Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the Mathematics of Higher Structures
77
0
0.0
(
0
)
Authors
Nils A. Baas
Ask ChatGPT about the research
No Arabic abstract
In this paper we will relate hyperstructures and the general $mathscr{H}$-principle to known mathematical structures, and also discuss how they may give rise to new mathematical structures. The main purpose is to point out new ideas and directions of investigation.
rate research
Read More
In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory of hyperstructures.
The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.
Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is currently independent of Euclidean spaces -have in the Isodimensional Discrete Mathematics (IDM) their roots in the DESs. This mathematics, which arises largely from the discretization of traditional mathematics, presents its foundations and concepts differently from the orthodox way, so at first glance it may seem that the IDM could be an exotic tool, or perhaps just a simple curiosity. However, the IDM dis-crete approaches have a great theoretical repercussion on traditional mathematics.
We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for the existence of complex structures from the almost-complex structure. It is a function, not a tensor, so it is easier to work with.
We formulate a general approach to higher concurrencies in general and neural codes in particular, and suggest how the higher order aspects may be dealt with in using topology.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
