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 ...

Dentistry and society have long recognized the benefits of using silver-based amalgams to restore and maintain the dental health of patients. However, recent studies by health and environment experts have shown that mercury is of great concern when it enters the biosphere as a contaminant. A rational approach to pollution prevention is mandatory. This article explains the relationship between m...

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...