Edge detection with trigonometric polynomial shearlets

In this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

Analysis of directional higher order jump discontinuities with trigonometric shearlets

<p style='text-indent:20px;'>In a recent article, we showed that trigonometric shearlets are able to detect directional step discontinuities along edges of periodic characteristic functions. In this paper, we extend these results to bivariate periodic functions which have jump discontinuities in higher order directional derivatives along edges. In order to prove suitable upper and lower bounds for the shearlet coefficients, we need to generalize the results about localization- and orientation-dependent decay properties of the corresponding inner products of trigonometric shearlets and the underlying periodic functions.</p>

Investigation on Fluidelastic Instability Accompanied by Wake Shedding With a Time-Domain Model

As the most dangerous flow-induced vibration (FIV) mechanism, fluid-elastic instability is always accompanied by the wake shedding. If both of the two FIV mechanisms are considered, fluid forces in this condition can be quite complex. In this paper, a time-domain model based on unsteady flow theory was used to investigate the fluid-elastic instability in a rotated triangular tube array. The vortex shedding forces were simplified as harmonic forces. Computational fluid dynamics (CFD) was used to get the fluid force coefficients with vortex shedding. The model was established by a finite element code with MATLAB software and simulation results agreed with the experiment results. The results showed the critical instability velocity can be influenced by vortex shedding forces, and double peaks can be found in the frequency spectrum of displacements of tubes. The time-domain displacements showed the phases had been impacted by the shedding and periodic characteristic was found in the displacements results. The model can also be adopted in fluid-elastic instability analysis in other tube arrangements and flow conditions.

Granular Mobility-Factor Analysis Framework for enriching Occupancy Sensing with Doppler Radar

With the growing need for adoption of smarter resource control system in existing infrastructure, the proliferation of occupancy sensing is slowly increasing its pace. After reviewing an existing system, we find that utilization of Doppler radar is less progressive in enhancing the accuracy of occupancy sensing operation. Therefore, we introduce a novel analytical model that is meant for incorporating granularity in tracing the psychological periodic characteristic of an object by emphasizing on the mobility and uncertainty movement of an object in the monitoring area. Hence, the model is more emphasized on identifying the rate of change in any periodic physiological characteristic of an object with the aid of mathematical modelling. At the same time, the model extracts certain traits of frequency shift and directionality for better tracking of the unidentified object behavior where its applicabilibility can be generalized in majority of the fields related to object detection.

Periodic Control of General Energy Flowing in Charging-Discharging-Storage Integrated Station

A novel scheme of charging-discharging-storage integrated station is put forward. In order to control energy/power flowing in the integrated station effectively, a new definition of general energy is fully discussed and its periodic characteristic is analyzed. General energy includes three parts: general energy of battery supply system, general energy of battery echelon utilization system and general energy of EVs, all of which is almost periodic. After analyzing steady operation curves of the three parts of general energy, their interrelation is discussed. On this basis, a periodic control strategy for general energy is proposed. Taking typical bus operation in Shanghai as a case, general energy curves of battery systems and EVs are described and analyzed under periodic control strategy, which obviously shows that the integrated station can maintain stable and economic operation by periodic control of general energy flowing in the integrated station.