Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

Spatial Patterns in Hyphal Growth and Substrate Exploitation within Norway Spruce Stems Colonized by the Pathogenic White-Rot Fungus Heterobasidion parviporum▿ †

In Norway spruce, a fungistatic reaction zone with a high pH and enrichment of phenolics is formed in the sapwood facing heartwood colonized by the white-rot fungus Heterobasidion parviporum. Fungal penetration of the reaction zone eventually results in expansion of this xylem defense. To obtain information about mechanisms operating upon heartwood and reaction zone colonization by the pathogen, hyphal growth and wood degradation were investigated using real-time PCR, microscopy, and comparative wood density analysis of naturally colonized trees with extensive stem decay. The hyphae associated with delignified wood at stump level were devoid of any extracellular matrix, whereas incipient decay at the top of decay columns was characterized by a carbohydrate-rich hyphal sheath attaching hyphae to tracheid walls. The amount of pathogen DNA peaked in aniline wood, a narrow darkened tissue at the colony border apparently representing a compromised region of the reaction zone. Vigorous production of pathogen conidiophores occurred in this region. Colonization of aniline wood was characterized by hyphal growth within polyphenolic lumen deposits in tracheids and rays, and the hyphae were fully encased in a carbohydrate-rich extracellular matrix. Together, these data indicate that the interaction of the fungus with the reaction zone involves a local concentration of fungal biomass that forms an efficient translocation channel for nutrients. Finally, the enhanced production of the hyphal sheath may be instrumental in lateral expansion of the decay column beyond the reaction zone boundary

Use of Biotechnology in Forestry Breeding Programs for Natural Resources and Biodiversity Conservation: Creating Super Trees for the Future

Owing to the increasing human population and the increasing global demand for wood, its consumption is exceeding the natural rate of regeneration in many areas worldwide. Despite only 3% of the world’s forested land is plantation forest, plantations are highly productive; and with further improvement in genetic composition of planting stock as well as applying biotechnology, additional productivity increases can be obtained. For this reason, it is necessary to enrich traditional breeding programs with biotechnological tools able to increase the quantity and quality of the forestry plants produced. FAO’s definition of forest biotechnology encompasses different techniques for cloning forest trees. Forestry companies are currently considering clonal propagation as a good source of forestry plants. Clonal propagation can be achieved by various means: grafting, rooting of cuttings, coppicing, or in vitro propagation. Several methods of clonal propagation are being practiced with conifers. Along this chapter, a summary of some of the different approaches to improve Pinus spp. clonal propagation will be described, particularly those made in our laboratory