Title and Abstract : The title and abstract is well formulated and indeed representative for the rest of the full text paper.
Following von Neumann's program, Kenneth Arrow and Gérard Debreu formulated abstract models of economic equilibria using convex sets and fixed point theory.
The modern, more abstract treatment, first formulated by Giuseppe Peano in 1888, encompasses more general objects than Euclidean space, but much of the theory can be seen as an extension of classical geometric ideas like lines, planes and their higher-dimensional analogs.
The missions of the energy cooperatives have many similarities when formulated in abstract statutory terms.
But Frege also explicitly formulated the abstract notion of a quantifier as a second-order relation, or, as he called it, a second level concept ("Begriff zweiter Stufe").
Although Proposition 2 is fairly abstract, the sufficient condition formulated there can readily be verified, as soon as a specific market model is adopted (see, for instance, Bielecki and Rutkowski (2015) and Nie and Rutkowski (2015,2016a,2017 (published online on 18 April 2017)).
A parsimonious model of such a system might have been formulated with abstract negative and positive feedback differentially influencing a simple kinetic proofreading scheme.
The network alignment problem in its abstract form can be formulated as an optimization problem with the goal of identifying an optimal mapping between the nodes of the input networks, which maximizes both sequence similarity of aligned proteins and conservation of their underlying interactions.
If formulated differently, their abstract provisions could subject the inequalities and indignities of late capitalism to withering attack.
Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980.
Then (3.5) can be formulated into the abstract form (1.1).
