Ecologists have proposed several incompatible definitions of ecological stability. Emulating physicists, mathematical ecologists commonly define it as Lyapunov stability. This formalizes the problematic concept by integrating it into a well-developed mathematical theory. The formalization also seems to capture the intuition that ecological stability depends on how ecological systems respond to ...

In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward extension of the real-valued situation. We apply this definition to introduce a stochastic integral with respect to cylindrical Wiener processes. Again, this defin...

We dwell on how a definition of a theoretical concept of an operating system, suitable to be incorporated in a mathematical theory of operating systems, could look like. This is considered a valuable preparation for the development of a mathematical theory of operating systems .

The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise mathematical definition exists. In this paper, we adopt an axiomatic approach to the problem, and attempt to produce a satisfactory measure.

This is a thesis about the mathematical characterisation of state events in the context of dynamical hybrid models. The structure of the thesis is designed in three major aspects. The first part addresses the mathematical definition of dynamical hybrid models, respectively dynamical hybrid systems. For this purpose, the system theory of a dynamical system described by a differential algebraic e...

Since Li and Yorke first gave the definition of chaos by using strict mathematical language in 1975 [1], the research on chaos has greatly influenced modern science, not just natural sciences but also several social sciences, such as economics, sociology, and philosophy. The theory of chaos convinced scientists that a simple definite system can produce complicated features and a complex system ...

In recent years physicists have been deeply interested in studying the behavior of complex systems. The result of this effort has been a conceptual revolution, a paradigmatic shift that has far reaching consequences for the very definition of physics. In the nutshell, physics is an experimental science in which theoretical predictions are compared to experiments. It differs from other sciences ...

The discussion in this paper gives several theorems and lemmas on the Sums of Squares consecutive Carol Numbers. These are proved by using definition carol numbers mathematical induction method. Here matrix form recursive sum squares is also given. properties derived.

We extend the scheme of quantum teleportation by walks introduced Wang et al. (2017). First, we introduce mathematical definition accomplishment this extended scheme. Secondly, show a useful necessary and sufficient condition that is accomplished rigorously. Our result classifies parameters setting for teleportation.

In earlier work, we had presented a definition of software fault as being any feature of a program that admits a substitution that would make the program more-correct. This definition requires, in turn, that we define the concept of relative correctness, i.e., what it means for a program to be more-correct than another with respect to a given specification. In this paper we broaden our earlier ...