THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.

Estimating Changes in Contact Patterns in China Over the First Year of the COVID-19 Pandemic:Implications for SARS-CoV-2 Spread—Four Cities,China,2020

Introduction:Previous studies have demonstrated significant changes in social contacts during the firstwave coronavirus disease 2019(COVID-19)in Chinese mainland.The purpose of this study was to quantify the time-varying contact patterns by age in Chinese mainland in 2020 and evaluate their impact on the transmission of severe acute respiratory syndrome coronavirus 2(SARS-CoV-2).Methods:Diary-based contact surveys were performed for four periods:baseline(prior to 2020),outbreak(February 2020),post-lockdown(March–May 2020),and post-epidemic(September–November 2020).We built a Susceptible-Infected-Recovered(SIR)model to evaluate the effect of reducing contacts on transmission.Results:During the post-epidemic period,daily contacts resumed to 26.7%,14.8%,46.8%,and 44.2%of the pre-COVID levels in Wuhan,Shanghai,Shenzhen,and Changsha,respectively.This suggests a moderate risk of resurgence in Changsha,Shenzhen,and Wuhan,and a low risk in Shanghai.School closure alone was not enough to interrupt transmission of SARS-CoV-2 Omicron BA.5,but with the addition of a 75%reduction of contacts at the workplace,it could lead to a 16.8%reduction of the attack rate.To control an outbreak,concerted strategies that target schools,workplaces,and community contacts are needed.Discussion:Monitoring contact patterns by age is key to quantifying the risk of COVID-19 outbreaks and evaluating the impact of intervention strategies.

Integrating of metal-organic framework UiO-66-NH2 and cellulose nanofibers mat for high-performance adsorption of dye rose bengal

UiO-66-NH2 is an efficient material for removing pollutants from wastewater due to its high specific surface area,high porosity and water stability.However,recycling them from wastewater is difficult.In this study,the cellulose nanofibers mat deacetylated from cellulose acetate nanofibers were used to combine with UiO-66-NH_(2)by the method of in-situ growth to remove the toxic dye,rose bengal.Compared to previous work,the prepared composite could not only provide ease of separation of UiO-66-NH_(2)from the water after adsorption but also demonstrate better adsorption capacity(683 mg∙g‒1(T=25°C,pH=3))than that of the simple UiO-66-NH_(2)(309.6 mg∙g^(‒1)(T=25℃,pH=3)).Through the analysis of adsorption kinetics and isotherms,the adsorption for rose bengal is mainly suitable for the pseudo-second-order kinetic model and Freundlich model.Furthermore,the relevant research revealed that the main adsorption mechanism of the composite was electrostatic interaction,hydrogen bonding andπ–πinteraction.Overall,the approach depicts an efficient model for integrating metal-organic frameworks on cellulose nanofibers to improve metal-organic framework recovery performance with potentially broad applications.

Nearly invariant subspaces for shift semigroups

Let{T(t)}_(t≥0) be a C_(0)-semigroupon an infinite-dimensional separable Hilbert space;a suitable definition of near{T(t)^(*)}_(t≥0) invariance of a subspace is presented in this paper.A series of prototypical examples for minimal nearly{S(t)^(*)}_(t≥0) invariant subspaces for the shift semigroup{S(t)}_(t≥0) on L^(2)(0,∞)are demonstrated,which have close links with near T_(θ)^(*)invariance on Hardy spaces of the unit disk for an inner functionθ.Especially,the corresponding subspaces on Hardy spaces of the right half-plane and the unit disk are related to model spaces.This work further includes a discussion on the structure of the closure of certain subspaces related to model spaces in Hardy spaces.