The hyperspace of the regions below of continuous maps is homeomorphic to c0

AbstractFor a compact metric space (X,d), we use ↓USC(X) and ↓C(X) to denote the families of the regions below of all upper semi-continuous maps and the regions below of all continuous maps from X to I=[0,1], respectively. In this paper, we consider the two spaces topologized as subspaces of the hyperspace Cld(X×I) consisting of all non-empty closed sets in X×I endowed with the Vietoris topology. We shall show that ↓C(X) is Baire if and only if the set of isolated points is dense in X, but ↓C(X) is not a Gδσ-set in ↓USC(X) unless X is finite. As the main result, we shall prove that if X is an infinite locally connected compact metric space then (↓USC(X),↓C(X))≈(Q,c0), where Q=[−1,1]ω is the Hilbert cube and c0={(xn)∈Q:limn→∞xn=0}

Subspaces of interval maps related to the topological entropy

For $a\in [0,+\infty)$, the function space $E_{\geq a}$ ($E_{>a}$; $E_{\leq a}$; $E_{<a}$) of all continuous maps from $[0,1]$ to itself whose topological entropies are larger than or equal to $a$ (larger than $a$; smaller than or equal to $a$; smaller than $a$) with the supremum metric is investigated. It is shown that the spaces $E_{\geq a}$ and $E_{>a}$ are homeomorphic to the Hilbert space $l_2$ and the spaces $E_{\leq a}$ and $E_{<a}$ are contractible. Moreover, the subspaces of $E_{\leq a}$ and $E_{<a}$ consisting of all piecewise monotone maps are homotopy dense in them, respectively.Comment: 12 pages, 1 figure, to appear in Topol. Methods Nonlinear Ana

Quasiexact posets and the moderate meet-continuity

The study of weak domains and quasicontinuous domains leads to the consideration of two types generalizations of domains. In the current paper, we define the weak way-below relation between two nonempty subsets of a poset and quasiexact posets. We prove some connections among quasiexact posets, quasicontinuous domains and weak domains. Furthermore, we introduce the weak way-below finitely determined topology and study its links to Scott topology and the weak way-below topology first considered by Mushburn. It is also proved that a dcpo is a domain if it is quasiexact and moderately meet continuous with the weak way-below relation weakly increasing

Spatiotemporal deformation characteristics of Outang landslide and identification of triggering factors using data mining

publishedVersio

Attention based surrogate model to predict load envelope of monopile supporting offshore wind turbines

publishedVersio

Protective effect of vanillin in streptozotocin-induced diabetes in neonatal rats via attenuation of oxidative stress and inflammation

Purpose: To evaluate the antidiabetic activity of vanillin in streptozotocin (STZ)-induced diabetic rats.Methods: Diabetes was induced in 2-day old male pups by intraperitoneal (i.p.) administration of STZ (90 mg/kg). The pups were then randomly assigned to four groups: control group which received citrate buffer only in place of STZ; negative control group, i.e., diabetic group; and vanillin-treated groups which received vanillin (100 or 200 mg/kg, p.o.) continuously from the 6th week of age to the 10th week. The antidiabetic effect of vanillin was determined by measuring the serum levels of insulin, triglycerides and glucose in the diabetic rats. Oral glucose tolerance, kidney and liver function tests were also performed at the end of the protocol. Moreover, the oxidative stress and inflammatory cytokines in liver tissues, and histopathological changes in pancreatic tissues were assessed.Results: Vanillin treatment significantly decreased serum glucose and triglyceride levels and increased the level of insulin, when compared to the negative control group. There was higher insulin sensitivity in the vanillin-treated group than in the negative control group. In addition, vanillin improved liver and renal functions in STZ-induced diabetic neonatal rats. Hepatic oxidative stress and inflammatory mediators, as well as histopathological changes in pancreas were attenuated by vanillin treatment.Conclusion: These results reveal that vanillin attenuates hyperglycemia in STZ-induced neonatal diabetic rat model by decreasing oxidative stress and inflammatory cytokines. There, further studies are required to develop the anti-diabetic potentials of vanillin for clinical applications.Keywords: Vanillin, Streptozotocin, Diabetes, Oxidative stress, Insulin, Neonata

Prevalence and Associated Factors of Elder Mistreatment in a Rural Community in People's Republic of China: A Cross-Sectional Study

Background: Current knowledge about elder mistreatment is mainly derived from studies done in Western countries, which indicate that this problem is related to risk factors such as a shared living situation, social isolation, disease burden, and caregiver strain. We know little about prevalence and risk factors for elder mistreatment and mistreatment subtypes in rural China where the elder population is the most vulnerable. Methods: In 2010, we conducted a cross-sectional survey among older adults aged 60 or older in three rural communities in Macheng, a city in Hubei province, China. Of 2245 people initially identified, 2039 were available for interview and this was completed in 2000. A structured questionnaire was used to collect data regarding mistreatment and covariates. Logistic regression analysis was used to identify factors related to elder mistreatment and subtypes of mistreatment. Results: Elder mistreatment was reported by 36.2 % (95 % CI: 34.1%–38.3%) of the participants. Prevalence rates of psychological mistreatment, caregiver neglect, physical mistreatment, and financial mistreatment were 27.3 % (95 % CI

The growth and shrinkage of water droplets at the oil-solid interface.

HYPOTHESIS: The mechanism for the spontaneous formation of water droplets at oil/solid interfaces immersed in water is currently unclear. We hypothesize that growth and shrinkage of droplets are kinetically controlled by diffusion of water through the oil, driven by differences in chemical potential between the solid substrate and the aqueous reservoir. EXPERIMENTS: The formation, growth and shrinkage of water droplets at an immersed oil/solid interface are investigated theoretically and experimentally with three silicone oils. The surface is hydrophobic and the droplets formed are truncated spheres with radius, a, less than 10 μm. The expansion and contraction of the droplets can be controlled by adjusting the difference in chemical potential. The growth kinetics are modelled in terms of water migration through the oil layer which predicts a2∝t. FINDINGS: This is the first study of possible mechanisms for the formation of such interfacial droplets. Several possible causes are shown to be unfavourable, negligible, or are eliminated by careful experiments controlling key parameters (such as oil viscosity, substrate chemistry). The rate constant for mass transport is proportional to difference in chemical potential and an estimate shows dissociation of surface groups on the substrate provides a driving chemical potential of the right magnitude.National Natural Science Foundation of China (21872078