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Zhao, Junfang,Ge, Weigao The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.
Junfang Zhao,Weigao Ge 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, (∅p(x'(t)))' + h(t)f(t, x(t), |x'(t)|) = 0, 0 < t < 1, x'(0) −δx(η) = 0, x'(1) + δx(η) = 0, where ∅p(s) = |s|p−2s, p > 1, δ > 0, 1 > η > ξ > 0, ξ +η= 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interestingpoint is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now. In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, (∅p(x'(t)))' + h(t)f(t, x(t), |x'(t)|) = 0, 0 < t < 1, x'(0) −δx(η) = 0, x'(1) + δx(η) = 0, where ∅p(s) = |s|p−2s, p > 1, δ > 0, 1 > η > ξ > 0, ξ +η= 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interestingpoint is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.
POSITIVE SOLUTION FOR SYSTEMS OF NONLINEAR SINGULAR BOUNDARY VALUE PROBLEMS ON TIME SCALES
Chunmei Miao,Dehong Ji,Junfang Zhao,Weigao Ge,Jiani Zhang 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.4
In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale T [수식] where [수식] and [수식] may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems [수식], and [수식] satisfying similar boundary conditions.
Enhanced adsorption of Orange II on bagasse-derived biochar by direct addition of CTAB
Guo-Ting Liang,Huiyuan Li,Xiao Mi,Weigao Zhao 한국화학공학회 2019 Korean Journal of Chemical Engineering Vol.36 No.8
Surface charge properties of an adsorbent always play an important role for the removal of contaminants from water. A cationic surfactant hexadecyl tri-methyl ammonium bromide (CTAB) was involved into adsorptive removal of Orange II (ORII) by bagasse biochars to realize an in-situ modification and an enhanced adsorption capability. Adsorption capacity of biochar (BC600) improved significantly from 1.66mg/g in the absence of CTAB to 4.42mg/g in the presence of 2.0mg/L CTAB. A more hydrophobic surface of bagasse biochar was favorable for the dye uptake in the presence of CTAB. Linear pseudo-second-order kinetic model fitted the kinetics data better at three pH conditions than pseudo-first-order kinetic model, whether in the presence and absence of CTAB. Both nonlinear pseudo-first-order and pseudo-second-order kinetic models were suitable to describe the experimental data. The maximal adsorption capacity in the absence of CTAB was very limited (41.4mg/g), while the adsorption isotherm curve in the presence of CTAB was almost linear, indicating a strong adsorption capability due to the introduction of CTAB. Direct addition of CTAB into wastewater is a potential technique for the enhanced removal of negatively-charged pollutants by bagasse biochar.
Leader-following Consensus of Second-order Multi-agent Systems With Input Delays
Wei Gao,Yan Ren,LiYun Zhao,Kai Weng,HuiMin Wang 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.9
This paper studies the leader-following consensus of second-order multi-agent systems with input delays. Firstly, a feedback-tracking control protocol with the leader’s delayed state derivative is proposed to guarantee the leader-following consensus. Secondly, considering the same input delay of the second-order multi-agent system, the explicit formula of the upper bound of delay for the asymptotic stability of the second-order multi-agent system is obtained by using the frequency domain analysis method. Compared with the latest existing controllers, the controller designed in this paper improves the convergence speed and tracking accuracy. Thirdly, a variety of diverse input delays are further considered, the feedback tracking controller is designed to improve the convergence speed and tracking accuracy, and sufficient conditions of leader-following consensus are given by using the generalized Nyquist stability criterion. Finally, simulation examples are given to show the effectiveness of our control protocol.
Wei Gao,Aodong Chen,Bowen Zhang,Ping Kong,Chenli Liu,Jie Zhao 아세아·태평양축산학회 2015 Animal Bioscience Vol.28 No.4
This study evaluated the in situ ruminal degradability, and subsequent small intestinal digestibility (SID) of dry matter, crude protein (CP), and amino acids (AA) of cottonseed meal (CSM), sunflower seed meal (SFSM) and distillers dried grains with solubles (DDGS) by using the modified three-step in vitro procedure. The ruminal degradability and subsequent SID of AA in rumen-undegradable protein (RUP-AA) varied among three protein supplements. The result show that the effective degradability of DM for SFSM, CSM, and DDGS was 60.8%, 56.4%, and 41.0% and their ruminal fermentable organic matter was 60.0%, 55.9%, and 39.9%, respectively. The ruminal degradable protein (RDP) content in CP for SFSM, CSM, and DDGS was 68.3%, 39.0%, and 32.9%, respectively, at the ruminal solid passage rate of 1.84%/h. The SFSM is a good source of RDP for rumen micro-organisms; however, the SID of RUP of SFSM was lower. The DDGS and CSM are good sources of RUP for lambs to digest in the small intestine to complement ruminal microbial AA of growing lambs. Individual RUP-AA from each protein source was selectively removed by the rumen micro-organisms, especially for Trp, Arg, His, and Lys (p<0.01). The SID of individual RUP-AA was different within specific RUP origin (p<0.01). Limiting amino acid was Leu for RUP of CSM and Lys for both RUP of SFSM and DDGS, respectively. Therefore, different protein supplements with specific limitations should be selected and combined carefully in growing lambs ration to optimize AA balance.