基于核心素养的“递进式活动导学”初探——“机械能”教学案例

从三维目标走向核心素养,是学科教学高度、深度和内涵的提升,是学科教学对人的真正的回归.基于核心素养的“递进式活动导学”,是以核心素养为主导,以“递进式活动”为抓手,将教学目标细化为行为目标并在课堂教学中落实.文章以“上教版”八年级物理第四章第3节“机械能”第一课时为例,从教学目标细化和“递进式活动”的设计两个方面,讲述基于核心素养的“递进式活动导学”的教学思路,以期对初中物理核心素养在课堂教学中的落实有所帮助.     

Finite-Data Error Bounds for Koopman-Based Prediction and Control

Journal of Nonlinear Science - This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational...     

Study of a transition in the qualitative behavior of a simple oscillator with Coulomb friction

A simple mass-spring system is submitted to a constant force in addition to a periodic perturbation of rectangular wave shape. It has been obtained in a previous study that the range of the period-amplitude plane of this perturbation, where the trajectories are sliding with no loss of contact, is divided into two parts, one in which there exist infinitely many equilibrium states and no periodic solutions, and another one where there exist periodic solutions and no equilibrium states. The present work focuses on the transition between these two parts. All along the transition line, there exists a single equilibrium state. Initial data out of equilibrium lead either to a periodic trajectory, or to a trajectory, which tends to the equilibrium or to a periodic solution, either in finite time or at infinity.     

Hard elastic polypropylene-nature,internal friction,and surface energy

Tensile tests were performed at low temperatures, both in liquid and gaseous nitrogen and also at room temperature, using a series of polypropylene (PP) samples with various technological parameters. Crystalline morphology was also measured for film samples. The results show that liquid nitrogen or solvents can induce materials to create hard elasticity, which strongly supports the bulk-microfibril composite structure proposed by Baer et al., and suggests that the nature of hard elasticity is essentially a craze phenomenon. Three conditions of forming hard elastic structure are discussed. The results from long-time relaxation of hard elastic polypropylene (HEPP) and the improvement of necking of the PP samples in ethanol and water suggest that elastic recovery is reduced by internal friction. The relation between morphology and elasticity is also discussed. The methods of estimating the contribution of surface energy in the recovery process and the increase of surface energy of HEPP during the stretching process are provided. The contribution of surface energy to recovery is about 43% to 66% in the first cycle and after relaxation for 1 h at a maximum of 50% strain. The increased surface energy during stretching is about twice the recovery work done by surface energy.     

EC-STM observation on electrochemical response of fluidic phospholipid monolayer on Au(1 1 1) modified with 1-octanethiol

Electrochemical scanning tunneling microscopy (EC-STM) was applied to observe phospholipid layers over thiol-modified gold substrates as a model biological cell membrane. On a monolayer of 1-octanethiol on Au (1 1 1), a synthetic lipid, 1,2-dihexanoyl-sn-glycero-3-phosphocholine, was introduced in a neutral 0.05 M NH₄ClO₄ buffer solution. The lipid molecules formed a fluidic layer at 0.0 V vs. RHE of the substrate electrode potential. By cycling the electrode potential between +0.2 V and −0.2 V, the lipid layer reversibly changed over between the fluidic phase and a striped/grainy structure. This structural change might involve partial decomposition and oligomerization of phospholipids. This method will contribute for molecular biology by revealing the nanometer-scale structure of cell membrane.     

FTIR spectroscopic and NMR studies of hard elastic polypropylene

The variation of amorphous orientation and crystalline regularity of hard elastic polypropylene (HEPP) films during cyclic deformation and stress relaxation processes were studied using a FTIR spectrometer. The result proves entropic elasticity and shows the orientational hysteresis in the amorphous region or within the microfibrils, and also shows that the amorphous orientation increases, but that the crystalline regularity decreases with the increase of extension rate.Three spin-spin relaxation timesT _2f,T _2m, andT _2s and associated mass fractionsF _f,F _m, andF _s of HEPP fibers were measured with a solid echo of NMR method at different elongations and after relaxation or recovery for a long time A new possible interpretation was proposed that, while the microfibrils are formed in HEPP, the medium decay component should be ascribed to inner molecules of the microfibrils, and the slow decay component to the surface molecules of the microfibrils. According to this interpretation, the results implied that subfibrillation is the main process when HEPP is stretched up to 15% strain, and that at above 15% strain thinning and lengthening of the microfibrils become the main process. Thickening of the microfibrils was found in the recovery and relaxation processes.     

Separation and determination of acrylamide in potato chips by micellar electrokinetic capillary chromatography

A simple and rapid method using micellar electrokinetic capillary chromatography (MEKC) was developed for the separation and determination of acrylamide in potato chips at low levels for the first time. The experimental conditions for the separation and quantification of acrylamide were optimized at first. The optimized conditions were: 50 mmol/L Na₂B₄O₇ and 40 mmol/L SDS at pH 10.0, 12 kV applied voltage, 76 cm total length (67 cm effective length) and 75 μm i.d. capillary, 198 nm wavelength, 15 cm high 25 s hydrodynamics sample injection, 20 °C air-cooling. The linear response of acrylamide concentration ranges from 0.5 to 100 μg/mL with high correlation coefficient (r = 0.9986, n = 9). The LOD and LOQ were estimated to be 0.1 and 0.33 μg/mL based on S/N = 3 and 10. The precision values (expressed as R.S.D.) of intra- and inter-day were 0.86-4.35% and 2.61-9.65%, respectively. Recoveries spiked at levels 2, 20, 60 μg/mL ranged between 90.86% and 99.6% with R.S.D. less than 6.5%. Finally, the developed method has been applied to the analysis of real samples and has achieved satisfactory results. All of these indicated that it was a reliable method for the quantification of acrylamide in potato chips.     

Oscillation theorems for nonlinear hyperbolic systems with impulses

In this paper, we are mainly concerned with the oscillation problems of nonlinear hyperbolic differential systems with impulses. Some sufficient conditions for oscillations of the solutions of nonlinear impulsive hyperbolic systems with Robin boundary conditions are obtained and the criteria of oscillation of the systems are established.     

Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

The temperature integral, which has no exact analytical solution, is involved in the analysis of the experiment data obtained under nonisothermal conditions. Some approximations for the temperature integral have been proposed in the literature for the determination of the kinetic parameters, in particular the activation energy. Those approximations are classified into two categories, that is, exponential and rational approximations. The precision of them for estimating the temperature integral was evaluated within a certain continuous range rather than at several discrete points. Some applications of the approximations in the kinetic methods were presented. The relative errors of the activation energy and pre-exponential factor with four rational approximations by employing model-fitting method were calculated. The relative errors of the activation energy for a series of conversion rate with four rational and four exponential approximations by employing linear integral isoconversional methods were evaluated.     

Existence and Uniqueness Theorems for the Two-Dimensional Ericksen–Leslie System

In this paper we study the two dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value problem in two situations: the space-periodic problem and the case of a bounded domain with spatial Dirichlet boundary conditions on the Eulerian velocity and the cross product of the director field with its time derivative. We also show that the speed of propagation of the director field is finite and give an upper bound for it.