Influence of Soldiers' Cardiorespiratory Fitness on Physiological Responses and Dropouts During a Loaded Long-distance March.

Introduction: In military service, marching is an important, common, and physically demanding task. Minimizing dropouts, maintaining operational readiness during the march, and achieving a fast recovery are desirable because the soldiers have to be ready for duty, sometimes shortly after an exhausting task. The present field study investigated the influence of the soldiers' cardiorespiratory fitness on physiological responses during a long-lasting and challenging 34 km march. Materials and methods: Heart rate (HR), body core temperature (BCT), total energy expenditure (TEE), energy intake, motivation, and pain sensation were investigated in 44 soldiers (20.3 ± 1.3 years, 178.5 ± 7.0 cm, 74.8 ± 9.8 kg, body mass index: 23.4 ± 2.7 kg × m-2, peak oxygen uptake ($\dot{\rm{V}}$O2peak): 54.2 ± 7.9 mL × kg-1 × min-1) during almost 8 hours of marching. All soldiers were equipped with a portable electrocardiogram to record HR and an accelerometer on the hip, all swallowed a telemetry pill to record BCT, and all filled out a pre- and post-march questionnaire. The influence of aerobic capacity on the physiological responses during the march was examined by dividing the soldiers into three fitness groups according to their $\dot{\rm{V}}$O2peak. Results: The group with the lowest aerobic capacity ($\dot{\rm{V}}$O2peak: 44.9 ± 4.8 mL × kg-1 × min-1) compared to the group with the highest aerobic capacity ($\dot{\rm{V}}$O2peak: 61.7 ± 2.2 mL × kg-1 × min-1) showed a significantly higher (P < .05) mean HR (133 ± 9 bpm and 125 ± 8 bpm, respectively) as well as peak BCT (38.6 ± 0.3 and 38.4 ± 0.2 °C, respectively) during the march. In terms of recovery ability during the break, no significant differences could be identified between the three groups in either HR or BCT. The energy deficit during the march was remarkably high, as the soldiers could only replace 22%, 26%, and 36% of the total energy expenditure in the lower, middle, and higher fitness group, respectively. The cardiorespiratory fittest soldiers showed a significantly higher motivation to perform when compared to the least cardiorespiratory fit soldiers (P = .002; scale from 1 [not at all] to 10 [extremely]; scale difference of 2.3). A total of nine soldiers (16%) had to end marching early: four soldiers (21%) in the group with the lowest aerobic capacity, five (28%) in the middle group, and none in the highest group. Conclusion: Soldiers with a high $\dot{\rm{V}}$O2peak showed a lower mean HR and peak BCT throughout the long-distance march, as well as higher performance motivation, no dropouts, and lower energy deficit. All soldiers showed an enormous energy deficit; therefore, corresponding nutritional strategies are recommended

On the strict majorant property in arbitrary dimensions

In this work we study $d$-dimensional majorant properties. We prove that a set of frequencies in ${\mathbb Z}^d$ satisfies the strict majorant property on $L^p([0,1]^d)$ for all $p> 0$ if and only if the set is affinely independent. We further construct three types of violations of the strict majorant property. Any set of at least $d+2$ frequencies in ${\mathbb Z}^d$ violates the strict majorant property on $L^p([0,1]^d)$ for an open interval of $p \not\in 2 {\mathbb N}$ of length 2. Any infinite set of frequencies in ${\mathbb Z}^d$ violates the strict majorant property on $L^p([0,1]^d)$ for an infinite sequence of open intervals of $p \not\in 2 {\mathbb N}$ of length $2$. Finally, given any $p>0$ with $p \not\in 2{\mathbb N}$, we exhibit a set of $d+2$ frequencies on the moment curve in ${\mathbb R}^d$ that violate the strict majorant property on $L^p([0,1]^d).$Comment: 22 page

Polynomial Carleson operators along monomial curves in the plane

We prove $L^p$ bounds for partial polynomial Carleson operators along monomial curves $(t,t^m)$ in the plane $\mathbb{R}^2$ with a phase polynomial consisting of a single monomial. These operators are "partial" in the sense that we consider linearizing stopping-time functions that depend on only one of the two ambient variables. A motivation for studying these partial operators is the curious feature that, despite their apparent limitations, for certain combinations of curve and phase, $L^2$ bounds for partial operators along curves imply the full strength of the $L^2$ bound for a one-dimensional Carleson operator, and for a quadratic Carleson operator. Our methods, which can at present only treat certain combinations of curves and phases, in some cases adapt a $TT^*$ method to treat phases involving fractional monomials, and in other cases use a known vector-valued variant of the Carleson-Hunt theorem.Comment: 27 page