Effects of Additional Rifle-Carriage Training on Physiological Markers and Roller-Skiing Performance in Well-Trained Biathletes

Purpose The purpose was to investigate whether an increased amount of training while carrying the rifle affects skiing in well-trained biathletes at submaximal and maximal workloads during a pre-season period lasting a minimum of 12 weeks. Methods Seventeen well-trained biathletes (9 females, 8 males) were assigned to an intervention (IG, n = 10) or control (CG, n = 7) group. Before (T1) and after (T2) the training intervention all participants performed, using treadmill roller-skiing, a submaximal test without the rifle on one day and two submaximal workloads and a maximal time trial (TT) with the rifle on a subsequent day. Between T1 and T2 all participants performed a minimum of 12 weeks of normal training, the only difference between groups being that IG performed more of their training sessions carrying the rifle. Results IG performed more training compared to CG (15.4 ± 1.1 vs. 11.2 ± 2.6 h/week, P < 0.05), including a higher amount of training with the rifle (3.1 ± 0.6 vs. 1.1 ± 0.3 h/week, P < 0.001). Speed at 4 mmol/L of blood lactate increased significantly for CG from T1 to T2 (P = 0.028), while only tended to increase for IG (P = 0.058). Performance during the TT, VO2max and the aerobic metabolic rate increased significantly from T1 to T2, although the differences disappeared when including the speed at baseline as a covariate. Conclusion According to the present results, increasing training while carrying the rifle by 2 h/week does not appear to improve skiing performance in well-trained biathletes. In addition, physiological markers at submaximal and maximal intensities while carrying the rifle were not affected after the training intervention.

Anisotropic Curvature Flow of Immersed Networks

We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the $$L^2$$ L 2 -norm of the anisotropic curvature blows up.

Maximal Time Spent at VO2max from Sprint to the Marathon

Until recently, it was thought that maximal oxygen uptake (VO2max) was elicited only in middle-distance events and not the sprint or marathon distances. We tested the hypothesis that VO2max can be elicited in both the sprint and marathon distances and that the fraction of time spent at VO2max is not significantly different between distances. Methods: Seventy-eight well-trained males (mean [SD] age: 32 [13]; weight: 73 [9] kg; height: 1.80 [0.8] m) performed the University of Montreal Track Test using a portable respiratory gas sampling system to measure a baseline VO2max. Each participant ran one or two different distances (100 m, 200 m, 800 m, 1500 m, 3000 m, 10 km or marathon) in which they are specialists. Results: VO2max was elicited and sustained in all distances tested. The time limit (Tlim) at VO2max on a relative scale of the total time (Tlim at VO2max%Ttot) during the sprint, middle-distance, and 1500 m was not significantly different (p > 0.05). The relevant time spent at VO2max was only a factor for performance in the 3000 m group, where the Tlim at VO2max%Ttot was the highest (51.4 [18.3], r = 0.86, p = 0.003). Conclusions: By focusing on the solicitation of VO2max, we demonstrated that the maintenance of VO2max is possible in the sprint, middle, and marathon distances.

Data-Driven Model Reduction for Stochastic Burgers Equations

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable’s trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system’s mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model.

Data-driven Model Reduction for Stochastic Burgers Equations

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables&rsquo; trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model&rsquo;s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system&rsquo;s mean CFL number agrees with the full model&rsquo;s.

Ricci flow of warped Berger metrics on $${\mathbb {R}}^{4}$$

We study the Ricci flow on $${\mathbb {R}}^{4}$$ R 4 starting at an SU(2)-cohomogeneity 1 metric $$g_{0}$$ g 0 whose restriction to any hypersphere is a Berger metric. We prove that if $$g_{0}$$ g 0 has no necks and is bounded by a cylinder, then the solution develops a global Type-II singularity and converges to the Bryant soliton when suitably dilated at the origin. This is the first example in dimension $$n > 3$$ n > 3 of a non-rotationally symmetric Type-II flow converging to a rotationally symmetric singularity model. Next, we show that if instead $$g_{0}$$ g 0 has no necks, its curvature decays and the Hopf fibres are not collapsed, then the solution is immortal. Finally, we prove that if the flow is Type-I, then there exist minimal 3-spheres for times close to the maximal time.

Global in Time Existence of Strong Solution to 3D Navier-Stokes Equations

The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in H1 initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of subdividing the time interval of existence into smaller sub-intervals carefully chosen. These sub-intervals are chosen based on the hypothesis that for any wavenumber m, one can find an interval of time on which the energy quantized in low-frequency components (up to m) of the solution u is lesser than the energy quantized in high-frequency components (down to m) or otherwise the opposite. We associate then a suitable number m to each one of the intervals and we prove that the norm ||u(t)||H1 is bounded in both mentioned cases. The process can be continued until reaching the maximal time of existence Tmax which yields the global in time existence of strong solution.

Global Existence of Strong Solution to 3D Periodic Navier-Stokes Equations

The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in H1 initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of subdividing the time interval of existence into smaller sub-intervals carefully chosen. These sub-intervals are chosen based on the hypothesis that for any wavenumber m, one can find an interval of time on which the energy quantized in low-frequency components (up to m) of the solution u is lesser than the energy quantized in high-frequency components (down to m) or otherwise the opposite. We associate then a suitable number m to each one of the intervals and we prove that the norm ||u(t)||H1 is bounded in both mentioned cases. The process can be continued until reaching the maximal time of existence Tmax which yields the global in time existence of strong solution.

Maximal time existence of unnormalized conical Kähler–Ricci flow

We generalize the maximal time existence of Kähler–Ricci flow in [G. Tian and Z. Zhang, On the Kähler–Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179–192] and [J. Song and G. Tian, The Kähler–Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519–595] to the conical case. Furthermore, if the log canonical bundle {K_{M}+(1-\beta)[D]} is big or big and nef, we can examine the limit behaviors of such conical Kähler–Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.

LARGE DEVIATIONS FOR THE LONGEST GAP IN POISSON PROCESSES

The longest gap $L(t)$ up to time $t$ in a homogeneous Poisson process is the maximal time subinterval between epochs of arrival times up to time $t$; it has applications in the theory of reliability. We study the Laplace transform asymptotics for $L(t)$ as $t\rightarrow \infty$ and derive two natural and different large-deviation principles for $L(t)$ with two distinct rate functions and speeds.