The free rectangular band of inverse semigroups on a set

AbstractThis paper provides a model for the free rectangular band of inverse semigroups on a set and the free perfect rectangular band of inverse monoids on a set, thus solving a problem originally posed by Pastijn (“Rectangular bands of inverse semigroups”, Simon Stevin 56 (1982) 3–95). It is shown that the free rectangular band of inverse semigroups and the free perfect rectangular band of inverse monoids on X may be described as suitable expansions of the free completely simple semigroup on X. A Rees representation for the free perfect rectangular band of inverse monoids on X is also provided

Subgroups of free idempotent generated semigroups: full linear monoid

We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix monoid of n x n matrices, n>2$ over a division ring Q has maximal subgroup isomorphic to the multiplicative subgroup of Q.Comment: We hope to use similar methods to study the higher rank component

The liturgy as drama

This thesis seeks to show that the presentation of the liturgy and the presentation of dramatic performances have something in common. The liturgy is a dramatic method” of presenting the message of salvation within a gathered worshipping community. It is a drama whose scenes are set in a whole range of contexts, each of which will have a bearing on the methods and appropriateness of presentation. The motivation for preparing this thesis lies in the fact that it is too easy to stumble across ill-conceived, ill-prepared and directionless liturgies where insufficient attention has been given to the sort of detail which is required if the drama is to succeed. We shall look at a number of contexts in which the liturgy is set, among them, the cultural context, the context of folk religion, of language and music and of the physical space before moving towards making recommendations about the ways in which the dramatic impact of the liturgy can be enhanced. Throughout the thesis we shall use a number of major examples drawn largely from the worshipping life of Durham Cathedral to illustrate the points being made

Amalgams of Inverse Semigroups and C*-algebras

An amalgam of inverse semigroups [S,T,U] is full if U contains all of the idempotents of S and T. We show that for a full amalgam [S,T,U], the C*-algebra of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam of C*(S) and C*(T) over C*(U). Using this result, we describe certain amalgamated free products of C*-algebras, including finite-dimensional C*-algebras, the Toeplitz algebra, and the Toeplitz C*-algebras of graphs

The mechanism of porosity formation during solvent-mediated phase transformations

Solvent-mediated solid-solid phase transformations often result in the formation of a porous medium, which may be stable on long time scales or undergo ripening and consolidation. We have studied replace- ment processes in the KBr-KCl-H2O system using both in situ and ex situ experiments. The replacement of a KBr crystal by a K(Br,Cl) solid solution in the presence of an aqueous solution is facilitated by the gen- eration of a surprisingly stable, highly anisotropic and connected pore structure that pervades the product phase. This pore structure ensures efficient solute transport from the bulk solution to the reacting KBr and K(Br,Cl) surfaces. The compositional profile of the K(Br,Cl) solid solu- tion exhibits striking discontinuities across disc-like cavities in the product phase. Similar transformation mechanisms are probably important in con- trolling phase transformation processes and rates in a variety of natural and man-made systems.Comment: 22 pages, 7 figure

Beyond Mixing-length Theory: a step toward 321D

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear {\it beyond} the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different P\'eclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.Comment: 22 pages, 4 figures, 2 tables; significantly re-written, critique of Pasetto, et al. model added, accepted for publication by Ap