Convergence and optimality of the adaptive Morley element method

This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the convergence analysis of the adaptive nonconforming method. By introducing a new parameter-dependent error estimator and further establishing a discrete reliability property, sharp convergence and optimality estimates are then fully proved for the fourth order elliptic problem

Converting normal insulators into topological insulators via tuning orbital levels

Tuning the spin-orbit coupling strength via foreign element doping and/or modifying bonding strength via strain engineering are the major routes to convert normal insulators to topological insulators. We here propose an alternative strategy to realize topological phase transition by tuning the orbital level. Following this strategy, our first-principles calculations demonstrate that a topological phase transition in some cubic perovskite-type compounds CsGeBr$_3$ and CsSnBr$_3$ could be facilitated by carbon substitutional doping. Such unique topological phase transition predominantly results from the lower orbital energy of the carbon dopant, which can pull down the conduction bands and even induce band inversion. Beyond conventional approaches, our finding of tuning the orbital level may greatly expand the range of topologically nontrivial materials

The convergence of subspace trust region methods

AbstractThe trust region method is an effective approach for solving optimization problems due to its robustness and strong convergence. However, the subproblem in the trust region method is difficult or time-consuming to solve in practical computation, especially in large-scale problems. In this paper we consider a new class of trust region methods, specifically subspace trust region methods. The subproblem in these methods has an adequate initial trust region radius and can be solved in a simple subspace. It is easier to solve than the original subproblem because the dimension of the subproblem in the subspace is reduced substantially. We investigate the global convergence and convergence rate of these methods

Notes on monotone Lindelöf property

summary:We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf

Application of Ultra-high Pressure Processing Technology

High pressure processing is an innovation for the traditional food processing and preservation method. Since the method of ultra-high pressure processing (HPP) exerts a very little influence on the covalent bond of food, its influence on the nutrition, taste, and texture of food is minimized. However, HPP food is perishable in long distance transportation and sales process. Since food freshness directly affects the final demand in market, how to use the appropriate strategy to manage commodity stocks effectively during the long time and distance in food transportation and match the supply and demand of HPP food to improve the competitiveness of companies are the challenges faced by HPP food companies in upstream and downstream supply chain. This paper describes of the different features of HPP foods compared to that of traditional processed foods, and analyzes the collaboration of HPP foods supply chain members

Cloud-Based Dynamic Programming for an Electric City Bus Energy Management Considering Real-Time Passenger Load Prediction

Electric city bus gains popularity in recent years for its low greenhouse gas emission, low noise level, etc. Different from a passenger car, the weight of a city bus varies significantly with different amounts of onboard passengers, which is not well studied in existing literature. This study proposes a passenger load prediction model using day-of-week, time-of-day, weather, temperatures, wind levels, and holiday information as inputs. The average model, Regression Tree, Gradient Boost Decision Tree, and Neural Networks models are compared in the passenger load prediction. The Gradient Boost Decision Tree model is selected due to its best accuracy and high stability. Given the predicted passenger load, dynamic programming algorithm determines the optimal power demand for supercapacitor and battery by optimizing the battery aging and energy usage in the cloud. Then rule extraction is conducted on dynamic programming results, and the rule is real-time loaded to onboard controllers of vehicles. The proposed cloud-based dynamic programming and rule extraction framework with the passenger load prediction shows 4% and 11% fewer bus operating costs in off-peak and peak hours, respectively. The operating cost by the proposed framework is less than 1% shy of the dynamic programming with the true passenger load information