Embedded exponential-type low-regularity integrators for KdV equation under rough data

BIT Numerical Mathematics - In this paper, we introduce a novel class of embedded exponential-type low-regularity integrators (ELRIs) for solving the KdV equation and establish their optimal...     

A multigrid method for the ground state solution of Bose–Einstein condensates based on Newton iteration

BIT Numerical Mathematics - In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose–Einstein condensates based on Newton iteration scheme. Instead of...     

Vanishing coefficients and identities concerning Ramanujan’s parameters

The Ramanujan Journal - In this paper we investigate several infinite products with vanishing Taylor coefficients in arithmetic progressions. These infinite products are closely related to...     

Anisotropic black phosphorene nanotube anodes afford ultrafast kinetic rate or extra capacities for Li-ion batteries

As an important anode material for fast-charging Li-ion batteries (LIBs), black phosphorus (BP) has attracted extensive attention. Black phosphorene nanotubes (BPNTs) can be theoretically produced by rolling up the black phosphorene nanosheet along armchair (a-BPNTs) and zigzag (z-BPNTs) directions. The effects of curvature, chirality, Li-storage concentrations and strain stress on the Li-storage performance such as Li diffusion barriers and mechanical stabilities of BPNTs are mainly investigated by first principles calculations. The theoretical calculations predict that the a-BPNTs and z-BPNTs have good maximum Li-storage capacities, and the z-BPNTs exhibit better flexibility than a-BPNTs. The mechanical stabilities and Li-migration are all related to the curvature of BPNTs. Additionally, both a-BPNTs and z-BPNTs exhibit fast Li-ion conductivity along the c-axis direction. Moreover, the average Poisson's ratio of a-BPNTs (0.68) is larger than that of z-BPNTs (0.17), indicating that the strain stress is more difficult to apply on a-BPNTs than z-BPNTs. Our calculations predict that the a-BPNTs can afford ultrafast kinetic rate for fast-charging and high-power LIBs, while the z-BPNTs can provide extra capacity for high-energy LIBs.     

基于Caputo导数的分数阶非线性振动系统响应计算

研究了含分数阶Caputo导数的非线性振动系统响应的数值计算方法。首先，由Caputo分数阶导数算子的叠加关系，得到含分数阶导数项非线性振动系统状态方程的标准形式。其次，基于Caputo导数与Riemann-Liouville导数和Grunwald-Letnikov导数间的关系，推导计算了Caputo导数的一般数值迭代格式。本文方法不要求状态方程中各分数阶导数阶数相等，弱化了已有算法中对分数阶导数阶数的限制，并可推广到多自由度的情形。随后，选择若干有解析解的算例验证了本文方法的正确性。最后，以多吸引子共存的分数阶Duffing振子系统为例，比较Caputo和GL两种算法所得结果，说明了用GL算法求解存在的问题。     

In Situ Electropolymerization Enables Ultrafast Long Cycle Life and High-Voltage Organic Cathodes for Lithium Batteries

Organic cathode materials have attracted extensive attention because of their diverse structures, facile synthesis, and environmental friendliness. However, they often suffer from insufficient cycling stability caused by the dissolution problem, poor rate performance, and low voltages. An in situ electropolymerization method was developed to stabilize and enhance organic cathodes for lithium batteries. 4,4′,4′′-Tris(carbazol-9-yl)-triphenylamine (TCTA) was employed because carbazole groups can be polymerized under an electric field and they may serve as high-voltage redox-active centers. The electropolymerized TCTA electrodes demonstrated excellent electrochemical performance with a high discharge voltage of 3.95 V, ultrafast rate capability of 20 A g⁻¹, and a long cycle life of 5000 cycles. Our findings provide a new strategy to address the dissolution issue and they explore the molecular design of organic electrode materials for use in rechargeable batteries.     

Transfer learning in deep neural network based under-sampled MR image reconstruction

In Magnetic Resonance Imaging (MRI), the success of deep learning-based under-sampled MR image reconstruction depends on: (i) size of the training dataset, (ii) generalization capabilities of the trained neural network. Whenever there is a mismatch between the training and testing data, there is a need to retrain the neural network from scratch with thousands of MR images obtained using the same protocol. This may not be possible in MRI as it is costly and time consuming to acquire data. In this research, a transfer learning approach i.e. end-to-end fine tuning is proposed for U-Net to address the data scarcity and generalization problems of deep learning-based MR image reconstruction. First the generalization capabilities of a pre-trained U-Net (initially trained on the human brain images of 1.5 T scanner) are assessed for: (a) MR images acquired from MRI scanners of different magnetic field strengths, (b) MR images of different anatomies and (c) MR images under-sampled by different acceleration factors. Later, end-to-end fine tuning of the pre-trained U-Net is proposed for the reconstruction of the above-mentioned MR images (i.e. (a), (b) and (c)). The results show successful reconstructions obtained from the proposed method as reflected by the Structural SIMilarity index, Root Mean Square Error, Peak Signal-to-Noise Ratio and central line profile of the reconstructed images.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

Effective suppression of beta oscillation in Parkinsonian state via a noisy direct delayed feedback control scheme

This work explores the function of the noisy direct delayed feedback(NDDF)control strategy in suppressing the pathological oscillations in the basal ganglia(BG)with Parkinson’s disease(PD).Deep brain stimulation(DBS)alleviates the PD state fantastically.However,due to its unclear mechanism and open-loop characteristic,it is challenging to further improve its effects with lower energy expenditure.The noise stimulus performs competitively in alleviating the PD state theoretically,but it cannot adapt to the neural condition timely and automatically due to its open-loop control scheme.The direct delayed feedback(DDF)control strategy is able to disturb excessive synchronous effectively.Therefore,the NDDF control strategy is proposed and researched based on a BG computational model,which can reflect the intrinsic properties of the BG neurons and their connections with thalamic neurons.Simulation results show that the NDDF control strategy with optimal parameters is effective in removing the pathological beta oscillations.By comparison,we find the NDDF control strategy performs more excellent than DDF in alleviating PD state.Additionally,we define the multiple-NDDF control strategy and find that the multiple-NDDF with appropriate parameters performs better than NDDF.The obtained results contribute to the cure for PD symptoms by optimizing the noise-induced improvement of the BG dysfunction.     

Semi-invariants of binary forms and Sylvester’s theorem

The Ramanujan Journal - We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in...