Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities

In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric difference. We also study a new nonlocal flow of convex plane curves and discuss its evolution behavior. In the second part of the paper we discuss necessary and sufficient conditions (in terms of the (mixed) isoperimetric ratio or (mixed) isoperimetric difference) for two convex closed curves to be homothetic or parallel.Comment: 23 page

Neural Feedback Scheduling of Real-Time Control Tasks

Many embedded real-time control systems suffer from resource constraints and dynamic workload variations. Although optimal feedback scheduling schemes are in principle capable of maximizing the overall control performance of multitasking control systems, most of them induce excessively large computational overheads associated with the mathematical optimization routines involved and hence are not directly applicable to practical systems. To optimize the overall control performance while minimizing the overhead of feedback scheduling, this paper proposes an efficient feedback scheduling scheme based on feedforward neural networks. Using the optimal solutions obtained offline by mathematical optimization methods, a back-propagation (BP) neural network is designed to adapt online the sampling periods of concurrent control tasks with respect to changes in computing resource availability. Numerical simulation results show that the proposed scheme can reduce the computational overhead significantly while delivering almost the same overall control performance as compared to optimal feedback scheduling.Comment: To appear in International Journal of Innovative Computing, Information and Contro

Fuzzy Feedback Scheduling of Resource-Constrained Embedded Control Systems

The quality of control (QoC) of a resource-constrained embedded control system may be jeopardized in dynamic environments with variable workload. This gives rise to the increasing demand of co-design of control and scheduling. To deal with uncertainties in resource availability, a fuzzy feedback scheduling (FFS) scheme is proposed in this paper. Within the framework of feedback scheduling, the sampling periods of control loops are dynamically adjusted using the fuzzy control technique. The feedback scheduler provides QoC guarantees in dynamic environments through maintaining the CPU utilization at a desired level. The framework and design methodology of the proposed FFS scheme are described in detail. A simplified mobile robot target tracking system is investigated as a case study to demonstrate the effectiveness of the proposed FFS scheme. The scheme is independent of task execution times, robust to measurement noises, and easy to implement, while incurring only a small overhead.Comment: To appear in International Journal of Innovative Computing, Information and Contro

catena-Poly[[[(acetato-κ2 O,O′)cadmium]-μ-acetato-κ3 O,O′:O′-μ-{1,2-bis­[4-(pyridin-3-yl)pyrimidin-2-ylsulfan­yl]ethane}-κ2 N 4,N 4′] trihydrate]

The title compound, {[Cd(CH3COO)2(C20H16N6S2)]·3H2O}n, exists as a one-dimensional zigzag polymer in which the CdII ion shows a seven-coordinate [CdO5N2] distorted penta­gonal–bipyramidal geometry with the N atoms in axial positions and an N—Cd—N angle of 176.94 (13)°. The metal atoms are bridged by 1,2-bis­[4-(pyridin-3-yl)pyrimidin-2-ylsulfan­yl]ethane ligands, giving a polymeric chain extending along the b axis. Adjacent chains related by an inversion center are further bridged by Cd—O bonds formed between the O atom of one of the acetate ligands and the metal atom. The five Cd—O bond lengths are in the range 2.329 (3)–2.485 (3) Å. There are π–π stacking inter­actions between the aromatic rings of adjacent polymeric chains, the centroid–centroid distances being 3.556 (3) and 3.698 (3) Å, organizing the chains into a three-dimensional framework. This framework is additionally stabilized by extensive O—H⋯O and O—H⋯N hydrogen bonding between water mol­ecules and the ligands