Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications

If a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper. In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable. The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, th…

On the stability of spline-collocation methods of multivalue type

In this paper the general classV of spline-collocation methods for first order systems of ordinary differential equations is investigated. The methods can in part be regarded as so-called multivalue methods. This type contains the generalized singly-implicit methods treated by Butcher.

Charakterisierung der Konvergenzordnung einer Klasse von Kollokationsverfahren

Algebraische Approximationen hoher Ordnung an die Exponentialfunktion

Im Zusammenhang mit der numerischen Behandlung von Anfangswertproblemen bei gewohnlichen Differentialgleichungen fuhrt der Begriff der absoluten Stabilitat bei sogenannten einwertigen Verfahren auf gewisse rationale Approximationen der Exponentialfunktion, wie z. B. Pade-Approximationen. Aus der Untersuchung dieser rationalen Approximationen haben sich verschiedene Theorien entwickelt, als Beispiel sei die Theorie der Ordnungssterne von Wanner, Hairer und Norsett genannt. Im selben Zusammenhang ergeben sich bei der Anwendung von mehrwertigen Verfahren algebraische Approximationen der Exponentialfunktion. In der vorliegenden Arbeit wird fur Butchers verallgemeinerte implizite Runge-Kutta Met…

Diagnosis in track and field performances past the 1988 Ben Johnson doping scandal

Beginning with the early 1960s, a lot of performance supporting effects have been integrated in the structure of track and field training, such as technical progress, theoretical knowledge of the training process, development of societies and medical steps, which among others include the forbidden use of steroids or other doping ‘techniques’. Since the integration of those effects took place quite fast, a logistic growth of world class performances concerning the years 1960–1988 can be observed in many disciplines especially if they were not far developed at the beginning of this period. Eight years (1989–1996) later, doping tests of world class athletes have spread (or should have spread) …

Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin-case

If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper. In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II. Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three-dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibri…

Loss of organic cation transporter 3 (Oct3) leads to enhanced proliferation and hepatocarcinogenesis

// Johanna Vollmar 1 , Anja Lautem 2 , Ellen Closs 3 , Detlef Schuppan 4 , Yong Ook Kim 4 , Daniel Grimm 1 , Jens U. Marquardt 1 , Peter Fuchs 1 , Beate K. Straub 5 , Arno Schad 5 , Dirk Grundemann 6 , Jorn M. Schattenberg 1 , Nadine Gehrke 1 , Marcus A. Worns 1 , Jan Baumgart 7 , Peter R. Galle 1 and Tim Zimmermann 1 1 Department of Internal Medicine, Gastroenterology and Hepatology, University Medical Center, Johannes Gutenberg-University Mainz, Mainz, Germany 2 Department of Hepatobiliary and Transplantation Surgery, University Medical Center, Johannes Gutenberg-University Mainz, Mainz, Germany 3 Department of Pharmacology, University Medical Center, Johannes Gutenberg-University Mainz, …

Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects

A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics. The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables. The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.

A-stable spline-collocation methods of multivalue type

In this paper the general classV of spline-collocation methods presented by Multhei is investigated. The methods ofV approximate solutions of first order initial value problems. ClassV contains as subclass the methods of so-called multivalue type, and in particular contains the generalized singly-implicit methods treated by Butcher.

General mathematical concept of compensation in sports science with quantitative analysis in the case of sprinting performance

In many of the known sports disciplines, especially in athletics, the criterion which determines the positions of the competitors is a simple physical value, mostly a time or a distance, and the athlete with the minimum or maximum, respectively, takes the first place. Moreover, sports science explains this criterion by a set of the so-called basic abilities. Compensation means the balance of the inferiority of such a basic ability by the superiority of another one. In the following paper, a general abstract concept to analyse compensation in a quantitative way is presented first. It can be applied to any discipline with a measurable criterion, if, in addition, the performance can be describ…