课程文献中心 更多>>

关键词： Representation of numbers   Repeating decimals   Limits   Infinity  

摘要： Equating 0.999 & mldr;(infinitely repeating nines after the decimal point) with 1 has provoked bewilderment, as well as various justifications, discussions and research engagements. The equality can also be seen as an example of a more general mathematical phenomenon, which begs the question, what does it exemplify? We introduce a theoretical construct "space of an example," as a variation on the notion of "example spaces," and explore how prospective secondary school teachers situate this particular equality within a broader mathematical space. Responding to the question "of what is this an example?" participants' highlighted ideas related to (i) different representations of numbers, (ii) infinity, and (iii) approximation and limits. We argue that the "space of an example" is a useful research tool to uncover ideas related to a particular concept.

关键词： chirality   density functional theory   surface science   scanning tunneling microscopy   self-assembly  

摘要： Understanding how chirality emerges from assemblies of achiral molecules is central to the study of symmetry breaking at surfaces. Here we show that achiral 1,10-phenanthroline adsorbed on Au(111) generates chirality through a pairing-driven hierarchical self-assembly pathway. Upon adsorption, molecules selectively form hydrogen-bonded pairs via weak but directional C & horbar;HN interactions. Steric and electrostatic constraints restrict this interaction to two molecules, forcing a choice between two symmetry-equivalent nitrogen sites and thereby producing left- or right-handed molecular pairs that act as local chiral motifs. These motifs organize through attractive intermolecular interactions into homochiral one-dimensional chains, which further assemble into two-dimensional chiral domains governed by repulsive interchain interactions. Scanning tunneling microscopy directly visualizes mirror-related left- and right-handed domains. Density functional theory calculations confirm that the face-to-face paired configuration is energetically preferred and stabilized by adsorption on Au(111). This work reveals a distinct route to surface chirality in which chirality originates at the level of a hydrogen-bonded molecular pair and is amplified into organized chiral architectures through weak intermolecular interactions.

关键词： contact Hamilton-Jacobi equations   long time behavior   C1,1 viscosity subsolutions  

摘要： We extend classical Hamiltonian systems to contact Hamiltonian systems, prove the existence of C1,1 viscosity subsolutions of contact Hamilton-Jacobi equations, and show their density in the subsolution space. Furthermore, we establish that the long time behavior of the Hamilton-Jacobi equation with a C1,1 initial value can determine the long time behavior of the equation with a Lipschitz initial value.

摘要： Introduction Peripheral intravenous catheters (PIVCs) are a vital part of care for hospitalized children. Despite commonality, up to 45% fail before treatment completion, with up to 20% of PIVCs resulting in an infusate-associated injury, such as infiltration or extravasation. Biosensors developed to detect preclinical signs of intravenous catheter dysfunction have the potential to prevent significant *** This multi-site, type 1 hybrid effectiveness-implementation randomized controlled trial will evaluate an IV biosensor for preventing infiltration/extravasation injuries in hospitalized neonates and infants. Participants up to 1 year of age who require a PIVC with continuous or moderate-high risk infusates will be recruited from three Australian hospitals. Participants (n = 532) will be randomized 1:1 to receive either standard observation plus IV biosensor or standard observation alone. The primary outcome is infiltration/extravasation injury occurrence, measured using the Cincinnati Children's Hospital Medical Centre Extravasation Harm Scale by the masked outcome assessment committee. Secondary outcomes include infiltration/extravasation severity, volume, treatment sequelae, quality of life, and cost-effectiveness. The implementation context exploration will use mixed methods, including ecological momentary assessments and semi-structured interviews, to evaluate barriers and facilitators for future *** The PATCH trial addresses a significant gap in evidence regarding the effectiveness and implementation of IV biosensor technology in preventing extravasation injuries in vulnerable infant and neonatal populations. The hybrid effectiveness-implementation study will provide comprehensive data to inform both clinical practice and future implementation *** Registration ACTRN12623000561684

关键词： closed-loop insulin delivery   glucose variability   HbA1c   meta-analysis   sensor-augmented pump   time in range   type 1 diabetes mellitus  

摘要： Aim Although hybrid closed-loop systems (HCLS) and sensor-augmented pump (SAP) therapy are advanced diabetes management technologies for type 1 diabetes, their relative efficacy in optimising glycaemic control is not fully established. This meta-analysis evaluated the impact of HCLS versus SAP therapy on glucose regulation across multiple randomised controlled trials (RCTs) and randomised crossover trials (RCOs). The primary aim was to determine the efficacy of HCLS in improving glycaemic control, reducing glucose variability and enhancing time in range (TIR) compared with SAP *** The review was prospectively registered with the International Prospective Register of Systematic Reviews as CRD42023488722. Data from 27 studies involving over 1000 participants were analysed. The studies included both RCTs and RCOs that compared HCLS with SAP therapy. Key metrics assessed were mean glucose levels, glucose variability (coefficient of variation and standard deviation), low blood glucose index (LBGI), high blood glucose index (HBGI), glycated haemoglobin (HbA1c) and TIR (3.9-10.0 mmol/L). Hyperglycaemia and hypoglycaemia outcomes were also *** HCLS significantly reduced mean glucose levels by 2.0 mg/dL compared with SAP therapy. It also decreased glucose variability, including CV and SD, and reduced LBGI, HBGI and HbA1c. HCLS increased TIR by 8.8%. Regarding hyperglycaemia, HCLS reduced the time spent above 10 mmol/L by 7.8%, above 13.9 mmol/L by 3.63% and above 16.7 mmol/L by 0.88%. Hypoglycaemia outcomes showed modest improvements, with reductions in time below 3 mmol/L by 0.10% and below 3.9 mmol/L by 0.72%.Conclusions Our findings support HCLS as a superior modality to SAP therapy in improving glycaemic control, particularly in paediatric populations. HCLS effectively reduces hyperglycaemia and increases TIR, with modest effects on hypoglycaemia. The clinical implications are significant, highlighting the advantages of HCLS in optimising glucos

关键词： association   CRF01_AE   Japan   MSM   phylogeny   Vietnam  

摘要： Objectives: The bidirectional increase of visitors between Vietnam and Japan has raised concerns about the spread of CRF01_AE;however, the epidemiological characteristics of CRF01_AE in Vietnam and its relationship with Japan remain unclear. We compared the CRF01_AE gene sequences from Vietnam and Japan to understand their epidemiolocal relationships. Design: A molecular-epidemiological observational study. Methods: We analyzed 753 protease--reverse transcriptase sequences from CRF01_AE-infected individuals in northern Vietnam and 500 CRF01_AE sequences from the Japanese Drug Resistance HIV-1 Surveillance Network's cluster database. We inferred the chronological phylogeny of these sequences with HIV-1 subtype references and identified statistically significant Vietnam-related clusters (VRCs). Individuals' sex, infection risk, age, collection year, collection site, and nationality were analyzed in relation to clustering and bilateral epidemiological relationships. Results: A total of 33 VRCs and 41 Vietnam-related pairs were identified. Of these, eight were linked to known Japanese domestic transmission clusters (dTCs). Two VRCs included Vietnamese individuals diagnosed in Japan. One Japanese dTC linked to Vietnam included numerous Philippine nationals who were diagnosed in Japan. Regression analysis revealed that VRCs with a higher proportion of young people had a higher number of MSM (adjR(2) = 0.422, P < 0.001). Although VRCs involved different risk groups in northern Vietnam, a strong association was observed between bilateral epidemic links and MSM (adjOR = 8.718, P < 0.001). Conclusion: CRF01_AE in northern Vietnam has spread through many different at-risk populations. Some MSM groups were associated with the epidemiological relationship between northern Vietnam and Japan.