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Let G = (V, E) be an undirected connected simple graph on n vertices. A cut-equivalent tree of G is an edge-weighted tree on the same vertex set V, such that for any pair of vertices s, t ∈ V, the minimum (s, t)-cut in the tree is also a minimum (s, t)-cut in G, and these two cuts have the same cut value. In a recent paper [Abboud, Krauthgamer and Trabelsi, STOC 2021], the authors propose the first subcubic time algorithm for constructing a cut-equivalent tree. More specifically, their algorithm has Õ(n^{2.5}) running time. Later on, this running time was significantly improved to n^{2+o(1)} by two independent works [Abboud, Krauthgamer and Trabelsi, FOCS 2021] and [Li, Panigrahi, Saranurak, FOCS 2021], and then to (m+n^{1.9})^{1+o(1)} by [Abboud, Krauthgamer and Trabelsi, SODA 2022]. In this paper, we improve the running time to Õ(n²) graphs if near-linear time max-flow algorithms exist, or Õ(n^{17/8}) using the currently fastest max-flow algorithm. Although our algorithm is slower than previous works, the runtime bound becomes better by a sub-polynomial factor in dense simple graphs when assuming near-linear time max-flow algorithms.

The corrosion behavior of 2205 duplex stainless steel (2205 DSS) was investigated by atomization tests, which was performed in an S-bearing thin electrolyte layer used as the artificial industrial-marine environment. Electrochemical methods and X-ray photoelectron spectroscopy (XPS), were conducted to reveal the protection properties and the composition evolution of the passive film. The results indicated that the corrosion time would weak the protectiveness of passive film, which was attributed to the accumulation of defects and metal sulfides in the passive film. The decrease of composition percentage of Cr2O3 made more negative effects on the protection properties of passive film than the increase of Cr(OH)3 and CrO3, whose formation was related to the adequate supply of oxygen and water molecules. The metal sulfides such as NiS and MoS2 formed during atomization tests reduced the content of alloy oxides in the passive film, and provided locations for the growth of defects., The corrosion behavior of 2205 duplex stainless steel (2205 DSS) was investigated by atomization tests, which was performed in an S-bearing thin electrolyte layer used as the artificial industrial-marine environment. Electrochemical methods and X-ray photoelectron spectroscopy (XPS), were conducted to reveal the protection properties and the composition evolution of the passive film. The results indicated that the corrosion time would weak the protectiveness of passive film, which was attributed to the accumulation of defects and metal sulfides in the passive film. The decrease of composition percentage of Cr2O3 made more negative effects on the protection properties of passive film than the increase of Cr(OH)3 and CrO3, whose formation was related to the adequate supply of oxygen and water molecules. The metal sulfides such as NiS and MoS2 formed during atomization tests reduced the content of alloy oxides in the passive film, and provided locations for the growth of defects.

Gas turbine is a widely-used propulsion device for power convection in marine dynamical system. Conventional coolants such as impingement cooling and thermal protection material have lower convective heat transfer efficiency on the target surface which can hinder the development of marine gas turbine combustor. In this paper, impact cooling simplification models are established, which have simulated the function of the transition segment of marine gas turbine combustor to be protected from high temperature. Being enlightened by the butterfly scale, four types of bionic ribs are designed on the simplification models. During the analysis, conservation equations for mass, momentum and energy are solved by using finite volume method with Realizable k−ε turbulence model. By comparing the four types bionic ribs models, the surface with Type 3 rib structure has the best cooling efficiency. The results show that the sharp corner and unequal length fins of bionic rib could affect the cooling efficiency. The inspire application of the bionic structures will provide a reference for new cooling structure design in marine gas turbine combustor.

Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph G=(V,E) with n vertices and m edges, the textbook algorithm takes O(n+m) time to construct a DFS tree. In this paper, we study the problem of maintaining a DFS tree when the graph is undergoing incremental updates. Formally, we show: Given an arbitrary online sequence of edge or vertex insertions, there is an algorithm that reports a DFS tree in O(n) worst case time per operation, and requires O (min {m log n, n^2}) preprocessing time. Our result improves the previous O(n log^3 n) worst case update time algorithm by Baswana et al. [Baswana et al., 2016] and the O(n log n) time by Nakamura and Sadakane [Nakamura and Sadakane, 2017], and matches the trivial Omega(n) lower bound when it is required to explicitly output a DFS tree. Our result builds on the framework introduced in the breakthrough work by Baswana et al. [Baswana et al., 2016], together with a novel use of a tree-partition lemma by Duan and Zhang [Duan and Zhang, 2016], and the celebrated fractional cascading technique by Chazelle and Guibas [Chazelle and Guibas, 1986a; Chazelle and Guibas, 1986b].