Narrow Results

Given a planar triangulation all of whose faces are initially white, we study the problem of colouring the faces black one by one so that the boundary between black and white faces as well as the number of connected black and white regions are small at all times. We call such a colouring sequence of the triangles a flooding. We prove that a flooding with boundary size and regions can be computed in time. We also prove that it is in general impossible to guarantee boundary size , for any ∊ > 0, and a number of regions that is o(log n), where n is the number of faces of the triangulation.

Let X be a zero-dimensional scheme in ℙ¹ × ℙ¹. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their Hilbert functions and depend only on their distributions of points in a grid of lines. Moreover, a minimal set of generators of the ideal of these schemes is given by curves split into the union of lines.

Aqueous zinc-ion batteries (AZIBs) are the most promising candidates for large-scale energy storage devices due to the advantages of low cost, high safety, environmental friendliness and high energy density. However, the low Coulombic efficiency (CE) and short cycle life of AZIBs caused by dendrite growth, hydrogen evolution reaction and corrosion of Zn anode, are limited the development and application of AZIBs in the future. To solve these problems, many works focused on the modification of Zn anode and electrolyte optimization have been widely reported. The separator–electrolyte interface and the separator–anode interface play a significant part in the behavior of zinc ions. Owing to the importance of separators for batteries, this paper reviews the requirements and optimization strategies of separators for AZIBs. It is mainly based on the surface modification of conventional separators (e.g. glass fiber, cellulose separators), the introduction of an intermediate membrane in the interlayer of the separator and anode, and the preparation of new-type separators to replace the conventional separators. In addition, this review proposes a further outlook on the future development of separators for AZIBs.

We present results of the recent research on sparse graphs and finite structures in the context of contemporary combinatorics, graph theory, model theory and mathematical logic, complexity of algorithms and probability theory. The topics include: complexity of subgraph- and homomorphism- problems; model checking problems for first order formulas in special classes; property testing in sparse classes of structures. All these problems can be studied under the umbrella of classes of structures which are Nowhere Dense and in the context of Nowhere Dense – Somewhere Dense dichotomy. This dichotomy presents the classification of the general classes of structures which proves to be very robust and stable as it can be defined alternatively by most combinatorial extremal invariants as well as by algorithmic and logical terms. We give examples from logic, geometry and extremal graph theory. Finally we characterize the existence of all restricted dualities in terms of limit objects defined on the homomorphism order of graphs.

Aqueous zinc-ion batteries (AZIBs) are the most promising candidates for large-scale energy storage devices due to the advantages of low cost, high safety, environmental friendliness and high energy density. However, the low Coulombic efficiency (CE) and short cycle life of AZIBs caused by dendrite growth, hydrogen evolution reaction and corrosion of Zn anode, are limited the development and application of AZIBs in the future. To solve these problems, many works focused on the modification of Zn anode and electrolyte optimization have been widely reported. The separator–electrolyte interface and the separator– anode interface play a significant part in the behavior of zinc ions. Owing to the importance of separators for batteries, this paper reviews the requirements and optimization strategies of separators for AZIBs. It is mainly based on the surface modification of conventional separators (e.g. glass fiber, cellulose separators), the introduction of an intermediate membrane in the interlayer of the separator and anode, and the preparation of new-type separators to replace the conventional separators. In addition, this review proposes a further outlook on the future development of separators for AZIBs.