Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Lewis, Andrew D."'
Autor:
Lewis, Andrew D., Zhang, Yanlei
We study time- and parameter-dependent ordinary differential equations in the geometric setting of vector fields and their flows. Various degrees of regularities in state are considered, including Lipschitz, finitely diferentiable, smooth, and holomo
Externí odkaz:
http://arxiv.org/abs/2310.12293
Autor:
Lewis, Andrew D.
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of these bundles
Externí odkaz:
http://arxiv.org/abs/2309.11121
Autor:
Lewis, Andrew D.
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental part of mech
Externí odkaz:
http://arxiv.org/abs/2309.10471
Autor:
Lewis, Andrew D.
It is well-known that the Lebesgue integral generalises the Riemann integral. However, as is also well-known but less frequently well-explained, this generalisation alone is not the reason why the Lebesgue integral is important and needs to be a part
Externí odkaz:
http://arxiv.org/abs/2309.08908
Autor:
Lewis, Andrew D.
Explicit formulae are given for the nine possible induced matrix norms corresponding to the 1-, 2-, and $\infty$-norms for Euclidean space. The complexity of computing these norms is investigated.
Externí odkaz:
http://arxiv.org/abs/2309.07190
Autor:
Lewis, Andrew D.
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new characterisation of t
Externí odkaz:
http://arxiv.org/abs/2009.09755
Autor:
Lewis, Andrew D.
In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological embedding of a s
Externí odkaz:
http://arxiv.org/abs/2009.09757
Autor:
Gharesifard, Bahman, Lewis, Andrew D.
We investigate a few problems in the theory of linear time-invariant systems that arise when the open-loop system possesses imaginary eigenvalues. The problems are: (1) the infinite horizon, minimum energy optimal control problem; (2) the matter of d
Externí odkaz:
http://arxiv.org/abs/2003.04374