Measurement uncertainty is a key topic in the university physics laboratory curriculum. In this study, we investigate students' ability to draw conclusions from measurement data and reasoning about ...measurement uncertainty in inquiry labs. This investigation centres around a task where students conclude whether measurements from two experiments that differ only by one setup agree or disagree. Surveys were administered in introductory physics courses before and after Workshop Physics instruction, which utilises an activity-based, guided-inquiry approach. Student reasoning was characterised using the point and set paradigms. Think-aloud interviews were conducted to gain deeper insights into students' interpretations of measurement uncertainty. The survey results showed that students tended to draw conclusions based on the means without appropriately accounting for uncertainty even if many recognised the need to evaluate uncertainty. The number of decimal places had no influence on students' ability to draw conclusions. After instruction, students' reasoning shifted from point toward set or mixed paradigm, but their ability to draw conclusions did not improve. During the interviews, students demonstrated sophisticated interpretations about measurement uncertainty and data analysis strategies they used. Students recognised measurement uncertainty is inevitable and were able to identify possible sources of uncertainty. We discuss implications for instruction around measurement uncertainty.
We introduce and study a class of free boundary models with “nonlocal diffusion”, which are natural extensions of the free boundary models in 16 and elsewhere, where “local diffusion” is used to ...describe the population dispersal, with the free boundary representing the spreading front of the species. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model in 16.
This paper is concerned with the spatial dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species becomes ...extinct in the habitat if the speed of the shifting habitat edge
c
>
c
∗
(
∞
)
, while the species persists and spreads along the shifting habitat at an asymptotic speed
c
∗
(
∞
)
if
c
<
c
∗
(
∞
)
, where
c
∗
(
∞
)
is determined by the nonlocal dispersal kernel, diffusion rate and the maximum linearized growth rate. Moreover, we demonstrate that for any given speed of the shifting habitat edge, the model system admits a nondecreasing traveling wave with the wave speed at which the habitat is shifting, which indicates that the extinction wave phenomenon does happen in such a shifting environment.
This work aims to determine the optimal conditions for emulsion cross-linking of chitosan (CHS) with various molecular weights using glutaraldehyde as a cross-linking agent to produce ...5-fluorouracil-loaded CHS microspheres (5-FU/CHS). Their drug loading and encapsulation efficiencies are found to be in the range of 3.87-12.35% and 20.13-70.45%, respectively. The dynamic light scattering results show that 5-FU/CHS microspheres are micron-sized with a uniform size distribution, and the scanning electron microscopy results show that they are spherical. The results of thermogravimetric analysis, X-ray diffraction, and Fourier transform infrared spectroscopy demonstrate that 5-FU is successfully incorporated into the microspheres. The
in vitro
release tests show that 5-FU/CHS have a prolonged, pH-responsive release pattern of 5-FU, and the cumulative release rate under acidic condition is much larger than that under neutral conditions. The drug release kinetic analysis further demonstrates that the release of 5-FU can be well described by the Fickian diffusion model.
This work aims to determine the optimal conditions for emulsion cross-linking of chitosan (CHS) with various molecular weights using glutaraldehyde as a cross-linking agent to produce 5-fluorouracil-loaded CHS microspheres (5-FU/CHS).
PEGylation changes the physical and chemical properties of the biomedical molecule, such as its conformation, electrostatic binding, and hydrophobicity, and results in an improvement in the ...pharmacokinetic behavior of the drug, while it also causes some disadvantages of which cannot be neglected. The available data manifests that polyethylene glycol (PEG) itself shows potential risk, such as immunogenicity of the PEG and PEG-containing vacuoles in cells observed with PEGylated biologicals. Decreased activity and heterogeneity are also the negative aspects of PEGylation. The unfavorable impacts which are brought by the PEGylation are described here with examples of modified therapeutic proteins on the market and used in the clinical trials.
We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, ...where humans get infected by the agents, and infected humans in return contribute to the growth of the agents. The model can be viewed as a nonlocal version of the free boundary model studied by Ahn, Beak and Lin 2, with its origin tracing back to Capasso et al. 5,6. We prove that the problem has a unique solution defined for all t>0, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local diffusion model in 2. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the model of 2, where the spreading has finite speed whenever spreading happens 33.
In this paper we study a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the spatial movement of individuals is described by a nonlocal ...(convolution) diffusion operator, the transmission rate and recovery rate are spatially heterogeneous, and the total population number is constant. We first define the basic reproduction number R0 and discuss the existence, uniqueness and stability of steady states of the nonlocal dispersal SIS epidemic model in terms of R0. Then we consider the impacts of the large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease. The obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease. In particular, our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease.
This paper is concerned with space periodic traveling wave solutions of the following Lotka–Volterra competition system with nonlocal dispersal and space periodic ...dependence,{∂u1∂t=∫RNκ(y−x)u1(t,y)dy−u1(t,x)+u1(a1(x)−b1(x)u1−c1(x)u1),x∈RN∂u2∂t=∫RNκ(y−x)u2(t,y)dy−u2(t,x)+u2(a2(x)−b2(x)u1−c2(x)u2),x∈RN. Under suitable assumptions, the system admits two semitrivial space periodic equilibria (u1⁎(x),0) and (0,u2⁎(x)), where (u1⁎(x),0) is linearly and globally stable and (0,u2⁎(x)) is linearly unstable with respect to space periodic perturbations. By sub- and supersolution techniques and comparison principals, we show that, for any given ξ∈SN−1, there exists a continuous periodic traveling wave solution of the form (u1(t,x),u2(t,x))=(Φ1(x−ctξ,ctξ),Φ2(x−ctξ,ctξ)) connecting (u1⁎(⋅),0) and (0,u2⁎(⋅)) and propagating in the direction of ξ with speed c>c⁎(ξ), where c⁎(ξ) is the spreading speed of the system in the direction of ξ. Moreover, for c<c⁎(ξ) there is no such solution. When the wave speed c>c⁎(ξ), we also prove the asymptotic stability and uniqueness of traveling wave solution using squeezing techniques.
This paper is concerned with the propagation dynamics of nonlocal dispersal monostable equations in time-space periodic habitats. We first show that such an equation admits a single spreading speed ...in every direction under certain conditions and then give several spreading properties in terms of spreading speeds such as asymptotic spreading ray speeds and asymptotic spreading sets. Furthermore, we consider the dependence of the spreading speed on the dispersal rate and reaction term and prove that taking the temporal average or spatial average can decrease the spreading speed. Finally, we employ the viscosity vanishing method to establish the existence of time-space periodic traveling fronts with the critical speed in every direction under the partially temporally homogeneous case and partially nearly flat case, which solves partially the open problem raised by Rawal, Shen, and Zhang (Discrete Contin. Dyn. Syst.35 (2015) 1609–1640).
This paper is concerned with propagation phenomena of a general class of partially degenerate nonlocal dispersal cooperative systems in time and space periodic habitats. We first show that such ...system has a finite spreading speed interval in any direction and there is a spreading speed for the partially degenerate system under certain conditions. Next, we prove that if the wave speed is greater than the spreading speed, there exists a time and space periodic traveling wave solution connecting the stable positive time and space periodic steady state and 0. Finally, we apply these results to two species partially degenerate competition systems and a partially degenerate epidemic model with nonlocal dispersal in time and space periodic habitats.
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