Abstract
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Highlights
Interdisciplinary studies represent one of main trends in the modern science
The point is that experts in a particular topic may be not so deep involved in related areas outside their competence For example, we observe very active development of mathematical modelings in the biology and ecology
The use of such models by experts from these disciplines is essentially restricted by the lack of mathematical techniques
Summary
Interdisciplinary studies represent one of main trends in the modern science. Several essential problems in the science and its applications need combination and interaction of methods and ideas from different areas of our knowledge. Some general analytic and geometric considerations for models on the cone of Radon measures have been carried out in [7, 11] Note that this approach differs from the so-called marked configuration spaces considered in [1, 12]. Tsilevich, Vershik and Yor [18] used this as a starting point to further analyze so-called Gamma processes As seen here, these measures supported on the cone K(Rd) appear naturally without any a priori restriction of the spaces or aspects of modeling. These measures supported on the cone K(Rd) appear naturally without any a priori restriction of the spaces or aspects of modeling There is another mathematical explanation why it makes sense to consider K(Rd). These configurations can be identified with objects in the cone, i.e. there exists a one-to-one correspondence between the so-called Plato space Π(R∗+ ×Rd) and the cone K(Rd) [4]
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