Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

Obstacles to Inter-Racial Understanding: Some Clinical Implications for Mental Health Practitioners in Predominantly White Institutions

in the context of predominantly white institutions. In this paper concepts such as projection, projective identification, splitting, scapegoating, superiority and denial will be employed to illustrate why racial prejudice is a deeply-rooted collective psychological disorder that affects even educated mental health practitioners. Clinicians have an ethical responsibility to demonstrate cultural sensitivity and empathy when working with minority clients, colleagues, staff and students, to examine and root out their own prejudices, and to encourage others to do the same.

Techniques for the In Vitro Production of Queens in Stingless Bees (Apidae, Meliponini)

Considering the ecological importance of stingless bees as caretakers and pollinators of a variety of native plants makes it necessary to improve techniques which increase of colonies' number in order to preserve these species and the biodiversity associated with them. Thus, our aim was to develop a methodology of in vitro production of stingless bee queens by offering a large quantity of food to the larvae. Our methodology consisted of determining the amount of larval food needed for the development of the queens, collecting and storing the larval food, and feeding the food to the larvae in acrylic plates. We found that the total average amount of larval food in a worker bee cell of E varia is approximately 26.70 +/- 3.55 mu L. We observed that after the consumption of extra amounts of food (25, 30, 35 and 40 mu L) the larvae differentiate into queens (n = 98). Therefore, the average total volume of food needed for the differentiation of a young larva of F. varia queen is approximately 61.70 +/- 5.00 mu L. In other words; the larvae destined to become queens eat 2.31 times more food than the ones destined to become workers. We used the species Frieseomelitta varia as a model, however the methodology can be reproduced for all species of stingless bees whose mechanism of caste differentiation depends on the amount of food ingested by the larvae. Our results demonstrate the effectiveness of the in vitro technique developed herein, pointing to the possibility of its use as a tool to assist the production of queens on a large scale. This would allow for the artificial splitting of colonies and contribute to conservation efforts in native bees.

Spectroscopic and Catalytic Characterization of a Functional (FeFeII)-Fe-III Biomimetic for the Active Site of Uteroferrin and Protein Cleavage

A mixed-valence complex, [Fe(III)Fe(II)L1(mu-OAc)(2)]BF4 center dot H2O, where the ligand H(2)L1 = 2-{[[3-[((bis-(pyridin-2-ylmethyl)amino)methyl)-2-hydroxy-5-methylbenzyl](pyridin-2-ylmethyl)amino]methyl]phenol}, has been studied with a range of techniques, and, where possible, its properties have been compared to those of the corresponding enzyme system purple acid phosphatase. The (FeFeII)-Fe-III and Fe-2(III) oxidized species were studied spectroelectrochemically. The temperature-dependent population of the S = 3/2 spin states of the heterovalent system, observed using magnetic circular dichroism, confirmed that the dinuclear center is weakly antiferromagnetically coupled (H = -2JS(1).S-2, where J = -5.6 cm(-1)) in a frozen solution. The ligand-to-metal charge-transfer transitions are correlated with density functional theory calculations. The (FeFeII)-Fe-III complex is electron paramagnetic resonance (EPR)-silent, except at very low temperatures (<2 K), because of the broadening caused by the exchange coupling and zero-field-splitting parameters being of comparable magnitude and rapid spin-lattice relaxation. However, a phosphate-bound Fe-2(III) complex showed an EPR spectrum due to population of the S-tot = 3 state (J= -3.5 cm(-1)). The phosphatase activity of the (FeFeII)-Fe-III complex in hydrolysis of bis(2,4-dinitrophenyl)phosphate (k(cat.) = 1.88 x 10(-3) s(-1); K-m = 4.63 x 10(-3) mol L-1) is similar to that of other bimetallic heterovalent complexes with the same ligand. Analysis of the kinetic data supports a mechanism where the initiating nucleophile in the phosphatase reaction is a hydroxide, terminally bound to Fe-III. It is interesting to note that aqueous solutions of [Fe(III)Fe(II)L1(mu-OAc)(2)](+) are also capable of protein cleavage, at mild temperature and pH conditions, thus further expanding the scope of this complex's catalytic promiscuity.

Interionic Interactions in Imidazolic Ionic Liquids Probed by Soft X-ray Absorption Spectroscopy

This work investigates pure ionic liquids (ILs) derived from an imidazolium ring with different carbonic chains and halides or bis(trifluoromethanesulfonilimide) (TFSI-) as anions, using X-ray absorption near edge spectroscopy (XANES) at different energies (N, S, O, F, and Cl edges) to probe the interionic interactions. XANES data show that the interaction with the anion is weaker when the cation is an imidazolium than when the salt is formed by smaller cations, as lithium, independently of the length of the carbonic chain attached to the imidazolium cation. The results also show that, for all studied as, it is not observed any influence of the anion on the XANES spectra of the cation, nor the opposite. 1-Methylimidazolium with Cl-, a small and strongly coordinating anion, presents in the N K XANES spectrum a splitting of the band corresponding to nitrogen in the imidazolic ring, indicating two different chemical environments. For this cation with TFSI-, on the contrary, this splitting was not observed, showing that the anion has a weaker interaction with the imidazolic ring, even without a lateral carbonic chain.

Spin coherence generation in negatively charged self-assembled (In,Ga)As quantum dots by pumping excited trion states

Spin coherence generation in an ensemble of negatively charged (In,Ga)As/GaAs quantum dots was investigated by picosecond time-resolved pump-probe spectroscopy measuring ellipticity. Robust coherence of the ground-state electron spins is generated by pumping excited charged exciton (trion) states. The phase of the coherent state, as evidenced by the spin ensemble precession about an external magnetic field, varies relative to spin coherence generation resonant with the ground state. The phase variation depends on the pump photon energy. It is determined by (a) pumping dominantly either singlet or triplet excited states, leading to a phase inversion, and (b) the subsequent carrier relaxation into the ground states. From the dependence of the precession phase and the measured g factors, information about the quantum dot shell splitting and the exchange energy splitting between triplet and singlet states can be extracted in the ensemble.

On the nu SiO infrared absorption of polysiloxane films

The infrared absorption of polysiloxanes involves a strong band at around 1050 cm(-1), attributed to the antisymmetric vibration of siloxane bridges. The splitting of this band into two components is generally attributed to coupling between next-neighbor siloxane groups along the polysiloxane chain. From a quantitative analysis of the spectra of these materials, we find that this splitting is larger when the material is in thin-film form, and that the relative intensity of the two components is polarization dependent. We show that these effects are fully understandable in the theoretical framework of infrared absorption by thin films, and are related to long-range dipolar interactions responsible for the longitudinal-transverse splitting effect in crystalline materials. As a consequence, the polarization dependence of the infrared absorption observed for thin films does not appear to be associated with an orientational ordering in the film. (c) 2012 Elsevier B.V. All rights reserved.

Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Magnetic and optical investigation of 40SiO(2)center dot 30Na(2)O center dot 1Al(2)O(3)center dot(29-x) B2O3 center dot xFe(2)O(3) glass matrix

Samples of 40SiO(2)center dot 30Na(2)O center dot 1Al(2)O(3)center dot(29 - x)B2O3 center dot xFe(2)O(3) (mol%), with 0.0 <= x <= 17.5, were prepared by the fusion method and investigated by electron paramagnetic resonance (EPR), optical absorption (OA) and Mossbauer spectroscopy (MS). The EPR spectra of the as-synthesized samples exhibit two well-defined EPR signals around g = 4.27 and g = 2.01 and a visible EPR shoulder around g = 6.4, assigned to isolated Fe3+ ion complexes (g = 4.27 and g = 6.4) and Fe3+-based clusters (g = 2.01). Analyses of both EPR line intensity and line width support the model picture of Fe3+-based clusters built in from two sources of isolated ions, namely Fe2+ and Fe3+; the ferrous ion being used to build in iron-based clusters at lower x-content (below about x = 2.5%) whereas the ferric ion is used to build in iron-based clusters at higher x-content (above about x = 2.5%). The presence of Fe2+ ions incorporated within the glass template is supported by OA data with a strong band around 1100 nm due to the spin-allowed E-5(g)-T-5(2g) transition in an octahedral coordination with oxygen. Additionally, Mossbauer data (isomer shift and quadrupole splitting) confirm incorporation of both Fe2+ and Fe3+ ions within the template, more likely in tetrahedral-like environments. We hypothesize that ferrous ions are incorporated within the glass template as FeO4 complex resulting from replacing silicon in non-bridging oxygen (SiO3O-) sites whereas ferric ions are incorporated as FeO4 complex resulting from replacing silicon in bridging-like oxygen silicate groups (SiO4). (C) 2012 Elsevier Masson SAS. All rights reserved.

Milky Way demographics with the VVV survey I. The 84-million star colour-magnitude diagram of the Galactic bulge

Context. The Milky Way (MW) bulge is a fundamental Galactic component for understanding the formation and evolution of galaxies, in particular our own. The ESO Public Survey VISTA Variables in the Via Lactea is a deep near-IR survey mapping the Galactic bulge and southern plane. Particularly for the bulge area, VVV is covering similar to 315 deg(2). Data taken during 2010 and 2011 covered the entire bulge area in the JHKs bands. Aims. We used VVV data for the whole bulge area as a single and homogeneous data set to build for the first time a single colour-magnitude diagram (CMD) for the entire Galactic bulge. Methods. Photometric data in the JHK(s) bands were combined to produce a single and huge data set containing 173 150 467 sources in the three bands, for the similar to 315 deg(2) covered by VVV in the bulge. Selecting only the data points flagged as stellar, the total number of sources is 84 095 284. Results. We built the largest colour-magnitude diagrams published up to date, containing 173.1+ million sources for all data points, and more than 84.0 million sources accounting for the stellar sources only. The CMD has a complex shape, mostly owing to the complexity of the stellar population and the effects of extinction and reddening towards the Galactic centre. The red clump (RC) giants are seen double in magnitude at b similar to -8 degrees-10 degrees, while in the inner part (b similar to -3 degrees) they appear to be spreading in colour, or even splitting into a secondary peak. Stellar population models show the predominance of main-sequence and giant stars. The analysis of the outermost bulge area reveals a well-defined sequence of late K and M dwarfs, seen at (J - K-s) similar to 0.7-0.9 mag and K-s greater than or similar to 14 mag. Conclusions. The interpretation of the CMD yields important information about the MW bulge, showing the fingerprint of its structure and content. We report a well-defined red dwarf sequence in the outermost bulge, which is important for the planetary transit searches of VVV. The double RC in magnitude seen in the outer bulge is the signature of the X-shaped MW bulge, while the spreading of the RC in colour, and even its splitting into a secondary peak, are caused by reddening effects. The region around the Galactic centre is harder to interpret because it is strongly affected by reddening and extinction.

Calculations of the spectral shifts and line profiles of alkaline earth atoms in liquid helium environment

Liquid configurations generated by Metropolis Monte Carlo simulations are used in time-dependent density functional theory calculations of the spectral line shifts and line profiles of the lowest lying excitation of the alkaline earth atoms, Be, Mg, Ca, Sr and Ba embedded in liquid helium. The results are in very good agreement with the available experimental data. Special attention is given to the calculated spectroscopic shift and the associated line broadening. The analysis specifies the inhomogeneous broadening of the three separate contributions due to the splitting of the s -> p transition of the alkaline earth atom in the liquid environment. (C) 2012 Elsevier B. V. All rights reserved.

Magnetic susceptibility study of Ce3+ in PbCeA (A=Te, Se, S)

The magnetic susceptibility of Pb(1-x)Ce(x)A (A=S, Se and Te) crystals with Ce3+ concentrations 0.006 <= x <= 0.036 was investigated in the temperature range from 2 K to 300 K. The magnetic susceptibility data was found to be consistent with a E-2(5/2) lowest manifold for Ce3+ ions with a crystal-field splitting Delta=E(Gamma(8))-E(Gamma(7)) of about 340 K, 440 K and 540 K for Pb1-xCexTe, Pb1-xCexSe, and Pb1-xCexS, respectively. For all the three compounds the doublet Gamma(7) lies below the Gamma(8) quadruplet which confirms the substitution of Pb2+ by Ce3+ ions in the host crystals. The observed values for the crystal-field splitting are in good agreement with the calculated ones based on the point-charge model. Moreover, the effective Lande factors were determined by X-band (similar to 9.5 GHz), electron paramagnetic measurements (EPR) to be g=1.333, 1.364, and 1.402 for Ce ions in PbA, A = S. Se and Te, respectively. The small difference with the predicted Lande factor g of 10/7 for the Gamma(7) (J=5/2) ground state was attributed to crystal-field admixture. (C) 2012 Elsevier B.V. All rights reserved.

Evolving decision trees with beam search-based initialization and lexicographic multi-objective evaluation

Decision tree induction algorithms represent one of the most popular techniques for dealing with classification problems. However, traditional decision-tree induction algorithms implement a greedy approach for node splitting that is inherently susceptible to local optima convergence. Evolutionary algorithms can avoid the problems associated with a greedy search and have been successfully employed to the induction of decision trees. Previously, we proposed a lexicographic multi-objective genetic algorithm for decision-tree induction, named LEGAL-Tree. In this work, we propose extending this approach substantially, particularly w.r.t. two important evolutionary aspects: the initialization of the population and the fitness function. We carry out a comprehensive set of experiments to validate our extended algorithm. The experimental results suggest that it is able to outperform both traditional algorithms for decision-tree induction and another evolutionary algorithm in a variety of application domains.

Resonant States in Negative Ions

Resonant states are multiply excited states in atoms and ions that have enough energy to decay by emitting an electron. The ability to emit an electron and the strong electron correlation (which is extra strong in negative ions) makes these states both interesting and challenging from a theoretical point of view. The main contribution in this thesis is a method, which combines the use of B splines and complex rotation, to solve the three-electron Schrödinger equation treating all three electrons equally. It is used to calculate doubly excited and triply excited states of 4S symmetry with even parity in He-. For the doubly excited states there are experimental and theoretical data to compare with. For the triply excited states there is only theoretical data available and only for one of the resonances. The agreement is in general good. For the triply excited state there is a significant and interesting difference in the width between our calculation and another method. A cause for this deviation is suggested. The method is also used to find a resonant state of 4S symmetry with odd parity in H2-. This state, in this extremely negative system, has been predicted by two earlier calculations but is highly controversial. Several other studies presented here focus on two-electron systems. In one, the effect of the splitting of the degenerate H(n=2) thresholds in H-, on the resonant states converging to this threshold, is studied. If a completely degenerate threshold is assumed an infinite series of states is expected to converge to the threshold. Here states of 1P symmetry and odd parity are examined, and it is found that the relativistic and radiative splitting of the threshold causes the series to end after only three resonant states. Since the independent particle model completely fails for doubly excited states, several schemes of alternative quantum numbers have been suggested. We investigate the so called DESB (Doubly Excited Symmetry Basis) quantum numbers in several calculations. For the doubly excited states of He- mentioned above we investigate one resonance and find that it cannot be assigned DESB quantum numbers unambiguously. We also investigate these quantum numbers for states of 1S even parity in He. We find two types of mixing of DESB states in the doubly excited states calculated. We also show that the amount of mixing of DESB quantum numbers can be inferred from the value of the cosine of the inter-electronic angle. In a study on Li- the calculated cosine values are used to identify doubly excited states measured in a photodetachment experiment. In particular a resonant state that violates a propensity rule is found.

Optically active photoresponsive multifunctional polymeric materials

In the last year [1], Angiolini and co-workers have synthesized and investigated methacrylic polymers bearing in the side chain the chiral cyclic (S)-3-hydroxypyrrolidine moiety interposed between the main chain and the trans-azoaromatic chromophore, substituted or not in the 4’ position by an electron-withdrawing group. In these materials, the presence of a rigid chiral moiety of one prevailing absolute configuration favours the establishment of a chiral conformation of one prevailing helical handedness, at least within chain segments of the macromolecules, which can be observed by circular dichroism (CD). The simultaneous presence of the azoaromatic and chiral functionalities allows the polymers to display both the properties typical of dissymmetric systems (optical activity, exciton splitting of dichroic absorptions), as well as the features typical of photochromic materials (photorefractivity, photoresponsiveness, NLO properties). The first part of this research was to synthesize analogue homopolymers and copolymers based on bisazoaromatic moiety and compare their properties to those of the above mentioned analogue derivatives bearing only one azoaromatic chromophore in the side chain. We focused also the attention on the effects induced on the thermal and chiroptical behaviours by the insertion of particulars achiral comonomers characterized by different side-chain mobility and grown hindrance (MMA, tert-BMA and TrMA). On the other hand carbazole containing polymers [2] have attracted much attention because of their unique features. The use of these materials in advanced micro- and nanotechnologies spreads in many different applications such as photoconductive and photorefractive polymers, electroluminescent devices, programmable optical interconnections, data storage, chemical photoreceptors, NLO, surface relief gratings, blue emitting materials and holographic memory. The second part of the work was focused on the synthesis and the characterization polymeric derivatives bearing in the side chain carbazole or phenylcarbazole moieties linked to the (S)- 2-hydroxy succinimide or the (S)-3-hydroxy pyrrolidinyl ring as chiral groups covalently linked to the main chain through ester bonds. The last objective of this research was to design, synthesize, and characterize multifunctional methacrylic homopolymers and copolymers bearing three distinct functional groups (i.e. azoaromatic, carbazole and chiral group of one single configuration) directly linked in the side chain. This polymeric derivatives could be of potential interest for several advanced application fields, such as optical storage, waveguides, chiroptical switches, chemical photoreceptors, NLO, surface relief gratings, photoconductive materials, etc.