Categorification of Fourier transforms, efficient computation and computing intelligence

Glazunov, Nikolaj

doi:10.1016/j.nima.2004.07.082

Cited by 1 publication

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In aviation and astronautics, transportation systems, and in other applied research, inverse problem occurs: given the trajectory x or its properties, find what forces as vector quantities should be applied to implement this trajectory. If we represent edges of such system as manifolds, and their correlations as mappings between them, we obtain the mathematical model of this system [21]. Models are various classes of manifolds and their generalizations with respective bundles on them and mappings between manifolds and bundles.…”

Section: Differential-algebraic Equationsmentioning

confidence: 99%

Differential–Algebraic Equations and Dynamic Systems on Manifolds

2016

View full text Add to dashboard Cite

The authors consider current problems of the modern theory of dynamic systems on manifolds, which are actively developing. A brief review of such trends in the theory of dynamic systems is given. The results of the algebra of dual numbers, quaternionic algebras, biquaternions (dual quaternions), and their application to the analysis of infinitesimal neighborhoods and infinitesimal deformations of manifolds (schemes) are presented. The theory of differential-algebraic equations over the field of real numbers and their dynamics, as well as elements of trajectory optimization of respective dynamic systems, are outlined. On the basis of connection in bundles, the theory of differential-algebraic equations is extended to algebraic manifolds and schemes over arbitrary fields and schemes, respectively.

show abstract

Section: Differential-algebraic Equationsmentioning

confidence: 99%