• 제목/요약/키워드: Boundedness

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비선형 상호작용을 갖는 전력계통의 비선형 분산 전압제어 (Decentralized Nonlinear Voltage Control of Multimachine Power Systems with Non linear Interconnections)

  • 이재원;윤태웅;김광연
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 A
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    • pp.47-50
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    • 2003
  • For large-scale systems which are composed of interconnections of many lower-dimensional subsystems, decentralized control is preferable since it can alleviate the computational burden, avoid communication between different subsystems, and make the control more feasible and simpler. A power system is such a large-scale system where generators are interconnected through transmission lines. Decentralized control is therefore considered for power systems. In this paper, a robust decentralized excitation control scheme for interactions is proposed to enhance the transient stability of multimachine power systems. First we employ a DFL(Direct Feedback Linearization) compensator to rancel most of the nonlinearities; however, the resulting model still contains nonlinear interconnections. Therefore, we design a robust controller in order to deal with Interconnection terms. In this procedure, an upper bound of interconnection terms is estimated by an estimator. The resulting adaptive scheme guarantees the uniform ultimate boundedness of the closed-loop dynamic systems in the presence of the uncertainties.

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ON A POSITIVE SUBHARMONIC BERGMAN FUNCTION

  • Kim, Jung-Ok;Kwon, Ern-Gun
    • 대한수학회보
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    • 제47권3호
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    • pp.623-632
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    • 2010
  • A holomorphic function F defined on the unit disc belongs to $A^{p,{\alpha}}$ (0 < p < $\infty$, 1 < ${\alpha}$ < $\infty$) if $\int\limits_U|F(z)|^p \frac{1}{1-|z|}(1+log)\frac{1}{1-|z|})^{-\alpha}$ dxdy < $\infty$. For boundedness of the composition operator defined by $C_{fg}=g{\circ}f$ mapping Blochs into $A^{p,{\alpha}$ the following (1) is a sufficient condition while (2) is a necessary condition. (1) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha}M_p(r,\lambda{\circ}f)^p\;dr$ < $\infty$ (2) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha+p}(1-r)^pM_p(r,f^#)^p\;dr$ < $\infty$.

LIPSCHITZ CONTINUOUS AND COMPACT COMPOSITION OPERATOR ACTING BETWEEN SOME WEIGHTED GENERAL HYPERBOLIC-TYPE CLASSES

  • Kamal, A.;El-Sayed Ahmed, A.;Yassen, T.I.
    • Korean Journal of Mathematics
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    • 제24권4호
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    • pp.647-662
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    • 2016
  • In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

DYNAMIC BEHAVIOR OF A PREDATOR-PREY MODEL WITH STAGE STRUCTURE AND DISTRIBUTED DELAY

  • Zhou, Xueyong
    • Journal of applied mathematics & informatics
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    • 제28권1_2호
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    • pp.193-207
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    • 2010
  • In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

A Discrete-Time Nonlinear Robust Controller for Current Regulation in PMSM Drives

  • Turker, Turker;Yanik, Gurcan;Buyukkeles, Umit;Bakan, Faruk;Mese, Erkan
    • Journal of Electrical Engineering and Technology
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    • 제12권4호
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    • pp.1537-1547
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    • 2017
  • In this paper, a discrete-time robust current controller is proposed for PMSM drives. The structure of the proposed controller is quite simple and does not require high computational resource. The only difference of the proposed controller from the classical dead-beat controller is the integral term which can easily be implemented in a PMSM drive. The stability analysis of the proposed controller is performed accounting in parametric uncertainties, unmodelled dynamics and disturbances in the mathematical model. The boundedness of the dynamical system and asymptotic convergence of dq-axes currents to their reference values are provided under certain conditions. Various simulation and experimental studies are performed and the results taken at different operation conditions show the validity of the proposed controller.

Lp BOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION

  • Wang, Feixing;Chen, Yanping;Yu, Wei
    • 대한수학회보
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    • 제49권4호
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    • pp.787-797
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    • 2012
  • In this paper the authors study the $L^p$ boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(y){\leq}t}\frac{\Omega(y)}{\rho(y)^{{\alpha}-1}}f(x-{\Phi}(y))dy$$ and ${\Omega}$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

BOUNDEDNESS FOR FRACTIONAL HARDY-TYPE OPERATOR ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT

  • Wu, Jianglong
    • 대한수학회보
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    • 제51권2호
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    • pp.423-435
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    • 2014
  • In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

ON SOME WEIGHTED HARDY-TYPE INEQUALITIES INVOLVING EXTENDED RIEMANN-LIOUVILLE FRACTIONAL CALCULUS OPERATORS

  • Iqbal, Sajid;Pecaric, Josip;Samraiz, Muhammad;Tehmeena, Hassan;Tomovski, Zivorad
    • 대한수학회논문집
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    • 제35권1호
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    • pp.161-184
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    • 2020
  • In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of [18,19]. We also prove the boundedness of the k-fractional integral operator on Lp[a, b].

A note on derivations of banach algebras

  • Kim, Gwang-Hui
    • 대한수학회보
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    • 제32권2호
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    • pp.367-372
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    • 1995
  • In 1955 Singer and Wermer [12] proved that every bounded derivation on a commutative Banach algebra maps into its radical. They conjectured that the continuity of the derivation in their theorm can be removed. In 1988 Thomas [13] proved their conjecture ; Every derivation on a commutative Banach algebra maps into its radical. For noncommutative versions, in 1984 B. Yood [15] proved that the continuous derivations on Banach algebras satisfing [D(a),b] $\in$ Rad(A) for all a, b $\in$ A have the radical range, where [a,b] will be denote the commutator ab-ba. In 1990 M.Bresar and J.Vukman [1] have generlized Yood's result, that is, the continuous linear Jordan derivation on Banach algebra that satisfies [D(a),a] $\in$ Rad(A) for all a $\in$ A has the radical range. In next year Mathieu and Murphy [5] proved that every bounded centralizing derivation on Banach algebras has its image in the radical. Mathieu and Runde [6] removed the boundedness of that.

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AN EXTERESION THEOREM FOR THE FOLLAND-STEIN SPACES

  • Kim, Yonne-Mi
    • 대한수학회논문집
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    • 제10권1호
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    • pp.49-55
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    • 1995
  • This paper is the third of a series in which smoothness properties of function in several variables are discussed. The germ of the whole theory was laid in the works by Folland and Stein [4]. On nilpotent Lie groups, they difined analogues of the classical $L^p$ Sobolev or potential spaces in terms of fractional powers of sub-Laplacian, L and extended several basic theorems from the Euclidean theory of differentaiability to these spaces: interpolation properties, boundedness of singular integrals,..., and imbeding theorems. In this paper we study the analogue to the extension theorem for the Folland-Stein spaces. The analogue to Stein's restriction theorem were studied by M. Mekias [5] and Y.M. Kim [6]. First, we have the space of Bessel potentials on the Heisenberg group introduced by Folland [4].

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