M.Ed. (Subject Didactics) / Please refer to full text to view abstract

Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a valuation domain. Since then it has also been proven that every lattice-ordered Abelian group can be recognized as the group of divisibility of a Bezont domain. Knowing these two facts allows us to use groups of divisibility to find examples of rings with highly exotic properties. For instance, we use them here to find examples of rings which admit elements that factor uniquely as the product of uncountably many primes. In addition to allowing us to create examples, groups of divisibility can he used to characterize some of the most important rings most commonly encountered in factorization theory, including valuation domains, UFD's, GCD domains, and antimatter domains. We present some of these characterizations here in addition to using them to create many examples of our own, including examples of rings which admit chains of prime ideals in which there are uncountably many primes in the chain. Moreover, we use groups of divisibility to prove that every fragmented domain must have infinite Krull dimension.

The problem of standardizing closed-canopy forest ringwidth series is investigated. A biological model for the tree-ring standardization problem indicated that one class of non-climatic variance frequently responsible for standardization problems could be objectively minimized in theory. This is the variance caused by endogenous stand disturbances which create fluctuations in ringwidth series that are non-synchronous or out-of-phase when viewed across trees in a stand. A time series method based on the autoregressive process is developed which minimizes the timewise influence of endogenous disturbances in detrended ringwidth series. Signal-to-noise ratio (SNR) properties of this method are derived which indicate that autoregressive modelling and prewhitening of detrended ringwidth indices will result in a higher SNR when endogenous disturbances are present in the series. This enables the verification of the SNR theory and the error variance reduction property of the standardization method.

published_or_final_version / Mathematics / Master / Master of Science

No description available.

Our objective was to document the effect of fire-history sampling on the mortality of mature ponderosa pine trees in Oregon. We examined 138 trees from which fire-scarred partial cross sections had been removed five to six years earlier, and 386 similarly sized, unsampled neighbor trees, from 78 plots distributed over about 5,000 ha. Mortality was low for both groups. Although mortality was significantly higher for the sectioned trees than their neighbors (8% versus 1 %), removing a partial section did not appear to increase a tree's susceptibility to death from factors such as wind or insect activity. Specifically, the few sectioned stems that broke did so well above sampling height. Most sectioned trees (79 %) had evidence of insect activity in 1994/95, while only an additional 5% had such evidence in 2000. Mortality among sectioned trees in this study was low probably because we removed relatively small sections, averaging 7 cm thick and 8% of the tree's cross-sectional area, from large trees of a species with effective, resin-based defenses against insects and pathogens. Sampling live ponderosa pine trees appears to be a non-lethal method of obtaining information on past fire regimes in this region because it only infrequently led to their death in the early years after sampling.

Dendrochronological analysis of fire scars requires tree survival of fire exposure. Trees survive fire exposure by: (1) avoidance of injury through constitutive protection and (2) induced defense. Induced defenses include (a) compartmentalization processes that resist the spread of injury and infection and (b) closure processes that restore the continuity of the vascular cambium after fire injury. Induced defenses are non-specific and are similar for fire and mechanical injury. Dissection of central hardwood species in a prescribed fire treatment area in southeastern Ohio provided an opportunity to place features seen in dendrochronological samples into their biological context. Terms for these features are proposed and further discussion is solicited.

We analyzed the radial growth response of seven boreal tree species growing on an island of Lake Duparquet, northwestern Québec. The species investigated were Betula papyrifera, Abies balsamea, Thuja occidentalis, Picea glauca, Picea mariana, Pinus banksiana and Pinus resinosa. Seven species chronologies were developed as well as seventy individual tree chronologies. Coniferous species were positively correlated to warm April and to cool-wet July. This indicates that early spring and positive water balance during the growth season favor radial growth. In contrast, the radial growth of B. papyrifera was mainly correlated to June precipitation. The response of individual trees to climate was variable but the differences between B. papyrifera and the coniferous species were maintained. No microsite factors or tree characteristics were associated with this variability. Except for B. papyrifera, it is speculated that climate change could have a similar qualitative physiological consequence on the growth of coniferous species found on homogeneous insular landscapes.

Three eastern hemlock (Tsuga canadensis (L.) Carr.) and three chestnut oak (Quercus prinus L.) ring-width chronologies were constructed from old-and second-growth stands in the Black Rock Forest in Cornwall. New York, the first developed for the highlands of southeastern New York State. The longest hemlock chronology extends from 1780-1992 and the longest oak chronology from 1806-1994. The oldest trees sampled had minimum ages of 275 and 300 years for hemlock and chestnut oak, respectively. The tree-ring chronologies were compared to monthly temperature and precipitation data from nearby West Point, NY for the 1850s-1990s and to Palmer Drought Severity Indices for 1911-1990. The chronologies provide forest growth information for the period prior to the initiation of meteorological measurements, begun in 1824 at West Point. Black Rock Forest eastern hemlock growth correlates positively with current July and prior September precipitation, with February-March temperature and with prior September Palmer Drought Severity Indices. It correlates negatively with prior June temperature. Black Rock Forest chestnut oak growth correlates positively with current June-July and prior September and December precipitation, with January temperature, and with prior September-October and current June-July Palmer Drought Severity Indices. It correlates negatively with current June-July temperature. The Black Rock Forest tree-ring records and analyses yield useful information for climate reconstruction and for assessing the potential impact of anthropogenic change (e.g. CO₂-induced climate effects, CO₂ and N fertilization, acid deposition, changes in soil chemistry due to atmospheric pollution).

A 280-year old white oak chronology was developed for south-central Virginia to verify the timber harvesting and construction dates of a cabin located on the Reynolds Homestead Research Center. A plaque on the cabin stated that the logs were harvested in 1814. However, the outer rings of the logs dated to 1875 and 1876. From the land-use history of the area, the cabin was most likely constructed to house tenant farmers after the Civil War. Most of the periods of below average growth identified in the 280-year chronology were related to drought events. Correlations between the radial growth of the white oak with temperature and precipitation data from a local weather station were examined. Precipitation had more influence on radial growth than temperature, and significant correlations (p = 0.05) existed between radial growth and precipitation from the previous September, the current April, and the current June.