Every ring has both left and right modules. In the theory of nearrings, only right modules are usually considered for left nearrings. The purpose of this report is to promote the study of an alternative type of nearring module. For left nearrings, these unusual modules are left modules. There are three reasons for studying left modules for left nearrings. These unusual nearring modules add an element of symmetry to the theory of nearrings. At the same time, comparing left and right modules of a left nearring illustrates how the theory of nearrings is distinct from ring theory. Finally, with two types of nearring modules, it is possible to carry over to nearring theory more concepts from ring theory; for example, duals of modules and bimodules. This report is an attempt to show that these reasons are valid. The first chapter is devoted to producing a well-reasoned definition for the unusual type of nearring module. It begins with a careful presentation of background material on nearrings, rings, and ring modules. This material is used to motivate the definitions for nearring modules, which are introduced in the third section. The second chapter is concerned with showing that the unusual type of nearring module can fit into the theory of nearrings. In the first section, several papers relevant to the study of these modules are summarized. The work of A. Frohlich on free additions is of primary importance. General construction methods for both types of nearring modules are then described. Finally, some general properties of left modules of left nearrings are examined. Examples of left modules for left nearrings are presented in the third chapter. First, the general constructions of the second chapter are applied in some particular cases. This leads naturally to structures that are analogous to bimodules and structures analogous to dual modules for ring modules. Here, free additions have a special role. Several dual nearring modules are examined in detail. The information needed to construct many more examples of nearring modules of the unusual type is also presented. Only small cyclic groups are used for these examples.

by Lam Che Pang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 85-87). / Chapter 1 --- Preliminaries --- p.2 / Chapter 1.1 --- Introduction --- p.2 / Chapter 1.2 --- Ideals of Γ-nearrings --- p.6 / Chapter 1.3 --- Pierce-decomposition theorem --- p.14 / Chapter 1.4 --- Left SΓ and Right RΓ-bimodules --- p.19 / Chapter 2 --- D.G. Γ-nearrings and its modules --- p.25 / Chapter 2.1 --- Distributively generated Γ-nearrings --- p.25 / Chapter 3 --- Near-rings and Automata --- p.40 / Chapter 3.1 --- Monoids of semiautomaton and automaton --- p.40 / Chapter 4 --- Derivation in Γ-nearrings --- p.66 / Chapter 4.1 --- Derivation in Γ-nearrings --- p.66 / Chapter 4.2 --- Abelian conditions --- p.70 / Chapter 4.3 --- Unitary Γ-nearrings --- p.76 / Chapter 4.4 --- Decomposition of right Rr-modules --- p.81

Prior to 1990, the only well known ideal-hereditary Kurosh-Amitsur radicals in the variety of zero-symmetric near-rings were the Jacobson type radicals Iv(N) , where ∨∈{2,3} and the Brown-McCoy radical. In 1990, Booth, Groenewald and Veldsman introduced the concept of an equiprime near-ring which leads to an ideal-hereditary Kurosh-Amitsur radical in N∘. The concept of an equiprime near-ring generalizes the concept of a prime ring to near-rings. Although the search for more ideal-hereditary radicals of near-rings was apparently the original motivation for the introduction of equiprime near-rings, it became clear that these near-rings are interesting in their own right. It is our aim in this treatise to give an exposition of the many interesting properties of equiprime near-rings. We begin with a brief reminder of near-ring rudiments; giving basic definitions and elementary results which are necessary for understanding and development of subsequent chapters. With the basics out of the way, our main task begins with a consideration of equiprime, strongly and completely equiprime left ideals. It is noted that any zero-symmetric near-ring can be embedded in an equiprime near-ring. Moreover, the class of equiprime near-rings is shown to be hereditary. Open questions arising out of the study of equiprime near-rings are highlighted along the way. In Chapter 3 we consider well known examples of near-rings and determine when such near-rings are equiprime. This provides more insight into the nature of equiprime near-rings and is a fertile ground for the birth of examples and counterexamples which may be used to close or solve some open question within the literature. We also prove some results which generalize some results of Booth and Hall [10] and Veldsman [29]. These results have not been previously presented elsewhere to the best of our knowledge. vii In Chapter 4, the equiprime near-rings are shown to yield an ideal-hereditary radical in N∘. It is shown that a special radical theory can be built on the equiprime nearrings in much the same way prime rings are used in ring theory to define special radical classes of rings.

In view of the facts that the definition of a ring led to the definition of a near- ring, the definition of a ring module led to the definition of a near-ring module, prime rings resulted in investigations with respect to primeness in near-rings, one is naturally inclined to attempt to define the notion of a group near-ring seeing that the group ring had already been defined and investigated into by, interalia, Groenewald in [7] . However, in trying to define the group near-ring along the same lines as the group ring was defined, it was found that the resulting multiplication was, in general, not associative in the near-ring case due to the lack of one distributive property. In 1976, Meldrum [19] achieved success in defining the group near-ring. How- ever, in his definition, only distributively generated near-rings were considered and the distributive generators played a vital role in the construction. In 1989, Le Riche, Meldrum and van der Walt [17], adopted a similar approach to that which led to a successful and fruitful definition of matrix near-rings, and defined the group near-ring in a more general sense. In particular, they defined R[G], the group near-ring of a group G over a near-ring R, as a subnear-ring of M(RG), the near-ring of all mappings of the group RG into itself. More recently, Groenewald and Lee [14], further generalised the definition of R[G] to R[S : M], the generalised semigroup near-ring of a semigroup S over any faithful R-module M. Again, the natural thing to do would be to extend the results obtained for R[G] to R[S : M], and this they achieved with much success.

Near-field thermophotovoltaic (NFTPV) devices have received great attention lately as attractive energy harvesting systems, whereby a heated thermal emitter exchanges super-Planckian near-field radiation with a photovoltaic (PV) cell to generate electricity. This work describes the advancement of NFTPV technology through both simulations of next-generation devices, and experimental research addressing the technical challenges faced by NFTVPs, including nanostructured material properties, and large-area near-field heat transfer. The first part of this work seeks to improve the performance of a possible NFTPV device by using a periodic tungsten grating as the thermal emission source. The effects on the electrical power generation and the conversion efficiency are investigated via simulations with different grating geometries. It is found that using the selected grating geometry the power output and efficiency could be increased by 40% and 6%, respectively, over a flat tungsten emitter. The reasoning behind the enhancement is attributed to a plasmonic resonance that shifts towards lower frequencies at large wavenumbers. Extensive experimental research is undertaken to investigate the technical challenges in NFTPVs. The optical properties of thin tungsten films, which may serve as an emitter material, are extracted through spectroscopic measurements, and are found to be significantly different from reported bulk values due to a wide range of crystal structures that are present in sputtered films. A heat transfer experiment is designed and built to measure near-field radiation between two doped-silicon slabs separated by a submicron vacuum gap. The details of this system and the sample fabrication show a robust and straightforward method of measuring large-area near-field radiative heat transfer at distances between 200 nm and 800 nm. The results of this experiment show the largest energy throughput of submicron near-field heat transfer to date, and serve to address technical challenges behind practical near-field thermophotovoltaic technology.

The family of planar nearrings enjoys quite a few geometric and combinatoric properties. Circular planar nearrings are members of this family which have the character of circles of the complex plane. On the other hand, they also have some properties which one may not find among the circles of the complex plane. In this dissertation, we first review the definition and characterization of a planar nearring, and some various ways of constructing planar nearrings, as well as various ways of constructing BIBD's from a planar nearring. Circularity of a planar nearring is then introduced, and examples of circularity planar nearrings are given. Then, some nonisomorphic BIBD's arising from the same additive group of a planar nearring are examined. To provide examples of nonabelian planar nearrings, the structures of Frobenius groups with kernel of order 64 are completely determined and described. On the other hand, examples of Ferrero pairs (N, Φ)'s with nonabelian Φ, which produce circular planar nearrings, are provided. Finally, we study the structures of circular planar nearrings generated from the finite prime fields from geometric and combinatoric points of view. This study is then carried back to the complex plane. In turn, it gives a good reason for calling a block from a circular planar nearring a "circle."

No description available.

When any method of surface wave testing that involves Rayleigh waves is performed, one important assumption is that plane Rayleigh waves are being measured. In the forward modeling or inversion procedure that is used to analyze the field dispersion curve to determine the field V[subscript s] profile, the analysis is based on the wave field consisting of plane Rayleigh waves. Therefore, field dispersion curves that contain near-field data could adversely distort the field V[subscript s] profile. To minimize the influence of near-field effects, several criteria have been recommended in the past. However, most of the criteria were based on empirical equations that implicitly assumed zones of influence, or numerical simulations. There is a lack of experimental investigation, particularly full-scale field investigations. Even, the numerical solutions have been based on simple soil profiles without significant velocity contrasts between soil layers and/or varying thicknesses of soil layers which can significantly influence near-field effects. Data from full-scale field test using the Spectral-Analysis-of-Surface-Waves (SASW) method was used in this thesis research. SASW tests performed at two stages in the construction of a deep, 90-ft thick backfill were studied. The V[subscript s] profiles were normally dispersive, with a substantial increase in the velocity of the layer beneath the backfill. The study shows the adverse distortions that can occur in the field dispersion curve from near-field effects when the spacing of the receiver pair is: (1) above the zone of rapidly increasing V[subscript s] near the surface and (2) less than the depth to the stiffer layer in deeper measurements. Other factors that affect the results are discussed and recommendations are presented to minimize the introduction of near-field effects, at least in these relatively simple V[subscript s] profiles. / text

No description available.

No description available.