The Generalization of the Decomposition of Functions by Energy Operators

This work starts with the introduction of a family of differential energy operators. Energy operators ($Psi_R^+$, $Psi_R^-$) were defined together with a method to decompose the wave equation in a previous work. Here the energy operators are defined following the order of their derivatives ($Psi_k^+$, $Psi_k^-$, k = {0,1,2,..}). The main part of the work is to demonstrate that for any smooth real-valued function f in the Schwartz space ($S^-(R)$), the successive derivatives of the n-th power of f (n in Z and n not equal to 0) can be decomposed using only $Psi_k^+$ (Lemma) or with $Psi_k^+$, $Psi_k^-$ (k in Z) (Theorem) in a unique way (with more restrictive conditions). Some properties of the Kernel and the Image of the energy operators are given along with the development. Finally, the paper ends with the application to the energy function.Comment: The paper was accepted for publication at Acta Applicandae Mathematicae (15/05/2013) based on v3. v4 is very similar to v3 except that we modified slightly Definition 1 to make it more readable when showing the decomposition with the families of energy operator of the derivatives of the n-th power of

Satellite mapping in cities and below cities: how good is it now?

Global navigation satellite systems (GNSS) have existed since the launch of the US global positioning system constellation in 1978. There is an increasing need for better maps in the digital age, particularly for buried utilities. One of the most convenient methods for creating accurate maps is the use of navigation satellites for positioning. However, built-up urban areas are not ideal for the use of this positioning technology. This paper provides an update on the situation regarding GNSS and assesses how new satellites and signals are contributing to better positioning availability by carrying out a test in a controlled environment. The results show that using combined satellite systems improves availability in urban canyons in some cases, but not in all scenarios. In addition, pipeline mapping technology has been tested and been shown to be an effective means of mapping pipes deep under the ground over short distances

Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis

The time evolution of geophysical phenomena can be characterised by stochastic time series. The stochastic nature of the signal stems from the geophysical phenomena involved and any noise, which may be due to, e.g., un-modelled effects or measurement errors. Until the 1990's, it was usually assumed that white noise could fully characterise this noise. However, this was demonstrated to be not the case and it was proven that this assumption leads to underestimated uncertainties of the geophysical parameters inferred from the geodetic time series. Therefore, in order to fully quantify all the uncertainties as robustly as possible, it is imperative to estimate not only the deterministic but also the stochastic parameters of the time series. In this regard, the Markov Chain Monte Carlo (MCMC) method can provide a sample of the distribution function of all parameters, including those regarding the noise, e.g., spectral index and amplitudes. After presenting the MCMC method and its implementation in our MCMC software we apply it to synthetic and real time series and perform a cross-evaluation using Maximum Likelihood Estimation (MLE) as implemented in the CATS software. Several examples as to how the MCMC method performs as a parameter estimation method for geodetic time series are given in this chapter. These include the applications to GPS position time series, superconducting gravity time series and monthly mean sea level (MSL) records, which all show very different stochastic properties. The impact of the estimated parameter uncertainties on sub-sequentially derived products is briefly demonstrated for the case of plate motion models. Finally, the MCMC results for weekly downsampled versions of the benchmark synthetic GNSS time series as provided in Chapter 2 are presented separately in an appendix

Cloning and characterization of a 9-lipoxygenase gene induced by pathogen attack from Nicotiana benthamiana for biotechnological application

<p>Abstract</p> <p>Background</p> <p>Plant lipoxygenases (LOXs) have been proposed to form biologically active compounds both during normal developmental stages such as germination or growth as well as during responses to environmental stress such as wounding or pathogen attack. In our previous study, we found that enzyme activity of endogenous 9-LOX in <it>Nicotiana benthamiana </it>was highly induced by agroinfiltration using a tobacco mosaic virus (TMV) based vector system.</p> <p>Results</p> <p>A <it>LOX </it>gene which is expressed after treatment of the viral vectors was isolated from <it>Nicotiana benthamiana</it>. As the encoded LOX has a high amino acid identity to other 9-LOX proteins, the gene was named as <it>Nb-9-LOX</it>. It was heterologously expressed in yeast cells and its enzymatic activity was characterized. The yeast cells expressed large quantities of stable 9-LOX (0.9 U ml^-1cell cultures) which can oxygenate linoleic acid resulting in high yields (18 μmol ml^-1cell cultures) of hydroperoxy fatty acid. The product specificity of Nb-9-LOX was examined by incubation of linoleic acid and Nb-9-LOX in combination with a 13-hydroperoxide lyase from watermelon (Cl-13-HPL) or a 9/13-hydroperoxide lyase from melon (Cm-9/13-HPL) and by LC-MS analysis. The result showed that Nb-9-LOX possesses both 9- and 13-LOX specificity, with high predominance for the 9-LOX function. The combination of recombinant Nb-9-LOX and recombinant Cm-9/13-HPL produced large amounts of C₉-aldehydes (3.3 μmol mg^-1crude protein). The yield of C₉-aldehydes from linoleic acid was 64%.</p> <p>Conclusion</p> <p>The yeast expressed Nb-9-LOX can be used to produce C₉-aldehydes on a large scale in combination with a <it>HPL </it>gene with 9-HPL function, or to effectively produce 9-hydroxy-10(<it>E</it>),12(<it>Z</it>)-octadecadienoic acid in a biocatalytic process in combination with cysteine as a mild reducing agent.</p

Transcriptome Analysis of H2O2-Treated Wheat Seedlings Reveals a H2O2-Responsive Fatty Acid Desaturase Gene Participating in Powdery Mildew Resistance

Hydrogen peroxide (H2O2) plays important roles in plant biotic and abiotic stress responses. However, the effect of H2O2 stress on the bread wheat transcriptome is still lacking. To investigate the cellular and metabolic responses triggered by H2O2, we performed an mRNA tag analysis of wheat seedlings under 10 mM H2O2 treatment for 6 hour in one powdery mildew (PM) resistant (PmA) and two susceptible (Cha and Han) lines. In total, 6,156, 6,875 and 3,276 transcripts were found to be differentially expressed in PmA, Han and Cha respectively. Among them, 260 genes exhibited consistent expression patterns in all three wheat lines and may represent a subset of basal H2O2 responsive genes that were associated with cell defense, signal transduction, photosynthesis, carbohydrate metabolism, lipid metabolism, redox homeostasis, and transport. Among genes specific to PmA, ‘transport’ activity was significantly enriched in Gene Ontology analysis. MapMan classification showed that, while both up- and down- regulations were observed for auxin, abscisic acid, and brassinolides signaling genes, the jasmonic acid and ethylene signaling pathway genes were all up-regulated, suggesting H2O2-enhanced JA/Et functions in PmA. To further study whether any of these genes were involved in wheat PM response, 19 H2O2-responsive putative defense related genes were assayed in wheat seedlings infected with Blumeria graminis f. sp. tritici (Bgt). Eight of these genes were found to be co-regulated by H2O2 and Bgt, among which a fatty acid desaturase gene TaFAD was then confirmed by virus induced gene silencing (VIGS) to be required for the PM resistance. Together, our data presents the first global picture of the wheat transcriptome under H2O2 stress and uncovers potential links between H2O2 and Bgt responses, hence providing important candidate genes for the PM resistance in wheat