The existence of relational products in categories of relations is strongly connected with the representability of that category. In this paper we propose a canonical weakening of the notion of a relational product. Unlike the strong version any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we investigate the categori...

The problematic of automatically searching series of broad patterns in technical documents is studied. Such series can be assumed to ordered information useful for the understanding of documents. The proposed methodology is able to extract successive patterns of different natures without a priori information about the shape. To make this, we consider the spatial location of triplets of similar ...

For an interger l > 1, the l-edge-connectivity λl(G) of G is defined to be the smallest number of edges whose removal leaves a graph with at least l components, if |V (G)| ≥ l; and λl(G) = |V (G)| if |V (G)| ≤ l. A graph G is (k, l)-edge-connected if the l-edge-connectivity of G is at least k. A sufficient and necessary condition for G to be minimally (k, k − 1)-edgeconnected is obtained in the...

Wepropose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set ...

We study an extension of the DeGroot model where part of the players may be rebels. The updating rule for rebels is quite different with that of normal players (which are referred to as conformists): at each step a rebel first takes the opposite value of the weighted average of her neighbors’ opinions, i.e. 1 minus that average (the opinion space is assumed to be [0,1] as usual), and then updat...

A simplified and shortened proof is presented for a theorem of Jordán and Szigeti [2] on detachments preserving local edge-connectivity.

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

We prove that for a finitely generated infinite nilpotent group G with a first order structure (G, ·, . . .), the connected component G of a sufficiently saturated extension G of G exists and equals ⋂ n∈N {g : g ∈ G}. We construct a first order expansion of Z by a predicate (Z,+, P ) such that the type-connected component Z ∅ is strictly smaller than Z. We generalize this to finitely generated ...