Topological partition relations to the form omega^*-> (Y)^1_2

Theorem: The topological partition relation omega^{*}-> (Y)^{1}_{2} (a) fails for every space Y with |Y| >= 2^c ; (b) holds for Y discrete if and only if |Y| <= c; (c) holds for certain non-discrete P-spaces Y ; (d) fails for Y= omega cup {p} with p in omega^{*} ; (e) fails for Y infinite and countably compact

Comparison of bone healing in four types of jaw cysts

Abstract no. 1019published_or_final_versio

Precompact noncompact reflexive abelian groups

We present a series of examples of precompact, noncompact, reflexive topological Abelian groups. Some of them are pseudocompact or even countably compact, but we show that there exist precompact non-pseudocompact reflexive groups as well. It is also proved that every pseudocompact Abelian group is a quotient of a reflexive pseudocompact group with respect to a closed reflexive pseudocompact subgroup

Sex differences in countermovement jump phase characteristics

The countermovement jump (CMJ) is commonly used to explore sex differences in neuromuscular function, but previous studies have only reported gross CMJ measures or have partly examined CMJ phase characteristics. The purpose of this study was to explore differences in CMJ phase characteristics between male and female athletes by comparing the force-, power-, velocity-, and displacement-time curves throughout the entire CMJ, in addition to gross measures. Fourteen men and fourteen women performed three CMJs on a force platform from which a range of kinetic and kinematic variables were calculated via forward dynamics. Jump height (JH), reactive strength index modified, relative peak concentric power, and eccentric and concentric displacement, velocity, and relative impulse were all greater for men (g = 0.58–1.79). Relative force-time curves were similar between sexes, but relative power-, velocity-, and displacement-time curves were greater for men at 90%–95% (immediately before and after peak power), 47%–54% (start of eccentric phase) and 85%–100% (latter half of concentric phase), and 65%–87% (bottom of countermovement and initial concentric phase) of normalized jump time, respectively. The CMJ distinguished between sexes, with men demonstrating greater JH through applying a larger concentric impulse and, thus, achieving greater velocity throughout most of the concentric phase, including take-off

Effectiveness of Hindman's theorem for bounded sums

We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified finite bound. Let $\mathsf{HT}^{\leq n}_k$ denote the assertion that for each $k$-coloring $c$ of $\mathbb{N}$ there is an infinite set $X \subseteq \mathbb{N}$ such that all sums $\sum_{x \in F} x$ for $F \subseteq X$ and $0 < |F| \leq n$ have the same color. We prove that there is a computable $2$-coloring $c$ of $\mathbb{N}$ such that there is no infinite computable set $X$ such that all nonempty sums of at most $2$ elements of $X$ have the same color. It follows that $\mathsf{HT}^{\leq 2}_2$ is not provable in $\mathsf{RCA}_0$ and in fact we show that it implies $\mathsf{SRT}^2_2$ in $\mathsf{RCA}_0$. We also show that there is a computable instance of $\mathsf{HT}^{\leq 3}_3$ with all solutions computing $0'$. The proof of this result shows that $\mathsf{HT}^{\leq 3}_3$ implies $\mathsf{ACA}_0$ in $\mathsf{RCA}_0$

Resistance training volume load with and without exercise displacement

Monitoring the resistance training volume load (VL) (sets × reps × load) is essential to managing resistance training and the recovery⁻adaptation process. Eight trained weightlifters, seven of which were at national level, participated in the study. VL was measured both with (VLwD) and without (VL) the inclusion of barbell displacement, across twenty weeks of training, in order to allow for comparisons to be made of these VL calculating methods. This consisted of recording the load, repetition count, and barbell displacement for every set executed. Comparisons were made between VL and VLwD for individual blocks of training, select training weeks, and select training days. Strong, statistically significant correlations (r ≥ 0.78, < 0.001) were observed between VL and VLwD between all training periods analyzed. -tests revealed statistically significant ( ≤ 0.018) differences between VL and VLwD in four of the seven training periods analyzed. The very strong relationship between VL and VLwD suggest that a coach with time constraints and a large number of athletes can potentially spare the addition of displacement. However, differences in percent change indicate that coaches with ample time should include displacement in VL calculations, in an effort to acquire more precise workload totals