain recurrent set, trapping region, attracting set and repelling set for a flow f on a TVS-cone metric space and prove that if f is a flow on a compact TVS-cone metric space, then 𝓡(f) = ⋂{A_U ∪ A*_U |U is a trapping region for f}.

• Journal of the Society of Disaster Information
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• v.3 no.1
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• pp.103-116
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• 2007

Der Begriff des Todes $h{\ddot{a}}ngt$ die einzelne Wertvorstellung ab, so dass die Unanschaulichkeit des Todes besteht und noch zu $kl{\ddot{a}}ren$ ist. Im koreanischen Recht, findet sich keine Legaldefinition des Todes. In der juristischen Literatur herrscht der Herztod, nach dem $f{\ddot{u}}r$ den Todeszeitpunkt der irreversible und $vollst{\ddot{a}}ndige$ Stillstand der $Herzt\ddot{a}tigkeit$ gehalten wird, $herk{\ddot{o}}mmlicherweise$ bis jetzt als Todesdefinition vor. Der Herztod basiert darauf, dass Individualtod des Menschen durch den $endg{\ddot{u}}ltigen$, nicht behebbaren Stillstands von Herzschlag nach Ausfall von Atmung eingetreten sind. Auch der medizinische Laie kann den Herztod einfach wahrnehmen und sicher feststellen. Darauf folgt der Herztod als sicheres Todeszeichen angesehen wird. In der Regel trete der Herztod letzte Mal im $nat{\ddot{u}}rlichen$ Sterbeprozess ein. Die $j{\ddot{u}}ngste$ $k{\ddot{u}}nstlichen$ Reanimationsma ${\SS}nahmen$ $erm{\ddot{o}}glicht$ es, die Atmungs- und Kreislauffunktion $f{\ddot{u}}r$ eine begrenzte Zeit $k{\ddot{u}}nstlich$ aufrecht zu erhalten. Die Entwicklung der Medizin machte es zu erkennen, dass das "Zentralorgan Gehirn" $f{\ddot{u}}r$ die Aufrechterhaltung der biologischen Lebensfunktion des Gesamtorganismus unverzichtbar ist. Die Verbesserung von Transplantationstechniken gab $gro{\SS}en$ Anlass neben $f{\ddot{u}}r$ den verbesserten Reanimationstechniken auch $f{\ddot{u}}r$ den Fortschritt auf dem Gebiet der toten Transplantation. Je frischer die Organe sind, desto $gr\ddot{o}{\SS}er$ sind die Chancen $f{\ddot{u}}r$ eine erfolgreiche Verpflanzung und $f{\ddot{u}}r$ $T{\ddot{a}}tigkeit$ im $Empf{\ddot{a}}ngerorganismus$. Die Organentnahme als solche wird $unzul{\ddot{a}}ssig$ nur durch Feststellung des Herztod bei lebenswichtigen Organe, besonders wie Herz. Der Herzstillstand allein ist aber kein sicheres Kriterimn $f{\ddot{u}}r$ die $Zul{\ddot{a}}ssigkeit$ der Organentnahme. Im Korea wurde das Gesetz ${\ddot{u}}ber$ die Transplantation von Organen (Gesetz-Nummer 5858) am 8. Februar 1999 ${\ddot{o}}ffentlich$ bekannt gemacht l1nd trat am 9. Febrllar 2000 in Kraft(${\S}$ 1 Schussvorschriften kTPG). Aus der Sicht des Gesamthirntod definiert das Transplantationsgesetz derjenige, dass nach Kriterien und Nachweisverfahren $f{\ddot{u}}r$ Hirntodfeststellung dieses Gesetzes der irreversible Ausfall der Gesamthirnfunktion festgestellt wird, als Hirntoter (${\S}$ 3 Nr.4 kTPG). Mit dieser Regelung wird die Feststellung des Gesamthimtodes als gesetzliche Mindestvoraussetzung $f{\ddot{u}}r$ die Organentnahme festgelegt. Es handelt sich um Kriterien und Nachweisverfahren $f{\ddot{u}}r$ Hirntodfeststellung des koreanischen Transplantationsgesetzes.