• Title/Summary/Keyword: derivation invariant

Search Result 20, Processing Time 0.021 seconds

REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS

  • Muhiuddin, G.
    • Communications of the Korean Mathematical Society
    • /
    • v.31 no.2
    • /
    • pp.229-235
    • /
    • 2016
  • In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.

NOTES ON A NON-ASSOCIATIVE ALGEBRA WITH EXPONENTIAL FUNCTIONS II

  • Choi, Seul-Hee
    • Bulletin of the Korean Mathematical Society
    • /
    • v.44 no.2
    • /
    • pp.241-246
    • /
    • 2007
  • For the evaluation algebra $F[e^{{\pm}x}]_M\;if\;M=\{{\partial}\}$, then $$Der_{non}(F[e^{{\pm}x}]_M)$$ of the evaluation algebra $(F[e^{{\pm}x}]_M)$ is found in the paper [15]. For $M=\{{\partial},\;{\partial}^2\}$, we find $Der_{non}(F[e^{{\pm}x}]_M))$ of the evaluation algebra $F[e^{{\pm}x}]_M$ in this paper. We show that there is a non-associative algebra which is the direct sum of derivation invariant subspaces.

On the Invariance of Primitive Ideals via φ-derivations on Banach Algebras

  • Jung, Yong-Soo
    • Kyungpook Mathematical Journal
    • /
    • v.53 no.4
    • /
    • pp.497-505
    • /
    • 2013
  • The noncommutative Singer-Wermer conjecture states that every derivation on a Banach algebra (possibly noncommutative) leaves primitive ideals of the algebra invariant. This conjecture is still an open question for more than thirty years. In this note, we approach this question via some sufficient conditions for the separating ideal of ${\phi}$-derivations to be nilpotent. Moreover, we show that the spectral boundedness of ${\phi}$-derivations implies that they leave each primitive ideal of Banach algebras invariant.

ON f-DERIVATIONS OF BE-ALGEBRAS

  • Kim, Kyung Ho;Davvaz, B.
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.28 no.1
    • /
    • pp.127-138
    • /
    • 2015
  • In this paper, we introduce the notion of f-derivation in a BE-algebra, and consider the properties of f-derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by f-derivations. Moreover, we prove that if d is a f-derivation of a BE-algebra, every f-filter F is a a d-invariant.

Exactly Solvable Potentials Derived from SWKB Quantization

  • Sun, Hosung
    • Bulletin of the Korean Chemical Society
    • /
    • v.35 no.3
    • /
    • pp.805-810
    • /
    • 2014
  • The shape invariant potentials are proved to be exactly solvable, i.e. the wave functions and energies of a particle moving under the influence of the shape invariant potentials can be algebraically determined without any approximations. It is well known that the SWKB quantization is exact for all shape invariant potentials though the SWKB quantization itself is approximate. This mystery has not been mathematically resolved yet and may not be solved in a concrete fashion even in the future. Therefore, in the present work, to understand (not prove) the mystery an attempt of deriving exactly solvable potentials directly from the SWKB quantization has been made. And it turns out that all the derived potentials are shape invariant. It implicitly explains why the SWKB quantization is exact for all known shape invariant potentials. Though any new potential has not been found in this study, this brute-force derivation of potentials helps one understand the characteristics of shape invariant potentials.

ON GENERALIZED DERIVATIONS OF BE-ALGEBRAS

  • Kim, Kyung Ho
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.27 no.2
    • /
    • pp.227-236
    • /
    • 2014
  • In this paper, we introduce the notion of a generalized derivation in a BE-algebra, and consider the properties of generalized derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by generalized derivations. Moreover, we prove that if d is a generalized derivation of a BE-algebra, every filter F is a d-invariant.

ON DERIVATIONS OF BE-ALGEBRAS

  • Kim, Kyung Ho;Lee, Sang Moon
    • Honam Mathematical Journal
    • /
    • v.36 no.1
    • /
    • pp.167-178
    • /
    • 2014
  • In this paper, we introduce the notion of derivation in a BE-algebra, and consider the properties of derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by derivations. Moreover, we prove that if d is a derivation of BE-algebra, every filter F is a d-invariant.

ON GENERALIZED (α, β)-DERIVATIONS IN BCI-ALGEBRAS

  • Al-Roqi, Abdullah M.
    • Journal of applied mathematics & informatics
    • /
    • v.32 no.1_2
    • /
    • pp.27-38
    • /
    • 2014
  • The notion of generalized (regular) (${\alpha},\;{\beta}$)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (${\alpha},\;{\beta}$)-derivation to be regular is provided. The concepts of a generalized F-invariant (${\alpha},\;{\beta}$)-derivation and ${\alpha}$-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (${\alpha},\;{\beta}$)-derivations are proved.

NILPOTENCY OF THE RICCI OPERATOR OF PSEUDO-RIEMANNIAN SOLVMANIFOLDS

  • Huihui An;Shaoqiang Deng;Zaili Yan
    • Bulletin of the Korean Mathematical Society
    • /
    • v.61 no.3
    • /
    • pp.867-873
    • /
    • 2024
  • A pseudo-Riemannian solvmanifold is a solvable Lie group endowed with a left invariant pseudo-Riemannian metric. In this short note, we investigate the nilpotency of the Ricci operator of pseudo-Riemannian solvmanifolds. We focus on a special class of solvable Lie groups whose Lie algebras can be expressed as a one-dimensional extension of a nilpotent Lie algebra ℝD⋉n, where D is a derivation of n whose restriction to the center of n has at least one real eigenvalue. The main result asserts that every solvable Lie group belonging to this special class admits a left invariant pseudo-Riemannian metric with nilpotent Ricci operator. As an application, we obtain a complete classification of three-dimensional solvable Lie groups which admit a left invariant pseudo-Riemannian metric with nilpotent Ricci operator.

Invariant Set Based Model Predictive Control of a Three-Phase Inverter System (불변집합에 기반한 삼상 인버터 시스템의 모델예측제어)

  • Lim, Jae-Sik;Park, Hyo-Seong;Lee, Young-Il
    • Journal of Institute of Control, Robotics and Systems
    • /
    • v.18 no.2
    • /
    • pp.149-155
    • /
    • 2012
  • This paper provides an efficient model predictive control for the output voltage control of three-phase inverter system which includes output LC filters. Use of SVPWM (Space Vector Pulse-Width-Modulation) and the rotating d-q frame is made to obtain an input constrained dynamic model of the inverter system. From the measured/estimated output current and reference output voltage, corresponding equilibrium values of the inductor current and the control input are computed. Derivation of a feasible and invariant set around the equilibrium state is made and then a receding horizon strategy which steers the current state deep into the invariant set is proposed. In order to remove offset error, use of disturbance observer is made in the form of state estimator. The efficacy of the proposed method is verified through simulations.