Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Inheritance and Characterization of Strong Resistance to Phosphine in Sitophilus oryzae(L.)

Sitophilus oryzae (Linnaeus) is a major pest of stored grain across Southeast Asia and is of increasing concern in other regions due to the advent of strong resistance to phosphine, the fumigant used to protect stored grain from pest insects. We investigated the inheritance of genes controlling resistance to phosphine in a strongly resistant S. oryzae strain (NNSO7525) collected in Australia and find that the trait is autosomally inherited and incompletely recessive with a degree of dominance of -0.66. The strongly resistant strain has an LC50 52 times greater than a susceptible reference strain (LS2) and 9 times greater than a weakly resistant strain (QSO335). Analysis of F2 and backcross progeny indicates that two or more genes are responsible for strong resistance, and that one of these genes, designated Sorph1, not only contributes to strong resistance, but is also responsible for the weak resistance phenotype of strain QSO335. These results demonstrate that the genetic mechanism of phosphine resistance in Soryzae is similar to that of other stored product insect pests. A unique observation is that a subset of the progeny of an F1 backcross generation are more strongly resistant to phosphine than the parental strongly resistant strain, which may be caused by multiple alleles of one of the resistance genes.

Historical demography of Lantana camara L. reveals clues about the influence of land use and weather in the management of this widespread invasive species

Weather is a general stochastic influence on the life history of weeds. In contrast, anthropogenic disturbance (e.g. land use) is an important deterministic influence on weed demography. Our aim with this study was to investigate the relative contributions of land use and weather on the demography of Lantana camara (lantana), a weed of agricultural and natural habitats, based on the intensive monitoring of lantana populations under three land uses (viz. farm[pasture], and burnt and grazed forests) in subtropical Australia. Lantana populations were growing vigorously across all land uses (asymptotic population growth rate, λ > 3). Examination of historical demography using retrospective perturbation analyses showed that weather was a strong influence on lantana demography with the transition from an El Niño (2008–09) to a La Niña (2009–10) year having a strong positive effect on population growth rate. This effect was most marked at the grazed site, and to a lesser extent at the burnt site, with seedling-to-juvenile and juvenile-to-adult transitions contributing most to these effects. This is likely the result of burning and grazing having eliminated/reduced interspecific competition at these sites. Prospective perturbation analyses revealed that λ was most sensitive to proportionate changes in growth transitions, followed by fecundity and survival transitions. Examination of context-specific patterns in elasticity revealed that growth and fecundity transitions are likely to be the more critical vital rates to reduce λ in wet years at the burnt and grazed forest sites, compared to the farm/pasture site. Management of lantana may need to limit the transition of juveniles into the adult stages, especially in sites where lantana is free from competition (e.g. in the presence of fire or grazing), and this particularly needs to be achieved in wet years. Collectively, these results shed light on aspects of spatial and temporal variation in the demography of lantana, and offer insights on its context-specific management.

Mechanism of glycine uptake by the silk glands of the silkworm Bombyx mori L

The transport of glycine in vitro into the silk glands of the silkworm has been studied. Glycine accumulates inside the tissue to a concentration higher than that present outside, indicating an active transport mechanism. The kinetics of uptake show a biphasic curve and two apparent Km values for accumulation, 0.33 mM and 5.00 mM. The effect of inhibitors on the energy metabolism of glycine transport is inconclusive. Exchange studies indicate the existence of two pools inside the gland, one that is easily removed by exchange and osmotic shock, and the other which is not. The results obtained conform with the carrier model of Britten and McClure concerning the amino-acid pool in E. coli.

Cadmium stress alters the redox reaction and hormone balance in oilseed rape (Brassica napus L.) leaves

In order to understand the physiological response of oilseed rape (Brassica napus L.) leaves to cadmium (Cd) stress and exploit the physiological mechanisms involved in Cd tolerance, macro-mineral and chlorophyll concentrations, reactive oxygen species (ROS) accumulation, activities of enzymatic antioxidants, nonenzymatic compounds metabolism, endogenous hormonal changes, and balance in leaves of oilseed rape exposed to 0, 100, or 200 μM CdSO4 were investigated. The results showed that under Cd exposure, Cd concentrations in the leaves continually increased while macro-minerals and chlorophyll concentrations decreased significantly. Meanwhile, with increased Cd stress, superoxide anion (O 2 • − ) production rate and hydrogen peroxide (H2O2) concentrations in the leaves increased significantly, which caused malondialdehyde (MDA) accumulation and oxidative stress. For scavenging excess accumulated ROS and alleviating oxidative injury in the leaves, the activity of enzymatic antioxidants, such as superoxide dismutase (SOD), peroxidase (POD), and catalase (CAT), was increased significantly at certain stress levels. However, with increased Cd stress, the antioxidant enzyme activities all showed a trend towards reduction. The nonenzymatic antioxidative compounds, such as proline and total soluble sugars, accumulated continuously with increased Cd stress to play a long-term role in scavenging ROS. In addition, ABA levels also increased continuously with Cd stress while ZR decreased and the ABA/ZR ratio increased, which might also be providing a protective role against Cd toxicity.

The combined effect of biological control with plant competition on the management of parthenium weed (Parthenium hysterophorus l.)

Parthenium hysterophorus L., (Asteraceae) commonly known as parthenium weed, is a highly invasive plant that has become a problematic weed of pasture lands in Australia and many other countries around the world. For the management of this weed, an integrated approach comprising biological control and plant competition strategies was tested in southern central Queensland. Two competitive pasture plant species (butterfly pea and buffel grass), selected for their high competitive ability, worked successfully with the biological control agent (Epiblema strenuana Walker) to synergistically reduce the biomass of parthenium weed, by between 62 and 69%. In the presence of biological control agent, the corresponding biomass of competitive plants, butterfly pea and buffel grass increased in comparison to when the biological control agent had been excluded, by 15 and 35%, respectively. This suggests that biological control and competitive plants can complement one another to bring about improved management of parthenium weed in Australia. Further, this approach may be adopted in countries where some of the biological control agents are already present including South Africa, Ethiopia, India, Pakistan and Nepal.

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Purification and Regulatory Properties of Mung Bean (Vigna Radiata L.) Serine Hydroxymethyltransferase 1

Serine hydroxymethyltransferase, the first enzyme in the pathway for interconversion of C1 fragments, was purified to homogeneity for the first time from any plant source. The enzyme from 72-h mung bean (Vigna radiata L.) seedlings was isolated using Blue Sepharose CL-6B and folate-AH-Sepharose-4B affinity matrices and had the highest specific activity (1.33 micromoles of HCHO formed per minute per milligram protein) reported hitherto. The enzyme preparation was extremely stable in the presence of folate or L-serine. Pyridoxal 5'-phosphate, ethylenediaminetetraacetate and 2-mercaptoethanol prevented the inactivation of the enzyme during purification. The enzyme functioned optimally at pH 8.5 and had two temperature maxima at 35 and 55°C. The Km values for serine were 1.25 and 68 millimolar, corresponding to Vmax values of 1.8 and 5.4 micromoles of HCHO formed per minute per milligram protein, respectively. The K0.5 value for L-tetrahydrofolate (H4folate) was 0.98 millimolar. Glycine, the product of the reaction and D-cycloserine, a structural analog of D-alanine, were linear competitive inhibitors with respect to L-serine with Ki values of 2.30 and 2.02 millimolar, respectively. Dichloromethotrexate, a substrate analog of H4folate was a competitive inhibitor when H4folate was the varied substrate. Results presented in this paper suggested that pyridoxal 5'-phosphate may not be essential for catalysis.The sigmoid saturation pattern of H4folate (nH = 2.0), one of the substrates, the abolition of sigmoidicity by NADH, an allosteric positive effector (nH = 1.0) and the increase in sigmoidicity by NAD+ and adenine nucleotides, negative allosteric effectors (nH = 2.4) clearly established that this key enzyme in the folate metabolism was an allosteric protein. Further support for this conclusion were the observations that (a) serine saturation exhibited an intermediary plateau region; (b) partial inhibition by methotrexate, aminopterin, O-phosphoserine, DL-{alpha}-methylserine and DL-O-methylserine; (c) subunit nature of the enzyme; and (d) decrease in the nH value from 2.0 for H4folate to 1.5 in presence of L-serine. These results highlight the regulatory nature of mung bean serine hydroxymethyltransferase and its possible involvement in the modulation of the interconversion of folate coenzymes.

Nitrogenase activity (acetylene reduction) associated with leaves of different cultivars of paddy (Oryza sativa L.)

An investigation was conducted to study the levels of nitrogen fixation on the leaf or sheath surfaces of four cultivars of paddy plants by using acetylene reduction technique. Varying levels of positive nitrogenase activity were observed on all the leaf surfaces. Sheath of IET 1991 cultivar showed a higher rate of fixation than the leaf surface. All the nitrogen-fixing organisms on the leaf or sheath surfaces belonged to the genus Beijerinckia. There was no correlation between the bacterial density and the level of fixation. Scanning electron microscopic data revealed that the upper surface of IET 1991 leaf was highly silicified and the microflora was either scanty or nil while the lower surface appeared quite different and harboured more micro-organisms. Similarly, the inner surface of sheath was devoid of silicification and showed the presence of micro-organisms.

L-Tyrosyl-L-glutarnie Acid Monohydrate, C14H18N206.H20

Mr=328.32, triclinic, P1, a=5.801 (1), b=7.977(1), c=9.110(2)A, ~t=102.33 (1), fl= 97.92 (1), y= 109.82 (1) °, v= 377.2 (1) A 3 at 293 K, Z=I, D x=1.45, D m=1.45 g cm -3, 2(MoKs)= 0.7107 A, ~ = 0.74 cm -1, F(000) = 174.0. R = 0.046 for 990 unique observed [F o > 4O(Fo)] reflections. The crystal structure is stabilized by extensive hydrogen bonding involving all N and O atoms.

Letter from Reverend M. L. M. Peixotto regarding Rabbi Corcos of Curaçao

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Genetic conservation of Phosphine Resistance in the Rice Weevil Sitophilus oryzae (L.)

High levels of resistance to phosphine in the rice weevil Sitophilus oryzae have been detected in Asian countries including China and Vietnam, however there is limited knowledge of the genetic mechanism of resistance in these strains. We find that the genetic basis of strong phosphine resistance is conserved between strains of S. oryzae from China, Vietnam and Australia. Each of four strongly resistant strains has an identical amino acid variant in the encoded dihydrolipoamide dehydrogenase (DLD) enzyme that was previously identified as a resistance factor in Rhyzopertha dominica and Tribolium castaneum. The unique amino acid substitution, Asparagine > Threonine (N505T) of all strongly resistant S. oryzae corresponds to the position of an Asparagine > Histidine variant (N506H) that was previously reported in strongly resistant R. dominica. Progeny (F16 and F18) from two independent crosses showed absolute linkage of N505T to the strong resistance phenotype, indicating that if N505T was not itself the resistance variant that it resided within 1 or 2 genes of the resistance factor. Non-complementation between the strains confirmed the shared genetic basis of strong resistance, which was supported by the very similar level of resistance between the strains, with LC50 values ranging from 0.20 to 0.36 mgL-1 for a 48 hour exposure at 25°C. Thus, the mechanism of high level resistance to phosphine is strongly conserved between R. dominica, T. castaneum and S. oryzae. A fitness cost associated with strongly resistant allele was observed in segregating populations in the absence of selection.

Letter to M. L. M. Peixotto to place Mrs. Brandley Isaacs on list of perpetual escaboth

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Letter from D. G. Seixas to M. L. M. Peixotto regarding Hebrew name of Mr. Solomons

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