Best Estimates of Weighted Eigenvalues of One-dimensional p-Laplacian

In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditions p(t)dt = M and max(e[0,T] p(t) = H. It is also explained for whatweights p the infimum and the supremum will be attained.

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

Existence,Multiplicity and Infinite Solvability of Positive Solutions for One-Dimensional p-Laplacian

The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.

MULTIPLICITY OF POSITIVE SOLUTIONS TO MULTIPOINT BOUNDARY VALUE PROBLEM WITH ONE-DIMENSIONAL p-LAPLACIAN

In this paper, we consider a multipoint boundary value problem for one-dimensional p-Laplacian. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the boundary value problem. In this problem, the nonlinear term explicitly involves a first-order derivative, which is different from some previous ones.

具有p-Laplacian算子的分数阶问题共振正解的存在性

本文研究了具有p-拉普拉斯算子的分数阶微分方程在两种边界条件下的共振正解存在的问题.利用Leggett-Williams范型定理的方法,获得了一些新的存在性结果,推广了该类问题已有的研究结果.

Existence Results for m-Point Boundary Value Problem at Resonance with One-dimensional p-Laplacian

By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper.

SOLVABILITY FOR m-POINT BOUNDARY VALUE PROBLEM AT RESONANCE WITH ONE-DIMENSIONAL p-LAPLACIAN

By using Mawhin＇s continuation theorem, the existence of solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of the paper.

具有脉冲效应的分数阶p-Laplacian方程耦合系统的可解性

本文研究了一类具有脉冲效应的分数阶p-Laplacian方程耦合系统的问题.利用变分方法,获得了该系统解存在的一些新结果.在证明过程中,弱化了系统中变系数和非线性项的条件,推广了已有结果.

Prediction of one-dimensional CrN nanostructure as a promising ferromagnetic half-metal

Searching for one-dimensional(1D)nanostructure with ferromagnetic(FM)half-metallicity is of significance for the development of miniature spintronic devices.Here,based on the first-principles calculations,we propose that the 1D CrN nanostructure is a FM half-metal,which can generate the fully spin-polarized current.The ab initio molecular dynamic simulation and the phonon spectrum calculation demonstrate that the 1D CrN nanostructure is thermodynamically stable.The partially occupied Cr-d orbitals endow the nanostructure with FM half-metallicity,in which the half-metallic gap(?s)reaches up to 1.58 eV.The ferromagnetism in the nanostructure is attributed to the superexchange interaction between the magnetic Cr atoms,and a sizable magnetocrystalline anisotropy energy(MAE)is obtained.Moreover,the transverse stretching of nanostructure can effectively modulate?s and MAE,accompanied by the preservation of half-metallicity.A nanocable is designed by encapsulating the CrN nanostructure with a BN nanotube,and the intriguing magnetic and electronic properties of the nanostructure are retained.These novel characteristics render the 1D CrN nanostructure as a compelling candidate for exploiting high-performance spintronic devices.

带p-Laplacian算子的分数阶微分方程半正系统正解的存在性

对一类带有p-Laplacian算子和含有分数阶积分的奇异非线性项的Riemann-Liouville型分数阶微分方程半正系统正解的存在性进行了分析与研究,其边界条件包括不同阶的分数阶导数、Riemann-Stieltjes积分和无穷点边值条件.基于相关Green函数的性质以及不动点指数定理,得到了参数属于合适区间时,该系统至少存在一个正解的充分条件.通过具体实例验证了所得结果的实用性.

Minimization of eigenvalues and construction of non-degenerate potentials for the one-dimensional p-Laplacian

We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for the one-dimensional p-Laplacian with the Dirichlet boundary condition. Such a class of nondegenerate potentials is a generalization of many known classes of non-degenerate potentials and will be useful in many problems of nonlinear differential equations.

Size effect on light propagation modulation near band edges in one-dimensional periodic structures

Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

Analysis of Dynamical Behavior of One-Dimensional Real Maps: An Executable Dynamical Programming Software Approach

The dynamical behavior of real-world phenomena is implausible graphically due to the complexity of mathematical coding. The present article has mainly focused on some one-dimensional real maps’ dynamical behavior irrespective of using coding. In continuation, linear, quadratic, cubic, higher-order, exponential, logarithmic, and absolute value maps have been used to scrutinize their dynamical behavior, including the characteristics of the orbit of points. Dynamical programming software (DPS.exe) will be proposed as a new technique to ascertain the dynamical behavior of said maps. Thus, a mathematician can automatically determine one-dimensional real maps’ dynamical behavior apart from complicated programming code and analytical solutions.

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

In this paper,we investigate the interfacial behavior of a thin one-dimensional(1D)hexagonal quasicrystal(QC)film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation.The contact interface is assumed to be nonslipping,with both perfectly bonded and debonded boundary conditions.The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress,which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials.The expressions are explicitly obtained for the phonon interfacial shear stress,internal normal stress,and stress intensity factors(SIFs).Finally,based on numerical calculations,we briefly discuss the effects of the material mismatch,the geometry of the QC film,and the debonded length and location on stresses and SIFs.

一类p-Laplacian问题正径向解的存在性与多解性

研究了p-Laplacian问题{-div(|∇u|^(p-2)∇u)=q(|x|)f(u),|x|>1,x∈R^(N),u(x)=b,|x|=1,u(x)→a,|x|→+∞,其中,1<p<N,a,b为正参数,q∈L^(1)_(loc)((1,+∞),[0,+∞)),f∈C([0,+∞),[0,+∞))。运用锥上的不动点定理、上下解方法和拓扑度理论,获得了p-Laplacian问题正解的存在性和多解性结果。

Periodic Eigenvalues of One-Dimensional p-Laplacian with Indefinite Weights

Rotation numbers are used in this paper to study the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic weight which changes sign. The analysis proves that for any nonnegative integer n, ρ -1(n/2) is the union of two closed intervals, one of which lies in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] + and the other in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] -, and the endpoints of these intervals yield the corresponding periodic and anti-periodic eigenvalues.

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL p-LAPLACIAN

We study the existence of positive solutions to boundary value problems for one- dimensional p-Laplacian under some conditions about the first eigenvalues correspon- ding to the relevant operators by the fixed point theory. The main difficulties are the computation of fixed point index and the subadditivity for positively 1-homogeneous operator.

带有p-Laplacian算子的分数阶非线性积分边值问题的唯一正解与和算子方法

该文研究了一类带有p-Laplacian算子并且非线性项f中含有分数阶导数项以及边界条件中含有非线性积分项的分数阶边值问题唯一正解的存在性.通过构造适当的辅助边值问题和锥上的等价类,利用锥理论与和算子方法获得了该边值问题唯一正解存在的充分条件,建立了一致收敛于唯一正解的单调迭代格式,最后给出了一个具体的例子作为所获结论的应用.