We define Ratner–Marklof–Strömbergsson measures (following Marklof and Strömbergsson (2014)). These are probability supported on cut-and-project sets in $\smash{\mathbb{R}^d}$ $(d \geq 2)$ which invariant ergodic for the action of groups $\operatorname{ASL}\_d(\mathbb{R})$ or $\operatorname{SL}\_d(\mathbb{R})$. classify that can arise terms algebraic homogeneous dynamics. Using classification, ...

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what will call Cut-for-Formulas Cut-for-Sets Theorem: for a set F and binary relation ⊢ on P ( ) $\mathcal {P}(F)$ , if finitary, monotonic, satisfies cut formulas, then it also sets. deduce CF/CS from Ultrafilter twice; each proof uses different order-theoretic variant of Tukey-Teichmüller...

Let G = (V; E) be a graph and T V be a node set. We call an edge set S a Steiner tree with respect to T if S connects all pairs of nodes in T. In this paper we address the following problem, which we call the weighted Steiner tree packing problem. Given a graph G = (V; E) with edge weights w e , edge capacities a Steiner tree with respect to T k , at most c e of these edge sets use edge e for e...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...

A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edge-cuts of fullerene graphs of sizes up to 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerated and non-degenerated cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-de...

In this paper, a new algorithm for edge detection based on fuzzyconcept is suggested. The proposed approach defines dynamic membershipfunctions for different groups of pixels in a 3 by 3 neighborhood of the centralpixel. Then, fuzzy distance and -cut theory are applied to detect the edgemap by following a simple heuristic thresholding rule to produce a thin edgeimage. A large number of experime...