Class Notes for Math 905: Commutative Algebra, Instructor Sylvia Wiegand

Topics include: Rings, ideals, algebraic sets and affine varieties, modules, localizations, tensor products, intersection multiplicities, primary decomposition, the Nullstellensatz

Class Notes for Math 918: Homological Conjectures, Instructor Tom Marley

This course was an overview of what are known as the “Homological Conjectures,” in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass’ Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, the Monomial Conjecture, the Syzygy Conjecture, and the big and small Cohen Macaulay Conjectures. Many of these are shown to imply others. This document contains notes for a course taught by Tom Marley during the 2009 spring semester at the University of Nebraska-Lincoln. The notes loosely follow the treatment given in Chapters 8 and 9 of Cohen-Macaulay Rings, by W. Bruns and J. Herzog, although many other sources, including articles and monographs by Peskine, Szpiro, Hochster, Huneke, Grith, Evans, Lyubeznik, and Roberts (to name a few), were used. Special thanks to Laura Lynch for putting these notes into LaTeX.

Class Notes for Math 918: Cohen Macaulay Modules, Instructor Roger Wiegand

Topics covered are: Cohen Macaulay modules, zero-dimensional rings, one-dimensional rings, hypersurfaces of finite Cohen-Macaulay type, complete and henselian rings, Krull-Remak-Schmidt, Canonical modules and duality, AR sequences and quivers, two-dimensional rings, ascent and descent of finite Cohen Macaulay type, bounded Cohen Macaulay type.

Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Skeletal muscle major histocompatibility complex class I and II expression differences in adult and juvenile dermatomyositis

OBJECTIVE: To analyze major histocompatibility complex expression in the muscle fibers of juvenile and adult dermatomyositis. METHOD: In total, 28 untreated adult dermatomyositis patients, 28 juvenile dermatomyositis patients (Bohan and Peter's criteria) and a control group consisting of four dystrophic and five Pompe's disease patients were analyzed. Routine histological and immunohistochemical (major histocompatibility complex I and II, StreptoABComplex/HRP, Dakopatts) analyses were performed on serial frozen muscle sections. Inflammatory cells, fiber damage, perifascicular atrophy and increased connective tissue were analyzed relative to the expression of major histocompatibility complexes I and II, which were assessed as negatively or positively stained fibers in 10 fields (200X). RESULTS: The mean ages at disease onset were 42.0 +/- 15.9 and 7.3 +/- 3.4 years in adult and juvenile dermatomyositis, respectively, and the symptom durations before muscle biopsy were similar in both groups. No significant differences were observed regarding gender, ethnicity and frequency of organ involvement, except for higher creatine kinase and lactate dehydrogenase levels in adult dermatomyositis (p<0.050). Moreover, a significantly higher frequency of major histocompatibility complex I (96.4% vs. 50.0%, p<0.001) compared with major histocompatibility complex II expression (14.3% vs. 53.6%, p = 0.004) was observed in juvenile dermatomyositis. Fiber damage (p = 0.006) and increased connective tissue (p<0.001) were significantly higher in adult dermatomyositis compared with the presence of perifascicular atrophy (p<0.001). The results of the histochemical and histological data did not correlate with the demographic data or with the clinical and laboratory features. CONCLUSION: The overexpression of major histocompatibility complex I was an important finding for the diagnosis of both groups, particularly for juvenile dermatomyositis, whereas there was lower levels of expression of major histocompatibility complex II than major histocompatibility complex I. This finding was particularly apparent in juvenile dermatomyositis.

Treatment times of Class II malocclusion: four premolar and non-extraction protocols

The purpose of this study was to retrospectively compare the treatment times of Class II division 1 malocclusion subjects treated with four first premolar extractions or a non- extraction protocol and fixed edgewise appliances. Eighty- four patients were selected and divided into two groups. Group 1, treated with four first premolar extractions, consisted of 48 patients (27 males and 21 females) with a mean age of 13.03 years and group 2, treated without extractions, consisted of 36 patients (18 males and 18 females) with a mean age of 13.13 years. Group 2 was subdivided into two subgroups, 2A consisting of 16 patients treated in one phase and 2B consisting of 20 patients treated in two phases. The initial and final Treatment Priority Index (TPI), initial ages, initial mandibular crowding, and treatment times of groups 1 and 2 were compared with t- tests. These variables were also compared between group 1 and the subgroups with analysis of variance followed by Tukey's tests. The treatment times for groups 1 and 2 and subgroups 2A and 2B were 2.36, 2.47, 2.25, and 2.64 years, respectively, which were not significantly different. Treatment times with non-extraction and four premolar extraction protocols are similar.

The identification of the pillars of education in the class comprehensiveness in healthcare

The objective of the present study was to verify, based on the analysis of student portfolio narratives, if the four pillars of education were approached in the class "Comprehensiveness in health care", part of the integrated curriculum of the Baccalaureate in Nursing Program of the University of Sao Paulo at Ribeirao Preto College of Nursing. A qualitative, documental study was performed using 46 portfolios constructed during the classes. Data collection was performed using an assessment tool that contained items addressing cognitive and affective dimensions. The data were submitted to thematic categorical analysis using the pillars of education as predefined categories. The results show that the pillars of education were, apparently, included in the class. Despite the present study findings, no evidence was found that the expected competencies were actually discussed among students and faculty, according to the records regarding the evaluations of each pedagogical cycle of the studied class.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Class-specific metrics for multidimensional data projection applied to CBIR

Content-based image retrieval is still a challenging issue due to the inherent complexity of images and choice of the most discriminant descriptors. Recent developments in the field have introduced multidimensional projections to burst accuracy in the retrieval process, but many issues such as introduction of pattern recognition tasks and deeper user intervention to assist the process of choosing the most discriminant features still remain unaddressed. In this paper, we present a novel framework to CBIR that combines pattern recognition tasks, class-specific metrics, and multidimensional projection to devise an effective and interactive image retrieval system. User interaction plays an essential role in the computation of the final multidimensional projection from which image retrieval will be attained. Results have shown that the proposed approach outperforms existing methods, turning out to be a very attractive alternative for managing image data sets.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

Finite element analysis of bonded model Class I 'restorations' after shrinkage

Objectives. The C-Factor has been used widely to rationalize the changes in shrinkage stress occurring at the tooth/resin-composite interfaces. Experimentally, such stresses have been measured in a uniaxial direction between opposed parallel walls. The situation of adjoining cavity walls has been neglected. The aim was to investigate the hypothesis that: within stylized model rectangular cavities of constant volume and wall thickness, the interfacial shrinkage-stress at the adjoining cavity walls increases steadily as the C-Factor increases. Methods. Eight 3D-FEM restored Class I 'rectangular cavity' models were created by MSC.PATRAN/MSC.Marc, r2-2005 and subjected to 1% of shrinkage, while maintaining constant both the volume (20 mm(3)) and the wall thickness (2 mm), but varying the C-Factor (1.9-13.5). An adhesive contact between the composite and the teeth was incorporated. Polymerization shrinkage was simulated by analogy with thermal contraction. Principal stresses and strains were calculated. Peak values of maximum principal (MP) and maximum shear (MS) stresses from the different walls were displayed graphically as a function of C-Factor. The stress-peak association with C-Factor was evaluated by the Pearson correlation between the stress peak and the C-Factor. Results. The hypothesis was rejected: there was no clear increase of stress-peaks with C-Factor. The stress-peaks particularly expressed as MP and MS varied only slightly with increasing C-Factor. Lower stress-peaks were present at the pulpal floor in comparison to the stress at the axial walls. In general, MP and MS were similar when the axial wall dimensions were similar. The Pearson coefficient only expressed associations for the maximum principal stress at the ZX wall and the Z axis. Significance. Increase of the C-Factor did not lead to increase of the calculated stress-peaks in model rectangular Class I cavity walls. (C) 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

56-month clinical performance of Class I and II resin composite restorations

Objective: This study evaluated the 56-month clinical performance of Class I and II resin composite restorations. Filtek P60 was compared with Filtek Z250, which are both indicated for posterior restorations but differ in terms of handling characteristics. The null hypothesis tested was that there is no difference in the clinical performance of the two resin composites in posterior teeth. Material and Methods: Thirty-three patients were treated by the same operator, who prepared 48 Class I and 42 Class II cavities, which were restored with Single Bond/Filtek Z250 or Single Bond/Filtek P60 restorative systems. Restorations were evaluated by two independent examiners at baseline and after 56 months, using the modified USPHS criteria. Data were analyzed statistically using Chi-square and Fisher's Exact tests (alpha=0.05). Results: After 56 months, 25 patients (31 Class I and 36 Class II) were analyzed. A 3% failure rate occurred due to secondary caries and excessive loss of anatomic form for P60. For both restorative systems, there were no significant differences in secondary caries and postoperative sensitivity. However, significant changes were observed with respect to anatomic form, marginal discoloration, and marginal adaptation. Significant decreases in surface texture were observed exclusively for the Z250 restorations. Conclusions: Both restorative systems can be used for posterior restorations and can be expected to perform well in the oral environment.