On the unitarization of linear representations of primitive partially ordered sets

We describe all weights which are appropriated for the unitarization of linear representations of primitive partially ordered sets of finite type

Orthoscalar representations of the partially ordered set (N, 4)

We obtain a one-parameter series of orthoscalar representations of the partially ordered set (N, 4). This proves that the classification of such representations is a problem of infinite type

A majorization relation for a certain class of *-quivers with an orthogonality condition

In [1, 2, 3], *-algebras and *-categories over the field C of complex numbers were quasi-ordered with respect to the complexity of the structure of their *-representations with a majorization relation >-. A notion of *-wildness was also introduced there for an algebra (a category) if the algebra majorizes the *-algebra C* (F2)- In this paper, we discuss some methods for proving that an algebra is *-wild and obtain criteria for certain "standard" *-categories (ensembles with an orthogonality condition) to be *-wild

Pines

Pinus is the most important genus within the Family Pinaceae and also within the gymnosperms by the number of species (109 species recognized by Farjon 2001) and by its contribution to forest ecosystems. All pine species are evergreen trees or shrubs. They are widely distributed in the northern hemisphere, from tropical areas to northern areas in America and Eurasia. Their natural range reaches the equator only in Southeast Asia. In Africa, natural occurrences are confined to the Mediterranean basin. Pines grow at various elevations from sea level (not usual in tropical areas) to highlands. Two main regions of diversity are recorded, the most important one in Central America (43 species found in Mexico) and a secondary one in China. Some species have a very wide natural range (e.g., P. ponderosa, P. sylvestris). Pines are adapted to a wide range of ecological conditions: from tropical (e.g., P. merkusii, P. kesiya, P. tropicalis), temperate (e.g., P. pungens, P. thunbergii), and subalpine (e.g., P. albicaulis, P. cembra) to boreal (e.g., P. pumila) climates (Richardson and Rundel 1998, Burdon 2002). They can grow in quite pure stands or in mixed forest with other conifers or broadleaved trees. Some species are especially adapted to forest fires, e.g., P. banksiana, in which fire is virtually essential for cone opening and seed dispersal. They can grow in arid conditions, on alluvial plain soils, on sandy soils, on rocky soils, or on marsh soils. Trees of some species can have a very long life as in P. longaeva (more than 3,000 years)