Wightman imposed axioms on polynomial algebras P(O) of smeared fields, i.e., sums of products of smeared fields in finite space-time regions O.
This approach was motivated by the operationalistic view that QFT is a statistical theory about local measurement outcomes with all the experimental information coming from measurements in finite space-time regions.
This paper develops the foundations of this notion for variables assuming values in finite spaces.
The notion of digital fundamental group was originated by Khalimsky [E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proc. IEEE Int. Conf. Syst. Man Cybernet. (1987) 227 234].
As a corollary, a refinement to Ostrowski's sufficient condition for local convergence in finite spaces is obtained, which applies to many models, e.g. in economics, ecology or game theory, where one has an interest in fixed point iterations and local stability of discrete dynamic processes.
This technique permits to transform the initial game problem, given in Banach space, to a static game given in finite dimensional space.
is a right-continuous Markov chain on the probability space taking values in finite state space, and is -dimensional independent standard Wiener process defined on the probability space, which is independent of the Markov chain.
But because of the difficulty of calculation, open domain problems are often simplified as equivalent model in the finite space in order to save time of modeling and analyzing in the computer.
Understanding the buckling behaviors of rods confined in a finite space is of paramount importance in a diversity of engineering fields.
Maurits Cornelis Escher uses a paving motif of the Poincaré disk of the hyperbolic plane in order to represent an infinite structure in a finite space.
This is as true of humans in the finite space of a planetary ecosystem as it is of gas molecules in a sealed flask.
