DEVELOPMENT OF Liriodendron EST-SSR MARKERS AND GENETIC COMPOSITION OF TWO Liriodendron tulipifera L. ORCHARDS

Liriodendron tulipifera L., commonly known as yellow-poplar, is a fast-growing hardwood tree species with great ecological and economic value and is native to eastern North America. Liriodendron occupies an important phylogenetic position as a basal angiosperm and has been used in studies of the evolution of flowering plants. Genomic resources, such as Expressed Sequence Taq (EST) databases and Bacterial Artificial Chromosome (BAC) libraries, have been developed for this species. However, no genetic map is available for Liriodendron, and very few molecular markers have been developed. In this study, a total of 119 informative genomic SSR markers suitable were identified for genetic linkage map construction with an F1 progeny from #UT108A × #UT23 cross, that have been developed. The full-sibship of 213 seedlings were validated. These informative SSR markers and full-sib seedlings are essential in construction of linkage maps. Linkage map will enable molecular breeding and quantitative trait locus (QTL) mapping, and provide framework for sequencing the Liriodendron genome. In addition we characterized 20 EST-SSR markers with 174 trees from two yellow-poplar seed orchards (residing in Knoxville, Tennesse, and Clemson, South Carolina, respectively), and the US National Arboretum, and provided a first look at the genetic diversity and allele richness among selections of this unique native species. Analysis revealed only one locus significantly deviating from Hardy-Weinberg proportions in the Clemson population, and 10 loci in Knoxville population (p\u3e0.05). In addition, the Clemson orchard exhibited higher values of observed and effective number of alleles, observed heterozygosity, and Nei\u27s expected heterozygosity than the Knoxville orchard, revealing larger genetic diversity in the Clemson seed orchard

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations

Overexpression of Pear (Pyrus pyrifolia) CAD2 in Tomato Affects Lignin Content

PpCAD2 was originally isolated from the ‘Wangkumbae’ pear (Pyrus pyrifolia Nakai), and it encodes for cinnamyl alcohol dehydrogenase (CAD), which is a key enzyme in the lignin biosynthesis pathway. In order to verify the function of PpCAD2, transgenic tomato (Solanum lycopersicum) ‘Micro-Tom’ plants were generated using over-expression constructs via the agrobacterium-mediated transformation method. The results showed that the PpCAD2 over-expression transgenic tomato plant had a strong growth vigor. Furthermore, these PpCAD2 over-expression transgenic tomato plants contained a higher lignin content and CAD enzymatic activity in the stem, leaf and fruit pericarp tissues, and formed a greater number of vessel elements in the stem and leaf vein, compared to wild type tomato plants. This study clearly indicated that overexpressing PpCAD2 increased the lignin deposition of transgenic tomato plants, and thus validated the function of PpCAD2 in lignin biosynthesis

PpNAC187 Enhances Lignin Synthesis in ‘Whangkeumbae’ Pear (Pyrus pyrifolia) ‘Hard-End’ Fruit

A disorder in pears that is known as ‘hard-end’ fruit affects the appearance, edible quality, and market value of pear fruit. RNA-Seq was carried out on the calyx end of ‘Whangkeumbae’ pear fruit with and without the hard-end symptom to explore the mechanism underlying the formation of hard-end. The results indicated that the genes in the phenylpropanoid pathway affecting lignification were up-regulated in hard-end fruit. An analysis of differentially expressed genes (DEGs) identified three NAC transcription factors, and RT-qPCR analysis of PpNAC138, PpNAC186, and PpNAC187 confirmed that PpNAC187 gene expression was correlated with the hard-end disorder in pear fruit. A transient increase in PpNAC187 was observed in the calyx end of ‘Whangkeumbae’ fruit when they began to exhibit hard-end symptom. Concomitantly, the higher level of PpCCR and PpCOMT transcripts was observed, which are the key genes in lignin biosynthesis. Notably, lignin content in the stem and leaf tissues of transgenic tobacco overexpressing PpNAC187 was significantly higher than in the control plants that were transformed with an empty vector. Furthermore, transgenic tobacco overexpressing PpNAC187 had a larger number of xylem vessel elements. The results of this study confirmed that PpNAC187 functions in inducing lignification in pear fruit during the development of the hard-end disorder. View Full-Tex

Positive Solutions of a General Discrete Dirichlet Boundary Value Problem

A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub- and supersolution technique, and monotone method. All obtained results are new and valid on any n-dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different

Positive Solutions of a General Discrete Dirichlet Boundary Value Problem

A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub-and supersolution technique, and monotone method. All obtained results are new and valid on any -dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different

Existence Of Traveling Waves Of Auto-Catalytic Systems With Decay

This article establishes the existence of traveling waves of a class of reaction–diffusion systems which model the pre-mixed isothermal autocatalytic chemical reaction of order m (m\u3e1) between two chemical species, a reactant and an auto-catalyst, and a linear decay. Moreover, our result shows that the set of speed is contained in a bounded interval for any fixed initial value at x=−∞. This is in strong contrast to either the reaction–diffusion systems of autocatalytic chemical reaction of the order m without decay, or to the systems which have the same order of decay, which were shown by various authors (e.g. [8,13,17,26]) that the set of traveling wave speeds contains [c⁎,∞) for some c⁎\u3e0. The same systems also appear in a mathematical model of microbial growth and competition in a flow reactor; see [2,24]