Aharoni and Howard and, independently, Huang et al. (2012) proposed the following rainbow version of the Erdős matching conjecture: For positive integers n, k and m with n ⩾ km, if each of the families \(F_{1},\ldots,F_{m}\subseteq\left(\begin{array}{c}[n]\\ k\end{array}\right)\) has size more than \(\max\{\left(\begin{array}{c}n\\ k\end{array}\right)-\left(\begin{array}{c}n-m+1\\ k\end{array}\right),\left(\begin{array}{c}km-1\\ k\end{array}\right)\}\), then there exist pairwise disjoint subsets e1,…,em such that ei ∈ Fi for all i ∈ [m]. We prove that there exists an absolute constant n0 such that this rainbow version holds for k = 3 and n ⩾ n0. We convert this rainbow matching problem to a matching problem on a special hypergraph H. We then combine several existing techniques on matchings in uniform hypergraphs: Find an absorbing matching M in H; use a randomization process of Alon et al. (2012) to find an almost regular subgraph of H − V(M); find an almost perfect matching in H − V(M). To complete the process, we also need to prove a new result on matchings in 3-uniform hypergraphs, which can be viewed as a stability version of a result of Łuczak and Mieczkowska (2014) and might be of independent interest.
Journal of Solid State Electrochemistry - High-voltage LiNi0.5Mn1.5O4 with a spinel structure is considered as important cathode materials for high-energy density Li-ion batteries (LIBs). In this... 相似文献
In view of the continuously worsening environmental problems, fossil fuels will not be able to support the development of human life in the future. Hence, it is of great importance to work on the efficient utilization of cleaner energy resources. In this case, cheap, reliable, and eco-friendly grid-scale energy storage systems can play a key role in optimizing our energy usage. When compared with lithium-ion and lead-acid batteries, the excellent safety, environmental benignity, and low toxicity of aqueous Zn-based batteries make them competitive in the context of large-scale energy storage. Among the various Zn-based batteries, due to a high open-circuit voltage and excellent rate performance, Zn-Ni batteries have great potential in practical applications. Nevertheless, the intrinsic obstacles associated with the use of Zn anodes in alkaline electrolytes, such as dendrite, shape change, passivation, and corrosion, limit their commercial application. Hence, we have focused our current efforts on inhibiting the corrosion and dissolution of Zn species. Based on a previous study from our research group, the failure of the Zn-Ni battery was caused by the shape change of the Zn anode, which stemmed from the dissolution of Zn and uneven current distribution on the anode. Therefore, for the current study, we selected K3[Fe(CN)6] as an electrolyte additive that would help minimize the corrosion and dissolution of the Zn anode. In the alkaline electrolyte, [Fe(CN)6]3– was reduced to [Fe(CN)6]4– by the metallic Zn present in the Zn-Ni battery. Owing to its low solubility in the electrolyte, K4[Fe(CN)6] adhered to the active Zn anode, thereby inhibiting the aggregation and corrosion of Zn. Ultimately, the shape change of the anode was effectively eliminated, which improved the cycling life of the Zn-Ni battery by more than three times (i.e., from 124 cycles to more than 423 cycles). As for capacity retention, the Zn-Ni battery with the pristine electrolyte only exhibited 40% capacity retention after 85 cycles, while the Zn-Ni battery with the modified electrolyte (i.e., containing K3[Fe(CN)6]) showed 72% capacity retention. Moreover, unlike conventional organic additives that increase electrode polarization, the addition of K3[Fe(CN)6] not only significantly reduced the charge-transfer resistance in a simplified three-electrode system, but also improved the discharge capacity and rate performance of the Zn-Ni battery. Importantly, considering that this strategy was easy to achieve and minimized additional costs, K3[Fe(CN)6], as an electrolyte additive with almost no negative effect, has tremendous potential in commercial Zn-Ni batteries.相似文献
Introducing chirality into the metal-halide hybrids has enabled many emerging properties including chiroptical activity, spin-dependent transport, and ferroelectricity. However, most of the chiral metal-halide hybrids to date are non-emissive, and the underlying mechanism remains elusive. Here, we show a new strategy to turn on the circularly polarized luminescence (CPL) in chiral metal-halide hybrids. We demonstrate that alloying Sb3+ into chiral indium-chloride hybrids dramatically increases the photoluminescence quantum yield in two new series of chiral indium-antimony chlorides. These materials exhibit strong CPL signals with tunable energy and a high dissymmetry factor up to 1.5×10−2. Mechanistic studies reveal that the emission originates from the self-trapped excitons centered in 5s2 Sb3+. Moreover, near-ultraviolet pumped white light is demonstrated with a polarization up to 6.0 %. Our work demonstrates new strategies towards highly luminescent chiral metal-halide hybrids. 相似文献
Mature microRNAs (miRNAs) in extracellular vesicles (EVs) are involved in different stages of cancer progression, yet it remains challenging to precisely detect mature miRNAs in EVs due to the presence of interfering RNAs (such as longer precursor miRNAs, pre-miRNAs) and the low abundance of tumor-associated miRNAs. By leveraging the size-selective ability of DNA cages and polyethylene glycol (PEG)-enhanced thermophoretic accumulation of EVs, we devised a DNA cage-based thermophoretic assay for highly sensitive, selective, and in situ detection of mature miRNAs in EVs with a low limit of detection (LoD) of 2.05 fM. Our assay can profile EV mature miRNAs directly in serum samples without the interference of pre-miRNAs and the need for ultracentrifugation. A clinical study showed that EV miR-21 or miR-155 had an overall accuracy of 90 % for discrimination between breast cancer patients and healthy donors, which outperformed conventional molecular probes detecting both mature miRNAs and pre-miRNAs. We envision that our assay can advance EV miRNA-based diagnosis of cancer. 相似文献
A visible light photosensitizing metal-organic cage is applied as an artificial supramolecular reactor to control the reaction of aryl radicals with terminal olefins under green light/solvent conditions, which facilitates selective transformation in the confined enzyme-mimicking environment to give a series of geometrically defined E/Z-alkenes. The hydrophobic cage displays good host–guest inclusion with aromatic substrates, promoting Meerwein arylation and protecting E-isomeric products during reaction; while a small amount of benzonitrile can turn on efficient E→Z isomerization. Besides π–π stacking, the hydrogen bonding and halogen bonding interactions also act as control forces for the arylation of aliphatic terminal olefins known as poor acceptors in classic Meerwein arylation. The application of this switchable cage-confined arylation catalysis has been demonstrated by the syntheses of Tapinarof and a marine natural product from the same substrate via controllable E/Z selectivity. 相似文献
Intercellular proximity labeling has emerged as a promising approach to enable the study of cell-cell interactions (CCIs), but the efficiency of current platforms is limited. Here, we use Ru(bpy)32+ to construct an efficient photocatalytic proximity labeling (PPL) system on the cell surface that allows the highly discriminative CCI detection with spatiotemporal resolution. Through the mechanism study and quantitative characterization on living cells, we demonstrate that the singlet-oxygen (1O2) mechanism is more efficient and specific than the single electron transfer (SET) mechanism in Ru-mediated PPL. Ru(bpy)32+ catalysts with different cell-anchoring moieties are prepared to facilitate the catalyst loading on primary cells. Finally, based on this system, we develop a “live” T cell receptor (TCR) multimer with TCR-T cells that could sensitively identify and discriminate cells presenting antigens of different affinity, providing a powerful tool to better understand the heterogeneity of antigen presenting cells. 相似文献
The utilization of carbon resources stored in plastic polymers through chemical recycling and upcycling is a promising approach for mitigating plastic waste. However, most current methods for upcycling suffer from limited selectivity towards a specific valuable product, particularly when attempting full conversion of the plastic. We present a highly selective reaction route for transforming polylactic acid (PLA) into 1,2-propanediol utilizing a Zn-modified Cu catalyst. This reaction exhibits excellent reactivity (0.65 g gcat−1 h−1) and selectivity (99.5 %) towards 1,2-propanediol, and most importantly, can be performed in a solvent-free mode. Significantly, the overall solvent-free reaction is an atom-economical reaction with all the atoms in reactants (PLA and H2) fixed into the final product (1,2-propanediol), eliminating the need for a separation process. This method provides an innovative and economically viable solution for upgrading polyesters to produce high-purity products under mild conditions with optimal atom utilization. 相似文献