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This paper is concerned { ut = ∆u− χ1∇·(u∇v) + µ1u(1−u−a1w) in Ω×(0,∞), 0 = ∆v−v+w in Ω×(0,∞), wt = ∆w− χ2∇·(w∇z) + µ2w(1−a2u−w) in Ω×(0,∞), 0 = ∆z−z+u in Ω×(0,∞), with stabilization in the two-species–two chemicals chemotaxis-competition system where Ω is a bounded domain in R n (n ≥ 2) with smooth boundary, X1,X2 and µ1,µ2 are constants satisfying some conditions. About this system Tu–Mu–Zheng–Lin (Discrete Contin. Dyn. Syst.;2018;38;3617– 3636) showed global existence and stabilization of solutions under some smallness conditions for χ1 and χ2. Here energy arguments for seeing stabilization in the previous work were based on ideas in Bai–Winkler (Indiana Univ. Math. J.;2016;65;553–583); however, these ideas were recently improved by the first author (Discrete Contin. Dyn. Syst. Ser. S;2020;13;269–278), which implies that the result about stabilization in the previous work seems not to be the best. This paper gives an improvement of conditions for stabilization in the previous work. The feature of the proof is to use the Sylvester criterion in deriving energy estimates. [ABSTRACT FROM AUTHOR]

We use data from a large-scale experiment conducted in Indiana in 2009-2010 to examine the impact of two interim assessment programs (mCLASS and Acuity) across the mathematics and reading achievement distributions. Specifically, we focus on whether the use of interim assessments has a particularly strong effect on improving outcomes for low achievers. Quantile regression is used to estimate treatment effects across the entire achievement distribution (i.e., provide estimates in the lower, middle, or upper tails). Results indicate that in Grades 3 to 8 (particularly third, fifth, and sixth) lower achievers seem to benefit more from interim assessments than higher achieving students. [ABSTRACT FROM AUTHOR]