Kobayashi-Royden pseudometric vs. Lempert function

We give an example showing that the Kobayashi-Royden pseudometric for a non-taut domain is, in general, not the derivative of the Lempert function.Comment: An essential mistake has been corrected in v2. Improved example in v3. v4: minor changes according to the referee remarks (Ann. Mat. Pura Appl.

The Lempert function of the symmetrized polydisc in higher dimensions is not a distance

We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance

ACTIVE MOBILITY AS AN ALTERNATIVE FOR THE DAILY COMMUTE. ISSUES AND CHANCES FOR THE CITY OF VARNA

There is a variety of synonyms to describe the transport of people that only use their physical activity for the need to travel, and active mobility is most commonly-used. Soft mobility, human-powered mobility, active travel, active transport, active transportation and active commute are also in the list. And beyond all doubt the most popular forms are walking and cycling.The current paper explores some problems of active mobility, regarding the need for sustainable daily commute. In this point having sustainable alternatives to private motorised transport is vital for the development of settlements but often the importance of soft mobility in their connectivity with industrial areas is underestimated. Using active forms of transport, mainly bicycle and pedestrian traffic, as well as a combination of them and public transit, is a chance to make urban spaces more livable.Many areas are difficult to be accessed without personal motorised transport and for the city of Varna the adjacent resorts and industrial territories are such a striking example as their connection with the rest of the settlement is full of barriers to cycling and walking commute.In this paper, regarding its topic, the author explores some issues that people face every day in the city of Varna and searches chances for future improvement based on a good practice example from Barcelona