A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

Validation of a new spot form of net blotch differential set and evidence for hybridisation between the spot and net forms of net blotch in Australia

A recently developed spot form of blotch differential set of 16 barley lines was tested for reaction response to 60 Pyrenophora teres f. maculata isolates from geographically disperse barley crops of Australia. Twelve barley lines (Arimont, Barque, Chebec, CI5286, CI5791, CI9214, CII6150, Dairokkaku, Esperance Orge 289, Galleon, Keel, Skiff, Torrens and TR250) provided differential response between the isolates. The susceptible controls Gairdner and Kombar provided indication of isolate virulence or avirulence. Abundant pathogenic diversity was revealed with 33 designated pathotypes, some of which related to geographic region. AFLP analysis also revealed abundant diversity with each of the isolates representing a unique genotype and one isolate that contained both AFLP bands unique to P. teres f. maculata and P. teres f. teres, the cause of spot form and net form of net blotch respectively, suggesting that sexual recombination between the net form and spot form isolates may have occurred naturally in the field.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

On Orlicz-Sobolev capacities

This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Sequence diversity and differential expression of major phenylpropanoid-flavonoid biosynthetic genes among three mango varieties

Background: Mango fruits contain a broad spectrum of phenolic compounds which impart potential health benefits; their biosynthesis is catalysed by enzymes in the phenylpropanoid-flavonoid (PF) pathway. The aim of this study was to reveal the variability in genes involved in the PF pathway in three different mango varieties Mangifera indica L., a member of the family Anacardiaceae: Kensington Pride (KP), Irwin (IW) and Nam Doc Mai (NDM) and to determine associations with gene expression and mango flavonoid profiles. Results: A close evolutionary relationship between mango genes and those from the woody species poplar of the Salicaceae family (Populus trichocarpa) and grape of the Vitaceae family (Vitis vinifera), was revealed through phylogenetic analysis of PF pathway genes. We discovered 145 SNPs in total within coding sequences with an average frequency of one SNP every 316bp. Variety IW had the highest SNP frequency (one SNP every 258bp) while KP and NDM had similar frequencies (one SNP every 369bp and 360bp, respectively). The position in the PF pathway appeared to influence the extent of genetic diversity of the encoded enzymes. The entry point enzymes phenylalanine lyase (PAL), cinnamate 4-mono-oxygenase (C4H) and chalcone synthase (CHS) had low levels of SNP diversity in their coding sequences, whereas anthocyanidin reductase (ANR) showed the highest SNP frequency followed by flavonoid 3'-hydroxylase (F3'H). Quantitative PCR revealed characteristic patterns of gene expression that differed between mango peel and flesh, and between varieties. Conclusions: The combination of mango expressed sequence tags and availability of well-established reference PF biosynthetic genes from other plant species allowed the identification of coding sequences of genes that may lead to the formation of important flavonoid compounds in mango fruits and facilitated characterisation of single nucleotide polymorphisms between varieties. We discovered an association between the extent of sequence variation and position in the pathway for up-stream genes. The high expression of PAL, C4H and CHS genes in mango peel compared to flesh is associated with high amounts of total phenolic contents in peels, which suggest that these genes have an influence on total flavonoid levels in mango fruit peel and flesh. In addition, the particularly high expression levels of ANR in KP and NDM peels compared to IW peel and the significant accumulation of its product epicatechin gallate (ECG) in those extracts reflects the rate-limiting role of ANR on ECG biosynthesis in mango. © 2015 Hoang et al.

Genome-wide association analysis and differential expression analysis of resistance to Sclerotinia stem rot in Brassica napus

Brassica napus is one of the most important oil crops in the world, and stem rot caused by the fungus Sclerotinia sclerotiorum results in major losses in yield and quality. To elucidate resistance genes and pathogenesis-related genes, genome-wide association analysis of 347 accessions was performed using the Illumina 60K Brassica SNP (single nucleotide polymorphism) array. In addition, the detached stem inoculation assay was used to select five highly resistant (R) and susceptible (S) B. napus lines, 48 h postinoculation with S. sclerotiorum for transcriptome sequencing. We identified 17 significant associations for stem resistance on chromosomes A8 and C6, five of which were on A8 and 12 on C6. The SNPs identified on A8 were located in a 409-kb haplotype block, and those on C6 were consistent with previous QTL mapping efforts. Transcriptome analysis suggested that S. sclerotiorum infection activates the immune system, sulphur metabolism, especially glutathione (GSH) and glucosinolates in both R and S genotypes. Genes found to be specific to the R genotype related to the jasmonic acid pathway, lignin biosynthesis, defence response, signal transduction and encoding transcription factors. Twenty-four genes were identified in both the SNP-trait association and transcriptome sequencing analyses, including a tau class glutathione S-transferase (GSTU) gene cluster. This study provides useful insight into the molecular mechanisms underlying the plant's response to S. sclerotiorum.

Differential scanning calorimetric studies on ammonium perchlorate

Differential scanning calorimetric studies on ammonium perchlorate have been carried out. The enthalpy values for the phase transition endotherm and the two exotherms have been reported in the present communication. A new method has been developed for the estimation of kinetic parameters from DSC the mograms. The values for activation energy as calculated by the above method for low temperature and high temperature exotherms are in close agreement with literature values. The present studies also confirm the presence of small exothermic peaks at the initial stages of high temperature exotherm. Explanation for the same has been given.

Inductor realisation using a finite gain differential amplifier

A finite gain differential amplifier is used along with a few passive RC elements to simulate an inductor. Methods for obtaining low Q inductance and frequency dependent high QI inductance are described. Sensitivity analysis when the gain varies is also included.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

Negative differential resistance in GaN nanocrystals above room temperature

Negative differential resistance (NDR) has been observed for the first time above room temperature in gallium nitride nanocrystals synthesized by a simple chemical route. Current-voltage characteristics have been used to investigate this effect through a metal-semiconductor-metal (M-S-M) configuration on SiO2. The NDR effect is reversible and reproducible through many cycles. The threshold voltage is similar to 7 V above room temperature.

The Pseudomonas syringae-derived HrpA pilins - molecular characterization and biotechnological application of the transcripts

Many Gram-negative bacteria pathogenic to plants and animals possess type III secretion systems that are used to cause disease. Effector proteins are injected into host cells using the type III secretion machineries. Despite vigorous studies, the nature of the secretion signal for type III secreted proteins still remains elusive. Both mRNA and proteinaceous signals have been proposed. Findings on coupling of translation to secretion by the type III secretion systems are also still contradictory. This study dealt with the secretion signal of HrpA from Pseudomonas syringae pathovar tomato. HrpA is the major component of the type III secretion system-associated Hrp pilus and a substrate for the type III secretion systems. The secretion signal was shown to reside in the first 15 codons or amino acids, a location typical for type III secretion signals. Translation of HrpA in the absence of a functional type III secretion system was established, but it does not exclude the possibility of coupling of translation to secretion when the secretion apparatus is present. The hrpA transcripts from various unrelated plant pathogenic bacteria were shown to be extremely stable. The biological relevance of this observation is unknown, but possible explanations include the high prevalence of HrpA protein, an mRNA secretion signal or timing of secretion. The hrpA mRNAs are stable over a wide range of temperatures, in the absence of translating ribosomes and even in the heterologous host Escherichia coli. The untranslated regions (UTRs) of hrpA transcripts from at least 20 pathovars of Pseudomonas syringae are highly homologous, whilst their coding regions exhibit low similarity. The stable nature of hrpA messenger RNAs is likely to be due to the folding of their 5 and 3 UTRs. In silico the UTRs seem to form stem-loop structures, the hairpin structures in the 3 UTRs being rich in guanidine and cytosine residues. The stable nature of the hrpA transcript redirected the studies to the stabilization of heterologous transcripts and to the use of stable messenger RNAs in recombinant protein production. Fragments of the hrpA transcript can be used to confer stability on heterologous transcripts from several sources of bacterial and eukaryotic origin, and to elevate the levels of production of the corresponding recombinant proteins several folds. hrpA transcript stabilizing elements can be used for improving the yields of recombinant proteins even in Escherichia coli, one of the most commonly used industrial protein production hosts.

A Nonmoving-Part Fluidic Display Using Photoelastic Effect

Digital fluidic and pneumatic systems incorporate displays for the presentation of information to the operator. Displays reported so far for such systems use moving pistons, tapes, and other mechanisms leading to lower reliability. This paper describes a nonmoving part fluidic display employing the photoelastic effect. The display is pressure actuated and has a long life. When fabricated from compatible materials, this device can withstand hostile environments like nuclear radiation, vibrations, etc. The display is compact, economical and is virtually maintenance free. The display unit has been tested in the laboratory for reliability and speed of response.

Mechanisms of KCC2 upregulation during development

Gamma-aminobutyric acid (GABA) acting through ionotropic GABAA receptors plays a crucial role in the activity of the central nervous system (CNS). It triggers Ca2+ rise providing trophic support in developing neurons and conducts fast inhibitory function in mature neuronal networks. There is a developmental change in the GABAA reversal potential towards more negative levels during the first two postnatal weeks in rodent hippocampus. This change provides the basis for mature GABAergic activity and is attributable to the developmental expression of the neuron-specific potassium chloride cotransporter 2 (KCC2). In this work we have studied the mechanisms responsible for the control of KCC2 developmental expression. As a model system we used hippocampal dissociated cultures plated from embryonic day (E) 17 mice embryos before the onset of KCC2 expression. We showed that KCC2 was significantly up-regulated during the first two weeks of culture development. Interestingly, the level of KCC2 upregulation was not altered by chronic pharmacological blockage of action potentials as well as GABAergic and glutamatergic synaptic transmission. By in silico analysis of the proximal KCC2 promoter region we identified 10 candidate transcription factor binding sites that are highly conserved in mammalian KCC2 genes. One of these transcription factors, namely early growth response factor 4 (Egr4), had similar developmental profile as KCC2 and considerably increased the activity of mouse KCC2 gene in neuronal cells. Next we investigated the involvement of neurotrophic factors in regulation of Egr4 and KCC2 expression. We found that in immature hippocampal cultures Egr4 and KCC2 levels were strongly up-regulated by brain derived neurotrophic factor (BDNF)and neurturin. The effect of neurotrophic factors was dependent on the activation of a mitogen activated protein kinase (MAPK) signal transduction pathway. Intact Egr4-binding site in proximal KCC2 promoter was required for BDNF-induced KCC2 transcription. In vitro data were confirmed by several in vivo experiments where we detected an upregulation of KCC2 protein levels after intrahippocampal administration of BDNF or neurturin. Importantly, a MAPK-dependent rise in Egr4 and KCC2 expression levels was also observed after a period of kainic acid-induced seizure activity in neonatal rats suggesting that neuronal activity might be involved in Egr4-mediated regulation of KCC2 expression. Finally we demonstrated that the mammalian KCC2 gene (alias Slc12a5) generated two neuron-specific isoforms by using alternative promoters and first exons. A novel isoform of KCC2, termed KCC2a, differed from the previously known KCC2b isoform by 40 unique N-terminal amino acid residues. KCC2a expression was restricted to CNS,remained relatively constant during postnatal development, and contributed 20 50% of total KCC2 mRNA expression in the neonatal mouse brainstem and spinal cord. In summary, our data provide insight into the complex regulation of KCC2 expression during early postnatal development. Although basal KCC2 expression seems to be intrinsically regulated, it can be further augmented by neurotrophic factors or by enhanced activity triggering MAPK phosphorylation and Egr4 induction. Additional KCC2a isoform, regulated by another promoter, provides basal KCC2 level in neonatal brainstem and spinal cord required for survival of KCC2b knockout mice.