The distribution of monomers along a linear polymer grafted on hard wall is modelled by determining the probability occupied vertices Dyck and ballot path models adsorbing polymers. For example, that passes through lattice site with coordinates $(\lfloor \epsilon n \rfloor,\lfloor \delta \sqrt{n}\rfloor)$ in square lattice, for $0 < 1$ $\delta\geq 0$, determined asymptotically as $n\to\infty$ t...

In a proper vertex coloring of a graph a subgraph is colorful if its vertices are colored with different colors. It is well-known that in every proper coloring of a k-chromatic graph there is a colorful path Pk on k vertices. If the graph is k-chromatic and triangle-free then in any proper coloring there is also a path Pk which is an induced subgraph. N.R. Aravind conjectured that these results...

A flow is a directed space structure on homotopy type. It already known that the underlying type of realization precubical set as equivalent to topological space. This depends non-canonical choice q-cofibrant replacement. We construct new functor from sets flows which previous one and does not depend any cofibrant replacement functor. The main tool notion natural $d$-path introduced by Raussen....

Stylistic paths give the colorful meaning of discourse; therefore they are usually used in literal text. One them, is irony. Irony a type stylistic technique that will be investigated this article. The purpose article to find out some its types. Moreover, literary works, including irony, illustrated.