AIM: The geographical extent and climatic tolerances of one- and two-needled pinyon pines (Pinus subsect. Cembroides) are the focus of questions in taxonomy, palaeoclimatology and modelling of future distributions. The identification of these pines, traditionally classified by one- versus two-needled fascicles, is complicated by populations with both one- and two-needled fascicles on the same t...

Cryptantha (Boraginaceae) is a group of approximately 200 annual and perennial species, representing two-thirds of the diversity within subtribe Cryptanthinae. The genus exhibits an amphitropic distribution, occurring in temperate and desert regions of western North and South America. Fifty samples of 45 species of Cryptantha s. l., exemplars of the related genera Amsinckia, Pectocarya, and Pla...

Circumscriptions of and relationships among many genera and suprageneric taxa of the diverse grass tribe Poeae remain controversial. In an attempt to clarify these, we conducted phylogenetic analyses of >2400 new DNA sequences from two nuclear ribosomal regions (ITS, including internal transcribed spacers 1 and 2 and the 5.8S gene, and the 3'-end of the external transcribed spacer (ETS)) and fi...

We consider the 2 x 2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called the p-system). We show that they can be reformulated as a kinetic equation, using an additional kinetic variable. Such a formulation was first obtained by the authors in the case of multidimensional scalar conservation laws. A new phenomenon occurs here, namely that the adve...

Gene frequencies at 13 isozyme loci were determined in three South American taxa of cultivated potatoes [the diploid group (gp.) Stenotomum, the diploid subgroups (subgp.) Goniocalyx, and the tetraploid gp. Andigena of S. tuberosum], in the diploid weed species S. sparsipilum, and in most of the main cultivars now raised in the Northern Hemisphere (the tetraploid gp. Tuberosum of S. tuberosum)....

Phylogenetic analyses are used to examine the morphological diversity and systematics of Synthyris and Besseya. The placement of Synthyris and Besseya in Veronicaceae is strongly supported in parsimony analyses of nuclear ribosomal ITS DNA sequences. Parsimony and maximum likelihood (ML) criteria provide consistent hypotheses of clades of Synthyris and Besseya based on the ITS data. The combina...

This paper discusses the anomaly of gradually inconsistent argumentations when reasoning under uncertainty. It is argued that in several domains, uncertain knowledge modeling experts’ opinions may induce inconsistencies to a certain degree in interim and final conclusions. In order to model gradual/partial inconsistency, complex certainty factors are introduced and their serial and parallel pro...

Verifying design instead of code can be an effective and practical approach to obtaining verified software. This paper argues that proof scores are an attractive method for verifying design, in that they achieve a balance in which the respective capabilities of humans and machines are utilized optimally. 1 Verifying Code or Design Although creation of a verifying compiler is a difficult challen...