Abstract The axiom system ACP of [10] was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics [7, 15] rather than weak bisimulation semantics [11, 20]. The version using relative timing is discussed extensively, versions using absolute and parametric timing are presented in brief. A term model and a graph model are pres...

We present a reorganisation of popular theories of “reasoning with relational flavour”, including allegories, Kleene algebras, and Dedekind categories, into an relatively symmetric picture using ordered categories as common base and defining converse independently from joins and meets. As an example application, we use this to regroup results about formalisation of algebraic graph rewriting and...

We develop mathematical switch-level models for static combinational CMOS networks. In contrast to other dVdihbk MOS models and theories, our models capture design principles that are special to CMOS, such as the use of transmission gates. First we study networks consisting of cascade connections of CMOS cells realizing negative functions. We then extend this model to incorporate transmission g...

Group consensus problems of multi-agent systems in directed networks with fixed and switching topologies are addressed in this note. Under mild assumptions, necessary and/or sufficient conditions of group consensus are derived, based on algebraic graph theories and matrix theories. For the fixed topology case, the group consensus can be guaranteed by the Hurwitz stability of coefficient matrice...

a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

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in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy’s equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. T...

This paper is aimed at examining the polarization and hierarchies arising in Europe in terms of air transport passengers’ flows and the possible levels of interaction and integration between nodes. In the paper we use Eurostat database of air passengers’ flows between the 27 EU countries as well as between city pairs. In this paper graph theory and network analysis are used, as well as a use of...

We will define the notions of abstract theorem-proving graph, abstract theorem-proving problem g and search strategy E for g. These concepts generalize the usual tree (or graph) searching problem and admit Hart, Nilsson and Raphael (1968) and Pohl (1969) theories of heuristic search. In particular the admissibility and optimality theorems of Hart, Nilsson and Raphael generalize for the classes ...