A Category of Restricted Modules for the Ovisenko-Roger Algebra

In this paper, we study a category of restricted modules for the Ovsienko-Roger algebra, which is an extension of the Virasoro algebra of its tensor density module of degree one. We construct and characterize simple modules in this category and give natural free field realizations of certain restricted modules using the Weyl vertex algebra.

     

Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m

In this paper, we study the explicit expansion of the first order Melnikov function near a double homoclinic loop passing through a nilpotent saddle of order m in a near-Hamiltonian system. For any positive integer $m(m\ge 1)$, we derive the formulas of the coefficients in the expansion, which can be used to study the limit cycle bifurcations for near-Hamiltonian systems. In particular, for $m=2$, we use the coefficients to consider the limit cycle bifurcations of general near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 and 16 (11, 13 and 16, respectively) limit cycles in the case that the homoclinic loop is of cuspidal type (smooth type, respectively) and their distributions. As an application, we consider a near-Hamiltonian system with a nilpotent saddle of order 2 and obtain the lower bounds of the maximal number of limit cycles.     

Photons can hide where they have been

Recently,the nested Mach–Zehnder interferometer[Phys.Rev.Lett.111,240402(2013)]was modified by adding Dove prisms in a paper[Quantum Stud.:Math.Found.2,255(2015)],and an interesting result is that,after the Dove prisms were inserted,a signal at the first mirror of the nested interferometer was obtained.But,according to the former original paper,the photons have never been present near that mirror.In this work,we interpret this result naturally by resorting to the three-path interference method.Moreover,we find that even though the photons have been somewhere,they can hide the trace of being there.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

H2S gas sensor based on integrated resonant dual-microcantilevers with high sensitivity and identification capability

Detection of trace-level hydrogen sulfide (H₂S) gas is of great importance whether in industrial production or disease diagnosis. This research presents a novel H₂S gas sensor based on integrated resonant dual-microcantilevers which can identify and detect trace-level H₂S in real-time. The sensor consists of two integrated resonant microcantilever sensors with different functions. One cantilever sensor can identify H₂S by outputting positive frequency shift signals, while the other cantilever sensor will detect H₂S as a normally used cantilever sensor with negative frequency shifts. Combined the two cantilever sensors, the proposed gas sensor can distinguish H₂S from a variety of common gases, and the detection limit to H₂S of the sensor is as sensitive as below 1 ppb.     

Asymmetric Hydrosilylation of Aromatic Ketones Catalyzed by an Economical and Effective Copper-Diphosphine Catalytic System in Air

In the presence of the inexpensive and non‐toxic polymethylhydrosiloxane, the combination of copper(II) acetate and a chiral diphosphine displayed high catalytic efficiency in the asymmetric hydrosilylation of a series of aromatic ketones in air atmosphere and at room temperature. (R)‐1‐Arylethanols were obtained with up to 99% yield and 93% enantiomeric excess. Meanwhile, the electron effect and steric hindrance of substituents on the aromatic ring had an interesting influence on both the yields and enantioselectivities. Furthermore, a possible mechanism was presented to explain the influence of some key factors on the reaction.     

Estimation of partially specified spatial panel data models with random-effects

In this article, we study estimation of a partially specified spatial panel data linear regression with random-effects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain sufficient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.     

phyphox软件介绍及其在物理教学中的应用

全面介绍了基于手机传感器应用的phyphox软件的功能,并对于每种传感器均给出了相应实例来说明并启发其在物理教学中的应用.文章最后尝试总结了phyphox软件的优缺点,并对phyphox在物理教学中的应用前景作了展望和思考,期望对广大物理教师和物理教育研究者提供有益参考.     

On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity

The limiting behavior of stochastic evolution processes with small noise intensity ε is investigated in distribution-based approaches.Let μ~ε be a stationary measure for stochastic process X~ε with small ε and X~0 be a semiflow on a Polish space.Assume that {μ~ε:0 ε≤ε_0} is tight.Then all their limits in the weak sense are X~0-invariant and their supports are contained in the Birkhoff center of X~0.Applications are made to various stochastic evolution systems,including stochastic ordinary differential equations,stochastic partial differential equations,and stochastic functional differential equations driven by Brownian motion or Levy processes.