Trajectory engineering via a space-fractional Schrodinger equation with dynamic linear index potential

We theoretically and numerically study the propagation dynamics of a Gaussian beam modeled by the fractional Schrodinger equation with different dynamic linear potentials. For the limited case α = 1(α is the Lévy index) in the momentum space, the beam suffers a frequency shift which depends on the applied longitudinal modulation and the involved chirp. While in the real space, by precisely controlling the linear chirp, the beam will exhibit two different evolution characteristics: one is the zigzag trajectory propagation induced by multi-reflection occurring at the zeros of spatial spectrum,the other is diffraction-free propagation. Numerical simulations are in full accordance with the theoretical results. Increase of the Lévy index not only results in the drift of those turning points along the transverse direction, but also leads to the delocalization of the Gaussian beam.

Effect of Si δ-Doping on the Linear and Nonlinear Optical Absorptions and Refractive Index Changes in InAlN/GaN Single Quantum Wells

In the framework of effective mass approximation, we theoretically investigate the electronic structure of the Si δ-doped InAIN/GaN single quantum well by solving numerically the coupled equations Schrodinger-Poisson self-consistently. The linear, nonlinear optical absorption coefficients and relative refractive index changes are calculated as functions of the doping concentration and its thickness. The obtained results show that the position and the amplitude of the linear and total optical absorption coefficients and the refractive index changes can be modified by varying the doping concentration and its thickness. In addition, it is found that the maximum of the optical absorption can be red-shifted or blue-shifted by varying the doping concentration. The obtained results are important for the design of various electronic components such as high-power FETs and infrared photonic devices.

Parallel Control for Continuous-Time Linear Systems:A Case Study

In this paper,a new parallel controller is developed for continuous-time linear systems.The main contribution of the method is to establish a new parallel control law,where both state and control are considered as the input.The structure of the parallel control is provided,and the relationship between the parallel control and traditional feedback controls is presented.Considering the situations that the systems are controllable and incompletely controllable,the properties of the parallel control law are analyzed.The parallel controller design algorithms are given under the conditions that the systems are controllable and incompletely controllable.Finally,numerical simulations are carried out to demonstrate the effectiveness and applicability of the present method.Index Terms-Continuous-time linear systems,digital twin,parallel controller,parallel intelligence,parallel systems.

Quantitative Structure-retention Relationship Study of Volatile Components from Rosa Banksiae Ait

In the present study,（QSRR） study had been carried out for volatile components from Rosa banksiae Ait.based on various quantum-chemical and physicochemical descriptors derived by B3LYP method.To build QSRR models,a multiple linear regression （MLR） stepwise method was used.The generated models have good predictive ability and are of high statistical significance with good correlation coefficients （R2≥0.734） and p values far less than 0.05.Preliminary results indicated that the application of the models,especially the prediction of GC retention time and linear retention index of volatile components from Rosa banksiae Ait.,will be helpful.The models contribute also to the identification of important quantum-chemical and physicochemical descriptors responsible for the retention time and linear retention index.It was found that the shape attribute （ShpA） and logP value play a vital role in determining component’s GC retention time and linear retention index which increase with the lipophilicity of volatile components.The larger the shape attribute of analyte is,the larger the deformability is,the stronger the interaction between analyte and stationary phase is,and the longer the GC retention time is,the larger the linear retention index is.The importance of E HOMO,q＋,and SEV is also embodied in models,but they are not dominant.

Tests for nonparametric parts on partially linear single index models

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

A New Prediction Model for Grain Yield in Northeast China Based on Spring North Atlantic Oscillation and Late-Winter Bering Sea Ice Cover

Accurate estimations of grain output in the agriculturally important region of Northeast China are of great strategic significance for guaranteeing food security.New prediction models for maize and rice yields are built in this paper based on the spring North Atlantic Oscillation index and the Bering Sea ice cover index.The year-to-year increment is first forecasted and then the original yield value is obtained by adding the historical yield of the previous year.The multivariate linear prediction model of maize shows good predictive ability,with a low normalized root-mean-square error（NRMSE）of 13.9%,and the simulated yield accounts for 81%of the total variance of the observation.To improve the performance of the multivariate linear model,a combined forecasting model of rice is built by considering the weight of the predictors.The NRMSE of the model is 12.9%and the predicted rice yield explains 71%of the total variance.The corresponding cross-validation test and independent samples test further demonstrate the efficiency of the models.It is inferred that the statistical models established here by applying year-to-year increment approach could make rational prediction for the maize and rice yield in Northeast China before harvest.The present study may shed new light on yield prediction in advance by use of antecedent large-scale climate signals adequately.

MULTIPLICITY OF SOLUTIONS TO ASYMPTOTICALLY LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL SYSTEM

In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.