Balanced carving turns in alpine skiing.

In this paper, we analyse the model of pure carving turns in alpine skiing and snowboarding based on the usual assumption of approximate balance between forces and torques acting on the skier during the turn. The approximation of torque balance yields both lower and upper limits on the skier speed, which depend only on the sidecut radius of skis and the slope gradient. We use the model to simulate carving runs on slopes of constant gradient and find that pure carving is possible only on slopes of relatively small gradient, with the critical slope angle in the range of .

Dynamics of carving runs in alpine skiing. II.Centrifugal pendulum with a retractable leg.

In this paper, we present an advanced model of centrifugal pendulum where its length is allowed to vary during swinging. This modification accounts for flexion and extension of skier's legs when turning. We focus entirely on the case where the pendulum leg shortens near the vertical position, which corresponds to the most popular technique for the transition between carving turns in ski racing, and study the effect of this action on the kinematics and dynamics of these turns.

Dynamics of carving runs in alpine skiing. I. The basic centrifugal pendulum.

We studied perfect carving turns of alpine skiing using the simple model of an inverted pendulum which is subject to the gravity force and the force mimicking the centrifugal force emerging in the turns. Depending on the turn speed the model describes two different regimes. In the subcritical regime, there exist three equilibrium positions of the pendulum where the total torque applied to the pendulum vanishes-the marginally stable vertical position and two unstable tilted positions on both sides of the vertical.

Stationary relativistic jets.

In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution . Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialised code for the time-independent equations.

[Use of permanent pacemakers in children].

The experience of pacemakers use in 24 children aged 6-15 years in the treatment of arrhythmias and conduction disturbances (CD) were summarized. Surgical intervention is indicated when a medical history of syncope or severe hemodynamic disturbances is present. In order to achieve a high quality of life of the child with arrhythmias and CD it is essential to use up-to-date pacemaker models with 2-chamber stimulation, frequency modulation, telemetry and prolonged expiry term.