Bi-exponential modelling of $$W^{^{\prime}}$$ reconstitution kinetics in trained cyclists

Purpose The aim of this study was to investigate the individual $$W^{^{\prime}}$$ W ′ reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe $$W^{^{\prime}}$$ W ′ reconstitution. Methods Ten trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; $$\dot{V}{\text{O}}_{2\max }$$ V ˙ O 2 max 58.6 ± 7.1 mL kg min−1) completed three incremental ramps (20 W min−1) to the limit of tolerance with varying recovery durations (15–360 s) on 5–9 occasions. $$W^{^{\prime}}$$ W ′ reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R2 and bias-corrected Akaike information criterion (AICc). Results A bi-exponential model outperformed the mono-exponential model of $$W^{^{\prime}}$$ W ′ reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adjR2 = 0.999) for the first recovery when optimised with parameters of fast component (FC) amplitude = 50.67%; slow component (SC) amplitude = 49.33%; time constant (τ)FC = 21.5 s; τSC = 388 s. Following the second recovery, W′ reconstitution reduced by 9.1 ± 7.3%, at 180 s and 8.2 ± 9.8% at 240 s resulting in an increase in the modelled τSC to 716 s with τFC unchanged. Individual bi-exponential models also fit well (adjR2 = 0.978 ± 0.017) with large individual parameter variations (FC amplitude 47.7 ± 17.8%; first recovery: (τ)FC = 22.0 ± 11.8 s; (τ)SC = 377 ± 100 s; second recovery: (τ)FC = 16.3.0 ± 6.6 s; (τ)SC = 549 ± 226 s). Conclusions W′ reconstitution kinetics were best described by a bi-exponential model consisting of distinct fast and slow phases. The amplitudes of the FC and SC remained unchanged with repeated bouts, with a slowing of W′ reconstitution confined to an increase in the time constant of the slow component.

On the oscillation of nonlinear delay differential equations and their applications

The oscillation of nonlinear differential equations is used in many applications of mathematical physics, biological and medical physics, engineering, aviation, complex networks, sociophysics and econophysics. The goal of this study is to create some new oscillation criteria for fourth-order differential equations with delay and advanced terms ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + ∑ j = 1 r β j ( x ) w k ( γ j ( x ) ) = 0 , {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+\mathop{\sum }\limits_{j=1}^{r}{\beta }_{j}(x){w}^{k}({\gamma }_{j}(x))=0, and ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + a 2 ( x ) h ( w ‴ ( x ) ) + β ( x ) f ( w ( γ ( x ) ) ) = 0 . {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+{a}_{2}(x)h({w}^{\prime\prime\prime }(x))+\beta (x)f(w(\gamma (x)))=0. The method is based on the use of the comparison technique and Riccati method to obtain these criteria. These conditions complement and extend some of the results published on this topic. Two examples are provided to prove the efficiency of the main results.

LHC constraints on $$W^\prime ,~Z^\prime $$ that couple mainly to third generation fermions

We use the results of CMS and ATLAS searches for resonances that decay to $$\tau \nu $$ τ ν or tb and $$\tau ^+\tau ^-$$ τ + τ - or $$t{\bar{t}}$$ t t ¯ final states to constrain the parameters of non-universal $$W^\prime $$ W ′ and $$Z^\prime $$ Z ′ gauge bosons that couple preferentially to the third generation. For the former we consider production from $$c\bar{b}$$ c b ¯ annihilation and find very weak constraints on the strength of the interaction and only for the mass range between 800 and 1100 GeV from the $$pp \rightarrow \tau _h p_T^{\mathrm{miss}}$$ p p → τ h p T miss channel. The constraints on the latter are much stronger and arise from both $$t{\bar{t}}$$ t t ¯ and $$\tau ^+\tau ^-$$ τ + τ - production. Treated separately, we find that the weak constraints on the $$W^\prime $$ W ′ still permit an explanation of the $$R(D^{(\star )})$$ R ( D ( ⋆ ) ) anomalies with a light sterile neutrino whereas the stronger constraints on the $$Z^\prime $$ Z ′ exclude significant light sterile neutrino contributions to the $$K \rightarrow \pi \nu \bar{\nu }$$ K → π ν ν ¯ rates. Within specific models the masses of $$W^\prime $$ W ′ and $$Z^\prime $$ Z ′ are of course related and we briefly discuss the consequences.

Exercise tolerance during flat over-ground intermittent running: modelling the expenditure and reconstitution kinetics of work done above critical power

Purpose We compared a new locomotor-specific model to track the expenditure and reconstitution of work done above critical power (W´) and balance of W´ (W´BAL) by modelling flat over-ground power during exhaustive intermittent running. Method Nine male participants completed a ramp test, 3-min all-out test and the 30–15 intermittent fitness test (30–15 IFT), and performed a severe-intensity constant work-rate trial (SCWR) at the maximum oxygen uptake velocity (vV̇O2max). Four intermittent trials followed: 60-s at vV̇O2max + 50% Δ1 (Δ1 = vV̇O2max − critical velocity [VCrit]) interspersed by 30-s in light (SL; 40% vV̇O2max), moderate (SM; 90% gas-exchange threshold velocity [VGET]), heavy (SH; VGET + 50% Δ2 [Δ2 = VCrit − VGET]), or severe (SS; vV̇O2max − 50% Δ1) domains. Data from Global Positioning Systems were derived to model over-ground power. The difference between critical and recovery power (DCP), time constant for reconstitution of W´ ($$\tau_{{W^{\prime}}}$$τW′), time to limit of tolerance (TLIM), and W´BAL from the integral (W´BALint), differential (W´BALdiff), and locomotor-specific (OG-W´BAL) methods were compared. Results The relationship between $$\tau_{{W^{\prime}}}$$τW′ and DCP was exponential (r2 = 0.52). The $$\tau_{{W^{{\prime}}}}$$τW′ for SL, SM, and SH trials were 119 ± 32-s, 190 ± 45-s, and 336 ± 77-s, respectively. Actual TLIM in the 30–15 IFT (968 ± 117-s) compared closely to TLIM predicted by OG-W´BAL (929 ± 94-s, P > 0.100) and W´BALdiff (938 ± 84-s, P > 0.100) but not to W´BALint (848 ± 91-s, P = 0.001). Conclusion The OG-W´BAL accurately tracked W´ kinetics during intermittent running to exhaustion on flat surfaces.

A new principle for arbitrary meromorphic functions in a given domain

This paper presents a new principle related to an arbitrary meromorphic function w in a given domain D. The main component of this principle gives (first time) lower bounds for {|w^{\prime}|} for a similar general class of functions. The principle can qualitatively be stated as follows: any set of simple a-points of w contains a “large” subset of complex values, where we have lower bounds for {|w^{\prime}|} and upper bounds for {|w^{(h)}|} , {h>1} .

Turbulence modifications induced by the bed mobility in intense sediment-laden flows

An experimental dataset of high-resolution velocity and concentration measurements is obtained under intense sediment transport regimes to provide new insights into the modification of turbulence induced by the presence of a mobile sediment bed. The physical interpretation of the zero-plane level in the law of the wall is linked to the bed-level variability induced by large-scale turbulent flow structures. The comparison between intrinsic and superficial Reynolds shear stresses shows that the observed strong bed-level variability results in an increased covariance between wall-normal ($w^{\prime }$) and streamwise ($u^{\prime }$) velocity fluctuations. This appears as an additional Reynolds shear stress in the near-wall region. It is also observed that the mobile sediment bed induces an increase of turbulence kinetic energy (TKE) across the boundary layer. However, the increased contribution of interaction events ($u^{\prime }w^{\prime }>0$, i.e. quadrants I and III in the ($u^{\prime },w^{\prime }$) plane) induces a decrease of the turbulent momentum diffusion and an increase of the turbulent concentration diffusion in the suspension region. This result provides an explanation for the modification of the von Kármán parameter and the turbulent Schmidt number observed in the literature for intense sediment transport.

NON-COMMUTATIVE LOCALIZATIONS OF ADDITIVE CATEGORIES AND WEIGHT STRUCTURES

In this paper we demonstrate thatnon-commutative localizationsof arbitrary additive categories (generalizing those defined by Cohn in the setting of rings) are closely (and naturally) related to weight structures. Localizing an arbitrary triangulated category$\text{}\underline{C}$by a set$S$of morphisms in the heart$\text{}\underline{Hw}$of a weight structure$w$on it one obtains a triangulated category endowed with a weight structure$w^{\prime }$. The heart of$w^{\prime }$is a certain version of the Karoubi envelope of the non-commutative localization$\text{}\underline{Hw}[S^{-1}]_{\mathit{add}}$(of$\text{}\underline{Hw}$by$S$). The functor$\text{}\underline{Hw}\rightarrow \text{}\underline{Hw}[S^{-1}]_{\mathit{add}}$is the natural categorical version of Cohn’s localization of a ring, i.e., it is universal among additive functors that make all elements of$S$invertible. For any additive category$\text{}\underline{A}$, taking$\text{}\underline{C}=K^{b}(\text{}\underline{A})$we obtain a very efficient tool for computing$\text{}\underline{A}[S^{-1}]_{\mathit{add}}$; using it, we generalize the calculations of Gerasimov and Malcolmson (made for rings only). We also prove that$\text{}\underline{A}[S^{-1}]_{\mathit{add}}$coincides with the ‘abstract’ localization$\text{}\underline{A}[S^{-1}]$(as constructed by Gabriel and Zisman) if$S$contains all identity morphisms of$\text{}\underline{A}$and is closed with respect to direct sums. We apply our results to certain categories of birational motives$DM_{gm}^{o}(U)$(generalizing those defined by Kahn and Sujatha). We define$DM_{gm}^{o}(U)$for an arbitrary$U$as a certain localization of$K^{b}(Cor(U))$and obtain a weight structure for it. When$U$is the spectrum of a perfect field, the weight structure obtained this way is compatible with the corresponding Chow and Gersten weight structures defined by the first author in previous papers. For a general$U$the result is completely new. The existence of the correspondingadjacent$t$-structure is also a new result over a general base scheme; its heart is a certain category of birational sheaves with transfers over$U$.