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Curriculum standards are a critical component of a nation's educational system and directly impact talent development and overall national development. Most studies on curriculum standards focus on a single competency. This study aims to understand the extent to which the competencies outlined in the OECD 2030-oriented learning framework are reflected in China's compulsory education biology curriculum as a whole and within individual content subjects. In this study, we conducted a content analysis of China's National Biology Curriculum Standards (Grades 7–9). The result shows that the standards cover 20 of the 28 competencies, focusing on foundational literacies, transformative competencies and competency development. We found that certain competencies, such as Action, Literacy, and Problem-solving, were emphasized across content subjects, while other competencies were uniquely emphasized within specific content subjects. This study provides a comprehensive view of China's National Biology Curriculum Standards (Grades 7–9) from the perspective of future literacy development and can inform efforts to reform the curriculum. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two conservative Crank–Nicolson type finite difference schemes and a Chebyshev collocation scheme for the nonlinear Schrödinger equation with a Dirac delta potential in 1D. The key to the proposed methods is to transform the original problem into an interface problem. Different treatments on the interface conditions lead to different discrete schemes and it turns out that a simple discrete approximation of the Dirac potential coincides with one of the conservative finite difference schemes. The optimal H 1 error estimates and the conservative properties of the finite difference schemes are investigated. Both Crank-Nicolson finite difference methods enjoy the second-order convergence rate in time, and the first-order/second-order convergence rates in space, depending on the approximation of the interface condition. Furthermore, the Chebyshev collocation method has been established by the domain-decomposition techniques, and it is numerically verified to be second-order convergent in time and spectrally accurate in space. Numerical examples are provided to support our analysis and study the orbital stability and the motion of the solitary solutions. [ABSTRACT FROM AUTHOR]

Compared with macroscopic conservation law for the solution of the derivative nonlinear Schrödinger equation (DNLS) with small mass in Klaus and Schippa (A priori estimates for the derivative nonlinear Schrödinger equation. Accepted by Funkcial. Ekvac), we show the corresponding microscopic conservation laws for the Schwartz solutions of DNLS with small mass. The new ingredient is to make use of the logarithmic perturbation determinant A (κ) introduced in Rybkin (in: Topics in Operator Theory, Birkhäuser Verlag, Basel, 2010), Simon (in: Trace ideals and their applications, American Mathematical Society, Providence, 2005) to show one-parameter family of microscopic conservation laws of the A (κ) flow and the DNLS flow, which is motivated by Harrop-Griffiths et al. (Sharp well-poseness for the cubic NLS and MKdV in H s . ), Killip and Visan (Ann Math 190:249–305, 2019), Killip et al. (Geom Funct Anal 28:1062–1090, 2018). [ABSTRACT FROM AUTHOR]

In this paper, we continue the study of the dynamics of the traveling waves for nonlinear Schrödinger equation with derivative (DNLS) in the energy space. Under some technical assumptions on the speed of each traveling wave, the stability of the sum of two traveling waves for DNLS is obtained in the energy space by Martel-Merle-Tsai's analytic approach in Martel et al. (Commun Math Phys 231(2):347-373, 2002, Duke Math J 133(3):405-466, 2006). As a by-product, we also give an alternative proof of the stability of the single traveling wave in the energy space in Colin and Ohta (Ann Inst Henri Poincaré Anal Non Linéaire 23(5):753-764, 2006), where Colin and Ohta made use of the concentration-compactness argument. [ABSTRACT FROM AUTHOR]