• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권4호
• /
• pp.237-246
• /
• 2014

Let M be a prime ${\Gamma}$-ring and let d be a derivation of M. If there exists a fixed integer n such that $(d(x){\alpha})^nd(x)=0$ for all $x{\in}M$ and ${\alpha}{\in}{\Gamma}$, then we prove that d(x) = 0 for all $x{\in}M$. This result can be extended to semiprime ${\Gamma}$-rings.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제25권3호
• /
• pp.181-191
• /
• 2018

In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying $(G([x,y])-[G(x),y])^n=0$ for all x, $y{\in}I$, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.

• 대한수학회보
• /
• 제48권5호
• /
• pp.917-922
• /
• 2011

Let R be a prime ring, H a generalized derivation of R, L a noncentral Lie ideal of R, and 0 ${\neq}$ a ${\in}$ R. Suppose that $au^sH(u)u^t$ = 0 for all u ${\in}$ L, where s; t ${\geq}$ 0 are fixed integers. Then H = 0 unless satisfies $S_4$, the standard identity in four variables.

• 대한수학회보
• /
• 제46권3호
• /
• pp.599-605
• /
• 2009

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that $u^sH(u)u^t$ = 0 for all u $\in$ L, where s $\geq$ 0, t $\geq$ 0 are fixed integers. Then H(x) = 0 for all x $\in$ R unless char R = 2 and R satisfies $S_4$, the standard identity in four variables.

• 충청수학회지
• /
• 제22권3호
• /
• pp.451-458
• /
• 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.

• 대한수학회보
• /
• 제46권5호
• /
• pp.857-866
• /
• 2009

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\mu$, $\nu$ be a pair of generalized derivations on R. If < $\mu^2(x)+\nu(x),\;x^n$ > = 0 for all x $\in$ R, then $\mu$ and $\nu$ are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center $C_R$ and d, g be a pair of derivations on R. If < $d^2(x)+g(x)$, $x^n$ > $\in$ $C_R$ for all x $\in$ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

• 대한안전경영과학회지
• /
• 제16권3호
• /
• pp.231-237
• /
• 2014

Construction of the external wall framing using construction Gang-Form withstand the load of a full lift safety is very important in lifting rings can be a lot of Gang-Form is now fixed in the manner that you are welding and applied, but this study is based on the safety of the lifting ring to seek improvements were bolt type fixing method applied to the bonding type were part of the lifting ring in a manner fixed to the concrete surface and was applied in consideration of safety.

• 융복합기술연구소 논문집
• /
• 제1권2호
• /
• pp.6-15
• /
• 2011

This paper reports the design and fabrication of a micro-electro-mechanical-system(MEMS)-based electrostatic angular microactuator for a dual-stage servo. The proposed actuator employs a novel electrode pattern named "skewed electrode array(SEA)" scheme. It is shown that SEA has better linearity than a parallel plate type actuator and stronger force than a comb-drive based actuator. The moving and the fixed electrodes are arranged to make the driving force perpendicular to the rotating moment of arm. By changing the electrode overlap length, the magnitude of electrostatic force and stable displacement will be changed. In order to optimize the design, an electrostatic FE analysis was carried out and an empirical force model was established for SEA. A new assembly method which will allow the active electrodes to be located beneath the slider was developed. The active electrodes are connected by inner and outer rings lifted on the base substrate, and the inner and outer rings are connected to platform on which the slider locates. Electrostatic force between active electrodes and platform can be used for exiting out of plane modes, so this provides the possibility of the flying height control. A microactuator that can position the pico-slider over ${\pm}0.5{\mu}m$ using under 20 volts for a 2 kHz fine-tracking servo was designed and fabricated using SoG process.

• Ocean and Polar Research
• /
• 제23권3호
• /
• pp.305-310
• /
• 2001

This paper describes a floating fish reef technology for enhancement of fisheries productivity in the muddy areas. The floating fish reef was composed of main fish cage, anchor rope and concrete anchor blocks. Main fish cage was made up of 12 steel buoys measuring 0.37m in diameter and 1.5m long, polyethylene (PE) netting and circular steel rings. Each steel buoy had buoyancy of 110kgf. The size of main fish cage was 1.96 m in diameter and 3.75m in length. Monitoring on its durability was made for eight months after installation. The steel buoys fixed on main fish cage and nettings were observed to be kept safely. The wet weight of fouling organisms per unit area$(m^2)$ was 26.6kgf after eight months. Reduction in the cross-section of steel buoys and circular steel rings of main fish cage were not found. In addition, any cracks on the concrete anchor blocks were not observed.

• 대한수학회보
• /
• 제58권3호
• /
• pp.659-668
• /
• 2021

Let R be a semiprime ring with maximal right ring of quotients Q_mr(R), and let n₁, n₂, …, n_k be k fixed positive integers. Suppose that R is (n₁+n₂+⋯+n_k)!-torsion free, and that f : 𝜌 → Q_mr(R) is an additive map, where 𝜌 is a nonzero right ideal of R. It is proved that if [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ 𝜌, then [f(x), x] = 0 for all x ∈ 𝜌. This gives the result of Beidar et al. [2] for semiprime rings. Moreover, it is also proved that if R is p-torsion, where p is a prime integer with p = Σ^k_i=1 n_i and if f : R → Q_mr(R) is an additive map satisfying [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ R, then [f(x), x] = 0 for all x ∈ R.