• Kyungpook Mathematical Journal
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• 제53권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권1호
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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.

• 대한수학회논문집
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• 제34권1호
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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.

• 한국컴퓨터그래픽스학회논문지
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• 제24권5호
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• pp.1-10
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• 2018

본 논문에서는 피사계 심도(DoF, Depth of field)가 포함된 사진을 자동으로 추상화 시켜주는 비 사실적 렌더링(NPR, Non-photorealistic rendering) 기술을 제안한다. 우리의 접근 방식은 RGB 채널을 이용하여 DoF 영역을 효율적으로 분류하고, DoF 크기에 따라 색상을 추상화하며, 라인의 두께를 자동으로 조절함으로 새롭게 필터링 하는 기술이다. DoF기반 필터링 방식은 성능과 디자인 관점에서 추상화의 품질을 크게 개선시켰으며, 간단하고 빨라 구현하기 쉽고, 사진으로부터 추상화나 일러스트레이션을 제작할 때 원본 사진이 갖고 있는 DoF의 특징과 스타일을 효율적으로 잘 표현한다.

• 전자통신동향분석
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• 제34권6호
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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.

• 충청수학회지
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• 제35권4호
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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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• 제38권5호
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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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• 제40권5_6호
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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.

• 대한수학회논문집
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• 제38권1호
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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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• 제22권1호
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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.