Symmetry and Localization in Periodic Crystals: Triviality of Bloch Bundles with a Fermionic Time-Reversal Symmetry

Acta Applicandae Mathematicae - We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons...     

The Tallest Column—A Dynamical System Approach Using a Symmetry Solution

A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the direction of the stable manifold, and solving backward numerically. This removes the need for an iterative integration method that was previously used. The method is shown to work for clamped or hinged boundary condition and can also be used for other problems involving singularities at the endpoints.     

六自由度机械臂的运动规划

为了使六自由度机械臂完成特定的动作,需要设计计算相应的指令序列.首先计算了机械臂位姿与指尖位置之间的关系公式,然后针对机械臂的到达问题、沿曲线运动问题和避障问题,分别提出目标位姿预测、曲线离散到达和受限目标到达三种解决方法,其中涉及的关键算法是自适应搜索法,该方法具有效率高、精度高、适用范围广的特点.在产生指令序列时采用贪心算法.通过以上方法得到的执行结果误差很小(<0.8mm),同时搜索收敛速度也很快.     

Robust Optimal Trajectory Planning for Robots by Stochastic Optimization

In the optimal control of industrial, field or service robots, the standard procedure is to determine first offline a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal Stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.     

Trajectory Planning and Feedforward Control Design for the Temperature Distribution in a Cuboid

The design of a feedforward tracking controller is considered for the temperature distribution in a cuboid, where the temperature on a single lateral surface can be arbitrarily prescribed by a control input. It is shown that there exists a so–called flat or basic output, which allows to explicitly derive the inverse infinite–dimensional system representation suitable for trajectory planning and for the determination of the respective control input necessary to track the desired trajectory in open–loop. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Decision Support System for Crew Planning in Passenger Transportation Using a Flexible Branch-and-Price Algorithm

This paper discusses a decision support system for airline and railway crew planning. The system is a state-of-the-art branch-and-price solver that is used for crew scheduling and crew rostering. Since it is far from trivial to build such a system from the information provided in the existing literature, technical issues about the system and its implementation are covered in more detail. We also discuss several applications. In particular, we focus on a specific aircrew rostering application. The computational results contain an interesting comparison of results obtained with the approach in which crew scheduling is carried out before crew rostering, and an approach in which these two planning problems are solved in an integrated manner.     

Tactical Planning for a Cutting Stock System

Wood processing on a centralized conversion site can be considered as a cutting stock problem. The multiperiod optimization of the production system is a very hard problem to solve. A balance has to be made between value recovery optimization and service rate maximization. In this research a decision support system was designed and built to support production planning. Strategic, tactical and operational planning are covered, but here the focus is primarily on tactical planning.     

Symmetry analysis for a thin film equation

In this work we give a complete group classification of the thin film equation u_t = –(f (u)_xxx )_x – kg (u)_x . By using Lie classical method the corresponding reductions are performed and some solutions are characterized. Some nonclassical symmetries for an associated potential system are derived. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Resonances Induced by Broken Symmetry in a System with a Singular Potential

We study a three-dimensional nonrelativistic quantum system with a delta-type potential. The support of this potential is determined by a circle and straight line in ${\mathbb{R}^3}$ . We show that a special symmetry of our system induces embedded eigenvalues, and breaking this symmetry leads to resonances.     

Symmetry reductions for a dissipation-modified KdV equation

In this paper we give a group classification for a dissipation-modified Korteweg-de Vries equation by means of the Lie method of the infinitesimals. We prove that, by using the nonclassical method, we get several new solutions which are unobtainable by Lie classical symmetries. We obtain nonclassical symmetries that reduce the dissipation-modified Korteweg-de Vries equation to ordinary equations with the Painlevé property. These solutions have not been derived elsewhere by the singular manifold method.     

Symmetry of solutions for a fractional system

We consider a pseudo-differential system involving different fractional orders. Through an iteration method, we obtain the key ingredients—the maximum principles—of the method of moving planes. Then we derive symmetry on non-negative solutions without any decay assumption at infinity.     

An Extension Principle for the Einstein-Vlasov System in Spherical Symmetry

We prove that “first singularities” in the non-trapped region of the maximal development of spherically symmetric asymptotically flat data for the Einstein-Vlasov system must necessarily emanate from the center. The notion of “first” depends only on the causal structure and can be described in the language of terminal indecomposable pasts (TIPs). This result suggests a local approach to proving weak cosmic censorship for this system. It can also be used to give the first proof of the formation of black holes by the collapse of collisionless matter from regular initial configurations. Communicated by Sergiu Klainerman submitted 15/11/04, accepted 17/02/05     

The Application of a Decision-support System for Planning Services within Hospitals

A paper in a previous issue of this journal described the development of a decision-support system for planning services within hospitals, the Hospital Planning Model. A crucial test of such a system is the actual change in the planning process its use brings about. Does it change and improve the planning process or do planners prefer to continue with historical practice? To demonstrate the potential impact of a decision-support system on planning, this paper describes a major application of the system undertaken in an inner London DHA. In this study, use of the system helped overturn management's original intention and resulted in savings of around £ 2 million.     

The Development of a Decision-support System for Planning Services within Hospitals

The planning of services within district health authorities is a complex task, but the process of planning is often crude: few options for addressing issues are considered, and these are inadequately assessed. These deficiencies led to research of which the aim was to identify the types of information and systems needed for improved planning. This paper describes the product of that research, the Hospital Planning Model. It is a decision-support system which gives planners fast access to relevant information for planning hospital services. This allows them to consider quickly a range of options for addressing a particular planning issue, and to test how sensitive the implications of proposals are to differing planning assumptions. The system has been shown to be generalizable, and is currently used in 28 health districts and other health organizations throughout the United Kingdom. The proposed reforms of the NHS are likely to increase the relevance of the system: the purchaser/provider market will result in a greater awareness by hospitals of the importance of identifying measures to improve the cost-effectiveness of care. Purchasers too may want to scrutinize hospitals in terms of their efficiency.     

Scheduler – A System for Staff Planning

In this paper we propose a unified formulation based on (min?,+) algebra to express the dynamics of pull control policies for serial single product manufacturing systems. For policies such as basestock, kanban, extended kanban and generalized kanban, the formulation has the same parametric form with different parameters for each policy. To calculate these parameters efficiently, (min?,+) algebra tools are used. This formulation allows us to identify under what parameter values two different policies have the same dynamics behavior. This has been applied to extended kanban and generalized kanban.     

Example of a System Whose Minimal Trajectory Attractor Does not Contain Solutions of the System

Mathematical Notes -