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A significant body of research identifies a large number of team composition characteristics that affect the success of individuals and teams in cooperative learning and project-based team environments. Controlling these factors when assigning students to teams should result in improved learning experiences. However, it is very difficult for instructors to consider more than a few criteria when assigning teams, particularly in large classes. As a result, most instructors allow students to self-select teams, randomly assign teams, or, at best, balance teams on a very limited number of criteria. This paper describes the design of "Team-Maker," a web-based software tool that surveys students about criteria that instructors want to use when creating teams and uses a max-min heuristic to determine team assignments based on distribution criteria specified by the instructor. The "Team-Maker" system was validated by comparing the team assignments generated by the "Team-Maker" software to assignments made by experienced faculty members using the same criteria. This validation experiment showed that "Team-Maker" consistently met the specified criteria more closely than the faculty members. We suggest that "Team-Maker" can be used in combination with the "Comprehensive Assessment of Team-Member Effectiveness" ("CATME") peer evaluation instrument to form a powerful faculty support system for team-based and cooperative learning and for a variety of research purposes. Internet access to both the "Team-Maker" and "CATME" systems is freely available to college faculty in all disciplines by selecting the "request faculty account" button at https://www.catme.org.

In this paper, we first investigate the regularity of finite energy solutions to the following Wolff type integral system: { u (x) = R 1 (x) W β , γ (v p u r) (x) , u (x) > 0 , x ∈ R N , v (x) = R 2 (x) W β , γ (u q v s) (x) , v (x) > 0 , x ∈ R N , where γ > 1 , β > 0 , β γ < N , W β , γ is the Wolff potential, R 1 , R 2 are double bounded functions in R N and p , q > max ⁡ { 1 , γ − 1 } , r , s ≥ 0 with p − s ≥ q − r > − γ + 1. We exploit the regularity lifting lemma to obtain the optimal integrability, boundedness and decaying property of finite energy solutions to the system. Secondly, we establish sharp pointwise estimates of positive finite energy solutions to the p -Laplacian and k -Hessian systems related to the above integral system, by using the previous regularity results, the interior Hölder estimates of solutions for the corresponding differential systems and a doubling lemma of Poláčik, Quittner and Souplet (Duke Math. J.,2007). These extend Vétois's decay results (Indiana Univ. Math. J.,2019) on the positive solutions of Laplacian systems to the p -Laplacian and k -Hessian cases. We remark that our methods do not need Harnack type inequalities and it can be applied to deal with the solutions without radial structures. As far as we know, this is the first attempt to derive sharp decay estimates for possibly non-radial solutions involving k -Hessian operators. We also obtain some decay estimates of the gradients at infinity. [ABSTRACT FROM AUTHOR]

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]

It is shown in this paper that suitable weak solutions to the 6D steady incompressible Navier-Stokes are Hölder continuous at 0 provided that ∫ B 1 | u (x) | 3 d x + ∫ B 1 | f (x) | q d x or ∫ B 1 | ∇ u (x) | 2 d x + ∫ B 1 | ∇ u (x) | 2 d x (∫ B 1 | u (x) | d x) 2 + ∫ B 1 | f (x) | q d x with q > 3 is sufficiently small, which implies that the 2D Hausdorff measure of the set of singular points is zero. For the boundary case, we also obtain that 0 is regular provided that ∫ B 1 + | u (x) | 3 d x + ∫ B 1 + | f (x) | 3 d x or ∫ B 1 + | ∇ u (x) | 2 d x + ∫ B 1 + | f (x) | 3 d x is sufficiently small. These results improve previous regularity theorems by Dong-Strain ([8] , Indiana Univ. Math. J., 2012), Dong-Gu ([7] , J. Funct. Anal., 2014), and Liu-Wang ([27] , J. Differential Equations, 2018), where either the smallness of the pressure or the smallness of the scaling invariant quantities on all balls is necessary. [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]