Forced Time-Dependent Harmonic Oscillators in Non-Commutative Space

For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis-Riesenfeld invariant. Coherent states are obtedned as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.

Solving the Inverse Problems of Wave Equation by a Boundary Functional Method

The inverse problems of wave equation to recover unknown space-time dependent functions of wave speed and wave source are solved in this paper, without needing of initial conditions and no internal measurement of data being required. After a homogenization technique, a sequence of spatial boundary functions at least the fourth-order polynomials are derived, which satisfy the homogeneous boundary conditions. The boundary functions and the zero element constitute a linear space, and then a new boundary functional is proved in the linear space, of which the energy is preserved for each dynamic energetic boundary function. The linear systems and iterative algorithms used to recover unknown wave speed and wave source functions with the dynamic energetic boundary functions as bases are developed, which converge fast at each time step. The input data are parsimonious, merely the measured boundary strains and the boundary values and slopes of unknown functions to be recovered. The accuracy and robustness of present methods are confirmed by comparing exact solutions with estimated results under large noises up to 20%.

基于C-DGCN的信息流行度预测

提出了一种基于上下文依赖的动态图卷积网络(context dependent dynamic graph convolutional network,CDGCN)对在线社交网络进行信息流行度预测,即根据信息的历史转发动态预测将来的流行度。根据信息转发动态构建转发网络,并将转发文本嵌入作为节点属性。C-DGCN基于扩散核的图卷积网络对转发网络进行嵌入,得到空间依赖表示,并输入循环神经网络(recurrent neural network,RNN)学习实时依赖表示。在2020年1月的微博数据集上进行了实验,并将C-DGCN与传统的基于特征设计、基于生成模型、基于深度学习的方法进行了比较。CDGCN的优势在于:1)充分考虑了文本内容对信息传播的驱动作用,建模表示了语义特性变化的影响,捕获了上下文依赖特性;2)扩散核是基于时间延迟特性的,循环神经网络能够捕获实时特性,充分建模表示了信息传播的时-空依赖。

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Wellposedness of some quasi-linear Schrdinger equations

This article is devoted to the study of a quasilinear Schrodinger equation coupled with an elliptic equation on the metric g. We first prove that, in this context, the propagation of regularity holds which ensures local wellposedness for initial data small enough in H1/2 and belonging to the Besov space B3/2 2,1. In a second step, we establish Strichartz estimates for time dependent rough metrics to obtain a lower bound of the time existence which only involves the B1＋ε 2,∞ norm on the initial data.

Bifurcation and spatiotemporal patterns of a density-dependent predator-prey model with Crowley-Martin functional response

In this paper, we consider a diffusive density-dependent predator-prey model with Crowley-Martin functional responses subject to Neumann boundary condition. We ana- lyze the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through the distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally, numerical simulations are given to verify our theoretical analysis.

Comparative analyses of current three-dimensional numerical solar wind models

We present a comparative study of the most advanced three-dimensional time-dependent numerical simulation models of solar wind. These models can be classified into two categories： （I） theoretical, empirical and numerically based models and （Ⅱ） self-consistent multi-dimensional numerical magnetohydrodynamic （MHD） models. The models of Category I are used to sep- arately describe the solar wind solution in two plasma flows regions： transonic/trans-Alfvrnic and supersonic/super-Alfvenic, respectively. Models of Category II construct a complete, single, numerical solar wind solution through subsonic/sub-Alfvrnic region into supersonic/super-Alfvrnic region. The Wang-Sheeley-Arge （WSA）/ENLIL in CISM is the most successful space weather model that belongs to Category I, and the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme （BATS-R-US） code in SWMF （Space Weather Modeling Framework） and the solar-interplanetary conservative element solution element MHD （SIP-CESE MHD） model in SWIM （Space Weather Integrated Model） are the most commonly-used models that belong to Category II. We review the structures of their frameworks, the main results for solar wind background studies that are essential for solar transient event studies, and discuss the common features and differences between these two categories of solar wind models. Finally, we conclude that the transition of these two categories of models to operational use depends on the availability of computational resources at reasonable cost and point out that the models＇ prediction capabilities may be improved by employing finer computational grids, incorporating more observational data and by adding more physical constraints to the models.

Neural circuit and its functional roles in cerebellar cortex

Objective To investigate the spike activities of cerebellar cortical cells in a computational network model con- structed based on the anatomical structure of cerebellar cortex. Methods and Results The multicompartment model of neuron and NEURON software were used to study the external influences on cerebellar cortical cells. Various potential spike patterns in these cells were obtained. By analyzing the impacts of different incoming stimuli on the potential spike of Purkinje cell, temporal focusing caused by the granule cell-golgi cell feedback inhibitory loop to Purkinje cell and spa- tial focusing caused by the parallel fiber-basket/stellate cell local inhibitory loop to Purkinje cell were discussed. Finally, the motor learning process of rabbit eye blink conditioned reflex was demonstrated in this model. The simulation results showed that when the afferent from climbing fiber existed, rabbit adaptation to eye blinking gradually became stable under the Spike Timing-Dependent Plasticity （STDP） learning rule. Conclusion The constructed cerebellar cortex network is a reliable and feasible model. The model simulation results confirmed the output signal stability of cerebellar cortex after STDP learning and the network can execute the function of spatial and temporal focusing.