• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.2
• /
• pp.125-136
• /
• 2022

The goal of this paper is to introduce the notion of generalized symmetric bi-f-derivations in lattices and to study some properties of generalized symmetric f-derivations of lattice. Moreover, we consider generalized isotone symmetric bi-f-derivations and fixed sets related to generalized symmetric bi-f-derivations.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.9-16
• /
• 2006

The purpose of this paper is to define the symmetric $bi-(\sigma,\;\tau)$ derivations on prime and semi prime Gamma rings and to prove some results concerning symmetric $bi-(\sigma,\;\tau)$derivations on prime and semi prime Gamma rings.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.959-967
• /
• 2011

Let A be a Banach algebra and let f : $A{\times}A{\rightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{\times}A{\rightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.

• East Asian mathematical journal
• /
• v.15 no.1
• /
• pp.105-109
• /
• 1999

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.819-826
• /
• 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 $D_1=0 \;and\; D_2=0$.

• Kyungpook Mathematical Journal
• /
• v.46 no.2
• /
• pp.153-167
• /
• 2006

We study permuting tri-derivations in ${\Gamma}$-rings and give an example.

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

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

• International journal of steel structures
• /
• v.18 no.4
• /
• pp.1440-1463
• /
• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.