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In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable vt(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded. 相似文献
14.
This paper develops a framework to deal with the unconditional superclose analysis of
nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example,
a new mixed finite element method (FEM) is established and the $τ$ -independent superclose
results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an
error splitting technique, with which the time-discrete and the spatial-discrete systems are
constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require
certain time step conditions. Finally, some numerical results are provided to confirm the
theoretical analysis, and show the efficiency of the proposed method. 相似文献
15.
Waleed A. El‐Said Mona A. Abdel‐Rahman Eman M. Sayed Aboel‐Magd A. Abdel‐Wahab 《Electroanalysis》2019,31(5):829-837
Here, we reported on a one‐step fabrication of magnetite Fe3O4 nanoparticles/indium tin oxide (ITO) electrode based on the direct growing of Fe3O4 nanoparticles on the ITO surface by using a solvothermal process. The modified electrode was used as electrochemical methotrexate (MTX) biosensor with high sensitivity based on cyclic voltammetry and square wave voltammetry techniques. The results demonstrated a linear relationship between the MTX concentration and its oxidation current peak over a wide range from 10?5 to 10?14 mole/L with a limit of detection of 0.4×10?15 M based on the square wave voltammetry (SWV) technique. In addition, Fe3O4/ITO electrode showed a good capability for measuring very low concentrations of MTX drug dissolved in human serum solution. Also, Fe3O4/ITO electrode was used for detecting MTX in blood serum samples collected from patients after their treatment with MTX. The prepared electrode showed the higher sensitivity that higher than the Viva‐E instrument, which opens the door for developing a cheap, simple and higher sensitive MTX sensor. 相似文献
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Diabetes mellitus (DM) is the fastest growing metabolic disorder in the world. Recently, more attention is paid to the study of natural products due to side effects of synthetic drugs. Stevia rebaudiana (Bertoni) is considered an encouraging starting point for the antidiabetic lead development. In the present study, the in vitro α-amylase inhibitory activity of the extracts of S. rebaudiana is investigated. In order to understand the molecular mechanism and future pharmacophore development, in silico study of secondary metabolites isolated from S. rebaudiana was carried out. Results indicated that water extract shows highest α-amylase inhibitory activity as compared to other extracts. Moreover, compound 20 (rebaudioside A) which has been previously reported and isolated from water extract showed the impressive binding profile with α-amylase. Therefore, our study suggests that S. rebaudiana could be used in the development of therapeutic drugs for the treatment of diabetes. 相似文献
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The electrochemical behavior of austenitic stainless steel (Type 304) in 3 M sulfuric acid with 3.5% recrystallized sodium chloride at specific concentrations of butan-1-ol was investigated with the aid of potentiodynamic polarization, open circuit measurement and weight loss technique. Butan-1-ol effectively inhibited the steel corrosion with a maximum inhibition efficiency of 78.7% from weight-loss analysis and 80.9% from potentiodynamic polarization test at highest concentration studied. Adsorption of the compound obeyed the Freundlich isotherm. Thermodynamic calculations reveal physiochemical interactions and spontaneous adsorption mechanism. Surface characterizations showed the absence of corrosion products and topographic modifications of the steel. Statistical analysis depicts the overwhelming influence and statistical significance of inhibitor concentration on the inhibition performance. 相似文献
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