Complex dynamic behavior in a viral model with state feedback control strategies

With the consideration of mechanism of prevention and control for the spread of viral diseases, in this paper, we propose two novel virus dynamics models where state feedback control strategies are introduced. The first model incorporates the density of infected cells (or free virus) as control threshold value; we analytically show the existence and orbit stability of positive periodic solution. Theoretical results imply that the density of infected cells (or free virus) can be controlled within an adequate level. The other model determines the control strategies by monitoring the density of uninfected cells when it reaches a risk threshold value. We analytically prove the existence and orbit stability of semi-trivial periodic solution, which show that the viral disease dies out. Numerical simulations are carried out to illustrate the main results.     

Synthesis,structural characterization and catalytic activity of benzimidazole‐functionalized Pd(II) N‐heterocyclic carbene complexes

Two Pd(II)–NHC complexes bearing benzimidazole and pyridine groups have been successfully prepared and fully characterized by NMR and X‐ray diffraction analysis. The structure of palladium complexes are a typical square‐planar with palladium surrounded by two pairs of trans‐arranged benzimidazole and carbene ligands. The Pd–NHC complexes have been proved to be a highly efficient catalyst for the Mizoroki–Heck coupling reaction of aryl halides with various substituted acrylates under mild conditions in excellent yields. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation and feature analysis for gas emboli Doppler ultrasound signals

The purpose of this study is to establish the simulation model of the gas emboli by analyzing reasons for features of gas emboli Doppler ultrasound signals.It is useful for the further classification of the solid emboli and gas emboli.First,the model of the radiation force and the drag force is used to calculate forces acting on the gas emboli.Second,the acceleration of the gas emboli is calculated in both the radial direction and the axial direction of the vessel, which is used to calculate the trajectory of the gas emboli in the vessel.Finally,the computer simulation model is established for the gas emboli.Doppler ultrasound signals of the gas emboli and the solid emboli are generated in the simulation experiment.Experimental results show that compared with the solid emboli,the gas emboli acted by the radiation force and the drag force will result in the frequency-domain broaden in the Doppler spectrogram.When the gas emboli circulate from the low speed area to the high speed one and then from the high speed area back to the low speed one,a "V" shape will be shown in the spectrogram of gas emboli signals.When the gas emboli circulate from the low speed area to the high speed one or from the high speed area to the low speed one,a diagonal shape will be shown for gas emboli signals. It is also shown that features of simulated gas emboli signals match with those of gas emboli signals sampled from clinic.All demonstrate that the simulation method of the gas emboli is reasonable.     

Existence of nontrivial solutions for fractional Schrödinger equations with critical or supercritical growth

In this paper, we study the following fractional Schrödinger equation with critical or supercritical growth where 0 < s < 1, N > 2s, λ > 0, , , ( ? Δ)^s denotes the fractional Laplacian of order s and f is a continuous superlinear but subcritical function. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 by variational methods. Our main contribution is related to the fact that we are able to deal with the case .     

Research Progress and Application of Ion Funnel Technique

Ion funnel is a new-style ion guider which can reduce spatial divergence and energy dispersity of the transmission ions by using radio frequency (RF) electric field to confine the ions radially and the direct current (DC) axial electric field to move the ions toward the exit, and thus it can greatly increase the ion transmission efficiency and improve the sensitivity of the mass spectrometry. Since ion funnel was invented in 1997, it has attracted a close attention of mass spectrometry scientists all over the world. Ion funnel has been used in various kinds of mass spectrometry, and built a bridge with high efficiency ion transmission between low vacuum ionization source and high vacuum mass analyzer. In this paper, the principle, technology development, and application progress of ion funnel are reviewed, and the future prospects are prospected.     

Asymmetric Wacker-Type Oxyallenylation and Azaallenylation of Cyclic Alkenes

Palladium-catalyzed three-component carboetherification of cyclic alkenes proceeded to give trans adducts exclusively with excellent enantioselectivity through a Wacker-type pathway. The reaction is also applicable to other oxygen nucleophiles, such as water, phenols, and carboxylic acids, as well as some electron-poor aryl amines.