Discretization of Planar Geometric Cover Problems

We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union of the translates in the collection contains all the points in $P$. We show that the geometric cover problem can be converted to a form of the geometric set cover, which has a given finite-size collection of translates rather than the infinite continuous solution space of the former. We propose a reduced finite solution space that consists of distinct canonical translates and present polynomial algorithms to find the reduce solution space for disks, convex/non-convex polygons (including holes), and planar objects consisting of finite Jordan curves.Comment: 16 pages, 5 figure

Nonflammable Lithium Metal Full Cells with Ultra-high Energy Density Based on Coordinated Carbonate Electrolytes

Coupling thin Li metal anodes with high-capacity/high-voltage cathodes such as LiNi0.8Co0.1Mn0.1O2 (NCM811) is a promising way to increase lithium battery energy density. Yet, the realization of high-performance full cells remains a formidable challenge. Here, we demonstrate a new class of highly coordinated, nonflammable carbonate electrolytes based on lithium bis(fluorosulfonyl)imide (UFSI) in propylene carbonate/fluoroethylene carbonate mixtures. Utilizing an optimal salt concentr ation (4 M LiFSI) of the electrolyte results in a unique coordination structure of Li+-FSI-solvent cluster, which is critical for enabling the formation of stable interfaces on both the thin Li metal anode and high-voltage NCM811 cathode. Under highly demanding cell configuration and operating conditions (Li metal anode = 35 mu m, areal capacity/charge voltage of NCM811 cathode = 4.8 mAh cm(-2)/4 .6 V, and anode excess capacity [relative to the cathode] = 0.83), the Li metal-based full cell provides exceptional electrochemical performance (energy densities = 679 Wh kg(cell)(-1)/1,024 Wh L-cell(-1)) coupled with nonflammability

Ti3C2Tx MXene core-shell spheres for ultrahigh removal of mercuric ions

Two-dimensional (2-D) titanium carbide MXene core (Ti3C2Tx) shell aerogel spheres (MX-SA) for mercuric ion removal were designed and fabricated with varying concentrations of Ti3C2Tx MXene and sodium alginate (SA) using a facile method. Owing to their unique inside structures, high porosities, large specific surface areas, oxygenated functional groups of MXene nanosheets, and available active binding sites, the synthesized microspheres constitute a unique adsorbent for heavy metals removal in water. The MX-SA4:20 spheres exhibit an exceptional adsorption capacity of 2+932.84 mg/g for Hg2+ , which is among the highest value reported for adsorbents. The adsorbent exhibits high single- and multi-component removal efficiencies, with 100% efficiency for Hg2+ and > 90% efficiency for five heavy metal ions. The synthesized materials are highly efficient for Hg2+ removal under extreme pH conditions (0.5–1.0 M HNO3 ) and have additional excellent reproducible properties. The micro-size and spherical shape of MX-SA4:20 also allow it to be used in column-packed devices

The genetic diversity among strawberry breeding resources based on SSRs

Cultivated strawberry (Fragaria × ananassa Duch.) is a high value horticultural crop. In this study, the genetic diversity of 160 strawberry accessions was determined using five highly polymorphic simple sequence repeat (SSR) markers. Sixty different alleles were identified, with allele frequencies in the range of 0.006 to1. Similarity scores were in the range of 0.034 to 0.963 (average: 0.507). The accessions were categorized into five groups. Group 1 contained two diploid Fragaria vesca species and one unknown accession. Group 2 contained one accession (F x ananassa). Group 3 contained 20 F × ananassa accessions and six unknown accessions. Group 4 contained 48 F. × ananassa accessions, one octaploid Fragaria chiloensis species, and six unknown accessions while Group 5 contained 69 F. × ananassa accessions and six unknown accessions. Accessions within a pedigree were frequently grouped together. A total of 30 novel accessions were categorized alongside existing accessions. These results will allow breeders to develop strategies which incorporate more genetic diversity into new cultivars