A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.     

Engineering nanostructures of CuO-based photocatalysts for water treatment: Current progress and future challenges

Nowadays, increasing extortions regarding environmental problems and energy scarcity have stuck the development and endurance of human society. The issue of inorganic and organic pollutants that exist in water from agricultural, domestic, and industrial activities has directed the development of advanced technologies to address the challenges of water scarcity efficiently. To solve this major issue, various scientists and researchers are looking for novel and effective technologies that can efficiently remove pollutants from wastewater. Nanoscale metal oxide materials have been proposed due to their distinctive size, physical and chemical properties along with promising applications. Cupric Oxide (CuO) is one of the most commonly used benchmark photocatalysts in photodegradation owing to the fact that they are cost-effective, non-toxic, and more efficient in absorption across a significant fraction of solar spectrum. In this review, we have summarized synthetic strategies of CuO fabrication, modification methods with applications for water treatment purposes. Moreover, an elaborative discussion on feasible strategies includes; binary and ternary heterojunction formation, Z-scheme based photocatalytic system, incorporation of rare earth/transition metal ions as dopants, and carbonaceous materials serving as a support system. The mechanistic insight inferring photo-induced charge separation and transfer, the functional reactive radical species involved in a photocatalytic reaction, have been successfully featured and examined. Finally, a conclusive remark regarding current studies and unresolved challenges related to CuO are put forth for future perspectives.     

Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit L² norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the H¹ norm of this solution. Note that the obtained upper-bound is not optimal.     

无绝缘高温超导双饼线圈的瞬态电热特性分析

无绝缘高温超导线圈具有良好的电热稳定性和机械紧凑性,但其充电过程中却有明显的磁场延迟现象。为详细了解无绝缘高温超导线圈励磁过程的瞬态特性,建立了无绝缘高温超导线圈的同轴圆环等效电路模型。通过绕制一个670匝的无绝缘高温超导双饼线圈,在液氮温度下进行不同充电速率的励磁实验,初步验证了等效电路模型的正确性。基于该模型,针对线圈励磁过程的充电和恒流阶段,仿真得到了线圈各匝的径向电流分布规律和电热损耗特性。     

Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.     

Turing patterns for a coupled two-cell generalized Schnakenberg model

ABSTRACT

We consider a system for a generalized Schnakenberg model, showing Turing pattern formation for a wide class of nonlinearities.     

Analytic and numerical solutions in the theory of elastic plates

ABSTRACT

Numerical approximations of the solution of a boundary value problem when an exact solution is not available can be constructed by means of a variety of methods. In this paper, we present a technique that is based on the integral representation of the solution of an elliptic problem and the properties of the associated layer potentials. The procedure is illustrated in application to the mathematical model of bending of plates with transverse shear deformation in a finite domain, in the presence of Dirichlet, Neumann, and Robin conditions prescribed on the boundary.     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。