Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Photonic and Device Design Principles for Ultrahigh-Efficiency (>50%), Spectrum-Splitting Photovoltaics

The sun has the potential to power the Earth's total energy needs, but electricity from solar power still constitutes an extremely small fraction of our power generation because of its high cost relative to traditional energy sources. Therefore, the cost of solar must be reduced to realize a more sustainable future. This can be achieved by significantly increasing the efficiency of modules that convert solar radiation to electricity. In this thesis, we consider several strategies to improve the device and photonic design of solar modules to achieve record, ultrahigh (> 50%) solar module efficiencies. First, we investigate the potential of a new passivation treatment, trioctylphosphine sulfide, to increase the performance of small GaAs solar cells for cheaper and more durable modules. We show that small cells (mm2), which currently have a significant efficiency decrease (~ 5%) compared to larger cells (cm2) because small cells have a higher fraction of recombination-active surface from the sidewalls, can achieve significantly higher efficiencies with effective passivation of the sidewalls. We experimentally validate the passivation qualities of treatment by trioctylphosphine sulfide (TOP:S) through four independent studies and show that this facile treatment can enable efficient small devices. Then, we discuss our efforts toward the design and prototyping of a spectrum-splitting module that employs optical elements to divide the incident spectrum into different color bands, which allows for higher efficiencies than traditional methods. We present a design, the polyhedral specular reflector, that has the potential for > 50% module efficiencies even with realistic losses from combined optics, cell, and electrical models. Prototyping efforts of one of these designs using glass concentrators yields an optical module whose combined spectrum-splitting and concentration should correspond to a record module efficiency of 42%. Finally, we consider how the manipulation of radiatively emitted photons from subcells in multijunction architectures can be used to achieve even higher efficiencies than previously thought, inspiring both optimization of incident and radiatively emitted photons for future high efficiency designs. In this thesis work, we explore novel device and photonic designs that represent a significant departure from current solar cell manufacturing techniques and ultimately show the potential for much higher solar cell efficiencies.

Graphs and Groups

This project is a combination of graphs and group theory in which the aim is to describe the automorphism group of some specific families of graphs. Finally, an example of the application of automorphism groups in reaction graphs is shown. The project is written in english.

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

Beam splitting of low-contrast binary gratings under second Bragg angle incidence

Beam splitting of low-contrast rectangular gratings under second Bragg angle incidence is studied. The grating period is between lambda and 2 lambda. The diffraction behaviors of the three transmitted propagating orders are illustrated by analyzing the first three propagating grating modes. From a simplified modal approach, the design conditions of gratings as a high-efficiency element with most of its energy concentrated in the -2nd transmitted order (similar to 90%) and of gratings as a 1 x 2 beam splitter with a total efficiency over 90% are derived. The grating parameters for achieving exactly the splitting pattern by use of rigorous coupled-wave analysis verified the design method. A 1 x 3 beam splitter is also demonstrated. Moreover, the polarization-dependent diffraction behaviors are investigated, which suggest the possibility of designing polarization-selective elements under such a configuration. The proposed concept of using the second Bragg angle should be helpful for developing new grating-based devices. (C) 2008 Optical Society of America.

Effect of hydroxyl groups on nonradiative decay of Er3+: I-4(13/2)-> I-4(15/2) transition in zinc tellurite glasses

A series of zinc tellurite glasses of 75TeO(2)-20ZnO-(5-x)La2O3-xEr(2)O(3) (x=0.02, 0.05, and 0.1 mol%) with the different hydroxl groups were prepared by the conventional melt-quenching method. Infrared spectra were measured in order to estimate the exact content of OH- groups in samples. The observed increase of the fluorescence lifetime with the oxygen bubbling time has been related to the reduction in the OH- content concentration as evidenced by IR transmission spectra. Various nonradiative decay rates from I-4(13/2) of Er3+ with. the change of OH content were determined from the fluorescence lifetime and radiative decay rates were calculated on the basis of Judd-Ofelt theory. (c) 2005 Elsevier B.V. All rights reserved.

The effect of OH- groups on the spectroscopic properties of erbium-doped tellurite glasses

A series of five different concentration erbium-doped tellurite glasses with various hydroxl groups were prepared. Infrared spectra of glasses were measured. In order to estimate the exact content of OH- groups in samples, various absorption coefficients of the OH- vibration band were analyzed under the different oxygen bubbling times. The absorption spectra of the glasses were measured, and the Judd-Ofelt intensity parameters Omega(i) of samples with the different erbium ions concentration and OH- contents were calculated on the basis of the Judd-Ofelt theory. The peak stimulated emission cross-section of (I13/2 ->I15/2)-I-4-I-4 transition of the samples was finally calculated by using the McCumber theory. The fluorescence spectra of Er3+:I-4(13/2)->I-4(15/2) transition and the lifetime of Er3+:I-4(13/2) level of the samples were measured. The effects of OH- groups on the spectroscopic properties of Er3+ doped samples with the different concentrations were discussed. The results showed that the OH- groups had great influences on the Er3+ lifetime and the fluorescence peak intensity. The OH- group is a main influence factor of fluorescence quenching when the doping concentration of Er2O3 is smaller than 1.0 mol%, but higher after this concentration, the energy transfer of Er3+ ions turns into the main function of the fluorescence quenching. And basically, there is no influence on the other spectroscopic properties (FWHM, absorption spectra, peak stimulated emission cross section, etc.).

The influence of OH groups on laser performance in phosphate glasses

Because of the influence of OH groups in phosphate glasses on the radiation of rare-earth ions, the laser performance is degraded. The laser efficiency and the small signal gain experiment of several phosphate glass samples have been done, the concentration of OH groups in glasses was calculated from the measured absorption coefficient at 3.47 μm. It is shown that the concentration of OH groups in phosphate glasses can seriously influence the laser output characteristics, and the OH groups have worse influence on the laser amplifier than laser oscillator.