A Study on the Cohesion of English Teaching Materials Between Primary and Junior High School

English teaching materials, as the main teaching media, play an important role in teaching. Many scholars have attached great importance to teaching materials, but they took little heed to the cohesion of teaching materials between different stages of basic education. This study intended to investigate the cohesion of primary-secondary teaching materials by exploring the problems in terms of language knowledge and language skills in the selected English teaching materials for primary and secondary schools, which was finally succeeded by some practical suggestions for the English teachers and the students alike to effectively facilitate the cohesion problems in the primary-secondary stages

Cohomologies of modified λ\lambda-differential Lie triple systems and applications

In this paper, we introduce the concept and representation of modified $\lambda$-differential Lie triple systems. Next, we define the cohomology of modified $\lambda$-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $\lambda$-differential Lie triple systems

The Coordination of Centromere Replication, Spindle Formation, and Kinetochore–Microtubule Interaction in Budding Yeast

The kinetochore is a protein complex that assembles on centromeric DNA to mediate chromosome–microtubule interaction. Most eukaryotic cells form the spindle and establish kinetochore–microtubule interaction during mitosis, but budding yeast cells finish these processes in S-phase. It has long been noticed that the S-phase spindle in budding yeast is shorter than that in metaphase, but the biological significance of this short S-phase spindle structure remains unclear. We addressed this issue by using ask1-3, a temperature-sensitive kinetochore mutant that exhibits partially elongated spindles at permissive temperature in the presence of hydroxyurea (HU), a DNA synthesis inhibitor. After exposure to and removal of HU, ask1-3 cells show a delayed anaphase entry. This delay depends on the spindle checkpoint, which monitors kinetochore–microtubule interaction defects. Overproduction of microtubule-associated protein Ase1 or Cin8 also induces spindle elongation in HU-arrested cells. The spindle checkpoint-dependent anaphase entry delay is also observed after ASE1 or CIN8 overexpression in HU-arrested cells. Therefore, the shorter spindle in S-phase cells is likely to facilitate proper chromosome–microtubule interaction

Numerical analysis of a time discretized method for nonlinear filtering problem with L\'evy process observations

In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is a unnormalized probability density function of the filter solution. Then we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis