Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of non-strict functional programs with lazy lists. One limitation of this basic calculus is that the ordi...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

Kingston (J Comb Theory (A) 20:357–363, 1976) and Anderson (J Comb Theory (A) 23:363, 1977) show that the probability that a given contestant wins a bestof-2k+1 series of asymmetric, zero-sum, binary-outcome games is, for a large class of assignment rules, independent of which contestant is assigned the advantageous role in each component game. We design a laboratory experiment to test this hyp...

In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{...

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete classification up to isometry, and also their isometry groups. The key tool is the so-called canonical decomposition of hyperbolic manifolds.

Recently some results have been presented which show that certain kinds of deterministic descriptions and indeterministic descriptions are observationally equivalent (Werndl 2009a, Werndl 2011). These results prompt interesting philosophical questions, such as what exactly they show or whether the deterministic or indeterministic description is preferable. There is hardly any philosophical disc...