Sharp Reilly-type inequalities for a class of elliptic operators on submanifolds

Let M be an $n(>2)$-dimensional closed orientable submanifold in an $(n+p)$-dimensional space form ${\mathbb{R}}^{n+p}(c)$. We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on M defined by $L_{T}f=-\text{div}(T\mathrm{\nabla }f)$, where T is a general symmetric, positive definite and divergence-free $(1,1)$-tensor on M. The upper bound is given in terms of an integration involving tr T and $|H_T{|}^2$, where tr T is the trace of the tensor T and $H_T={\sum }_{i=1}^{n}A(T{e}_i,e_i)$ is a normal vector field associated with T and the second fundamental form A of M. Furthermore, we give the sufficient and necessary conditions when the upper bound is attained. Our main theorem can be viewed as an extension of the famous “Reilly inequality”. The operator $L_T$ can be regarded as a natural generalization of the well-known operator $L_r$ which is the linearized operator of the first variation of the $(r+1)$-th mean curvature for hypersurfaces in a space form. As applications of our main theorem, we generalize the results of Grosjean [17] and Li–Wang [20] in codimension one to arbitrary codimension.     

Meta-analysis on thermo-migration of tiny/nano-sized particles in the motion of various fluids

The importance of thermophoresis and its essential role in particle migration have led to many published reports (i.e. aim and objectives). However, there exists no report on thermo-migration of tiny/nano-sized particles in the motion of various fluids. A meta-analysis on the significance of either nano or tiny particles exposed to thermophoretic force owing to temperature gradient during the dynamics of liquid substances is deliberated upon in this report. The method of slope linear regression through the data point was adopted to scrutinize sixty (60) published reports in which the effects of thermophoresis (thermodiffusion) is deliberated upon. The outcome of the study shows that different responses to the force of a temperature gradient are sufficient enough to enhance the temperature distribution and the concentration of non-Newtonian fluid due to an increase in thermophoresis. Thermophoretic effect increases the concentration of fluids in which the relationship between the shear stress and shear strain is non-linear. Skin friction coefficients is a decreasing function of thermophoresis. Increase in thermophoretic deposition is achievable due to an increase in thermophoresis. The effect of haphazard motion of nanoparticles should be investigated when it increases negligibly and considerably large. Thermal radiation strongly influences the significance of thermo-migration of tiny particles on fluid flow.     

Laplacian Perfect State Transfer in Extended Neighborhood Coronas

Acta Mathematica Sinica, English Series - In this paper, we give some sufficient conditions for extended neighborhood coronas to have Laplacian perfect state transfer. We also give some conditions...     

Molecular Bridging Enables Isolated Iron Atoms on Stereoassembled Carbon Framework To Boost Oxygen Reduction for Zinc-Air Batteries

Realizing the synergy between active site regulation and rational structural engineering is essential in the electrocatalysis community but still challenging. Here, a matrix-confined co-pyrolysis strategy based on molecular bridging is demonstrated to realize highly dispersed Fe atoms on stereoassembled carbon framework. Both polyacrylonitrile matrix and organic linker from metal–organic frameworks (MOFs) provide sufficient N-anchoring sites for the generation of Fe−N₄ moieties. A high Fe loading of 2.9 wt.% is readily achieved based on the scalable approach without post-treatment. Owing to the presence of highly exposed Fe−N−C sites and well-tuned pore structures, isolated Fe atoms on porous carbon nanofiber framework (Fe−SA/NCF) exhibits decent oxygen reduction activity and stability in alkaline conditions via a near four-electron path, demonstrating superior performance as air cathode for zinc-air batteries (ZABs) to commercial Pt/C catalyst.     

A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

High-resolution semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations

We introduce a high resolution fifth-order semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations. The numerical fluxes of the scheme are constructed by Hermite polynomials which can be obtained by using the short-time assignment of the first derivatives. The extensions of the proposed semi-discrete Hermite central-upwind scheme to multidimensional cases are straightforward. The accuracy, efficiency and stability properties of our schemes are finally demonstrated via a variety of numerical examples.     

Enhanced mechanical properties of unidirectional basalt fiber/epoxy composites using silane-modified Na+-montmorillonite nanoclay

This study explores the effects of 3-glycidoxypropyltrimethoxysilane (3-GPTS) modified Na-montmorillonite (Na-Mt) nanoclay addition on mechanical response of unidirectional basalt fiber (UD-BF)/epoxy composite laminates under tensile, flexural and compressive loadings. Fourier transform infrared (FT-IR), X-ray diffraction (XRD) and simultaneous thermal analysis (STA) data confirmed the reaction mechanism between the silane compound and Mt. It was demonstrated that addition of 5 wt % 3-GPTS/Mt resulted in 28%, 11% and 35% increase in flexural, tensile and compressive strengths. Scanning electron microscopy (SEM) clarified the improvement in the adhesion between the basalt fibers and matrix in the case of Mt-enhanced epoxy specimens. Also, a theoretical route based on a Euler-Bernoulli beam-based approach was employed to estimate the compressive properties of the composites. The results demonstrated good agreement between theoretical and experimental approaches. Totally, the results of the study show that matrix modification is an effective strategy to improve the mechanical behavior of fibrous composites.     

Salient region detection using background priors

In this paper, we introduce a novel salient region detection algorithm by using background priors. Because of the fact that superpixel is perceptually more meaningful than pixel, and which can reduce the complexity of image processing, we use the superpixel algorithm to reprocess original images. In addition, we hold the point that the colors in the image boundary could mainly represent all background colors, hence we compute the color contrast between the intern colors and the boundary colors. Since the nearer the patches are close to center, the more they affect other patches, we propose a new distribution-based model. Finally, experimental results demonstrate that the proposed method outperforms the state-of-the-art approaches.     

太阳帆塔轨道和姿态耦合动力学建模及辛求解

在建立太阳帆塔太阳能电站简化模型的基础上,将系统的动力学方程从Lagrange体系导入到了Hamilton体系,给出了带约束的Hamilton正则方程;进而采用祖冲之类算法和辛Runge-Kutta方法分析了太阳帆塔轨道和姿态耦合系统的动力学特性,并讨论了算法的保能量、保约束特性;最后,数值模拟了系统的动力学特性,说明了所提方法的有效性.