Non-perturbative positive Lyapunov exponent of Schrödinger equations and its applications to skew-shift mapping

We first study the discrete Schrödinger equations with analytic potentials given by a class of transformations. It is shown that if the coupling number is large, then the Lyapunov exponent equals approximately to the logarithm of this coupling number. When the transformation becomes the skew-shift mapping, we prove that the Lyapunov exponent is weak Hölder continuous, and the spectrum satisfies Anderson Localization and contains large intervals. Moreover, all of these conclusions are non-perturbative.     

A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field

Conformal mapping and analytic continuation are employed to prove the existence of an internal uniform electroelastic field inside a non-elliptical piezoelectric inhomogeneity interacting with a screw dislocation. We focus specifically on the case when the piezoelectric matrix surrounding the inhomogeneity is subjected to uniform remote anti-plane mechanical and in-plane electrical loading and a constraint is imposed between the remote loading and the screw dislocation. The constraint can be expressed in a relatively simple decoupled form by utilizing orthogonality relationships between two corresponding eigenvectors. The internal uniform electroelastic field is found to be independent of the presence of the screw dislocation; moreover, it can be expressed in decoupled form.     

Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.     

Multi-objective optimal design of feedback controls for dynamical systems with hybrid simple cell mapping algorithm

This paper presents a study of multi-objective optimal design of full state feedback controls. The goal of the design is to minimize several conflicting performance objective functions at the same time. The simple cell mapping method with a hybrid algorithm is used to find the multi-objective optimal design solutions. The multi-objective optimal design comes in a set of gains representing various compromises of the control system. Examples of regulation and tracking controls are presented to validate the control design.     

Issues Mapping: A problem structuring method for addressing science and technology conflicts

There are new opportunities for the application of problem structuring methods to address science and technology risk conflicts through stakeholder dialogue. Most previous approaches to addressing risk conflicts have been developed from a traditional risk communication perspective, which tends to construct engagement between stakeholders based on the assumption that scientists evaluate technologies using facts, and lay participants do so based on their values. ‘Understanding the facts’ is generally privileged, so the value framings of experts often remain unexposed, and the perspectives of lay participants are marginalized. When this happens, risk communication methodologies fail to achieve authentic dialogue and can exacerbate conflict. This paper introduces ‘Issues Mapping’, a problem structuring method that enables dialogue by using visual modelling techniques to clarify issues and develop mutual understanding between stakeholders. A case study of the first application of Issues Mapping is presented, which engaged science and community protagonists in the genetic engineering debate in New Zealand. Participant and researcher evaluations suggest that Issues Mapping helped to break down stereotypes of both scientists and environmental activists; increased mutual understanding; reduced conflict; identified common ground; started building trust; and supported the emergence of policy options that all stakeholders in the room could live with. The paper ends with some reflections and priorities for further research.     

思维导图促进分析化学课堂思政教学的探索——以“酸碱滴定法基本原理”为例

在分析化学课程的教学中,通过充分发掘其中的思政元素,将其与教学内容进行有机结合,达到育人的目的。通过引入思维导图教学法,搭建思政元素与教学内容的桥梁,学生可以快速把握所学知识。通过学生的表现,分析教学效果,存在的问题等,为课堂思政与本科化学教学有机结合提供一定的借鉴。     

Strong Convergence Theorems for the Generalized Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in the Intermediate Sense in Hilbert Spaces

Abstract

The aim of this paper is to introduce the generalized viscosity implicit rules of one asymptotically nonexpansive mapping in the intermediate sense in Hilbert spaces. We obtain some strong convergence theorems under certain assumptions imposed on the parameters. We also give a numerical example to support our main results. The results obtained in this paper improve and extend many recent ones in this culture.     

Heat flow disturbed by periodic array of insulated interface cracks

The thermal effects of an interface crack between two dissimilar half-spaces is considered. The interface cracks are partially or fully insulated, and spaced in a periodic array. Using the complex variable technique, the temperature and fluxes are found in closed form, and the interactions between heat flows due to nearby cracks are determined.     

Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-?-nonexpansive mappings in Banach spaces

In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-?-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. The results presented in the paper improve and extend some recent results.     

Real-time sensing and three-dimensional display of far outdoor scenes based on asymmetric integral imaging

A new asymmetric integral imaging (AII) system for real-time pickup and three-dimensional (3-D) display of far outdoor scenes based on dynamic-pixel-mapping (DPM) is proposed. DPM is a digital process to transform the elemental images captured with a lens array into the perspective-variant object images (POIs) whose structures are matched with those of display lenses, where the orders of pixels in each POI are reversely mapped, and then capture a set of virtual elemental images (EIs) at the specific depth planes from the back-propagated POIs. This DPM enables an asymmetrical use of pickup and display lens arrays, allowing the long-ranged pickup of far outdoor scenes and their resolution-enhanced 3-D reconstruction. Experiments with a pair of pickup and display lens arrays whose pitches and focal lengths are given by 7.5 mm, 30 mm and 1.2 mm, 8 mm, respectively, show that the effective pickup-range and resolution of the proposed system have been increased up to 6 m and 1600×1600 pixels, respectively, from 0.064 m and 480×480 pixels of the conventional systems employing the same pickup and display lens arrays. In addition, experiments with an implemented test bed confirms that the proposed system can provide real-time 3-D images in 25 frames per second.