The interface separating a liquid from its vapor phase is diffuse; the composition varies continuously one to other over finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al., Europhys. Lett. 102, 44001 (2013)] identified diffuse between jammed and unjammed disks. In both cases, thickness of diverges as critical transition approached. We investigate g...

Let a be an l-sequence generated by a feedback-with-carry shift register with connection integer q = pe, where p is an odd prime and e 1. Goresky and Klapper conjectured that when pe = 2 f5; 9; 11; 13g, all decimations of a are cyclically distinct. When e = 1 and p > 13, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, ...

Continuing after the previous papers of this series, attention is devoted to RR-systems having two towns (i.e., to compact 3-manifolds with spines corresponding to group presentations having two generators). An interesting kind of symmetry is noted and then used to derive some useful results. Specifically, the following theorems are proved: Theorem 1. Let tf> be a group presentation correspondi...

The convex feasibility problem, that is, finding a point in the intersection of finitely many closed convex sets in Euclidean space, arises in various areas of mathematics and physical sciences. It can be solved by the classical method of cyclic orthogonal projections, where, by projecting cyclically onto the sets, a sequence is generated that converges to a point in the intersection. In 1967, ...

A snark is a cubic cyclically 4–edge connected graph with edge chromatic number four and girth at least five. We say that a graph G is odd 2–factored if for each 2–factor F of G each cycle of F is odd. In this paper, we present a method for constructing odd 2–factored snarks. In particular, we construct two new odd 2–factored snarks that disprove a conjecture by some of the authors. Moreover, w...