• East Asian mathematical journal
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• v.15 no.2
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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.

• Honam Mathematical Journal
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• v.31 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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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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• v.5 no.3
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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 $D_1=0 \;and\; D_2=0$.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.469-479
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• 2000

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

• Aerospace Engineering and Technology
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• v.6 no.1
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• pp.136-145
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• 2007

A computation was made to predict the movement of the thrust center position due to the rocket nozzle deflection. Three dimensional computations were done for the nozzle deflection angles of 0/1/3 degrees, and the oscillation of aerodynamic coefficients, not observed for the axisymmetric cases, was encountered. The position of the thrust center was found to be at -16 mm and -4 mm for the deflection angles of 1 and 3 degrees, respectively, and it can be concluded that the thrust center movement due to nozzle deflection is negligible. In addition to the computational results, the mechanism of thrust generation in a rocket engine is described with a brief mathematical derivation as it is sometimes mistaken. Also presented are some descriptions on the problem of pressure center definition for symmetric cases such as a rocket external flow problem and the nozzle deflection case.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.3
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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.