The cardiac electrical field is important not only because of its diagnostic significance, but also as a biological and biophysical phenomenon. As such, it has become a research target of biologists, biophysicists and biomathematicians. It has also been an impetus for constructing more and more sophisticated measuring devices. Criteria for the diagnostic evaluation of body surface potential maps have often been derived from clinical studies based on a restricted number of cases. Further clinical research is therefore a conditio sine qua non for the acceptance of mapping as a routine diagnostic procedure. In the future, body surface potential distributions will be used as the input for computer simulation of potential distribution and activation chronograms on the geometric surface closely encompassing the heart. In such a way, electrocardiographic signals will be interpreted in terms of activation and repolarization sequences on the cardiac surface.
In this paper we extend the notion of $n$-weak amenability of a Banach algebra $\mathcal A$ when $n\in \mathbb{N}$. Technical calculations show that when $\mathcal A$ is Arens regular or an ideal in $\mathcal A^{**}$, then $\mathcal A^*$ is an $\mathcal A^{(2n)}$-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of $n$-weak amenability to $n \in \mathbb{Z}$.
In this paper I discuss two questions on p-Laplacian type operators: I characterize sets that are removable for Hölder continuous solutions and then discuss the problem of existence and uniqueness of solutions to−div(|∇u| p−2∇u) = µ with zero boundary values; here µ is a Radon measure. The joining link between the problems is the use of equations involving measures.
The requirements on transportation systeins concern not only the quantitative and qualitative aspects of transportation activities, but also still more aspects of their reliability and safety. This concerns not only the transported subjects or goods, but also environment.
The losses caused by failures of transportation activities reach even now a very high level and, if they are not limited by systematic research and preventive activity, they will reach a quite tremendous level soon.
However, practically all the contemporary transportation vehicles, trains, ships and planes and also all the transportation systems need, for their proper operation, interaction with human beings who drive them, control them or use them and maintain them.
In spite of the fact that a significant progress was made in recent years as concerns the transportation systems automation; the fully automatic transportation system in use is still for-seen in considerably far future.
Analyzing the reliability and safety of transportation, one finds that the activity of human being is the weakest point. The technical reliability of almost all transportation tools hais improved quite a lot in recent years; however, the human subject interacting with them has not changed too much, as concerns his/her reliability and safety of the respective necessary interaction.
Therefore there is an urgent necessity to improve it, and possibilities how to increase it will stay more and more in the focus of our interest.
In this contribution, the overview of the related problems is being made and open problems for further research in this area are discussed.