The strength and conditioning practices and perspectives of soccer coaches and players

Strength and conditioning (S&C) is implemented across various sports and levels, but there is limited understanding of the personnel responsible for this, including their S&C practices and perspectives. Whereas recent evidence has shown that coaches and players are often tasked with the responsibility. Therefore, this study aimed to investigate: 1) the personnel responsible for delivering S&C across different levels of soccer, 2) the practices and perspectives of soccer coaches and players, and 3) to ascertain whether the practices employed align with contemporary evidence and guidelines. Forty-two soccer coaches and 30 soccer players completed an online survey with six sections: (a) informed consent, (b) background information, (c) education, qualifications, and prescription, (d) views on S&C, (e) exercise selection and preferences, and (f) issues and improvements. Frequency analysis was used to report responses to fixed-response questions and thematic analysis for open-ended questions. Most respondents reported S&C to be ‘important’ to ‘very important’ for all soccer, physical fitness, and injury parameters, with perspectives being predominantly aligned with S&C guidelines and research in soccer. Although S&C coaches were mostly responsible for delivering S&C sessions, over 60% of respondents disclosed S&C sessions were delivered independently or by support staff. This is problematic given only four coaches held S&C qualifications, and issues and improvements were mostly regarding a lack of S&C expertise and education. This study provides valuable information for S&C and soccer organizations. Particularly regarding the additional support required to ensure those responsible for delivering S&C in soccer have the appropriate knowledge and qualifications.

$$\alpha $$-Modulation Spaces for Step Two Stratified Lie Groups

We define and investigate $$\alpha $$ α -modulation spaces $$M_{p,q}^{s,\alpha }(G)$$ M p , q s , α ( G ) associated to a step two stratified Lie group G with rational structure constants. This is an extension of the Euclidean $$\alpha $$ α -modulation spaces $$M_{p,q}^{s,\alpha }({\mathbb {R}}^n)$$ M p , q s , α ( R n ) that act as intermediate spaces between the modulation spaces ($$\alpha = 0$$ α = 0 ) in time-frequency analysis and the Besov spaces ($$\alpha = 1$$ α = 1 ) in harmonic analysis. We will illustrate that the group structure and dilation structure on G affect the boundary cases $$\alpha = 0,1$$ α = 0 , 1 where the spaces $$M_{p,q}^{s}(G)$$ M p , q s ( G ) and $${\mathcal {B}}_{p,q}^{s}(G)$$ B p , q s ( G ) have non-standard translation and dilation symmetries. Moreover, we show that the spaces $$M_{p,q}^{s,\alpha }(G)$$ M p , q s , α ( G ) are non-trivial and generally distinct from their Euclidean counterparts. Finally, we examine how the metric geometry of the coverings $${\mathcal {Q}}(G)$$ Q ( G ) underlying the $$\alpha = 0$$ α = 0 case $$M_{p,q}^{s}(G)$$ M p , q s ( G ) allows for the existence of geometric embeddings $$\begin{aligned} F:M_{p,q}^{s}({\mathbb {R}}^k) \longrightarrow {} M_{p,q}^{s}(G), \end{aligned}$$ F : M p , q s ( R k ) ⟶ M p , q s ( G ) , as long as k (that only depends on G) is small enough. Our approach naturally gives rise to several open problems that is further elaborated at the end of the paper.

Frequency Analysis of the Nonstationary Annual Runoff Series Using the Mechanism-Based Reconstruction Method

Due to climate change and human activities, the statistical characteristics of annual runoff series of many rivers around the world exhibit complex nonstationary changes, which seriously impact the frequency analysis of annual runoff and are thus becoming a hotspot of research. A variety of nonstationary frequency analysis methods has been proposed by many scholars, but their reliability and accuracy in practical application are still controversial. The recently proposed Mechanism-based Reconstruction (Me-RS) method is a method to deal with nonstationary changes in hydrological series, which solves the frequency analysis problem of the nonstationary hydrological series by transforming nonstationary series into stationary Me-RS series. Based on the Me-RS method, a calculation method of design annual runoff under the nonstationary conditions is proposed in this paper and applied to the Jialu River Basin (JRB) in northern Shaanxi, China. From the aspects of rationality and uncertainty, the calculated design value of annual runoff is analyzed and evaluated. Then, compared with the design values calculated by traditional frequency analysis method regardless of whether the sample series is stationary, the correctness of the Me-RS theory and its application reliability is demonstrated. The results show that calculation of design annual runoff based on the Me-RS method is not only scientific in theory, but also the obtained design values are relatively consistent with the characteristics of the river basin, and the uncertainty is obviously smaller. Therefore, the Me-RS provides an effective tool for annual runoff frequency analysis under nonstationary conditions.