The paper deals with dynamics and control of a special type of mobile robot designed to act as a small platform to carry sensing devices or actuators in an environment where stability of the platform is critical, like in surveying unstructured hostile industrial environment or exploring other planets, or simply being a part of a human place, like office or home, which has not been designed for ...

The Parkinson’s disease is a neurodegenerative disorder with a range of symptoms such as slowness, rigidity, resting tremor (trembling), and an impairment of postural balance leading to disturbance of gait and falling. Continuous exercises are an effective strategy to maintain the patient’s movement abilities, slowing down the progression of the disease. Self-directed exercises in addition to s...

Abstract. Here we solve the problem posed by Comte and Lachand-Robert in [8] (2001). Take a bounded domain Ω ⊂ R and a piecewise smooth non-positive function u : Ω̄ → R vanishing on ∂Ω. Consider a flow of point particles falling vertically down and reflected elastically from the graph of u. It is assumed that each particle is reflected no more than once (no multiple reflections are allowed); the...

In this paper an optimization problem for a cylindrical shell under an applied dynamical loading is discussed. The aim is to look for an optimal thickness of a shell to minimize the deformation when the shell is subject to an external timedependent force together with an initial impact. The volume of the shell has to stay constant during optimization. A model for the deflection is derived and a...

Lorenz’s mathematical model of the weather, made in 1963, describes the motion of the air through the atmosphere. More precisely, Lorenz observed the hot air rising up into the atmosphere, then cooling down and eventually falling to the ground. While observing the weather conditions, Lorenz noticed that the weather does not always behave in a foreseen manner. In his attempt of introducing a mat...

Restless legs syndrome (RLS and also known as Willis-Ekbom disease) is a disorder that's characterized by annoying and sometimes painful sensations in the legs that are brought about by sitting or lying down. These sensations can include creeping, tingling, burning, tugging, or aching in the calves, thighs, or feet. Getting up and moving around is usually the only way to find some relief. Also,...

A significant deviation from the Debye model of rotational diffusion in the dynamics of orientational degrees of freedom in an equimolar mixture of ellipsoids of revolution and spheres is found to begin at a temperature at which the average inherent structure energy of the system starts falling with drop in temperature. We argue that this onset temperature corresponds to the emergence of the pr...

We derive generic equations for a vector field driving the evolution of flat homogeneous isotropic universe and give a comparison with a scalar filed dynamics in the cosmology. Two exact solutions are shown as examples, which can serve to describe an inflation and a slow falling down of dynamical " cosmological constant " like it is given by the scalar quintessence. An attractive feature of vec...

A 78-year-old patient presented with shortness of breath after falling down. Transthoracic echocardiogram showed an extensive thrombus in the right atrium (RA), extensive thrombosis of the inferior vena cava (IVC), and abdominal aortic aneurysm (AAA). A magnetic resonance confirmed the thrombosis of the RA extending to the IVC, which was apparently fused to the abdominal aortic aneurysm (compre...

We derive generic equations for a vector field driving the evolution of flat homogeneous isotropic universe and give a comparison with a scalar filed dynamics in the cosmology. Two exact solutions are shown as examples, which can serve to describe an inflation and a slow falling down of dynamical " cosmological constant " like it is given by the scalar quintessence. An attractive feature of vec...