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The full Kondrachov compactness theorem for Sobolev imbeddings of the type W (G)→ W (G) on bounded domains G in Ris extended to a large class of unbounded domains with 'reasonable' n- 1 dimensional boundaries. A Poincaré inequality is obtained for such domains and a compactness theorem for traces of functions in W (G) on lower dimensional hyperplanes is also proved. [ABSTRACT FROM AUTHOR]

Foliage and bark samples were collected from the tree that provided the type specimen for Juniperus deppeana var. sperryi Correll, as well as from trees from populations of J. pinchotii Sudw., J. flacida Schl., and J. deppeana Steud. var. deppeana. These four taxa were compared using terpenoid and morphological characters. The terpenoid data suggest that J. deppeana var. sperryi is most closely related to J. deppeana var. deppeana; no evidence of relict or present hybridization with J. flaccida was detected. The morphological data showed J. deppeana var. sperryi to be intermediate in several characters between J. deppeana var. deppeana and J. flacdda. The probability of a hybrid origin for this taxon is discussed. Due to the scattered occurrence of trees referable to J. deppeana var. sperryi, it is proposed that this taxon be reduced in rank to J. deppeana forma sperryi. [ABSTRACT FROM AUTHOR]

The effects of random and nonrandom errors were analyzed. Four types of nonrandom errors were simulated and examined in detail: 1. misidentification of compounds; 2. unresolved components; 3. errors in the quantification of individual compounds; and 4. errors in the quantification of a series of analyses. These cases were compared using data from studies in Juniperus. Misidentification of 1 of 40 components had only a slight effect on the resulting classification even when that error accounted for 20% of the total character weights. Unresolved components also had only a slight effect. Nonrandom errors in the quantification of individual compounds (throughout a study) were shown to have no effect on the similarity measure used in this study. Errors in the quantification of a series of analyses (such as encountered in seasonal variations) appeared to be the most serious source of error and were shown to be of considerable importance in chemosystematic studies. Several preventative procedures are suggested. [ABSTRACT FROM AUTHOR]