Decomposition Space Theory and the Bing Shrinking Criterion

‘Decomposition Space Theory and the Bing Shrinking Criterion’ gives a proof of the central Bing shrinking criterion and then provides an introduction to the key notions of the field of decomposition space theory. The chapter begins by proving the Bing shrinking criterion, which characterizes when a given map between compact metric spaces is approximable by homeomorphisms. Next, it develops the elements of the theory of decomposition spaces. A key fact is that a decomposition space associated with an upper semi-continuous decomposition of a compact metric space is again a compact metric space. Decomposition spaces are key in the proof of the disc embedding theorem.

Effect of Silicon Content on the Decomposition of Austenite in 0.4C Steel during Quenching and Partitioning Treatment

Although quenched and partitioned (Q&P) steels are traditionally alloyed with Si, its precise role on microstructural mechanisms occurring during the partitioning process is not thoroughly investigated. In this study, a systematic investigation has been carried out to reveal the influence of Si on austenite decomposition, phase transformation and carbide precipitation during Q&P treatment. Using a Gleeble thermomechanical simulator, three medium carbon steels with varying Si contents (0.25, 0.70 and 1.5 wt.%) were hot-rolled, reaustenitized, quenched into the Ms -Mf range, retaining about 20% austenite at the quench-stop temperature (TQ), and held for 1000 seconds above TQ in the temperature range of 200-300°C in order to better understand the mechanisms operating during partitioning. Dilatometric measurements combined with microstructural characterization using SEM-EBSD, TEM, and XRD clearly revealed the occurrence of various mechanisms. The effect of partitioning temperature/time on the hardness of the Q&P samples was correlated with the microstructural features. Steel containing low Si content (0.25%) was incapable of promoting carbon enrichment of austenite during partitioning, leading to its continuous decomposition into isothermal martensite and/or bainite without any detectable austenite retained even holding at 300°C. In comparison, 1.5% Si content promoted retention of about 19% austenite under similar Q&P conditions. Small fractions of bainite and high-carbon martensite formed during final cooling in both steels after partitioning at 200°C. Moreover, carbide precipitation was strongly retarded by high Si content.

Characteristics of Sedimentary Organic Matter and Phosphorus in Minor Rivers Discharging into Zhejiang Coast, China

In this study, the spatial distribution of lignin-derived phenols, bulk elemental composition and different phosphorus (P) species in surface sediments along six rivers discharging into Zhejiang coast, Southeast China, were investigated to improve the understanding of the carbon and P dynamics in these small river systems. The Shuang, Jiao, Ximen, Feiyun and Ao Rivers have total organic carbon (TOC) ranging from 0.29% to 2.77% and Λ (total lignin in mg/100 mg TOC) ranging from 0.24 to 4.24; Qiantang River has the lowest Λ (0.08–0.19) but the highest TOC (1.05%–6.46%). Jiao, Ximen, Feiyun and Ao Rivers have mean the total P (TP) and bioavailable P (BAP) of 34 to 124 mg/kg and 29 to 89 mg P/kg, and mean OC/OP molar ratio of 397–917. Qiantang River has the lowest mean TP and BAP of 13 mg P/kg and 7 mg P/kg, and highest OC/OP of 18,753; whereas Shuang River has the highest mean TP and BAP of 645 mg P/kg and 559 mg P/kg, and lowest mean OC/OP of 90. The lowest Λ, TP and BAP, but highest OC/OP, in the Qiantang River could be due to tidal bore causing rapid cycling of carbon and P. Trends of slight decrease in abundance of OC, Λ, TP and BAP, but increasing ratios of vanillic acid to vanillin [(Ad/Al)v], syringic acid to syringaldehyde [(Ad/Al)s] and OC/OP farther downstream of the rivers indicate a continuous decomposition of organic matter during transport along the rivers.

Boosting Electrochemical Performances of High-Voltage NCA/LTO Cells by Cathode Electrolyte Interface Nano Film Formation in Ionic Liquid Electrolyte

LiTFSI/EMITFSI ionic liquid was applied in this study as an electrolyte to enhance electrochemical performances of LiNi0.8 Co0.15 Al0.05 O2 /Li4 Ti5 O12 (NCA/LTO) batteries at a high charging cutoff voltage of 3.2 V. Li-EMITFSI electrolyte generated extremely stable and uniform cathode electrolyte interface (CEI) nano film on the cathode surface. This CEI film not only inhibited the continuous decomposition of electrolyte, but also stabilized the high operating voltage of NCA/LTO batteries, resulting in enhanced discharge gravimetric specific capacity (Cg) and cyclic stability of NCA/LTO batteries. With Li-EMITFSI electrolyte, the NCA/LTO batteries achieved higher C g of 172 mAhg –1 at 0.1 C and good capacity retention of 75% over 50 cycles at 1.4 ~ 3.2 V, compared to traditional commercial electrolytes.

Pure point/continuous decomposition of translation-bounded measures and diffraction

In this work we consider translation-bounded measures over a locally compact Abelian group$\mathbb{G}$, with a particular interest in their so-called diffraction. Given such a measure$\unicode[STIX]{x1D714}$, its diffraction$\widehat{\unicode[STIX]{x1D6FE}}$is another measure on the Pontryagin dual$\widehat{\mathbb{G}}$, whose decomposition into the sum$\widehat{\unicode[STIX]{x1D6FE}}=\widehat{\unicode[STIX]{x1D6FE}}_{\text{p}}+\widehat{\unicode[STIX]{x1D6FE}}_{\text{c}}$of its atomic and continuous parts is central in diffraction theory. The problem we address here is whether the above decomposition of$\widehat{\unicode[STIX]{x1D6FE}}$lifts to$\unicode[STIX]{x1D714}$itself, that is to say, whether there exists a decomposition$\unicode[STIX]{x1D714}=\unicode[STIX]{x1D714}_{\text{p}}+\unicode[STIX]{x1D714}_{\text{c}}$, where$\unicode[STIX]{x1D714}_{\text{p}}$and$\unicode[STIX]{x1D714}_{\text{c}}$are translation-bounded measures having diffraction$\widehat{\unicode[STIX]{x1D6FE}}_{\text{p}}$and$\widehat{\unicode[STIX]{x1D6FE}}_{\text{c}}$, respectively. Our main result here is the almost sure existence, in a sense to be made precise, of such a decomposition. It will also be proved that a certain uniqueness property holds for the above decomposition. Next, we will be interested in the situation where translation-bounded measures are weighted Meyer sets. In this context, it will be shown that the decomposition, whether it exists, also consists of weighted Meyer sets. We complete this work by discussing a natural generalization of the considered problem.