Generalized Bruhat Cells and Completeness of Hamiltonian Flows of Kogan-Zelevinsky Integrable Systems

Let $G$ be any connected and simply connected complex semisimple Lie group, equipped with a standard holomorphic multiplicative Poisson structure. We show that the Hamiltonian flows of all the Fomin-Zelevinsky twisted generalized minors on every double Bruhat cell of $G$ are complete in the sense that all the integral curves of their Hamiltonian vector fields are defined on ${\mathbb{C}}$. It follows that all the Kogan-Zelevinsky integrable systems on $G$ have complete Hamiltonian flows, generalizing the result of Gekhtman and Yakimov for the case of $SL(n, {\mathbb{C}})$. We in fact construct a class of integrable systems with complete Hamiltonian flows associated to {\it generalized Bruhat cells} which are defined using arbitrary sequences of elements in the Weyl group of $G$, and we obtain the results for double Bruhat cells through the so-called open {\it Fomin-Zelevinsky embeddings} of (reduced) double Bruhat cells in generalized Bruhat cells. The Fomin-Zelevinsky embeddings are proved to be Poisson, and they provide global coordinates on double Bruhat cells, called {\it Bott-Samelson coordinates}, in which all the Fomin-Zelevinsky minors become polynomials and the Poisson structure can be computed explicitly.Comment: Title slightly changed; Section 1.3 expanded; some typos correcte

Investigation of the properties of reactive MgO-based cements and their effect on performance

Reactive MgO cement (RMC) is a promising alternative cementitious material benefiting from a relatively low calcination temperature during its production and strength development in concrete formulations linked with its CO2 sequestering capacity. One of the main challenges with RMC is the variations in its performance in line with the significant differences observed in the properties of the main phase, MgO. To identify and analyze the effects of these properties on the performance of RMC, this study presents a detailed characterization of 9 commercial RMC powders from different sources and precursors and an investigation of their performance in terms of reaction mechanisms and strength development. The results showed that the progress of hydration was highly dependent on the reactivity of RMC, whilst the early stages of the reaction were influenced by the purity. Additionally, agglomeration ratio revealed a strong correlation with the strength after 7 days of carbonation curing and 28 days of hydration. Finally, a regression analysis was employed to propose a model for the prediction of strength based on the initial properties of the RMC powder. The results emerging from this study can serve as a guideline for the selection of most suitable RMC-based binders for various building applications.</p

Passivation of reinforcing steel in reactive MgO cement blended with Portland cement

Reactive MgO cement (RMC) has an ability to gain strength by carbonation. One of the main concerns in RMC systems is the potential corrosion of reinforcing steel in structural applications. This study evaluated the feasibility of replacing small proportions of RMC with Portland cement (PC) to promote the passivation of reinforcing steel. Reinforcing steels embedded in RMC with different proportions of PC were investigated by electrochemical measurements and microstructural analysis. Pore solutions extracted from these pastes were evaluated for their chemical compositions. Inclusion of ≥2% PC enabled the passivation of steel. Passive film forming in RMC-PC blends consisted of Fe3O4 and Mg(OH)2, which was thicker than those in pure PC mixes. The formation of passive film was mainly attributed to the increased pH of the pore solution, which reached over 12 in RMC mixes containing only 2% PC. These findings highlighted the potential of using RMC mixes in reinforced concrete applications.</p

Negligible effect of vitamin D supplementation on exacerbation in patients with chronic obstructive pulmonary disease: meta-analysis

IntroductionThe focus of this meta-analysis was how vitamin D supplementation influences exacerbations in patients with chronic obstructive pulmonary disease (COPD) and vitamin D deficiency (VDD). Materials and methodsCochrane Library, Web of Science, Embase, and PubMed databases have been systematically searched in an attempt to collect randomized controlled trials related to vitamin D supplementation in COPD patients with VDD published in English available by July 2022. Primary outcome indicators included the mean number of exacerbation and rate of exacerbation. Secondary outcome indicators included forced expiratory volume in the first second (FEV1), FEV1/forced vital capacity (FVC) ratio, and serum 25-hydroxyvitamin D (25(OH)D) concentration. ResultsFive studies involving 522 COPD patients with VDD (defined as 25(OH)D < 50 nmol/L) were included, among them 61 were severely deficient in vitamin D (25(OH)D < 25 nmol/L). The results showed that vitamin D supplementation did not decrease the mean number of exacerbation (standardized mean difference (SMD): - 0.10, 95% CI: - 0.29 to 0.09) and the rate of exacerbation (relative risk (RR): 0.89, 95% CI: 0.76 to 1.04, P = 0.179). Also, its effect on FEV1 (SMD: - 0.06, 95% CI: - 0.30 to 0.17) and FEV1/FVC (SMD: -0.10, 95% CI: - 0.48 to 0.27) remained negligible. However, it could increase the serum 25(OH)D concentration (SMD: 2.44, 95 CI%: 2.20 to 2.68, P < 0.001). ConclusionsThe effects of vitamin D supplementation on decreasing exacerbation and improving pulmonary function were not significant