Exponential energy decay for the kadomtsev-petviashvili (KP-II) equation

In this paper we study the exponential decay of the energy of the externally damped Kadomtsev-Petviashvili (KP-II) equation. Our main tool is the classical dissipation-observability method. We use multiplier techniques to establish the main estimates, and obtain exponential decay result.Fundação para a Ciência e a Tecnologia (FCT

Evaluation of tomato accessions for flavour and flavour-contributing components

Flavour is one of the most highly demanded consumer traits of tomato at present; poor flavour is one of the most commonly heard complaints associated with modern varieties of tomato. In order to combine flavour with other desirable fruit traits in improved cultivars, it is important to determine how much variability exists in the crucial compounds that contribute most to flavour. The objective of the present study was to determine the variability of flavour-contributing components including total soluble solids (TSS) and total titratable acids (TTA) among other subjective traits related to flavour in a core collection of tomato accessions. The core collection was comprised of 173 tomato accessions with a wide genetic background from the United States Department of Agriculture (USDA), Agricultural Research Services (ARS) Plant Genetic Resources Unit repository. The TTA varied from 0.20 to 0.64%, whereas the TSS ranged from 3.4 to 9.0%, indicating the availability of broad variation for these traits. Rinon (PI 118783), Turrialba, Purple Calabash and LA2102 were among the high TTA (>0.45%) containing accessions, whereas those with high TSS (>7.0%) were AVRDC#6, Sponzillo and LA2102. A positive correlation of overall flavour with TTA (r=0.33; P<0.05) and TSS (r=0.37; P<0.05) indicated that these two components play an important role in determining the overall flavour in tomato. Subjectively measured other traits including fruity odour and fruity flavour had positive correlations with overall flavour. Overall flavour is discussed in the context of other traits including fruit firmness. Information obtained from this study may be useful for tomato breeders aiming to improve tomato flavou

Global well-posedness for a coupled modified kdv system

We prove the sharp global well-posedness result for the initial value problem (IVP) associated to the system of the modi ed Korteweg-de Vries (mKdV) equation. For the single mKdV equation such result has been obtained by using Mirura's Transform that takes the KdV equation to the mKdV equation [8]. We do not know the existence of Miura's Transform that takes a KdV system to the system we are considering. To overcome this di culty we developed a new proof of the sharp global well-posedness result for the single mKdV equation without using Miura's Transform. We could successfully apply this technique in the case of the mKdV system to obtain the desired result.Fundação para a Ciência e a Tecnologia (FCT

On the ill-posedness result for the BBM equation

We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.Fundação para a Ciência e a Tecnologia (FCT

Transcriptome Profiling of Citrus Fruit Response to Huanglongbing Disease

Huanglongbing (HLB) or “citrus greening” is the most destructive citrus disease worldwide. In this work, we studied host responses of citrus to infection with Candidatus Liberibacter asiaticus (CaLas) using next-generation sequencing technologies. A deep mRNA profile was obtained from peel of healthy and HLB-affected fruit. It was followed by pathway and protein-protein network analysis and quantitative real time PCR analysis of highly regulated genes. We identified differentially regulated pathways and constructed networks that provide a deep insight into the metabolism of affected fruit. Data mining revealed that HLB enhanced transcription of genes involved in the light reactions of photosynthesis and in ATP synthesis. Activation of protein degradation and misfolding processes were observed at the transcriptomic level. Transcripts for heat shock proteins were down-regulated at all disease stages, resulting in further protein misfolding. HLB strongly affected pathways involved in source-sink communication, including sucrose and starch metabolism and hormone synthesis and signaling. Transcription of several genes involved in the synthesis and signal transduction of cytokinins and gibberellins was repressed while that of genes involved in ethylene pathways was induced. CaLas infection triggered a response via both the salicylic acid and jasmonic acid pathways and increased the transcript abundance of several members of the WRKY family of transcription factors. Findings focused on the fruit provide valuable insight to understanding the mechanisms of the HLB-induced fruit disorder and eventually developing methods based on small molecule applications to mitigate its devastating effects on fruit production