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.     

A high accuracy flow segmentation method in crowded scenes based on streakline

Flow segmentation based on similar motion patterns in crowded scenes remains an open problem in computer vision due to inherent complexity and vast diversity found in such scenes. To solve this problem, the streakline framework based on Lagrangian fluid dynamics had been proposed recently. However, this framework computed optical flow field using conventional optical flow method (Lucas Kanade method) which has poor anti-interference performance, and serious deviation would be brought to the computation of optical flow field. Moreover, our experimental results show that using the formulation of streak flow similarity in this framework can result in incorrect flow segmentation. Therefore, we combine this framework with a high accurate variational model, and modify the corresponding formulation of streak flow similarity after analyzing the streakline framework in detail. Finally, an improved method is proposed to solve flow segmentation in crowded scenes. Experiments are done to compare these two methods and results verify the validity and accuracy of our method.     

Silver(I)-mediated reaction of trimethylsilylated arylacetylenes with sulfonyl chlorides:Unexpected formation of vinvl sulfones

A novel reaction of trimethylsilylated arylacetylenes with sulfonyl chlorides was performed in the presence of silver nitrate or triflate.Conjugated vinyl sulfones as dramatic products were obtained in moderate yields and with Z-selectivity.A free radical mechanism has been proposed to account for the formation of the products.     

Quantum Theory of Two-Photon Ghost Interference

In this paper, we study two-photon ghost interference with the approach of photon quantum theory, and calculate the coincidence counts of D ₁ and D ₁ detectors. With specific attention to the two-photon interference experiment carried out by Milena D’Angelo et al. (Phys. Rev. Lett. 87:013602, 2001), and find the theoretical result is accordance with experiment data.