• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.565-571
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• 2013

In this paper, we investigate the commutativity of a semiprime ring R admitting a generalized derivation F with associated derivation D satisfying any one of the properties: (i) $F(x){\circ}D(y)=[x,y]$, (ii) $D(x){\circ}F(y)=F[x,y]$, (iii) $D(x){\circ}F(y)=xy$, (iv) $F(x{\circ}y)=[F(x) y]+[D(y),x]$, and (v) $F[x,y]=F(x){\circ}y-D(y){\circ}x$ for all x, y in some appropriate subsets of R.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.21-31
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• 2017

In this paper, we introduce and solve the following additive (${\rho}_1$, ${\rho}_2$)-functional inequality $${\Large{\parallel}}2f(\frac{x+y}{2})-f(x)-f(y){\Large{\parallel}}{\leq}{\parallel}{\rho}_1(f(x+y)+f(x-y)-2f(x)){\parallel}+{\parallel}{\rho}_2(f(x+y)-f(x)-f(y)){\parallel}$$ where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with $\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1$, ${\rho}_2$)-functional inequality (1) in complex Banach spaces.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.55-82
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• 2019

Given ${\sigma}:G{\rightarrow}G$ an involutive automorphism of a semigroup G, we study the solutions and stability of the following functional equations $$f(x{\sigma}(y))=f(x)g(y)+g(x)f(y),\;x,y{\in}G,\\f(x{\sigma}(y))=f(x)f(y)-g(x)g(y),\;x,y{\in}G$$ and $$f(x{\sigma}(y))=f(x)g(y)-g(x)f(y),\;x,y{\in}G$$, from the theory of trigonometric functional equations. (1) We determine the solutions when G is a semigroup generated by its squares. (2) We obtain the stability results for these equations, when G is an amenable group.

• Journal of the Korea Computer Graphics Society
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• v.24 no.5
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• pp.1-10
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• 2018

In this paper, we present a non-photorealistic rendering technique that automatically delivers a stylized abstraction of a photograph with DoF(Depth of field). Our approach is a new filtering method that efficiently classifies DoF regions using RGB channels and automatically adjusts the color abstraction and extracted line quality based on this classification. This DoF-based filtering is simple, fast, and easy to implement and significantly improves the abstraction performance in terms of feature enhancement and stylization.

• Electronics and Telecommunications Trends
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• v.34 no.6
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• pp.156-163
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• 2019

As a primitive immersive video technology, a three degrees of freedom (3DoF) $360^{\circ}$ video can currently render viewport images that are dependent on the rotational movements of the viewer. However, rendering a flat $360^{\circ}$ video, that is supporting head rotations only, may generate visual discomfort especially when objects close to the viewer are rendered. 3DoF+ enables head movements for a seated person adding horizontal, vertical, and depth translations. The 3DoF+ $360^{\circ}$ video is positioned between 3DoF and six degrees of freedom, which can realize the motion parallax with relatively simple virtual reality software in head-mounted displays. This article introduces the standardization trends for the 3DoF+ video in the MPEG-I visual group.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.315-327
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• 2022

In this paper, we investigate the transferred superstability for the p-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from the p-radical functional equations: $$f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)g(y),\;\\f({\sqrt[p]{x^p+y^p}})+f({\sqrt[p]{x^p-y^p}})={\lambda}g(x)h(y),$$ where p is an odd positive integer, λ is a positive real number, and f is a complex valued function. Furthermore, the results are extended to Banach algebras. Therefore, the obtained result will be forced to the pre-results(p=1) for this type's equations, and will serve as a sample to apply it to the extension of the other known equations.

• East Asian mathematical journal
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• v.38 no.5
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• pp.643-647
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• 2022

Let F² denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F². We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.

• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.243-256
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• 2023

We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin [54]. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism f of a compact smooth manifold M has the robustly pointwise inverse pseudoorbit tracing property, f is structurally stable. (ii) For a C1 generic diffeomorphism f of a compact smooth manifold M, if f has the pointwise inverse pseudo-orbit tracing property, f is structurally stable. (iii) If a diffeomorphism f has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set Λ, then Λ is hyperbolic for f. Finally, (iv) for C¹ generically, if a diffeomorphism f has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set Λ, then Λ is hyperbolic for f. In addition, we investigate cases of volume preserving diffeomorphisms.

• Animal Systematics, Evolution and Diversity
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• v.22 no.1
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• pp.87-89
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• 2006

The mitochondrial cytochrome b gene of the Korean subspecies (Falco tinnunculus interstinctus) of the common kestrel has been analyzed. According to the molecular phylogeny of six subspecies of common kestrel, six subspecies of the common kestrel were divided into two clades: the first clade is composed of the South African subspecies (F. t. rupicolus) and the second clade includes 5 subspecies (F. t. tinnunculus, F. t. rufescens, F. t. interstinctus, F. t. canariensis and F. t. dacotiae) of the common kestrel. Korean subspecies, F. t. interstinctus was closely related to F. t. rufescens and original subspecies F. t. tinnunculus.