Friedrichs extensions for a class of singular discrete linear Hamiltonian systems

This paper is concerned with the characterizations of the Friedrichs extension for a class of singular discrete linear Hamiltonian systems. The existence of recessive solutions and the existence of the Friedrichs extension are proved under some conditions. The self-adjoint boundary conditions are obtained by applying the recessive solutions and then the characterization of the Friedrichs extension is obtained in terms of boundary conditions via linear independently recessive solutions

Partial sequencing of the bottle gourd genome reveals markers useful for phylogenetic analysis and breeding

<p>Abstract</p> <p>Background</p> <p>Bottle gourd [<it>Lagenaria siceraria </it>(Mol.) Standl.] is an important cucurbit crop worldwide. Archaeological research indicates that bottle gourd was domesticated more than 10,000 years ago, making it one of the earliest plants cultivated by man. In spite of its widespread importance and long history of cultivation almost nothing has been known about the genome of this species thus far.</p> <p>Results</p> <p>We report here the partial sequencing of bottle gourd genome using the 454 GS-FLX Titanium sequencing platform. A total of 150,253 sequence reads, which were assembled into 3,994 contigs and 82,522 singletons were generated. The total length of the non-redundant singletons/assemblies is 32 Mb, theoretically covering ~ 10% of the bottle gourd genome. Functional annotation of the sequences revealed a broad range of functional types, covering all the three top-level ontologies. Comparison of the gene sequences between bottle gourd and the model cucurbit cucumber (<it>Cucumis sativus</it>) revealed a 90% sequence similarity on average. Using the sequence information, 4395 microsatellite-containing sequences were identified and 400 SSR markers were developed, of which 94% amplified bands of anticipated sizes. Transferability of these markers to four other cucurbit species showed obvious decline with increasing phylogenetic distance. From analyzing polymorphisms of a subset of 14 SSR markers assayed on 44 representative China bottle gourd varieties/landraces, a principal coordinates (PCo) analysis output and a UPGMA-based dendrogram were constructed. Bottle gourd accessions tended to group by fruit shape rather than geographic origin, although in certain subclades the lines from the same or close origin did tend to cluster.</p> <p>Conclusions</p> <p>This work provides an initial basis for genome characterization, gene isolation and comparative genomics analysis in bottle gourd. The SSR markers developed would facilitate marker assisted breeding schemes for efficient introduction of desired traits.</p

Dual-Level Regulation of ACC Synthase Activity by MPK3/MPK6 Cascade and Its Downstream WRKY Transcription Factor during Ethylene Induction in Arabidopsis

Plants under pathogen attack produce high levels of ethylene, which plays important roles in plant immunity. Previously, we reported the involvement of ACS2 and ACS6, two Type I ACS isoforms, in Botrytis cinerea–induced ethylene biosynthesis and their regulation at the protein stability level by MPK3 and MPK6, two Arabidopsis pathogen-responsive mitogen-activated protein kinases (MAPKs). The residual ethylene induction in the acs2/acs6 double mutant suggests the involvement of additional ACS isoforms. It is also known that a subset of ACS genes, including ACS6, is transcriptionally induced in plants under stress or pathogen attack. However, the importance of ACS gene activation and the regulatory mechanism(s) are not clear. In this report, we demonstrate using genetic analysis that ACS7 and ACS11, two Type III ACS isoforms, and ACS8, a Type II ACS isoform, also contribute to the B. cinerea–induced ethylene production. In addition to post-translational regulation, transcriptional activation of the ACS genes also plays a critical role in sustaining high levels of ethylene induction. Interestingly, MPK3 and MPK6 not only control the stability of ACS2 and ACS6 proteins via direct protein phosphorylation but also regulate the expression of ACS2 and ACS6 genes. WRKY33, another MPK3/MPK6 substrate, is involved in the MPK3/MPK6-induced ACS2/ACS6 gene expression based on genetic analyses. Furthermore, chromatin-immunoprecipitation assay reveals the direct binding of WRKY33 to the W-boxes in the promoters of ACS2 and ACS6 genes in vivo, suggesting that WRKY33 is directly involved in the activation of ACS2 and ACS6 expression downstream of MPK3/MPK6 cascade in response to pathogen invasion. Regulation of ACS activity by MPK3/MPK6 at both transcriptional and protein stability levels plays a key role in determining the kinetics and magnitude of ethylene induction

Error Estimate of Eigenvalues of Perturbed Higher-Order Discrete Vector Boundary Value Problems

This paper is concerned with the eigenvalues of perturbed higher-order discrete vector boundary value problems. A suitable admissible function space is first introduced, a new variational formula of eigenvalues is then established under certain nonsingularity conditions, and error estimates of eigenvalues of problems with small perturbation are finally given by using the variational formula. As a direct consequence, continuous dependence of eigenvalues on boundary value problems is obtained under the nonsingularity conditions. In addition, two special perturbed cases are discussed

Cerium oxide nanoparticle-loaded polyvinyl alcohol nanogels delivery for wound healing care systems on surgery

This study was designed to establish the composition of wound bandages based on Cerium nanoparticle (CeNP)-loaded polyvinyl alcohol (PVA) nanogels. The CeNP nanogel (Ce-nGel) was fabricated by the fructose-mediated reduction of Cerium oxide solutions within the PVA matrix. The influences of different experimental limitations on PVA nanogel formations were examined. The nanogel particle sizes were evaluated by transmission electron microscopy and determined to range from ∼10 to 50 nm. Additionally, glycerol was added to the Ce-nGels, and the resulting compositions (Ce-nGel-Glu) were coated on cotton fabrics to generate the wound bandaging composite. The cumulative drug release profile of the Cerium from the bandage was found to be ∼38% of the total loading after two days. Additionally, antibacterial efficacy was developed for Gam positive and negative microorganisms. Moreover, we examined in vivo healing of skin wounds formed in mouse models over 24 days. In contrast to the untreated wounds, rapid healing was perceived in the Ce-nGel-Glu-treated wound with less damage. These findings indicate that Ce-nGel-Glu-based bandaging materials could be a potential candidate for wound healing applications in the future