• East Asian mathematical journal
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• 제15권2호
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• pp.165-176
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• 1999

After the derivation was defined in [19] by Posner a lot of researchers studied the derivations in ring theory in different manners such as in [2], [4], [5], ..., etc. Furthermore, many researches followed the definition of the generalized derivation([3], [6], [7], ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.

• 호남수학학술지
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• 제31권2호
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• pp.203-217
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• 2009

In this note, we introduce a symmetric generalized 3-derivation in near-rings and investigate some conditions for a nearring to be a commutative ring.

• 충청수학회지
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• 제29권3호
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• pp.491-502
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• 2016

In this paper, as a generalization of symmetric bi-derivations and symmetric bi-f-derivations of a lattice, we introduce the notion of symmetric bi-(f, g)-derivations of a lattice. Also, we define the isotone symmetric bi-(f, g)-derivation and obtain some interesting results about isotone. Using the notion of $Fix_a(L)$ and KerD, we give some characterization of symmetric bi-(f, g)-derivations in a lattice.

• 충청수학회지
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• 제29권3호
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• pp.443-451
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• 2016

In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

• 충청수학회지
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• 제22권3호
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• pp.451-458
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• 2009

Let $n{\geq}2$ be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring. Suppose that there exists a symmetric n-derivation $\Delta$ : $R^{n}{\rightarrow}R$ such that the trace of $\Delta$ is centralizing on R. Then the trace is commuting on R. If R is a n!-torsion free prime ring and $\Delta{\neq}0$ under the same condition. Then R is commutative.

• 대한수학회논문집
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• 제39권1호
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• pp.79-91
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• 2024

This article examines the connection between 3-derivations and the commutativity of a prime ring R with an involution * that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.819-826
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• 1998

The purpose of this paper is to prove the following results; (1) Let R be a prime ring of char $(R)\neq 2$ and I a nonzero left ideal of R. The existence of a nonzero symmetric bi-derivation D : $R\timesR\;\longrightarrow\;$ such that d is sew-commuting on I where d is the trace of D forces R to be commutative (2) Let m and n be integers with $m\;\neq\;0.\;or\;n\neq\;0$. Let R be a noncommutative prime ring of char$ (R))\neq \; 2-1\; p_1 \;n_1$ where p is a prime number which is a divisor of m, and I a nonzero two-sided ideal of R. Let $D_1$ ; $R\;\times\;R\;\longrightarrow\;and\;$ $D_2\;:\;R\;\times\;R\;longrightarrow\;R$ be symmetric bi-derivations. Suppose further that there exists a symmetric bi-additive mapping B ; $R\;\times\;R\;\longrightarrow\;and\;$ such that $md_1(\chi)\chi ＋ n\chi d_2(\chi)=f(\chi$) holds for all $\chi$$\in$I, where $d_1 \;and\; d_2$ are the traces of $D_1 \;and\; D_2$ respectively and f is the trace of B. Then we have $D_1=0 \;and\; D_2=0$.

• 대한수학회논문집
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• 제15권3호
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• pp.469-479
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• 2000

We define and study the extended centroid of a prime $\Gamma$-ring.

• 항공우주기술
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• 제6권1호
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• pp.136-145
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• 2007

로켓 노즐의 변위에 따라 추력 중심이 어떻게 이동되는지를 예측하기 위해 전산유동해석을 수행하였다. 노즐 변위각을 0/1/3도로 하여 3차원 계산을 수행하였으며, 축대칭 계산에서 보지 못했던 공력계수의 진동이 관찰되었다. 변위각 1도 및 3도 조건에 대하여 추력중심 위치가 -16 mm 및 -4 mm로 나타났으며, 노즐 변위에 따른 추력 중시의 변화는 무시할 만한 정도라고 볼 수 있다. 이와 더불어 오해하기 쉬운 로켓 엔진의 추력 발생 원리를 간략히 수학적으로 기술하였으며, 로켓 외부 유동이나 노즐 변위와 같은 대칭 조건에서 압력 중심을 어떻게 정의해야 할 것인지에 대해서도 논하였다.

• 한국군사과학기술학회지
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• 제14권3호
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• pp.364-371
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• 2011

This paper presents experimental results and derived experimental equations to investigate the turbulent wake characteristics generated by the self-propelled SUBOFF submarine model. A self-propelled SUBOFF model which was assumed as an axial-symmetric body was used to create wake, and a thin strut was mounted on the topside of the model. The experiments were conducted in a circulating water channel(CWC), and the hot-film was used to measure the turbulence in wake cross-section at the distance range of 0.0~2.0L from the model. The hot film anemometer measured turbulent velocity fluctuations, and the time-averaged mean velocity and turbulent intensity are obtained from the acquired time-series data. Measured results show well the general characteristics of turbulent intensity, kinetic energy and mean velocity distribution. Also, this paper presents derived experimental equations, which is extended result to the reference [1]. These experimental equations show well the general characteristics of the turbulent wake behind the self-propelled submerged body.