Like Hilbert he characterized the structure of a two-dimensional manifold F by a system of neighbourhoods Up, each of which, U ⊂ F would contain p and be supplemented by a bijective map ψ: U→ V∈ ℂ, with V an open disk with center ψ(p). The totality of neighbourhoods was ...
The great advantage of the axiomatic method is that it makes totally explicit just what our initial assumptions are. It is sometimes said that “mathematics can be embedded in set theory.” This means that mathematical objects (such as numbers and differentiable functions) can be defined to be ...
Methodology of this study borrows many ideas of contemporary French philosopher Alain Badiou, who thinks that mathematical results are not solely mathematical, but might point to the ontological structure of realityEgorychev,IlyaProceedings of Petrozavodsk State University Social Scienc...
constrained structure and motionmaximum likelihood estimatorWe define the very rich language of composed conditionals on a three-valued logic and use this language as the communication tool between man and machine. Communication takes place for three reasons: knowledge acquisition, query, and response. ...
The Combinatorial System Generator, F:G(X), (read as "The attributive functor, F, maps the logic generator, G(X), into world theory" or "The world is an attributive combinatorial function of logic"). II. The Hamiltonian System Operating Theorem, h (an theory‐category structure). III. ...
An important achievement is the definition of the natural numbers and their fulfillment of the Peano axioms. Also the concept of recursion is discussed. Although the presentation is axiomatic the results shall match the mathematical usage. Therefore the set theoretic axiom system of A. P. ...
This work is concerned with the geometrical structure of flat spacetimes, especially Minkowski spacetime. In Part 1 we develop synthetic or axiomatic repre... BH Mundy 被引量: 1发表: 1982年 Generalized axiomatic scale-space theory We have also described how a different time-causal and time-rec...
The framework of locally covariant field theory is a plausible system of axioms for a generally covariant field theory. Before we enter the problem of constructing examples of 4 quantum field theory satisfying these axioms, we describe the corresponding structure in classical field theory (Sect. 4)...
Proofs of theorems are sketched in some forms being accessible both for researchers on mathematical physics and phenomenology of particle physics. We prefer the so-called abstract geometric method for proofs and emphasize the possibility of alternative N-adapted variational approaches. Certain technical de...
However, it should be stressed that several mathematical and physical problems will not be addressed in this paper. Among them, let us mention the mathematical structure of the distribution-valued f...G. Puccini and H. Vucetich, “Steps towards the axiomatic foundations of the relativistic ...