An algorithm to compute the Hilbert depth

We present an algorithm which computes the Hilbert depth of a graded module based on a theorem of Uliczka. Connected to a Herzog's question we see that the Hilbert depth of a direct sum of modules can be strictly bigger than the Hilbert depth of all the summands.Comment: to appear in: Journal of Symbolic Computatio

The effect of different imagery ratios on learning and performing a gymnastic floor routine

The purpose of this study was to observe the effect of different imagery ratios to physical practice needed to learn and perform a gymnastic floor routine. It was assumed that an increase in imagery ability would reflect positively on the floor routine performance. Twenty-seven school-aged, male and female, skilled gymnasts participated in the study. They were randomly separated into four experimental groups: two groups received three imagery sessions per week and two groups received one imagery session per week. The only delimitation was the use of proficiency levels, the imagery ability levels, and gender to ensure the homogeneity of the four experimental groups. After five-week imagery training for motor skill learning and performance, the overall imagery ability increased significantly. There were no significant differences in imagery ability with regard to the gender, proficiency level, and practice conditions. There was no significant difference in performance outcomes. Several possible barriers preventing the imagery ability increase from being translated into performance increase included a possible ceiling effect in performance, a short treatment period, and the subjective human factor occurring in scoring the gymnastics routines