Let X be a compact metric space and $\mathcal {M}_{X}$ be the set of isometry
classes of compact metric spaces Y such that the Lipschitz distance d L (X,Y) is
finite. We show that $(\mathcal {M}_{X}, d_{L})$ is not separable when X is a
closed interval, or an infinite union of shrinking closed intervals.... hiện toàn bộ
We analyze the Hunter vs. Rabbit game on a graph, which is a model of
communication in adhoc mobile networks. Let G be a cycle graph with N nodes. The
hunter can move from a vertex to a vertex along an edge. The rabbit can jump
from any vertex to any vertex on the graph. We formalize the game using the
random walk framework. The strategy of the rabbit is formalized using a one
dimensional random w... hiện toàn bộ
Derivatives and integrals of non-integer orders have a wide application to
describe complex properties of physical systems and media including nonlocality
of power-law type and long-term memory. We suggest an extension of the standard
variational principle for fractional nonlocal media with power-law type
nonlocality that is described by the Riesz-type derivatives of non-integer
orders. As example... hiện toàn bộ
In the literature, it has been hypothesized that the solar wind released by the
Sun affects the Earth as a trigger to cause earthquakes. This hypothesis is on
the basis of the observation that the frequency of earthquakes rises at the
period of solar minimum. In recent years, various physical measurements on the
solar wind like velocity and temperature etc. became available. With these data,
we fo... hiện toàn bộ
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