Abstract Algebra: An Inquiry-Based Approach, Second Edition, Supplemental Material

This text is a supplement to Abstract Algebra: An Inquiry-Based Approach, Second Edition. It includes applications of algebra to RSA encryption, check digits, the games of NIM and the 15 Puzzle, and the determination of groups of small order. In addition, reference material that could be useful for some students appears in the appendices, such as background material on functions, methods of proof (including the equivalencies of the Well-Ordering Principle and different versions of mathematical induction), and complex roots of unity. The appendices also contain a complete proof that polynomial rings are rings, a proof of the Fundamental Theorem of Algebra, and a derivation of the formula for solving any cubic equation.https://scholarworks.gvsu.edu/books/1029/thumbnail.jp

Material condition assessment with eddy current sensors

Eddy current sensors and sensor arrays are used for process quality and material condition assessment of conducting materials. In an embodiment, changes in spatially registered high resolution images taken before and after cold work processing reflect the quality of the process, such as intensity and coverage. These images also permit the suppression or removal of local outlier variations. Anisotropy in a material property, such as magnetic permeability or electrical conductivity, can be intentionally introduced and used to assess material condition resulting from an operation, such as a cold work or heat treatment. The anisotropy is determined by sensors that provide directional property measurements. The sensor directionality arises from constructs that use a linear conducting drive segment to impose the magnetic field in a test material. Maintaining the orientation of this drive segment, and associated sense elements, relative to a material edge provides enhanced sensitivity for crack detection at edges

Macro- and microscopic properties of strontium doped indium oxide

Solid state synthesis and physical mechanisms of electrical conductivity variation in polycrystalline, strontium doped indium oxide In2O3:(SrO)x were investigated for materials with different doping levels at different temperatures (T=20-300 C) and ambient atmosphere content including humidity and low pressure. Gas sensing ability of these compounds as well as the sample resistance appeared to increase by 4 and 8 orders of the magnitude, respectively, with the doping level increase from zero up to x=10%. The conductance variation due to doping is explained by two mechanisms: acceptor-like electrical activity of Sr as a point defect and appearance of an additional phase of SrIn2O4. An unusual property of high level (x=10%) doped samples is a possibility of extraordinarily large and fast oxygen exchange with ambient atmosphere at not very high temperatures (100-200 C). This peculiarity is explained by friable structure of crystallite surface. Friable structure provides relatively fast transition of samples from high to low resistive state at the expense of high conductance of the near surface layer of the grains. Microscopic study of the electro-diffusion process at the surface of oxygen deficient samples allowed estimation of the diffusion coefficient of oxygen vacancies in the friable surface layer at room temperature as 3x10^(-13) cm^2/s, which is by one order of the magnitude smaller than that known for amorphous indium oxide films.Comment: 19 pages, 7 figures, 39 reference

Cannabinoid exposure during zebra finch sensorimotor vocal learning persistently alters expression of endocannabinoid signaling elements and acute agonist responsiveness

<p>Abstract</p> <p>Background</p> <p>Previously we have found that cannabinoid treatment of zebra finches during sensorimotor stages of vocal development alters song patterns produced in adulthood. Such persistently altered behavior must be attributable to changes in physiological substrates responsible for song. We are currently working to identify the nature of such physiological changes, and to understand how they contribute to altered vocal learning. One possibility is that developmental agonist exposure results in altered expression of elements of endocannabinoid signaling systems. To test this hypothesis we have studied effects of the potent cannabinoid receptor agonist WIN55212-2 (WIN) on endocannabinoid levels and densities of CB₁immunostaining in zebra finch brain.</p> <p>Results</p> <p>We found that late postnatal WIN treatment caused a long-term global disregulation of both levels of the endocannabinoid, 2-arachidonyl glycerol (2-AG) and densities of CB₁immunostaining across brain regions, while repeated cannabinoid treatment in adults produced few long-term changes in the endogenous cannabinoid system.</p> <p>Conclusions</p> <p>Our findings indicate that the zebra finch endocannabinoid system is particularly sensitive to exogenous agonist exposure during the critical period of song learning and provide insight into susceptible brain areas.</p

Protein Function Assignment through Mining Cross-Species Protein-Protein Interactions

Background: As we move into the post genome-sequencing era, an immediate challenge is how to make best use of the large amount of high-throughput experimental data to assign functions to currently uncharacterized proteins. We here describe CSIDOP, a new method for protein function assignment based on shared interacting domain patterns extracted from cross-species protein-protein interaction data. Methodology/Principal Findings: The proposed method is assessed both biologically and statistically over the genome of H. sapiens. The CSIDOP method is capable of making protein function prediction with accuracy of 95.42 % using 2,972 gene ontology (GO) functional categories. In addition, we are able to assign novel functional annotations for 181 previously uncharacterized proteins in H. sapiens. Furthermore, we demonstrate that for proteins that are characterized by GO, the CSIDOP may predict extra functions. This is attractive as a protein normally executes a variety of functions in different processes and its current GO annotation may be incomplete. Conclusions/Significance: It can be shown through experimental results that the CSIDOP method is reliable and practical in use. The method will continue to improve as more high quality interaction data becomes available and is readily scalable t

Resolving the Ortholog Conjecture: Orthologs Tend to Be Weakly, but Significantly, More Similar in Function than Paralogs

The function of most proteins is not determined experimentally, but is extrapolated from homologs. According to the “ortholog conjecture”, or standard model of phylogenomics, protein function changes rapidly after duplication, leading to paralogs with different functions, while orthologs retain the ancestral function. We report here that a comparison of experimentally supported functional annotations among homologs from 13 genomes mostly supports this model. We show that to analyze GO annotation effectively, several confounding factors need to be controlled: authorship bias, variation of GO term frequency among species, variation of background similarity among species pairs, and propagated annotation bias. After controlling for these biases, we observe that orthologs have generally more similar functional annotations than paralogs. This is especially strong for sub-cellular localization. We observe only a weak decrease in functional similarity with increasing sequence divergence. These findings hold over a large diversity of species; notably orthologs from model organisms such as E. coli, yeast or mouse have conserved function with human proteins