The triangle scheduling problem

This paper introduces a novel scheduling problem, where jobs occupy a triangular shape on the time line. This problem is motivated by scheduling jobs with different criticality levels. A measure is introduced, namely the binary tree ratio. It is shown that the Greedy algorithm solves the problem to optimality when the binary tree ratio of the input instance is at most 2. We also show that the problem is unary NP-hard for instances with binary tree ratio strictly larger than 2 and provide a quasi-polynomial time approximation scheme. The approximation ratio of Greedy on general instances is shown to be between 1.5 and 1.05.     

Layered Platinum Dichalcogenides (PtS2, PtSe2, and PtTe2) Electrocatalysis: Monotonic Dependence on the Chalcogen Size

Presently, research in layered transition metal dichalcogenides (TMDs) for numerous electrochemical applications have largely focused on Group 6 TMDs, especially MoS₂ and WS₂, whereas TMDs belonging to other groups are relatively unexplored. This work unravels the electrochemistry of Group 10 TMDs: specifically PtS₂, PtSe₂, and PtTe₂. Here, the inherent electroactivities of these Pt dichalcogenides and the effectiveness of electrochemical activation on their charge transfer and electrocatalytic properties are thoroughly examined. By performing density functional theory (DFT) calculations, the electrochemical and electrocatalytic behaviors of the Pt dichalcogenides are elucidated. The charge transfer and electrocatalytic attributes of the Pt dichalcogenides are strongly associated with their electronic structures. In terms of charge transfer, electrochemical activation has been successful for all Pt dichalcogenides as evident in the faster heterogeneous electron transfer (HET) rates observed in electrochemically reduced Pt dichalcogenides. Interestingly, the hydrogen evolution reaction (HER) performance of the Pt dichalcogenides adheres to a trend of PtTe₂ > PtSe₂ > PtS₂ whereby the HER catalytic property increases down the chalcogen group. Importantly, the DFT study shows this correlation to their electronic property in which PtS₂ is semiconducting, PtSe₂is semimetallic, and PtTe₂ is metallic. Furthermore, Pt dichalcogenides are effectively activated for HER. Distinct electronic structures of Pt dichalcogenides account for their different responses to electrochemical activation. Among all activated Pt dichalcogenides, PtS₂ shows most accentuated improvement as a HER electrocatalyst with an exceptional 50% decline in HER overpotential. Knowledge on Pt dichalcogenides provides valuable insights in the field of TMD electrochemistry, in particular, for the currently underrepresented Group 10 TMDs.     

Bipolar Electrochemical Synthesis of WS2 Nanoparticles and Their Application in Magneto‐Immunosandwich Assay

WS₂ nanoparticles are prepared using bipolar electrochemistry. Obtained material exhibits high activity for hydrogen evolution reaction (HER) and it is used as a label in standard magneto‐immunosandwich assay for protein detection through HER. This new system shows high analytical performance in terms of a wide range, selectivity, sensitivity, and reproducibility.     

Ternary polymer electrolytes with 1-methylimidazole based ionic liquids and aprotic solvents

New polymer gel electrolytes containing ionic liquids were developed for modern chemical power sources—supercapacitors and lithium-ion batteries. Ternary systems polymer-ionic liquid-aprotic solvent as well as materials containing also lithium salts (LiClO₄ or LiPF₆) were prepared by direct, thermally initiated polymerisation. Poly(2-ethoxyethyl methacrylate) PEOEMA was combined with various ionic liquids based on 1-methylimidazole. Only 1-butyl-3-methylimidazolium hexafluorophosphate BMIPF₆ formed a homogenous and slightly translucent polymer electrolyte, where aprotic solvents—propylene carbonate and ethylene carbonates were used as plasticisers. Materials were studied using the electrochemical and thermogravimetric methods and exhibit high ionic conductivity up to 0.94 mS cm⁻¹ at 25 °C together with high electrochemical stability: the accessible potential window on the glassy carbon was found ca. 4.3 V. Prepared non-volatile materials are long-term and thermally stable up to 150 °C.