• 대한수학회논문집
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• 제27권1호
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• pp.69-76
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• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

• 한국수학교육학회지시리즈A:수학교육
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• 제26권2호
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• pp.55-61
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• 1988

이 논문에서는 CS-Semistratifiable 공간보다 더 일반화된 공간 Cn-Semistratifiable을 정의 하며 그에 따른 여러가지 성질들을 조사하였다. 위상 공간(X, $\tau$)에 대하여 $\alpha$$\times$$\tau$에서 X의 폐집합족으로의 함수 S가 존재하여 다음 조건들을 만족할 때 공간X는 Cn-Semistratifiable over $\alpha$라 정의한다. a) 임의의 개집합 U에 대하여 U=U{S($\beta$, U) : $\beta$<$\alpha$} b) U, V가 X의 개집합이고 U⊂CV이면 모든 $\beta$<$\alpha$에 대하여 S($\beta$, V)⊂S($\beta$, V)이다. c) 만약 ${\gamma}$<$\beta$<$\alpha$ 이라면 임의의 개집합 U에 대하여 S(${\gamma}$, U)⊂S($\beta$, U)이다. d) X의 수렴하는 net $X_{\beta}$$\longrightarrow$X와 X를 품는 임의의 개집합 U에 대하여 적당한 $\beta$<$\alpha$가 존재하여 X$\in$S($\beta$. U)이고 { $X_{\beta}$}는 S($\beta$, U)안에 eventual하게 들어간다. 위의 정의에 의하여 다음과 같은 성질들이 증명되었다. 1 . Strstifiable over $\alpha$$\longrightarrow$cn-semistratifiable over$\longrightarrow$semistratifiable over $\alpha$ 2, 어떤 공간이 cn-Semistratifiable over $\alpha$이기 위한 필요충분 조건은 그것이 linearly cushioned cn-pairnet를 갖는 것이다. 3. cn-semistratifiable over $\alpha$의 부분공간 역시 cn-semistratifiabie over $\alpha$ 하다. 4. on-semistratifiable over $\alpha$의 유한개의 적공간 역시 cn-semistratifiabie over $\alpha$한다. 5. 폐 cn-semistratifiable over $\alpha$ 부분공간들의 합공간 역시 on-semistrbtifiable over $\alpha$ 하다. 6. 폐연속 net-cevering 함수에 의하여 cn-semistratifiable over $\alpha$ 성질이 보존된다.

• 대한수학회논문집
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• 제33권1호
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• pp.73-83
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• 2018

Let R be an associative ring with involution * and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an $({\alpha},{\beta})^*$-derivation of R if $d(xy)=d(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $F:R{\rightarrow}R$ is called a generalized $({\alpha},{\beta})^*$-derivation of R associated with an $({\alpha},{\beta})^*$-derivation d if $F(xy)=F(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [12], and a theorem of Daif and El-Sayiad [6], moreover, we generalize a theorem of Ali et al. [4] and a theorem of Huang and Koc [9] related to generalized Jordan triple $({\alpha},{\beta})^*$-derivations.

• 대한수학회지
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• 제60권5호
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• pp.931-957
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• 2023

For an arbitrary integer x, an integer of the form $$T(x)={\frac{x^2+x}{2}}$$ is called a triangular number. Let α₁, ... , α_k be positive integers. A sum ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=\{\alpha}_1T(x_1)+\,{\cdots}\,+{\alpha}_kT(x_k)$ of triangular numbers is said to be almost universal with one exception if the Diophantine equation ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=n$ has an integer solution (x₁, ... , x_k) ∊ ℤ^k for any nonnegative integer n except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of "15-theorem" of Conway, Miller, and Schneeberger.

• 대한수학회논문집
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• 제32권3호
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• pp.535-542
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• 2017

Let R be an associative ring and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an (${\alpha},{\beta}$)-derivation of R if $d(xy)=d(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $D:R{\rightarrow}R$ is called a generalized (${\alpha},{\beta}$)-derivation of R associated with an (${\alpha},{\beta}$)-derivation d if $D(xy)=D(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [5], and a theorem of Daif and El-Sayiad [2].

• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.255-263
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• 2009

For an endomorphism ${\alpha}$ of R, in [1], a module $M_R$ is called ${\alpha}$-compatible if, for any $m{\in}M$ and $a{\in}R$, ma = 0 iff $m{\alpha}(a)$ = 0, which are a generalization of ${\alpha}$-reduced modules. We study on the relationship between the quasi-Baerness and p.q.-Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [2] and some results in [9]. In particular, we show: for an ${\alpha}$-compatible module $M_R$ (1) $M_R$ is p.q.-Baer module iff $M[x;{\alpha}]_{R[x;{\alpha}]}$ is p.q.-Baer module. (2) for an automorphism ${\alpha}$ of R, $M_R$ is p.q.-Baer module iff $M[x,x^{-1};{\alpha}]_{R[x,x^{-1};{\alpha}]}$ is p.q.-Baer module.

• 한국작물학회지
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• 제33권4호
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• pp.323-328
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• 1988

본 연구는 호프 주산지인 강원도 횡성에서 호프 발육기 동안의 기상요소 변화에 따른 $\alpha$-acid 함량 예측모형을 작성하고, $\alpha$-acid 생성에 관여하는 기상요소를 구명하고자 1978년부터 1986년까지 9개년 간의 연평균 $\alpha$-acid 함량과 발육단계별 기상요소를 분석 검토한 결과는 다음과 같다. 1. $\alpha$-acid 함량 예측을 위하여 선택된 기상요소는 화아분화기(5월 21일~6월 20일)의 최고기온, 개화기(6월 11일~7월 10일)의 최고기온, 일조시수 그리고 강수량, 구화형성기(7월 21일~8월 20일) 최고기온이었다. 2. 개화기의 일조시수(X$_1$), 개화기의 최고기온(X$_3$), 개화분화기의 최고기온(X$_4$), 개화기의 강수량(X$_{5}$), 그리고 구화성숙기의 최고기온(X$_{6}$)의 $\alpha$-acid 함량 증가에 영향을 주었다. 3. $\alpha$-acid 함량 예측의 중선형 회귀모형은 Y=28.369-0.003 X$_1$＋1.508 X$_2$-1.953X$_3$-0.335X$_4$-0.003X$_{5}$-0.119X$_{6}$로 MSEp=0.004, Rp$^2$=0.9987, Rap$^2$=0.9949, Cp=7.00이었다.

• Molecules and Cells
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• 제40권5호
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• pp.355-362
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• 2017

The ${\beta}2$ integrins are cell surface transmembrane proteins regulating leukocyte functions, such as adhesion and migration. Two members of ${\beta}2$ integrin, ${\alpha}M{\beta}2$ and ${\alpha}X{\beta}2$, share the leukocyte distribution profile and integrin ${\alpha}X{\beta}2$ is involved in antigen presentation in dendritic cells and transendothelial migration of monocytes and macrophages to atherosclerotic lesions. ${\underline{R}}eceptor$ for ${\underline{a}}dvanced$ ${\underline{g}}lycation$ ${\underline{e}}nd$ ${\underline{p}}roducts$ (RAGE), a member of cell adhesion molecules, plays an important role in chronic inflammation and atherosclerosis. Although RAGE and ${\alpha}X{\beta}2$ play an important role in inflammatory response and the pathogenesis of atherosclerosis, the nature of their interaction and structure involved in the binding remain poorly defined. In this study, using I-domain as a ligand binding motif of ${\alpha}X{\beta}2$, we characterize the binding nature and the interacting moieties of ${\alpha}X$ I-domain and RAGE. Their binding requires divalent cations ($Mg^{2+}$ and $Mn^{2+}$) and shows an affinity on the sub-micro molar level: the dissociation constant of ${\alpha}X$ I-domains binding to RAGE being $0.49{\mu}M$. Furthermore, the ${\alpha}X$ I-domains recognize the V-domain, but not the C1 and C2-domains of RAGE. The acidic amino acid substitutions on the ligand binding site of ${\alpha}X$ I-domain significantly reduce the I-domain binding activity to soluble RAGE and the alanine substitutions of basic amino acids on the flat surface of the V-domain prevent the V-domain binding to ${\alpha}X$ I-domain. In conclusion, the main mechanism of ${\alpha}X$ I-domain binding to RAGE is a charge interaction, in which the acidic moieties of ${\alpha}X$ I-domains, including E244, and D249, recognize the basic residues on the RAGE V-domain encompassing K39, K43, K44, R104, and K107.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.1-12
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• 2015

Let R be a ring and $D:R^n{\longrightarrow}R$ be n-additive mapping. A map $d:R{\longrightarrow}R$ is said to be the trace of D if $d(x)=D(x,x,{\ldots}x)$ for all $x{\in}R$. Suppose that ${\alpha},{\beta}$ are endomorphisms of R. For any $a,b{\in}R$, let < a, b > $_{({\alpha},{\beta})}=a{\alpha}(b)+{\beta}(b)a$. In the present paper under certain suitable torsion restrictions it is shown that D = 0 if R satisfies either < d(x), $x^m$ > $_{({\alpha},{\beta})}=0$, for all $x{\in}R$ or ${\ll}$ d(x), x > $_{({\alpha},{\beta})}$, $x^m$ > $_{({\alpha},{\beta})}=0$, for all $x{\in}R$. Further, if < d(x), x > ${\in}Z(R)$, the center of R, for all $x{\in}R$ or < d(x)x - xd(x), x >= 0, for all $x{\in}R$, then it is proved that d is commuting on R. Some more related results are also obtained for additive mapping on R.

• 한국수학교육학회지시리즈A:수학교육
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• 제16권2호
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• pp.22-26
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• 1978

($\alpha$$_{x}$, $\alpha$X)와 ($\alpha$$_{Y}$ , $\alpha$Y)를 T$_2$ 공간 X와 Y의 Alexandroff base Compactification이라 할 때 $\alpha$fㆍ$\alpha$$_{x}$=$\alpha$$_{Y}$ f를 만족하는 open이고 연속인 함수 $\alpha$f:$\alpha$X$\longrightarrow$$\alpha$Y가 존재하는 연속함수 f:X$\longrightarrow$Y는 유일한 $\alpha$-extension $\alpha$f를 가지며 Category ABC를 T$_2$ 공간과 위와 같은 연속함수 f들의 Category라고 할 때 open이고 연속인 함수와 Compact space들의 Category는 Category ABC의 epireflective subcategory임을 밝혔다.