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Surjective endomorphisms of projective surfaces -- the existence of infinitely many dense orbits
Let be a surjective endomorphism of a normal projective
surface. When , applying an (iteration of)
-equivariant minimal model program (EMMP), we determine the geometric
structure of . Using this, we extend the second author's result to singular
surfaces to the extent that either has an -invariant non-constant
rational function, or has infinitely many Zariski-dense forward orbits;
this result is also extended to Adelic topology (which is finer than Zariski
topology)
Distant Reading Methods for Historical Chinese Newspaper: The Case of Reading Tianyi Bao with Topic Modeling
This is the presentation slides for DH course
Screening for calcium phosphate solubilizing Rhizobium leguminosarumi
Rhizobium leguminosarum are well known for their ability to fix nitrogen (N). In addition, their capacity to solubilize phosphate has been receiving attention in recent years. The work presented in this thesis examined two aspects of screening and evaluating dicalcium phosphate (Pi) (CaHPO4) solubilizing R. leguminosarum. The objectives of this study were to: 1) identify a medium that is sensitive and effective as a screening tool for phospahte solubilizing R. leguminosarum; 2) determine the effect of N and carbon (C) on growth and P solubilization of R. leguminosarum isolates; 3) determine the relationship between the ability to solubilize CaHPO4 by R. leguminosarum isolates on solid medium and in liquid broth of same composition; and 4) assess and compare the ability of R. leguminosarum isolates to solubilize different P sources in soil under growth chamber conditions.In this study, 30 R. leguminosarum isolates were evaluated for phosphate solubilization in broth and solid formulations of three different media, Yeast Mannitol Extract (YEM), Botanical Research Institute Phosphate Nutrient medium (MNBRI) and Pikovskaya Phosphate medium (PVK). All media contain CaHPO4 as the only phosphorus (P) source. The R. leguminosarum isolates were selected on the basis of their different plasmid profiles, indicative of genetically distinct isolates. All 30 isolates increased the Pi concentration in solution to varying degrees in liquid cultures but performance varied from one medium to another. The highest average solution Pi concentration achieved by the 30 R. leguminosarum isolates was obtained from PVK cultured broth. CaHPO4 solubilization by R. leguminosarum isolates in liquid was associated with a decrease in pH. Among the three tested media, the lowest pH by the thirty R. leguminosarum isolates was obtained in PVK. Ability of the isolates to solubilize CaHPO4 on the solid media was not comparable to the performance of the isolates grown in liquid because only fewer R. leguminosarum isolates showed visible P solubilization on the solid media.The composition and formulation of medium influence the ability of the R. leguminosarum isolates to solubilize CaHPO4. Effects of N and C concentrations on the growth and CaHPO4 solubilization by nine R. leguminosarum isolates were examined in liquid formulation. Ammonium N had a greater influence on the growth and CaHPO4 solubilization by R. leguminosarum isolates than C at the tested levels. The growth of isolates was inhibited by ammonium N at 0.5 g L-1 as (NH4)2SO4 meaning there were less viable cells in this N concentration than were of ammonium N at 0.1 g L-1. The ability of isolates to solubilize Pi however was not affected by ammonium N at 0.5 g L-1 as (NH4)2SO4. The media containing low N (0.1 g (NH4)2S04 L-1) both Pi solubilization and growth of R. leguminosarum isolates were not affected.R. leguminosarum isolates were tested for their effects on growth and P uptake of canola plants in P-deficient soils amended with different P sources. R. leguminosarum isolates were selected separately based on their ability to solubilize CaHPO4 from the three screening media. A quadrant model was used based on the ability of the 30 R. leguminosarum isolates to solubilize CaHPO4 on both solid and liquid formulations within a medium. The effect of R. leguminosarum on canola dry mass, tissue Pi content and total Pi uptake varied from one isolate to another, but was not different from the controls. The quadrant model failed to correlate isolates able to solubilize CaHPO4 in laboratory screening to isolates able to solubilize P in the growth chamber. Despite the influence of the medium composition and formulation, none of tested media predicted Pi solubilization ability by the R. leguminosarum isolates in soils under growth chamber conditions, from their Pi solubilization of laboratory screenings. The work of this thesis demonstrates that phosphate solubilization is a complex process that depends on both organism and soil. Growth condition is an important factor for a R. leguminosarum isolate to express its ability to solubilize CaHPO4. Liquid media screenings illustrate an isolate’s ability to solubilize CaHPO4 under nonstressful conditions, but solid media screenings demonstrate the P solubilization result of an isolate under more stressful conditions. The lack of relationship in P solubilization ability by R. leguminosarum isolates, between laboratory methods to soil test, means neither liquid or solid media can provide a definitive selection process. Additional parameters should be investigated to modify the soil bioassay protocols and ultimate selection procedures. These include pH conditions, isolate colonization, growth, and survival on plants and rhizosphere
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