Meirong Zhang
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View article: A novel and application-oriented inverse nodal problem for Sturm-Liouville operators
A novel and application-oriented inverse nodal problem for Sturm-Liouville operators Open
This paper develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications in seismic wave analysis and submarine underwater radar (son…
View article: Platelet-Rich Plasma Versus Corticosteroids in the Treatment of Plantar Fasciitis
Platelet-Rich Plasma Versus Corticosteroids in the Treatment of Plantar Fasciitis Open
Objective This study aims to compare the efficacy of platelet-rich plasma and corticosteroids in treating plantar fasciitis, focusing on pain relief, foot function, and plantar fascia thickness to identify the optimal treatment approach. D…
View article: Asymptotic stability of the spectra of generalized indefinite strings
Asymptotic stability of the spectra of generalized indefinite strings Open
This paper focuses on the asymptotic stability of the spectra of generalized indefinite strings (GISs). A unitarily equivalent linear relation is introduced for GISs. It is shown that the solutions of the corresponding differential equatio…
View article: On the Meromorphic Integrability of the Critical Systems for Optimal Sums of Eigenvalues
On the Meromorphic Integrability of the Critical Systems for Optimal Sums of Eigenvalues Open
The popularity of estimation to bounds for sums of eigenvalues started from P. Li and S. T. Yau for the study of the Pólya conjecture. This subject is extended to different types of differential operators. This paper explores for the sums …
View article: On Planar Shadowing Curves to Closed Escaping Curves
On Planar Shadowing Curves to Closed Escaping Curves Open
We introduce a new dynamical system model called the shadowing problem, where a shadower chases after an escaper by always staring at and keeping the distance from him. When the escaper runs along a planar closed curve, we associate to the…
View article: On the structure of periodic eigenvalues of the vectorial <i>p</i>-Laplacian
On the structure of periodic eigenvalues of the vectorial <i>p</i>-Laplacian Open
In this paper we will solve an open problem raised by Manásevich and Mawhin twenty years ago on the structure of the periodic eigenvalues of the vectorial p -Laplacian. This is an Euler–Lagrangian equation on the plane or in higher dimensi…
View article: Relationships between Perturbations of a Linear Relation and Its Operator Part
Relationships between Perturbations of a Linear Relation and Its Operator Part Open
In this study, we establish some relationships between perturbations of a linear relation and its operator part by constructing an operator, which is induced by two linear relations including their closedness, hermiticity, self‐adjointness…
View article: The rotation number for almost periodic potentials with jump discontinuities and $δ$-interactions
The rotation number for almost periodic potentials with jump discontinuities and $δ$-interactions Open
We consider one-dimensional Schrödinger operators with generalized almost periodic potentials with jump discontinuities and $δ$-interactions. For operators of this kind we introduce a rotation number in the spirit of Johnson and Moser. To …
View article: Three-fold Weyl points in the Schrödinger operator with periodic potentials
Three-fold Weyl points in the Schrödinger operator with periodic potentials Open
Weyl points are degenerate points on the spectral bands at which energy bands intersect conically. They are the origins of many novel physical phenomena and have attracted much attention recently. In this paper, we investigate the existenc…
View article: Quantum (dual) Grassmann superalgebra as $\mathcal U_q(\mathfrak{gl}(m|n))$-module algebra and beyond
Quantum (dual) Grassmann superalgebra as $\mathcal U_q(\mathfrak{gl}(m|n))$-module algebra and beyond Open
We introduce and define the quantum affine $(m|n)$-superspace (or say quantum Manin superspace) $A_q^{m|n}$ and its dual object, the quantum Grassmann superalgebra $Ω_q(m|n)$. Correspondingly, a quantum Weyl algebra $\mathcal W_q(2(m|n))$ …
View article: On the Stability of Symmetric Periodic Orbits of the Elliptic Sitnikov Problem
On the Stability of Symmetric Periodic Orbits of the Elliptic Sitnikov Problem Open
Motivated by the recent works on the stability of symmetric periodic orbits of the elliptic Sitnikov problem, for time-periodic Newtonian equations with symmetries, we will study symmetric periodic solutions which are emanated from noncons…
View article: On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials
On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials Open
The works of V. A. Vinokurov have shown that eigenvalues and normalized eigenfunctions of Sturm-Liouville problems are analytic in potentials, considered as mappings from the Lebesgue space to the space of real numbers and the Banach space…
View article: Periodic solutions and their stability of some higher-order positively homogenous differential equations
Periodic solutions and their stability of some higher-order positively homogenous differential equations Open
View article: Limit cycles by perturbing quadratic isochronous centers inside piecewise smooth polynomial differential systems
Limit cycles by perturbing quadratic isochronous centers inside piecewise smooth polynomial differential systems Open
In the present paper, we study the number of zeros of the first order Melnikov function for piecewise smooth polynomial differential system, to estimate the number of limit cycles bifurcated from the period annulus of quadratic isochronous…
View article: An optimal class of non-degenerate potentials for second-order ordinary differential equations
An optimal class of non-degenerate potentials for second-order ordinary differential equations Open
By considering the Dirichlet boundary condition $x(0)=x(1)=0$ , we say that $q\in L^{1}[0,1]$ is a non-degenerate potential if the ordinary differential equation $x''+q(t) x=0$ has only the trivial solution $x(t)\equiv0$ which verifies the…