Results 51 to 60 of about 476,467 (270)
Applied Philosophy in Mathematics [PDF]
arXiv, 2020 We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
arxiv
Topology on cohomology of local fields
, 2015 Arithmetic duality theorems over a local field $k$ are delicate to prove if $\mathrm{char} k > 0$. In this case, the proofs often exploit topologies carried by the cohomology groups $H^n(k, G)$ for commutative finite type $k$-group schemes $G$. These "\v{
Cesnavicius, Kestutis
core +1 more source
Edge‐Connectivity Between Edge‐Ends of Infinite Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In infinite graph theory, the notion of ends, first introduced by Freudenthal and Jung for locally finite graphs, plays an important role when generalizing statements from finite graphs to infinite ones. Nash‐Williams' Tree‐Packing Theorem and MacLane's Planarity Criteria are examples of results that allow a topological approach, in which ends
Leandro Aurichi, Lucas Real
wiley +1 more source
Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers
PLoS ONE, 2016 The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data.
M. Andjelković +4 more
semanticscholar +1 more source
Conformal Hypergraphs: Duality and Implications for the Upper Clique Transversal Problem
Journal of Graph Theory, EarlyView.ABSTRACT Given a hypergraph H ${\rm{ {\mathcal H} }}$, the dual hypergraph of H ${\rm{ {\mathcal H} }}$ is the hypergraph of all minimal transversals of H ${\rm{ {\mathcal H} }}$. The dual hypergraph is always Sperner, that is, no hyperedge contains another.
Endre Boros +3 more
wiley +1 more source
Universal topological representation of geometric patterns [PDF]
, 2018 We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product space of 0 and 1, in which a partition with a specific topological structure determines a character of each ...
arxiv +1 more source
Motivic homotopy theory of group scheme actions
, 2015 We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category.
Heller, Jeremiah +2 more
core +1 more source
Algebraic and Topological Tools in Linear Optimization
Notices of the American Mathematical Society, 2019 The Linear Optimization Problem This is a story about the significance of diverse viewpoints in mathematical research. I will discuss how the analysis of the linear optimization problem connects in elegant ways to algebra and topology.
J. D. Loera
semanticscholar +1 more source
Design of a Tracking Controller Based on Machine Learning
International Journal of Mechanical System Dynamics, EarlyView.ABSTRACT Tracking control of multibody systems is a challenging task requiring detailed modeling and control expertise. Especially in the case of closed‐loop mechanisms, inverse kinematics as part of the controller may become a game stopper due to the extensive calculations required for solving nonlinear equations and inverting complicated functions ...
Dieter Bestle, Sanam Hajipour
wiley +1 more source
We review the differential topology underlying the topological protection of energy band crossings in Weyl semimetals, and how they lead to the experimental signature of surface Fermi arcs.
arxiv +1 more source