Order continuous extensions of positive compact operators on Banach lattices

Let $E$ and $F$ be Banach lattices. Let $G$ be a vector sublattice of $E$ and $T: G\rightarrow F$ be an order continuous positive compact (resp. weakly compact) operators. We show that if $G$ is an ideal or an order dense sublattice of $E$, then $T$ has a norm preserving compact (resp. weakly compact) positive extension to $E$ which is likewise order continuous on $E$. In particular, we prove that every compact positive orthomorphism on an order dense sublattice of $E$ extends uniquely to a compact positive orthomorphism on $E$.Comment: 7 page

Low-cost and low-topography fabrication of multilayer interconnections for microfluidic devices

Multilayer interconnections are needed for microdevices with a large number of independent electrodes. A multi-level photolithographic process is commonly employed to provide multilayer interconnections in integrated circuit (IC) devices, but it is often too expensive for large-area or disposable devices frequently needed for microfluidics. The printed circuit board (PCB) can provide multilayer interconnection at low cost, but its rough topography poses a challenge for small droplets to slide over. Here we report a low-cost fabrication of low-topography multilayer interconnects by selective and controlled anodization of thin-film metal layers. The process utilizes anodization of metal (tantalum in this paper) or, more specifically, repetitions of a partial anodization to form insulation layers between conductive layers and a full anodization to form isolating regions between electrodes, replacing the usual process of depositing, planarizing, and etching insulation layers. After verifying the electric connections and insulations as intended, the developed method is applied to electrowetting-on-dielectric (EWOD), whose complex microfluidic products are currently built on PCB or thin-film transistor (TFT) substrates. To demonstrate the utility, we fabricated a 3 metal-layer EWOD device with steps (surface topography) less than 1 micrometer (vs. > 10 micrometers of PCB EWOD devices) and confirmed basic digital microfluidic operations

Optimized Hierarchical Power Oscillations Control for Distributed Generation Under Unbalanced Conditions

Control structures have critical influences on converter-interfaced distributed generations (DG) under unbalanced conditions. Most of previous works focus on suppressing active power oscillations and ripples of DC bus voltage. In this paper, the relationship between amplitudes of the active power oscillations and the reactive power oscillations are firstly deduced and the hierarchical control of DG is proposed to reduce power oscillations. The hierarchical control consists of primary and secondary levels. Current references are generated in primary control level and the active power oscillations can be suppressed by a dual current controller. Secondary control reduces the active power and reactive power oscillations simultaneously by optimal model aiming for minimum amplitudes of oscillations. Simulation results show that the proposed secondary control with less injecting negative-sequence current than traditional control methods can effectively limit both active power and reactive power oscillations.Comment: Accepted by Applied Energ

Optimal relaying in heterogeneous delay tolerant networks

In Delay Tolerant Networks (DTNs), there exists only intermittent connectivity between communication sources and destinations. In order to provide successful communication services for these challenged networks, a variety of relaying and routing algorithms have been proposed with the assumption that nodes are homogeneous in terms of contact rates and delivery costs. However, various applications of DTN have shown that mobile nodes should be divided into different classes in terms of their energy requirements and communication ability, and real application data have revealed the heterogeneous contact rates between node pairs. In this paper, we design an optimal relaying scheme for DTNs, which takes into account nodes’ heterogeneous contact rates and delivery costs when selecting relays to minimise the delivery cost while satisfying the required message delivery probability. Extensive results based on real traces demonstrate that our relaying scheme requires the least delivery cost and achieves the largest maximum delivery probability, compared with the schemes that neglect nodes’ heterogeneity