A lemma of Tits establishes a connection between the simple connectivity of an incidence geometry and the universal completion of an amalgam induced by a sufficiently transitive group of automorphisms of that geometry. In the present paper, we generalize this lemma to intransitive geometries, thus opening the door for numerous applications. We treat ourselves some amalgams related to intransiti...

In this thesis we primarily consider saturated fusion systems which are of essential rank 1, i.e. which contain only one conjugacy class of essential subgroups. We prove that they all can be realized by an amalgam of two finite groups. This leads us to the application of amalgam related methods like pushing up techniques and results about FF-modules. As a first key result, in fusion systems of ...

A commutative loop is Jordan if it satisfies the identity x2(yx) = (x2y)x. Using an amalgam construction and its generalizations, we prove that a nonassociative Jordan loop of order n exists if and only if n ≥ 6 and n 6= 9. We also consider whether powers of elements in Jordan loops are well-defined, and we construct an infinite family of finite simple nonassociative Jordan loops.

Let 1 < p, q < ∞ and s, r ∈ R. It is proved that any function in the amalgam space W (H p′(R ), l∞), where p ′ is the conjugate exponent to p and H p′(R ) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space M p,q(R ), whenever r > |s|+ d.

We extend F. Holland’s definition of the space of resonant classes of functions, on the real line, to the space R(#pq) (I p, q ) of resonant classes of measures, on locally compact abelian groups. We characterize this space in terms of transformable measures and establish a realatlonship between R(pq) and the set of positive definite functions for amalgam spaces. As a consequence we answer the ...

We study inverse semigroup amalgams [S1, S2;U ], where S1 and S2 are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S1 and S2. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the R-classes of S1 ∗U S2 to state sufficient conditions for the amalgamated free products S1 ∗...

Patient safety has been an under-recognised and under-researched concept until recently. It is now high on the healthcare quality agenda in many countries of the world including the UK. The recognition that human error is inevitable in a highly complex and technical field like medicine is a first step in promoting greater awareness of the importance of systems failure in the causation of accide...

X-ray micro-analysis was used to determine the elemental composition of the tooth, amalgam, and base material of ten aged, amalgam-restored, posterior teeth after they had been fractured across the amalgam-tooth interface. Subsequently, replicas were used to remove marginal seal material from each interface for examination by x-ray micro-analysis. The results show that P and Sn were present in ...

A finite group amalgam of index (k,m) is a 5-tuple (L,φ,B, ψ,R) where L, B, and R are finite groups, φ : B → L and ψ : B → R are monomorphisms, and the indices of B and B in L and R are k and m, respectively. The amalgam is faithful if N ≤ B, N C L, and N C R implies N = 1. It is well known that the finite faithful amalgams of index (k, 2) are in a bijective correspondence with (the conjugacy c...

This paper investigates an inference (which we call cessation) that no state of the kind described currently holds. We propose that this inference occurs in a sentence φ when: (a) φ has stative verb in the past tense and (b) there is a present tense alternative to φ that shares a common reference time concept and is not vacuously false. We show how (a) and (b) correlate with the availability of...