Le débit maximal d’oxygène (VO2max), aussi appelé consommation maximale d’oxygène, est actuellement l’un des paramètres central pour la compréhension de la physiologie humaine lors d’un effort physique. Plus ce débit est important et plus le sujet, sportif ou non, est capable de fournir une grande quantité d’énergie pour courir, sauter, voir courir plus vite, sauter plus haut… Ainsi, le temps pendant lequel l’homme est capable de soutenir cette valeur de débit maximal (endurance au VO2max) est l’un des facteurs déterminant de la performance. Plus ce temps est long et plus le sujet maintient une haute vitesse de course. C’est pourquoi, de nombreuses études dans le domaine de la physiologie humaine et sportive se sont attachées à analyser les facteurs limitants le VO2max et l’endurance au VO2max. Néanmoins, si les facteurs limitants du VO2max sont aujourd’hui largement acceptés, les facteurs limitant l’endurance au VO2max restent encore à déterminer. La mise en place d’un modèle expérimental innovant utilisant comme variable indépendante la VO2max et non la puissance, comme cela était fait habituellement, a permis de mettre en évidence les facteurs limitant l’endurance au VO2max. Grâce à ce modèle, nous avons démontré que l’endurance au VO2max dépend de variations de puissance (ou de vitesse) durant cet effort au VO2max. Cette variation de puissance permet d’épargner les réserves du métabolisme anaérobie. Ainsi, nous avons montré que ces réserves anaérobies sont également un facteur limitant de l’endurance au VO2max. De plus, l’endurance au VO2max n’est pas corrélée au VO2max des sujets. Autrement dit, un sujet, avec un VO2max bas sera capable de soutenir longtemps son VO2max, s’il a en contre partie une grande capacité anaérobie et s’il est capable d’adapter sa vitesse de façon adéquate lors de sa course. L’endurance au VO2max sera identique au niveau de la mer ou en altitude (3000m) et ne dépendra pas des facteurs cardiovasculaires intervenant dans l’équation de Fick, principaux facteurs limitants de l’amplitude du VO2max. L’ensemble de ses résultats a donc permis, pour la première fois, de déterminer des facteurs limitant l’endurance au 2max qui sont différents des facteurs limitant l’amplitude du VO2max. Ces nouvelles connaissances sur l’endurance trouveront des applications dans la planification des entraînements sportifs afin d’améliorer la qualité des entraînements et en épargnant le surentraînement aux sportifs. De plus, ces données pourraient être également mise en œuvre chez les sujets dont les capacités physiques ont été endommagées par des pathologies (cardiaques, respiratoires par exemple). / Maximal Oxygen uptake (VO2max) is currently one of the central parameters for the comprehension of human physiology during a physical activity. Higher is this oxygen uptake is and greater is the energy supply to run or jump for trained or untrained subjects … Thus, the time during which the subject is able to support this maximal oxygen uptake (endurance at VO2max) is one of the factors determining the performance. Longer is this endurance at VO2max Higher is the speed of race maintains by the subjects this is why, Among the numerous studies in the field of human and sporting physiology, the limiting factors of VO2max and the limiting factors of endurance at VO2max were studied. Nevertheless, if the limiting factors of VO2max today are well accepted, the factors limiting the endurance at VO2max still remain to be determined.The development of an innovating experimental model using VO2max as independent variable and not the power, as that was usually done, highlight the factors limiting the endurance at VO2max. Thanks to this model, we showed that the endurance at VO2max depends on variations of power (or speed) during this effort at VO2max. This variation of power minimizes the anaerobic metabolism reserve utilization during the 2max plateau. Thus, we showed that these anaerobic reserves are also a limiting factor of the endurance at VO2max. Moreover, the endurance at VO2max was not correlated with the VO2max. In other words, a subject, with a low VO2max may be able to support VO2max for a long time, if the anaerobic capacity is important and if the speed variation is properly adapted during the race. The endurance at VO2max is identical at sea level and in hypoxic condition (3000m) and that not depend on the cardiovascular factors entering in the Fick equation, known as limiting factors of VO2max amplitude. For the first time, all of these results determine factors limiting the endurance at VO2max which are different from the factors limiting the amplitude of VO2max. This new knowledge about endurance will find applications in the planning of the sport training in order to improve its quality and by saving athletes overtraining. Moreover, these data could also be implemented for subjects whose physical capacities are damaged by pathologies (cardiac, respiratory impairments for example).

Hwang Cheuk Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 34-35). / Abstracts in English and Chinese. / Chapter 1 --- Introduction and Main Results --- p.5 / Chapter 2 --- Some qualitative results --- p.9 / Chapter 3 --- Existence result --- p.13 / Chapter 4 --- Asymtoptic behavior of the gound state solution --- p.21 / Bibliography --- p.34

No description available.

Thesis (M.S.)--University of Michigan, 1980.

The purpose of this thesis is to study the factors involved in determining a most efficient method for the numerical integration of the differential equation x' = f(t,x) . By "a most efficient method" we mean a method requiring a minimum of computation to obtain a solution within prescribed error bounds. We outline two computational procedures and derive estimates for the propagated error of a general multi-step method when based on either procedure. These estimates, lead us to conclude that a stable single-iterate procedure, involving one evaluation of f at each step, will determine a solution most efficiently. In particular, this procedure based on Adams formulas is recommended. Experimental results support our conclusion in all stable cases. However, these results also indicate that the role of stability in the choice of a most efficient procedure is in need of further investigation. / Science, Faculty of / Mathematics, Department of / Graduate

A comprehensive study of potential symmetries admitted by partial differential equations is given using the wave equation utt = c²(x)uxx as a given prototype equation, R. Methods are given for the construction of various conserved forms for R. Potential symmetries for R are nonlocal symmetries realized as local symmetries of auxiliary systems obtained from conserved forms of R. The existence of potential symmetries for R can be determined algorithmically and automatically by the use of a symbolic manipulation program. Most importantly, the potential symmetries obtained through one auxiliary system may or may not include and/or extend those obtained through another auxiliary system. The work in this thesis significantly extends the previously known classes of potential symmetries admitted by R and results in a better understanding of the limits in the construction of potential symmetries for R. / Science, Faculty of / Mathematics, Department of / Graduate

I present a new time-domain method for solving for the stress and particle velocity of normally incident plane waves propagating in a smoothly varying one-dimensional medium. Both the Young's modulus E and the density ⍴ are allowed to vary smoothly with depth. The restriction of geometrical optics, that the wavelength be much less than the material stratification length, is not required in this new method. The infinite geometrical optics expansion is truncated after n terms, imposing a condition on the acoustic impedance I for exact solutions to exist. For the case ռ = 2 there are three general classes of impedance functions for which the resultant expansion is uniform and exact. To check the numerical validity of the "truncated asymptotic" (TA) solution results are calculated for the case of a medium with a linear velocity gradient for which there is an exact solution in the frequency domain. Since a linear velocity gradient is not one of the foregoing classes of impedance functions, a curve-fitting approach is necessary. The TA method compares favourably to the exact solution and is accurate to within the error of the required curve fit. Two classes of synthetic seismograms are calculated for smooth velocity and density variations. The same impedance as a function of traveltime is used for both classes. In the first class the principal variation in impedance is due to velocity, while in the second it is mainly due to density. The amplitudes in both classes of synthetic seismograms are very similar, but, as expected, the traveltime curves for each class are widely separated. For the case ⍴ = constant the TA solution is used as a bench-mark to analyse a two-term WKBJ approximation for three classes of velocity functions. The velocity functions are such that the TA solutions are exact. For two of the classes the WKBJ solution performs well when the length of the transition zone is of the same order, or larger, than the length of the applied wavelet. For steeper velocity gradients the WKBJ solution begins to differ significantly from the exact TA solution. The WKBJ solution for the third class performs extremely well even for steep gradients. Equations governing the validity of the WKBJ solution are examined to explain the above results. Equations are derived to describe the distortion of a stress pulse propagating through a transition zone. For small velocity gradients (relative to the length of the applied pulse) the wavelet changes amplitude but its phase is not effected. As the gradient increases and the velocity function becomes a discontinuity at z = 0 the wavelet travels through undistorted. Only when the transition zone width is of the order of the length of the wavelet is there any visible phase distortion. Reflection and transmission coefficients as functions of time are calculated for low, intermediate and high gradient transition zones. The transmission coefficient is a delta function in each case. The reflection coefficient has the shape of a Hilbert transform for low gradients. For higher gradients the reflection coefficient approaches the shape of a delta function. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

We consider the problems of simulation and control for Burgers' equation with mixed boundary conditions. We first conduct numerical experiments to test the convergence and stability of two standard finite element schemes for various Robin boundary conditions and a variety of Reynolds numbers. These schemes are used to compute LQR feedback controllers for Burgers' equation with boundary control. Numerical studies of these feedback control laws are used to evaluate the performance and practicality of this approach to boundary control of non-linear systems. / Master of Science

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 126-131). Available also in a digital version from Dissertation Abstracts.

Thesis (M.S.)--Brigham Young University. Dept of Mathematics, 2007. / Includes bibliographical references (p. 100-102).