Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime

We provide in this paper a first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime by using the conformal geometric approach. We will show that the existing decay results for the solutions of the Regge-Wheeler and Zerilli equations obtained recently by L. Anderson, P. Blue and J. Wang \cite{ABlu} is sufficient to obtain the conformal scattering.Comment: 20 pages, 3 firgure

Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime

In this paper, we study the Cauchy and Goursat problems of the spin-$n/2$ zero rest-mass equations on Minkowski spacetime by using the conformal geometric method. In our strategy, we prove the wellposedness of the Cauchy problem in Einstein's cylinder. Then we establish pointwise decays of the fields and prove the energy equalities of the conformal fields between the null conformal boundaries \scri^\pm and the hypersurface $\Sigma_0=\left\{ t=0 \right\}$. Finally, we prove the wellposedness of the Goursat problem in the partial conformal compactification by using the energy equalities and the generalisation of H\"ormander's result.Comment: 42 pages, 3 figure

Geological characteristics, genesis and ore controlling factors of the Tick Hill Au deposit, Dajarra District, NW Queensland, Australia

Truong Le studied the Tick Hill gold deposit near Mt Isa. He found that the gold was deposited in two stages, around 1780 and 1520 million years ago. The mineralisation style is unique to the Mt Isa Block, but resembles gold mineralisation in the Tennant Creek area. Truong Le has provided a new exploration model for high-grade gold in NW Queensland which will be of benefit to the mineral exploration industry

Conformal scattering theory for the Dirac field on Kerr spacetime

We investigate to construct a conformal scattering theory of the spin-$1/2$ massless Dirac equation on the Kerr spacetime by using the conformal geometric method and under an assumption on the pointwise decay of the Dirac field. In particular, our construction is valid in the exteriors of Schwarzschild and very slowly Kerr black hole spacetimes, where the pointwise decay was established.Comment: 39 pages, 2 figures. arXiv admin note: text overlap with arXiv:2106.0405

13C-Metabolic flux analysis of soybean somatic embryos for identification of metabolic control points in developing seed

Of the world\u27s major agronomic food crops soybeans rank highest in protein content (~40% Dwt) while also containing significant quantities of oil (~20% Dwt). Based on these unique characteristics soy has become a mainstay in world agriculture, providing a protein source for livestock and human nutrition (68% of global vegetable protein meal consumption in 2011) as well as a primary source of vegetable oil (28% of global vegetable oil consumption in 2011; http://www.soystats.com/2012). The value of soy is therefore found both in its oil and protein content and increasing the content of both is therefore desirable. Research aimed at increasing the oil content, while leaving the protein content unchanged, has exposed a fundamental lack of understanding of resource partitioning and the factors that influence protein and oil content in the soybean seed. Somatic embryos have proven to be a highly productive platform for testing gene combinations designed to change soybean composition and provide a useful model for performing physiological and biochemical studies. Soybean somatic embryos cultured in Soybean Histodifferentiation and Maturation (SHaM) medium were examined for their suitability as a model system for developing an understanding of assimilate partitioning and metabolic control points for protein and oil biosynthesis in soybean seed. It was postulated that at media compositions that were sufficient to support maximal growth rates, changes in the C:N ratio are likely to influence the partitioning of resources between the various storage products, especially protein and oil. As postulated, at steady-state growth rates embryo protein content was strongly correlated to decreasing C: N ratios and increasing glutamine consumption rates. However, oil content remained relatively unchanged across the C: N ratio range tested and resources were instead directed towards the starch and residual biomass (estimated by mass balance) pools in response to increasing C: N ratios. Protein and oil were inversely related only at media sucrose concentrations below 88 mM, where carbon limited growth and no starch was found to accumulate in the tissues. This work describes the in-depth studies of zygotic and SHaM embryos under similar culture conditions and carbon and nitrogen sources. There is no significantly different in relative growth rate for both embryos. Both protein and oil content were lower for SHaM embryos than in zygotic embryos; however, starch contents were comparable, and the balance of the biomass differences, which was accounted for by the residual (structural carbohydrate) pool, was higher in the SHaM embryos. Flux analysis in cultured embryos resulted changes in nitrogen uptake and flux into oil biosynthesis, respiratory flux (CO2), glutamine biosynthesis flux, fluxes in the total of plastic and cytosolic of triose phosphate to phosphoenolpyruvate pathway, as well as an increase in tricarboxylic acid cycle activity for zygotic embryos. However, fluxes into structure and non-structure carbohydrates were significantly higher in SHaM embryos. Despite these differences, the NMR relative intensities of proteinogenic amino acids and labeling patterns of protein and starch-related glucosyl units were comparable between the two embryo types. Carbon labeling patterns of SHaM embryos well fitted with the metabolic network model of zygotic embryos with three compartments: cytosol, plastid, and mitochondrion. The observations described here shed light onto metabolic pathways of SHaM embryos, especially as compared to soybean seed. This thesis describes experiments in which we have used Metabolic Flux Analysis to investigate the influence of transgenic perturbations and nutritional status on resource partitioning in a soybean somatic embryo system. SHaM embryos of transgenic cultures with the plastidic phosphoglucomutase (PGM) gene knocked out (PGM-KO), and the control (PGM-null) are cultured in sucrose concentrations ranged from 88 to 234 mM as a carbon source and initial glutamine concentrations ranged from 20 to 60 mM as a nitrogen source. These concentrations correspond to C:N ratios ranging from 8.8 to 70.2. Two C: N mole ratio conditions are further examined through metabolic flux analysis with labeling experiment of U-13C12 sucrose for both PGM culture. The result indicates that: (1) protein and oil of PGM-KO were consistently higher than the PGM-null; (2) content in PGM-KO shows nearly two fold as compared to PGM-null; and (3) for both PGM culture, protein content is strongly correlated with the glutamine uptake rate. Fluxes through cytosolic glucose-6-phosphate isomerase, transketolase, and transaldolase, contributed significantly to the soluble sugar content for PGM-KO culture. These fluxes changed in response to the absence of starch synthesis

Peeling of Dirac fields on Kerr spacetimes

In a recent paper with J.-P. Nicolas [J.-P. Nicolas and P.T. Xuan, Annales Henri Poincare 2019], we studied the peeling for scalar fields on Kerr metrics. The present work extends these results to Dirac fields on the same geometrical background. We follow the approach initiated by L.J. Mason and J.-P. Nicolas [L. Mason and J.-P. Nicolas, J.Inst.Math.Jussieu 2009; L. Mason and J.-P. Nicolas, J.Geom.Phys 2012] on the Schwarzschild spacetime and extended to Kerr metrics for scalar fields. The method combines the Penrose conformal compactification and geometric energy estimates in order to work out a definition of the peeling at all orders in terms of Sobolev regularity near $\mathscr{I}$, instead of ${\mathcal C}^k$ regularity at $\mathscr{I}$, then provides the optimal spaces of initial data such that the associated solution satisfies the peeling at a given order. The results confirm that the analogous decay and regularity assumptions on initial data in Minkowski and in Kerr produce the same regularity across null infinity. Our results are local near spacelike infinity and are valid for all values of the angular momentum of the spacetime, including for fast Kerr metrics.Comment: 29 page

An explicit computation of the Hecke operator and the ghost conjecture

In this paper, we investigate the Hecke operator at p = 5 and show that the upper minors of the matrix have non zero corank and, interestingly, follow the same ghost pattern in the Ghost conjecture of Bergdall and Pollack. Due to this facts, we conjecture that the slope of Hecke action in this case can be computed using an appropriate variant of ghost series. Assume this result, we achieve an upper bound for the slopes that is similar to the Gouvea's (k-1)/(p+1) conjecture

Green Scheduling of Control Systems

Electricity usage under peak load conditions can cause issues such as reduced power quality and power outages. For this reason, commercial electricity customers are often subject to demand-based pricing, which charges very high prices for peak electricity demand. Consequently, reducing peaks in electricity demand is desirable for both economic and reliability reasons. In this thesis, we investigate the peak demand reduction problem from the perspective of safe scheduling of control systems under resource constraint. To this end, we propose Green Scheduling as an approach to schedule multiple interacting control systems within a constrained peak demand envelope while ensuring that safety and operational conditions are facilitated. The peak demand envelope is formulated as a constraint on the number of binary control inputs that can be activated simultaneously. Using two different approaches, we establish a range of sufficient and necessary schedulability conditions for various classes of affine dynamical systems. The schedulability analysis methods are shown to be scalable for large-scale systems consisting of up to 1000 subsystems. We then develop several scheduling algorithms for the Green Scheduling problem. First, we develop a periodic scheduling synthesis method, which is simple and scalable in computation but does not take into account the influence of disturbances. We then improve the method to be robust to small disturbances while preserving the simplicity and scalability of periodic scheduling. However the improved algorithm usually result in fast switching of the control inputs. Therefore, event-triggered and self-triggered techniques are used to alleviate this issue. Next, using a feedback control approach based on attracting sets and robust control Lyapunov functions, we develop event-triggered and self-triggered scheduling algorithms that can handle large disturbances affecting the system. These algorithms can also exploit prediction of the disturbances to improve their performance. Finally, a scheduling method for discrete-time systems is developed based on backward reachability analysis. The effectiveness of the proposed approach is demonstrated by an application to scheduling of radiant heating and cooling systems in buildings. Green Scheduling is able to significantly reduce the peak electricity demand and the total electricity consumption of the radiant systems, while maintaining thermal comfort for occupants

Conformal scattering theory for a tensorial Fackerell-Ipser equation on the Schwarzschild spacetime

In this paper, we prove that the existence of the energy and pointwise decays for the fields satisfying the tensorial Frackerell-Ipser equations (which are obtained from the Maxwell and spin $\pm 1$ Teukolsky equations) on the Schwarzschild spacetime is sufficient to obtain a conformal scattering theory. This work is the continuation of the recent work \cite{Pha2020} on the conformal scattering theory for the Regge-Wheeler and Zerilli equations arising from the linearized gravity fields and the spin $\pm 2$ Teukolsky equations.Comment: 27 pages, 3 figures. arXiv admin note: text overlap with arXiv:2005.1204