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'''''Davenport–Schinzel Sequences and Their Geometric Applications''''' is a book in [[discrete geometry]]. It was written by [[M ...rt]] and [[Andrzej Schinzel]], who applied them to certain problems in the theory of [[differential equation]]s.{{r|ph}} They are finite sequences of symbols ...

...d to have been used as early as 1827 by [[August Ferdinand Möbius]] in his theory of [[homogeneous coordinates]].<ref>D. Pedoe ''Notes on the History of Geom The theory of mass points is defined according to the following definitions:<ref>H. S. ...

...of [[mathematics]], is the study of algebraic structures on the [[homology theory|homology]] of [[free loop space]]s. The field was started by {{harvs|txt|fi ...ke their product <math>x\times y \in H_{p+q}(M\times M)</math> and make it transversal to the diagonal <math>M\hookrightarrow M\times M</math>. The intersection i ...

...int sets|disjoint]]. It is an extension of the notion of [[Matching (graph theory)|matching in a graph]].<ref name="lp">{{Cite Lovasz Plummer}}</ref>{{rp|466 ...E'')}}, where {{mvar|V}} is a [[Set (mathematics)|set]] of [[Vertex (graph theory)|vertices]] and {{mvar|E}} is a set of [[subset]]s of {{mvar|V}} called ''h ...

...cetime|space-time]]. Gravitation theory is formulated as [[classical field theory]] on [[general covariant transformations|natural bundles]] over a world man ...tions are [[gauge symmetry (mathematics)|gauge symmetries]] of gravitation theory on a world manifold. ...

...6|doi=10.1215/s0012-7094-58-02537-7}}</ref> studied these games from a non-geometric viewpoint. Jane W. DiPaola studied the minimum blocking coalitions in all t ...transversal (combinatorics)|transversal]]" is used, but in some contexts a transversal of <math>H</math> is a subset <math>T</math> of <math>X</math> that meets e ...

...s not exist (if the lines are [[parallel lines|parallel]]). Other types of geometric intersection include: Determination of the intersection of [[flat (geometry)|flats]] – linear geometric objects embedded in a higher-[[dimension]]al space – is a simple task of [[ ...

...ed to construct new [[homology theories]]. For example, they provide a new geometric model for ordinary homology. The concept of stratifolds was invented by [[M ...ifferential topology of stratifolds to show that these define a [[homology theory]]. Clearly, <math>SH_k(\text{point}) = 0</math> for <math>k > 0</math> sinc ...

...u/bitstream/1840.4/2172/1/ISMS_1963_378.pdf}}</ref> in connection with the theory of [[translation plane]]s. In these papers, it is shown that a spread of <m ...three elements of <math>R</math>, called a ''[[Transversal (combinatorics)|transversal]]'', meets every element of <math>R</math> ...

...on <math>T M</math> admit a compatible metric, and therefore, [[Chern–Weil theory]] cannot be used in general to write down the Euler class in terms of the c ...at counts the Euler number of a flat vector bundle in terms of vertices of transversal open coverings.<ref>{{cite arXiv|eprint=1603.07248v3|class=math.DG|first1=H ...

...celestial mechanics, dynamical systems, Hamiltonian dynamics, and ergodic theory. In his dissertation, he solved the [[Painlevé conjecture]], a long-standin ...ce of invariant tori in volume-preserving diffeomorphisms |journal=Ergodic Theory and Dynamical Systems |volume=12 |issue=3 |year=1992 |pages=621–631 |doi=10 ...

*[[Knot (mathematics)|Knots]] and [[Link (knot theory)|links]] in [[knot theory]], when [[Trivial knot|nontrivial]], always have quadrisecants, and the exi ...ontrivial]] [[Tame knot|tame]] [[Knot (mathematics)|knot]] or [[Link (knot theory)|link]] has a quadrisecant. Originally established in the case of knotted [ ...

...the graph's [[Vertex (graph theory)|vertices]] into two [[Complement (set theory)|complementary set]]s {{mvar|S}} and {{mvar|T}}, such that the number of ed ...where each edge is associated with a real number, its [[Glossary of graph theory#weighted graph|weight]], and the objective is to maximize the total weight ...

...so on came with fixed embeddings into projective space, whereas in scheme theory they are more often considered as abstract varieties. For example, a [[Vero ...were often considered only up to birational isomorphism, whereas in scheme theory they are usually considered up to biregular isomorphism. {{harv|Semple|Roth ...

...oved for [[convex preferences]] to non-convex preferences. In optimization theory, it can be used to explain the successful solution of minimization problems The definition of a convex&nbsp;set implies that the ''[[intersection (set theory)|intersection]]'' of two convex&nbsp;sets is a convex set. More generally, ...