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.

Cereal cultivars can be ranked consistently for resistance to root-lesion nematodes (Pratylenchus thornei & P. neglectus) using diverse procedures

The root-lesion nematodes (RLN) Pratylenchus thornei and P. neglectus are widely distributed in Australian grain producing regions and can reduce the yield of intolerant wheat cultivars by up to 65 , costing the industry ~123 M AUD/year. Consequently, researchers in the northern, southern and western regions have independently developed procedures to evaluate the resistance of cereal cultivars to RLN. To compare results, each of the three laboratories phenotyped a set of 26 and 36 cereal cultivars for relative resistance/susceptibility to P. thornei and P. neglectus respectively. The northern and southern regions also investigated the effects of planting time and experiment duration on RLN reproduction and cultivar ranking. Results show the genetic correlation between cultivars tested using the northern and southern procedures evaluating P. thornei resistance was 0.93. Genetic correlations between experiments using the same procedure, but with different planting times, were 0.99 for both northern and southern procedures. The genetic correlation between cultivars tested using the northern, southern and western procedures evaluating P. neglectus resistance ranged from 0.71 to 0.95. Genetic correlations between experiments using the same procedure but with different planting times ranged from 0.91 to 0.99. This study established that, even though experiments were conducted in different geographic locations and with different trial management practices, the diverse nematode resistance screening procedures ranked cultivars similarly. Consequently, RLN resistance data can be pooled across regions to provide national consensus ratings of cultivars.

[Liebe Verwandte, liebe Freunde].

A letter to friends and relatives from Eva and Wolfgang on occasion of their son’s birth, explaining why they chose for him the Jewish biblical name Elias.

Isotope shifts and hyperfine structure in the 555.8-nm S-1(0) -> P-3(1) line of Yb

We apply our technique of using a Rb-stabilized ring-cavity resonator to measure the frequencies of various spectral components in the 555.8-nm 1S0-->3P1 line of Yb. We determine the isotope shifts with 60 kHz precision, which is an order-of-magnitude improvement over the best previous measurement on this line. There are two overlapping transitions, 171Yb(1/2-->3/2) and 173Yb(5/2-->3/2), which we resolve by applying a magnetic field. We thus obtain the hyperfine constants in the 3P1 state of the odd isotopes with a significantly improved precision. Knowledge of isotope shifts and hyperfine structure should prove useful for high-precision calculations in Yb necessary to interpret ongoing experiments testing parity and time-reversal symmetry violation in the laws of physics.

Cotton root systems and recovery of applied P and K fertilisers

With potential to accumulate substantial amounts of above-ground biomass, at maturity an irrigated cotton crop can have taken up more than 20 kg/ha phosphorus and often more than 200 kg/ha of potassium. Despite the size of plant accumulation of P and K, recovery of applied P and K fertilisers by the crop in our field experiment program has poor. Processing large amounts of mature cotton plant material to provide a representative sample for chemical analysis has not been without its challenges, but the questions regarding mechanism of where, how and when the plant is acquiring immobile nutrients remain. Dry matter measured early in the growing season (squaring, first white flower) have demonstrated a 50% increase in crop biomass to applied P (in particular), but it represents only 20% of the total P accumulation by the plant. By first open boll (and onwards), no response in dry matter or P concentration could be detected to P application. A glasshouse study indicated P recovery was greater (to FOB) where it was completely mixed through a profile as opposed to a banded application method suggesting cotton prefers a more diffuse distribution. The relative effects of root morphology, mycorrhizal fungi infection, seasonal growth patterns and how irrigation is applied are areas for future investigation on how, when and where cotton acquires immobile nutrients.

Luokan P loogisesta karakterisoinnista

Deskriptiivisessä vaativuusteoriassa tutkitaan laskennan vaativuuteen liittyviä kysymyksiä logiikan työkalujen avulla. Tällöin käsitellään tilannetta, jossa laskennan syötteenä toimivat äärelliset mallit. Tässä kehyksessä erinäisiä vaativuusluokkia voidaan karakterisoida etsimällä logiikoita, joilla on kyseistä vaativuusluokkaa vastaava ilmaisuvoima. Klassiset esimerkit tällaisista tuloksista ovat Faginin esittämä epädeterministisen polynomiaalisen ajan karakterisaatio logiikan Σ_1^1 avulla ja Immermanin, Livchakin ja Vardin esittämä deterministisen polynomiaalisen ajan karakterisaatio ensimmäisen kertaluvun inflatorisen kiintopistelogiikan avulla. Tässä opinnäytetyössä tarkastellaan Gurevichin esittämää kysymystä polynomiaalisessa ajassa ratkeavien kielten luokan P vahvasta loogisesta karakterisaatiosta. Kyseinen kysymys on yksi äärellisen malliteorian haastavimpia ongelmia. Kysymyksen esittelyyn tarvittavan peruskoneiston läpikäynnin lisäksi tässä käsi- tellään myös sen yhteyksiä laskennan vaativuusteoriassa keskeiseen P-NP-ongelmaan. Gurevichin kysymyksestä voidaan esittää myös rajoitetumpia versioita, mikäli käsitellään tilannetta, jossa laskennan syötteenä voi olla vain kiinnitetyn malliluokan K malleja. Tällöin luokan P karakterisointi helpottuu, ainakin jos luokka K on riittävän suppea. Tässä opinnäytetyössä käydään läpi Grohen esittämä tulos siitä, että mikäli luokaksi K valitaan 3-yhtenäisten tasoverkkojen luokka, niin ensimmäisen kertaluvun inflatorinen kiintopistelogiikka karakterisoi polynomiaalisessa ajassa laskettavat kielet.

Dedication of new synagogue in Surinam (Dutch)

Digital image

Recommendation of Jacques Judah Lyons from Surinam

Digital image

Shochet's certificate

Digital image

Response to deep placed P, K and S in central Queensland

Two field experiments were established in central Queensland at Capella and Gindie to investigate the immediate and then residual benefit of deep placed (20 cm) nutrients in this opportunity cropping system. The field sites had factorial combinations of P (40 kg P/ha), K (200 kg K/ha) and S (40 kg S/ha) and all plots received 100 kg N/ha. No further K or S fertilizers were added during the experiment but some crops had starter P. The Capella site was sown to chickpea in 2012, wheat in 2013 and then chickpea in 2014. The Gindie site was sown to sorghum in 2011/12, chickpea in 2013 and sorghum in early 2015. There were responses to P alone in the first two crops at each site and there were K responses in half the six site years. In year 1 (a good year) both sites showed a 20% grain yield response to only to deep P. In year 2 (much drier) the effects of deep P were still evident at both sites and the effects of K were clearly evident at Gindie. There was a suggestion of an additive P+K effect at Capella and a 50% increase for P+K at Gindie. Year 3 was dry and chickpeas at Capella showed a larger response to P+K but the sorghum at Gindie only responded to deep K. These results indicate that responses to deep placed P and K are durable over an opportunity cropping system, and meeting both requirements is important to achieve yield responses.

Conversion of (+/-)-synephrine into p-hydroxyphenylacetaldehyde by Arthrobacter synephrinum: A novel enzymic reaction

A partically purified enzyme from Arthrobacter synephrinum was found to catalyse the conversion of (+/-)-synphrine into p-hydroxyphrenylacetaldehyde and methylamine. The enzyme is highly specific for synephrine and is distinctly different from monoamine oxidase.

The business of myth-making: Mary Poppins, P.L. Travers and the Disney effect

In just one of the many extraordinary moments during the spectacular Opening Ceremony of the 2012 London Olympic Games, thirty Mary Poppinses floated into the stadium on their umbrellas to battle a 40 foot-long inflatable Lord Voldemort. This multi-million pound extravaganza was telecast to a global audience of over one billion people, highlighting in an extremely effective manner the grandeur and eccentricities of the host nation, and featuring uniquely British icons such as Mr Bean, James Bond, The Beatles and Harry Potter, as well as those quintessential icons of Englishness, the Royal Family, double-decker red buses and the National Health Service.

Poll of an election

Digital image

Minutes of trustees meetings

Digital image

Schneeberger-Saenger Collection 1837-1845

Business ledger in Yiddish (1837-1845)