This dissertation has two principal components: the dimension of posets with planar cover graphs, and the cartesian product of posets whose cover graphs have hamiltonian cycles that parse into symmetric chains. Posets of height two can have arbitrarily large dimension. In 1981, Kelly provided an infinite sequence of planar posets that shows that the dimension of planar posets can also be arbitrarily large. However, the height of the posets in this sequence increases with the dimension. In 2009, Felsner, Li, and Trotter conjectured that for each integer h at least 2, there exists a least positive integer c(h) so that if P is a poset with a planar cover graph (the class of posets with planar cover graphs includes the class of planar posets) and the height of P is h, then the dimension of P is at most c(h). In the first principal component of this dissertation we prove this conjecture. We also give the best known lower bound for c(h), noting that this lower bound is far from the upper bound. In the second principal component, we consider posets with the Hamiltonian Cycle--Symmetric Chain Partition (HC-SCP) property. A poset of width w has this property if its cover graph has a hamiltonian cycle which parses into w symmetric chains. This definition is motivated by a proof of Sperner's theorem that uses symmetric chains, and was intended as a possible method of attack on the Middle Two Levels Conjecture. We show that the subset lattices have the HC-SCP property by showing that the class of posets with the strong HC-SCP property, a slight strengthening of the HC-SCP property, is closed under cartesian product with a two-element chain. Furthermore, we show that the cartesian product of any two posets from this strong class has the (weak) HC-SCP property.

Over-height trucks are not only a hazard to the over-height trucks themselves, but they pose a threat to the bridges they come into contact with, and most importantly the other drivers on the road way when a collision takes place with a low clearance structure. Therefore, there is a need for an over-height detection system that is affordable yet also reliable. At this time there exist over-height detection systems using laser and infrared beam devices however, they are expensive. This high cost makes it impossible for Department of Transportations across the nation to implement these systems at all low-clearance headroom roadways. In this research a machine vision based system is proposed to detect the height of trucks and provide a warning for over-height vehicles. The height determination will be completed using line detection and blob tracking; these two methods will be overlapped where an upper point of the truck can be compared to a lower point on the ground. These 2D coordinates will then be translated into 3D world coordinates that will provide an approximation of the truck height. If the truck is over the set height then a warning will sound. The accuracy of the test proves that the method is a reliable method of height determination, achieving a 96.59% accuracy rate for measured trucks. The method does have an error rate of 3.3%. The merit of this work is the creation of an automatic image based method which can provide height determination of trucks and is a low cost alternative to the current expensive laser and infrared detection systems.

In 1955, Cassels proved a now celebrated theorem giving a search bound algorithm for determining whether a quadratic form has a nontrivial zero over the rationals. Since then, his work has been greatly generalized, but most of these newer techniques do not follow his original method of proof. In this thesis, we revisit his 1955 proof, modernize his tools and language, and use this machinery to prove more general theorems regarding height bounds for the common zeros of a system of polynomials in terms of the heights of those polynomials. We then use these theorems to give a short proof of a more general (albeit, known) version of Cassels' Theorem and give some weaker results concerning the rational points of a cubic or a pair of quadratics. / text

In this thesis, we introduce and study several norms constructed to satisfy an extremal property with respect to the Mahler measure. These norms naturally generalize the metric Mahler measure introduced by Dubickas and Smyth. We show that bounding these norms on a certain subspace implies Lehmer's conjecture and in at least one case that the converse is true as well. We evaluate these norms on a class of algebraic numbers that include Pisot and Salem numbers, and for surds. We prove that the infimum in the construction is achieved in a certain finite dimensional space for all algebraic numbers in one case, and for surds in general, a finiteness result analogous to that of Samuels and Jankauskas for the t-metric Mahler measures. Next, we generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a Q-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over Q retain their linear independence over R. / text

3 pp. / “Summer slump” is a decline in growth of alfalfa usually beginning in July in areas where maximum daily temperature exceeds 100 °F, such as the low elevation deserts of Southwestern U.S (Fig. 1). In more temperate regions, there is a gradual decrease in alfalfa yield in successive harvests throughout the year, but the yield decline in the summer is not as sharp as in hot summer regions. The term summer slump has also been applied to reduction in growth of perennial cool season grasses such as tall fescue during the summer.

The superior growth of Grand fir (Abies grandis) compared to Douglas-fir (Pseudostuga menziesii) on suitable coastal sites has previously been recognized on the basis of qualitative observations with little empirical evidence. For example, D.E. McMullan (1977, pers. comm.) reported 18% higher volume for a grand fir tree of the same height and age as a 108-year old Douglas-fir plus tree (No. 622) This study was undertaken by Bernardy (1988) to examine possible differences in the growth of grand fir and Douglas-fir growing in a mixed 40-year-old plantation of unknown origin. Trends in height, diameter and annual volume increment between the two species over time were examined. Expected growth performance (i.e. volume and form) of each species was inferred from trends identified at time of sampling.

Abstract Validity of waist-to-height ratio as a screening tool for type 2 diabetes risk in non-Hispanic Whites, non-Hispanic Blacks, and Mexican American Adult Women, from the ages 20-65 years of age. Background: A prominent screening measure for type 2 diabetes is a simple measure of waist circumference. Waist circumference is an aggregate measurement of the actual amount of total and abdominal fat accumulation and is a crucial correlate of the complexities found among obese and overweight patients. However, waist circumference does not take into consideration the frame of an individual. Hence, recent epidemiologic data have suggested the use of height adjusted waist circumference (waist-to-height ratio). The use of waist-to-height ratio in screening for type 2 diabetes is poorly understood. Aims: The aim of this study is to determine racial/ethnic differences in the association of the independent variables waist-to-height ratio and waist circumference, with type 2 diabetes in non-Hispanic Whites, non-Hispanic Blacks, and Mexican American adult women, ages 20-65 years old. Methods: Data from the NHANES 2007-2008 surveys were used. Race/ethnic specific odds ratios from univariate and multivariate logistic regression models were to estimate the associations of waist-to-height ratio and waist circumference with type 2 diabetes. In the multivariate models, adjustments were made for age and alcohol use. Results: In the univariate models, WC was associated with 1.06, 1.07 and 1.04 increased odds of type 2 diabetes in Mexican Americans, non-Hispanic Whites and non-Hispanic Blacks, respectively. The corresponding values waist-to-height ratio were 2.85, 3.20 and 1.88, respectively. On adjusting for confounders, WC was associated with 1.07, 1.05, and 1.05 increased odds of type 2 diabetes in Mexican Americans, non-Hispanic Whites and non-Hispanic Blacks, respectively. WHtR was associated with 2.95, 2.38, and 2.37 increased odds of type 2 diabetes in Mexican Americans, non-Hispanic Whites and non-Hispanic Blacks, respectively. Conclusion: This study indicates that WHtR may be a powerful anthropometric predictor of risk for type 2 diabetes for Mexican American, non-Hispanic White and non-Hispanic Black American women ages 20-65.The literature on WHtR as a screening tool for type 2 diabetes in American women is lacking. This study is one of the first to examine the association between WHtR across varying races of American women. Future researchers should explore populations of women and men in the US with more races represented.

A number of parameters have been identified as characteristic of the walking pattern in patients with INPH. Most of these have been identified through qualitative surveys and manually conducted test batteries. In order to obtain quantitative, standardized and objective measures, which enable studies based on larger patient populations and comparable results, there is a need for a user-friendly system that can measure specific key parameters over time in a reliable manner in everyday clinical work. Step height, width and the variability in the gait cycle are such parameters which are interesting research areas for this group of patient. Problems with balance and gait are very common in other patient groups as well, particularly in neurological diseases such as Parkinson's disease, multiple sclerosis and stroke. This is the reason that the development of this gait analyzer is performed. Giving access to a simple and objective method for estimating gait and balance ability in clinical routine investigations would increase the ability to provide the right kind of treatment, confirm treatment results, and conducting larger research studies. Therefore, this equipment can contribute to the assessment of diseases which contain impaired gait. As a first test of the usability and for the validation of accuracy and repeatability of the equipment a group of healthy volunteers was used. Results from tests on healthy subjects show god repeatability between measurements, for step width at normal gait the difference was -0,2 ±0,34 cm (mean, ±SD) and step height 0,69 ±3,34 cm. The stride time variability in the healthy group where very small 0,00048 ±0,00028 s2 with a difference between test of 0,000019 ±0,00038 s2. Three pilot patients have been tested where we have clearly seen indications of increased stride time variability and reduced step height.

Objective: Lifting-seat devices are designed to raise the seat height to reduce biomechanical and neuromuscular demands of a sit-to-stand (STS). The goal of this thesis was to understand how seat height and lifting-seat devices with different mechanisms affect trunk, hip, and knee biomechanics and neuromuscular activity of surrounding muscles, and determine whether the effects are altered by age. Four conditions were tested; 1) no device normal seat height (ND-normal), 2) Seat Assist™ (SA), 3) Power Seat™ (PS), 4) no device raised height (ND-raised). Using a cross-sectional design, two objectives were completed. Objective one compared ND-normal and ND-raised to determine the effects of seat height. Objective two compared ND-raised, PS, SA to determine the effects of lifting-seats. Design: 10 healthy older and 10 healthy younger adults performed five trials of each STS condition. Bilateral lower limb and trunk three-dimensional motion, ground reaction forces and electromyography (EMG) from five muscles were collected.

Due to recent climate change and energy consumption concerns, several markets have emerged for agricultural biomass in the province of Ontario, Canada. Understanding variation of residue nutrient concentrations across the province and the causal factors is crucial for determining the feasibility of crop residue use in Ontario. The purpose of this study was to survey variation of Ontario winter wheat, soybean and corn residue nutrient concentrations and removals, as well as to determine the effect of altering cutting height and delaying harvest on the nutrient concentrations and removals of these residues. It was found that across-site nutrient concentration and removal variation were greater than within-site concentration and removal variation, and that site-scale climatological events, such as precipitation, are largely responsible. Concentration and removals differed significantly by year. Variation of nutrient concentration and removal did not correlate with crop grain yield, or soil characteristics such as organic matter, pH or texture. A leaching treatment significantly reduced residue nutrient concentrations and removals, but had no significant effect on the variation among residue samples. Finally, concentrations and removals differed significantly with cutting height and harvested corn component, highlighting the importance of harvest method in the system nutrient balances. / Ontario Soil and Crop Improvement Association, Ontario Ministry of Agriculture Food and Rural Affairs, University of Guelph