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This paper focuses on the structure of the subspace \(T_c\) of the BMO Teichmüller space \(T_b\) corresponding to chord-arc curves, which contains the VMO Teichmüller space \(T_v\). We prove that \(T_c\) is not a subgroup with respect to the group structure of \(T_b\), but it is preserved under the inverse operation and the left and the right translations by any element of \(T_v\). Moreover, we show that \(T_b\) has a fiber structure induced by \(T_v\), and the complex structure of \(T_b\) can be projected down to the quotient space \(T_v \backslash T_b\). Then, we see that \(T_c\) consists of fibers of this projection, and its quotient space also has the induced complex structure.

We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling–Ahlfors extension by heat kernel introduced by Fefferman et al. (Ann Math 134:65–124, 1991). Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

We present a new characterization of Muckenhoupt A ∞ A_{\infty } -weights whose logarithm is in vanishing mean oscillation ( R ) (\mathbb {R}) in terms of vanishing Carleson measures on R + 2 \mathbb {R}_+^2 and vanishing doubling weights on R \mathbb {R} . This also gives a novel description of strongly symmetric homeomorphisms on the real line by using a geometric quantity.

We interpolate a new family of Teichm\"uller spaces $T_{\sharp}^X$ between the universal Teichm\"uller space $T$ and its little subspace $T_0$, which we call the Teichm\"uller space of piecewise symmetric homeomorphisms. This is defined by prescribing a subset $X$ of the unit circle. The inclusion relation of $X$ induces a natural inclusion of $T_{\sharp}^X$, and an approximation of $T$ is given by an increasing sequence of $T_{\sharp}^X$. In this paper, we discuss the fundamental properties of $T_{\sharp}^X$ from the viewpoint of the quasiconformal theory of Teichm\"uller spaces. We also consider the quotient space of $T$ by $T_{\sharp}^X$ as an analog of the asymptotic Teichm\"uller space., Comment: arXiv admin note: text overlap with arXiv:1908.06618

The coexistence of pulmonary tuberculosis (PTB) and human immunodeficiency virus (HIV) infection leads to high morbidity and mortality in these populations. Although antiretroviral therapy (ART) has decreased TB incidence in HIV-infected patients, this coexistence still prevails in China. Patients with HIV-PTB admitted to Beijing You An Hospital from 2014 to 2018 were retrospectively enrolled, and information on demographics, clinical characteristics, and laboratory findings were extracted from medical records. Predictors of death, including age (adjusted hazard ratio [AHR]: 1.03; 95% confidence interval [CI]: 1.00-1.05), tobacco use (AHR: 2.76; 95% CI: 1.54-4.94), history of tuberculosis (AHR: 3.53; 95% CI: 1.82-6.85), not being on ART (AHR: 2.94; 95% CI: 1.31-6.63), extrapulmonary tuberculosis (AHR: 2.391; 95% CI: 1.37-4.18), sputum smear positivity (AHR: 2.84; 95% CI: 1.61-4.99), CD4+ T cell count ≤ 50 cells/µl (AHR: 3.45; 95% CI: 1.95-6.10), and initiating ART ≥ 8 weeks after the initiation of antituberculous therapy (odds ratio: 3.30; 95% CI: 1.09-10.04). By contrast, there were no deaths among the six patients who began ART within 8 weeks after the initiation of antituberculous therapy. Age, tobacco use, not being on ART, extrapulmonary tuberculosis, sputum smear positivity, and CD4+ T cell count ≤50 cells/µl predict those patients at high risk of death among HIV-infected patients with PTB, and the time of initiating ART after the initiation of antituberculous therapy is also important for prognosis.

Severe acute respiratory syndrome coronavirus clade 2 (SARS-CoV-2) is an emerging pathogen, which is similar to previous SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV) occurrences. However, we only get few understandings about the pathogenesis of SARS-CoV-2, which need to further be studied. The discovery of an agent that has a treatment efficacy against SARS-CoV-2 is very urgent. In this review, we briefly discuss the virology of this pathogen and focus on the available understanding of the pathogenesis and treatments of this pathogen including the uses of nucleoside analogues, protease inhibitors, interferons, and other small-molecule drugs, on the basis previous comprehensions of SARS and MERS. These reviewed concepts may be beneficial in providing new insights and potential treatments for COVID-19.

We introduce the concept of a new kind of symmetric homeomorphism on the unit circle, which is derived from the generalization of symmetric homeomorphisms on the real line. By the investigation of the barycentric extension for this class of circle homeomorphisms and the biholomorphic automorphisms induced by trivial Beltrami coefficients, we show that the Bers Schwarzian derivative map is a holomorphic split submersion and endow a complex Banach manifold structure on the Teichmüller space of those generalized symmetric homeomorphisms.

In [6] the equivalence among three definitions of BMO-Teichmuller spaces associated with a Fuchsian group was proven using the Douady–Earle extension operator. In this paper, we show that these equivalences are actually biholomorphisms. In [6] it was further shown that the Douady–Earle extension operator is continuous at the origin. We improve this result by showing Gâteaux-differentiability at this point.

This study developed a hybrid stochastic-fuzzy model with Green-Z scenario (HFSG) for coordinating regional irrigated production and forest protection (IPFP) under stresses of water and land resources with multiple informations. The novelty of proposed HFSG is that the improvement of handling capacity for various uncertainties can facilitate to generate a practical landscape scale planning and water resources management (land-water plan) with a more robust manner. It not only has advantage of reflecting the meteorological impact (e.g., precipitation) presented as probability distribution, but also identifies natural or artificial vagueness in the process of decision-making. Moreover, Green-Z scenario analysis associated with the risk-averse attitude, threshold of acceptability and coefficient of robustness can discern the tradeoff between expected targets and outcomes under different risk preferences of decision makers. Through the application of proposed HFSG model in a practical land-water plan issue, numbers of results associated with optimized planting scales (including cultivation withdraw and forest recovery), stresses of water and land resources, pollutant mitigations, ecological effects and system benefits under varied Green-Z scenarios can be obtained. The results can support policymaker to produce cleaner strategies for alleviating conflict between irrigated activities and environmental protection, achieving socio-economic and eco-environmental sustainability.

In an important paper [24] , Reimann showed that the flow mappings of a continuous vector field of Zygmund class Λ ⁎ are quasisymmetric homeomorphisms. In this paper, we will discuss the flow mappings when the vector field belongs to the smooth Zygmund class λ ⁎ or the Sobolev class H 3 2 .

We show an example of a symmetric homeomorphism $h$ of the real line $\mathbb{R}$ onto itself such that $h^{-1}$ is not symmetric. This implies that the set of all symmetric self-homeomorphisms of $\mathbb{R}$ does not constitute a group under the composition. We also deal with strongly symmetric self-homeomorphisms of $\mathbb{R}$ along the same line. These results reveal the difference of the sets of such self-homeomorphisms of the real line from those of the unit circle., Title is changed and Section 5 is added (v2)

Household education expenditure is critical for children's human capital accumulation; however, households may experience leverage load and thus may reduce their spending on children. In this paper, we employ a unique survey conducted by the Tsinghua University China Center for Financial Research (CCFR) in 2011 and 2012 to examine the relationship between leverage and household education expenditure. Our results reveal that higher leverage may constrain households’ spending on children's education, and the adverse effect can be worsened when households are conducting investments. The findings suggest that easing the leverage load for households may help to improve their education expenditure.

Douady–Earle extension provides a quasiconformal extension of a quasisymmetric homeomorphism to the unit disk and induces a continuous self-map σ of Beltrami coefficients. In this note, we show that σ is also continuous (under a stronger topology) on those Beltrami coefficients which induce vanishing Carleson measures and thus project to the VMO-Teichmuller space. An immediate consequence is that the VMO-Teichmuller space is contractible.

Astala–Zinsmeister [2] introduced a new topology on the set of all strongly quasisymmetric homeomorphisms of the unit circle denoted by SQS ( S 1 ) by means of BMO norm. Under this new topology, we prove that SQS ( S 1 ) is a partial topological group, and the characteristic topological subgroup of SQS ( S 1 ) consists of strongly symmetric homeomorphisms.

We study the relation between the boundary of a simply connected domain being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk onto the domain. As an application, we characterize the chord-arc curve with small norm and the asymptotically smooth curve in terms of the complex dilatation of some quasiconformal reflection with respect to the curve., Comment: 11 pages

Following Semmes and Zinsmeister, we continue the study of Carleson measures and their invariance under pull-back and push-forward operators. We also study the analogous statements for vanishing Carleson measures. As an application, we show that some quotient space of the space of chord-arc curves has a natural complex structure., 21 pages

In a previous paper [31] we established the complex analytic manifold theory of the BMO-Teichmuller space. In this paper we identify the function space which is the tangent space to the BMO-Teichmuller space.

We introduce a kernel function induced by a continuous function f on the unit circle, and show that the corresponding integral operator on the standard Bergman space is a bounded, compact or Hilbert–Schmidt operator precisely when f belongs to the big Zygmund class Λ ∗ , the little Zygmund class λ ∗ or the Sobolev class H 3 2 , respectively. This may be considered as the infinitesimal version of the main result obtained in Hu and Shen (2012) [9] by two of the authors.

Ischemia/reperfusion (I/R) has been known to cause damages to ventricular myocytes. Isorhamnetin, one member of flavonoid compounds, has cardioprotective effect, the effect that suggests a possible treatment for I/R damages. In the present investigation, we found that isorhamnetin could significantly promote the viability of neonatal rat ventricular myocytes that were exposed to ischemia/reperfusion (I/R) in vitro. Ventricular myocytes were obtained from neonatal SD rats, and then were divided randomly into three groups, namely I/R−/isor−, I/R+/isor− and I/R+/isor+ group. Before the whole experiment, the most appropriate concentration of isorhamnetin (4 μM) was determined by MTT assay. Our results showed that isorhamnetin could alleviate the damages of I/R to ventricular myocytes through inhibiting lactate dehydrogenase (LDH) activity, and repressing apoptosis. Compared with the counterpart of the I/R+/isor− group, LDH activity in the isorhamnetin-treated group weakened, halving from 24.1±2.3 to 11.4±1.2 U/L. Additionally, flow cytometry showed the apparently increased apoptosis rate induced by I/R, the result that was further confirmed by transmission electron microscope. Administration of isorhamnetin, however, assuaged the apoptosis induced by I/R. Corresponding to the reduced apoptosis rate in the I/R+/isor+ group, western blotting assay showed increased amount of Bcl-2 and p53, decreased amount of Bax, and nuclear accumulation of NF-κB/p65.

Isorhamnetin is one member of flavonoid components which has been used in the treatment of heart disease. Recently the in vitro anti-cancer effect of isorhamnetin on human esophageal squamous carcinoma cell line Eca-109 was investigated in our lab. When Eca-109 cells were in vitro exposed to the graded doses of isorhamnetin (0-80 microg/ml) for 48 h, respectively, isorhamnetin exhibited cytostatic effect on the treated cells, with an IC(50) of 40+/-0.08 microg/ml as estimated by MTT assay. Inhibition on proliferation by isorhamnetin was detected by trypan blue exclusion assay, clone formation test, immunocytochemical assay of PCNA and (3)H-thymidine uptake analysis. Cell cycle distribution was measured by FCM. It was found that the viability of Eca-109 cells was significantly hampered by isorhamnetin. Compared with the negative control group, the treated group which was exposed to isorhamnetin had increased population in G(0)/G(1) phase from 74.6 to 84 while had a significant reduction in G(2)/M phase from 11.9 to 5.8. In addition to its cytostatic effect, isorhamnetin also showed stimulatory effect on apoptosis. Typical apoptotic morphology such as condensation and fragmentation of nuclei and blebbing membrane of the apoptotic cells could be observed through transmission electron microscope. Moreover, the sharp increase in apoptosis rate between the control and treated group were detected by FCM from 6.3 to 16.3. To explore the possible molecular mechanisms that underlie the growth inhibition and apoptosis stimulatory effects of isorhamnetin, the expressions of six proliferation- and death-related genes were detected by FCM. Expressions of bcl-2, c-myc and H-ras were downregulated whereas Bax, c-fos and p53 were upregulated. However, the in vivo experiments were required to further confirm the anti-cancer effects of isorhamnetin. In conclusion, isorhamnetin appears to be a potent drug against esophageal cancer due to its in vitro potential to not only inhibit proliferation but also induce apoptosis of Eca-109 cells.

We first give some new characterizations on BMOA–Teichmuller space and various characterizations on VMOA–Teichmuller space as well. In particular, we prove that a quasisymmetric conformal welding h corresponds to an asymptotically smooth curve in the sense of Pommerenke (1978) [32] precisely when h is absolutely continuous with log h ′ ∈ VMO . We then show that these BMO–Teichmuller spaces have natural complex structures.