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THE GEOMETRIC CONVEXITY OF A FUNCTION INVOLVING GAMMA FUNCTION WITH APPLICATIONS
Chu, Yuming,Zhang, Xiaoming,Zhang, Zhihua Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.3
In this paper, we prove that $(\Gamma(x))^{\frac{1}{x-1}}$ is geometrically convex on (0, $\infty$). As its applications, we obtain some new estimates for $\frac{[\Gamma(x+1)]^{\frac{1}{x}}} {[\Gamma(y+1)]^{\frac{1}{y}}}$.
OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES
Cheng, Jinfa,Chu, Yuming Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.2
Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive $(x(t)+{\sum\limits^n_{i=1}}c_ix(t-{\sigma}_i))'+px(t-{\tau})=0$, $t{\neq}t_{\kappa}$, ${\Delta}(x(t_{\kappa})+{\sum\limits^n_{i=1}}c_ix(t_{\kappa}-{\sigma}_i))+p_0x(t_{\kappa}-{\tau})=0$, $c_i{\geq}0$, $i=1,2,{\ldots}n$, $p{\tau}$>0, $p_0{\tau}$>0, ${\Delta}(x_{\kappa})=x(t^+_{\kappa})-x(t_{\kappa})$. Explicit sufficient and necessary condition are established when $c_i$ = 0, i = 1, 2, ${\ldots}$, n.
Three Characteristic Beltrami System in Even Dimensions (I): p-Harmonic Equation
Gao, Hongya,Chu, Yuming,Sun, Lanxiang Department of Mathematics 2007 Kyungpook mathematical journal Vol.47 No.3
This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.
Delay-Dependent H_∞ Control for Jumping Delayed Systems with Two Markov Processes
Hao Shen,Yuming Chu,Shengyuan Xu,Zhengqiang Zhang 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.3
This paper addresses the H_∞ control problem for jumping delayed systems with two separable Markov processes. The objective is to design a controller such that the resulting closed-loop system is exponentially mean-square stable with a given decay rate and satisfies a prescribed H_∞ performance level. A decay-rate-dependent condition is obtained for the existence of admissible controllers in term of linear matrix inequalities. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.
$\bar{WT}$-Classes of Differential Forms on Riemannian Manifolds
Hongya, Gao,Zhihua, Gu,Yuming, Chu Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.1
The purpose of this paper is to study the relations between quasilinear elliptic equations on Riemannian manifolds and differential forms. Two classes of differential forms are introduced and it is shown that some differential expressions are connected in a natural way to quasilinear elliptic equations.
New Two-Weight Imbedding Inequalities for A-Harmonic Tensors
GAO, HONGYA,CHEN, YANMIN,CHU, YUMING 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.1
In this paper, we first define a new kind of two-weight-A_(r)^(λ_(3))(λ_(1), λ_(2), Ω)-weight, and then prove the imbedding inequalities for A-harmonic tensors. These results can be used to study the weighted norms of the homotopy operator T from the Banach space L^(P)(D, ∧^(l)) to the Sobolev space W^(1, p)(D, ∧^(l-l), l= 1, 2, · · , n, and to establish the basic weighted L^(P)-estimates for A-harmonic tensors.
EXPONENT-QUASIADDITIVE PROPERTIES AND APPLICATION
Wang, Gendi,Zhang, Xiaohui,Chu, Yuming Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.2
In this paper the authors study the properties of the so-called exponent-quasiadditive functions and an application to the generalized $Gr\ddot{o}tzsch$ ring function of quasiconformal theory is specified.
Adaptive Prescribed Performance Output Regulation of Nonlinear Systems with Nonlinear Exosystems
Fujin Jia,Cui Lei,Junwei Lu,Yuming Chu 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.8
The paper studies the prescribed performance output regulation problem for a class of nonlinear uncertain strict-feedback systems which are driven by nonlinear exosystems. Fuzzy logic systems (FLSs) are used to approximate the unknown functions. A fuzzy adaptive observer is designed to estimate the system state. A fuzzy internal model is designed to reject disturbance. Simultaneously, a parameter-type Lyapunov function and L function are designed to ensure the prescribed performance of the system. As illustrated by example, the proposed prescribed performance fuzzy adaptive output feedback control scheme is shown to guarantee semi-globally uniformly ultimately bounded, and the dynamic performance and steady-state performance of the tracking error are dependent on the prescribed performance functions.
Observer Design for A Class of Uncertain State-Delayed Nonlinear Systems
Junwei Lu,Chunmei Feng,Shengyuan Xu,Yuming Chu 대한전기학회 2006 International Journal of Control, Automation, and Vol.4 No.4
This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.
Degenerate Weakly (k<sub>1</sub>, k<sub>2</sub>)-Quasiregular Mappings
Gao, Hongya,Tian, Dazeng,Sun, Lanxiang,Chu, Yuming Department of Mathematics 2011 Kyungpook mathematical journal Vol.51 No.1
In this paper, we first give the definition of degenerate weakly ($k_1$, $k_2$-quasiregular mappings by using the technique of exterior power and exterior differential forms, and then, by using Hodge decomposition and Reverse H$\"{o}$lder inequality, we obtain the higher integrability result: for any $q_1$ satisfying 0 < $k_1({n \atop l})^{3/2}n^{l/2}\;{\times}\;2^{n+1}l\;{\times}\;100^{n^2}\;\[2^l(2^{n+3l}+1)\]\;(l-q_1)$ < 1 there exists an integrable exponent $p_1$ = $p_1$(n, l, $k_1$, $k_2$) > l, such that every degenerate weakly ($k_1$, $k_2$)-quasiregular mapping f ${\in}$ $W_{loc}^{1,q_1}$ (${\Omega}$, $R^n$) belongs to $W_{loc}^{1,p_1}$ (${\Omega}$, $R^m$), that is, f is a degenerate ($k_1$, $k_2$)-quasiregular mapping in the usual sense.