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Graded Hecke algebras are deformations of skew group algebras which arise from a group acting on a polynomial ring. Over fields of characteristic zero, these deformations have been studied in depth and include both symplectic reflection algebras and rational Cherednik algebras as examples. In Lusztig's graded affine Hecke algebras, the action of the group is deformed, but not the commutativity of the vectors. In Drinfeld's Hecke algebras, the commutativity of the vectors is deformed, but not the action of the group. Lusztig's algebras are all isomorphic to Drinfeld's algebras in the nonmodular setting. We find new deformations in the modular setting, i.e., when the characteristic of the underlying field divides the order of the group. We use Poincare-Birkhoff-Witt conditions to classify these deformations arising from the symmetric group acting on a polynomial ring in arbitrary characteristic, including the modular case.

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The purpose of this study was to determine whether or not differences exist in heart rate (HR) between jogging on the track and jogging on the treadmill at the same speed. Twenty-four college-age (19-31 years old) male (n = 12) and female (n = 12) recreational runners volunteered to participate in this study. Each participant performed a maximal graded exercise test (GXT) and four exercise sessions. During the first exercise session, participants completed a 1-mile steady-state jog on either the track or treadmill at a self-selected submaximal pace that could be maintained for 30 minutes. The following three exercise sessions were completed at the same pace as the first exercise session. Two of the exercise sessions were performed on the treadmill and two were performed on an indoor track. The order of the four sessions were counterbalanced. Participants were randomly assigned to an order of sessions. Heart rate was recorded every minute and the participants were asked to give an RPE at the end of every session. Statistical analysis revealed no significant differences in pace (mph) between the trials within the two track or two treadmill trials (p = 0.5812), in the HR response. Therefore, gender and trials were excluded from the final model, and the final model included only the treatment effect (track, treadmill). There was a significant treatment effect (F 1,94 = 39.126, p < 0.0001) indicating that significant differences in the HR responses between track and treadmill jogging at the same pace. Jogging on the treadmill elicited an average HR of 5.16 bpm (S.E. = 0.82) less than that observed while jogging on an indoor track at the same pace. We conclude that jogging on the treadmill and track at the same, self-selected speed results in HR values that differ significantly by 5 bpm. Differences in air resistance, biomechanics, and muscle activity most likely contributed to the observed differences in HR. The results of this study are applicable to various individuals who often train or exercise on the treadmill or overground. Use of a HR monitor is recommended to determine personal responses to exercise on a treadmill and overground.

Bifactor Item Response Theory (IRT) models are presented as a plausible structure for psychological measures with a primary scale and two or more subscales. A bifactor graded response model, appropriate for polytomous categorical data, was fit to two university counseling center datasets (N=4,679 and N=4,500) of Outcome-Questionnaire-45.2 (OQ) psychotherapy intake data. The bifactor model showed superior fit compared to a unidimensional IRT model. IRT item parameters derived from the bifactor model show that items discriminate well on the primary scale. Items on the OQ's subscales maintain some discrimination ability over and above the primary scale. However, reliability estimates for the subscales, controlling for the primary scale, suggest that clinical use should likely proceed with caution. Item difficulty or severity parameters reflected item content well, in that increased probability of endorsement was found at high levels of distress for items tapping severe symptomatology. Increased probability of endorsement was found at lower levels of distress for items tapping milder symptomatology. Analysis of measurement invariance showed that item parameters hold equally across gender for most OQ items. A subset of items was found to have item parameters non-invariant across gender. Implications for research and practice are discussed, and directions for future work given.

<p dir="ltr">This thesis consists of four parts that study different topics in commutative algebra. The main results of the first part of the dissertation are in Chapter 3, which is based on the author’s paper [1]. Let R be a commutative Noetherian ring graded by a torsionfree abelian group G. We introduce the notion of G-graded irreducibility and prove that G-graded irreducibility is equivalent to irreducibility in the usual sense. This is a generalization of a result by Chen and Kim in the Z-graded case. We also discuss the concept of the index of reducibility and give an inequality for the indices of reducibility between any radical non-graded ideal and its largest graded subideal. The second topic is developed in Chapter 4 which is based on the author’s paper [2]. In this chapter, we prove that if P is a prime ideal of inside a polynomial ring S with dim S/P = r, and adjoining s general linear forms to the prime ideal changes the (r − s)-th Hilbert coefficient of the quotient ring by 1 and doesn’t change the 0th to (r − s − 1)-th Hilbert coefficients where s ≤ r, then the depth of S/P is n − s − 1. This criterion also tells us about possible restrictions on the generic initial ideal of a prime ideal inside a polynomial ring. The third part of the thesis is Chapter 5 which is based on the author’s paper [3]. Let R be a polynomial ring over a field. We introduce the concept of sequentially almost Cohen-Macaulay modules, describe the extremal rays of the cone of local cohomology tables of finitely generated graded R-modules which are sequentially almost Cohen-Macaulay, and also describe some cases when the local cohomology table of a module of dimension 3 has a nontrivial decomposition. The last part is Chapter 6 which is based on the author’s paper [4]. We introduce the notion of strongly Lech-independent ideals as a generalization of Lech-independent ideals defined by Lech and Hanes, and use this notion to derive inequalities on multiplicities of ideals. In particular, we prove a new case of Lech’s conjecture, namely, if (R, m) → (S, n) is a flat local extension of local rings with dim R = dim S, the completion of S is the completion of a standard graded ring over a field k with respect to the homogeneous maximal ideal, and the completion of mS is the completion of a homogeneous ideal, then e(R) ≤ e(S).</p>

Stabilization of poorly graded sand in full-scale applications is challenging. This thesis evaluated cement-stabilized sand and had two objectives: (1) evaluation of stabilized material using the PM device to quantify engineering properties for future comparison to alterative materials and to investigate the effectiveness of the device with sand and (2) investigation of the merits of alternative application of cement to sand to benchmark against other topically applied materials. The PM device was successfully used to recommend 10% cement for field studies with one sand, successfully allowed data collection in laboratory and field applications, and its potential in sand seems promising though more overarching conclusions on characterization of sand using the PM device are withheld for subsequent efforts. Topical application methods developed in this thesis were able to percolate cement into sand and produce an average estimated unconfined compressive strength of 245 psi measured on cores that were 2.5 inches thick.

The method of optical emission spectroscopy has been used with Fe-Ni and other complex alloys to investigate in-situ compositional control for additive manufacturing. Although additive manufacturing of metallic alloys is an emerging technology, compositional control will be a challenge that needs to be addressed for a multitude of industries going forward for next-gen applications. This current scope of work includes analysis of ionized species generated from laser and metal powder interaction that is inherent to the laser engineered net shaping (LENS) process of additive manufacturing. By quantifying the amount of a given element's presence in the electromagnetic (EM) spectrum, this amount can be compared to the actual amount present in the sample via post-processing and elemental dispersive x-ray (EDX) data analysis. For this work a commercially available linear silicon CCD camera captured metallic ion peaks found within the ultraviolet (UV) region to avoid background contamination from blackbody radiation. Although the additive manufacturing environment can prove difficult to measure in-situ due to time dependent phenomena, extreme temperatures, and defect generation, OEM was able to capture multiple data points over a time series that showed a positive correlation between an element's peak intensity and the amount of that element found in the final deposit.

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