Let k be an integer and M be a closed 2-manifold with Euler characteristic χ(M) ≤ 0. We prove that each polyhedral map G on M with minimum degree δ and large number of vertices contains a k-path P , a path on k vertices, such that: (i) for δ ≥ 4 every vertex of P has, in G, degree bounded from above by 6k − 12, k ≥ 8 (It is also shown that this bound is tight for k even and that for k odd this ...

In the literature, there are a lot of methods concerning the problem of ordering the interval numbers k , ~ ] , [y,g], ... (', ') or the fuzzy ones A, B , ... (see 4, and for a n overview of methods). All of these methods can be classified a s belonging t o two different approaches. (i) Ordering t h e crisp or the fuzzy intervals using binary order relations: [ c , ~ ] 4 [ y , ~ ] , A 5 B, .......

pollen morphology of some species of the genus malus (rosaceae) was investigatedtaxonomically. all species are characteristic by tricolpate pollens. exine sculpturing is variable but is mostlystriate. however, species may differ in degree of density of ridges and their orientation. the exine patterns inm. trilobata and m. florentina are very similar and were characterized by short and very bran...

Every Boolean function on n variables can be expressed as a unique multivariate polynomial modulo p for every prime p. In this work, we study how the degree of a function in one characteristic affects its complexity in other characteristics. We establish the following general principle: functions with low degree modulo p must have high complexity in every other characteristic q. More precisely,...

The goal of this note is to reduce the existing upper bound for essential dimension central simple algebras degree 8 and exponent 2 over fields characteristic from 10 9.