A notion of open bisimulation is formulated for the spi calculus, an extension of the π-calculus with cryptographic primitives. This notion of open bisimulation is based on the so-called hedged bisimulation, due to Borgström and Nestmann. Open bisimulation is shown to be sound with respect to hedged bisimulation, and futher, open bisimilarity is shown to be a congruence relation on finite spi p...

By calculating the Fermat limit of certain q–Fermat functions, we get explicit surgery formulae for the second and third Ohtsuki invariants for homology 3–spheres. The surgery formula of the second Ohtsuki invariant λ2 , combined with an argument using the general theory of finite type invariants of homology 3–spheres, leads to a congruence relation between the first and second Ohtsuki invarian...

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform π0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of π0 and other automorphic forms. We a...

Each Gr-functor of the type (φ, f) of a Gr-category of the type (Π, C) has the obstruction be an element k ∈ H(Π, C). When this obstruction vanishes, there exists a bijection between congruence classes of Gr-functors of the type (φ, f) and the cohomology group H(Π,C). Then the relation of Gr-category theory and the group extension problem can be established and used to prove that each Gr-catego...

This paper comments on nine aspects of the Region Connection Calculus (the RCC theory) with conclusions as follows: (1) regions in the RCC theory shall not be points; (2) the identical relation is a deviation from its classic usage; (3) the ι operator is un-determinate; (4) it is unclear about the notion of region in the theory; (5) atomic regions have zero thickness, instead of non-zero thickn...

9 The theory of chi processes with the mismatch operator is studied. Four congruence relations are investigated. These are late open congruence, early open congruence, ground congruence and 11 barbed congruence. The late and early open congruence relations are the chi calculus counterparts of the weak late and early congruence relations of pi calculus. Both turn out to be special cases 13 of th...

The aim of this paper is to study the actions of the groups on lattices and to give some connections between the structure of a group and the structure of its subgroup lattice. Moreover, we shall introduce the concept of direct ∨-sum of G-sublattices and we shall present a generalization of a result about finite nilpotent groups. 1 Preliminaries Let (G, ·, e) be a monoid and L be a G–set (relat...

We study the resource calculus, an extension of the λ-calculus allowing to model resource consumption. We achieve an internal separation result, in analogy with Böhm’s theorem of λ-calculus. We define an equivalence relation on the terms, which we prove to be the maximal non-trivial congruence on normalizable terms respecting β-reduction. It is significant that this equivalence extends the usua...

In this paper, we focus on Dyck paths with peaks and valleys, avoiding an arbitrary set of heights. The generating functions of such types of Dyck paths can be represented by continued fractions. We also discuss a special case that requires all peak and valley heights to avoid congruence classes modulo k. We study the shift equivalence on sequences, which in turn induces an equivalence relation...

legg-calvé-perthes disease (lcpd) is an idiopathic osteonecrosis of the femoral head with variable complications and resultant deformity of the femoral head and osteoarthritis. suggested risk factors are acetabular retroversion, obesity, latitude, hyperactivity, and coagulopathy. the most commonly applied classification is based on radiolucency in the lateral pillar of the femoral head, which i...