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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]

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]

The results of this investigation would indicate that the smallersize letters (elite and pica) should be avoided in the preparation of projectuals-certainly for viewing distances beyond 20 feet. Further investigation could be, and probably should be, conducted at distances less than 20 feet to determine if anything significant would be lost by employing these smaller sizes for the closer distances. The smaller sizes are likely to be sufficient for distances of 20 feet or less. At further distances where larger-size letters are needed, probably the most feasible approach would be to use the primer typeavailable in many schools. It is quite interesting to note that four of the five grades found the 6/32 inch primer size type with serif to be more readable than the 6/32 inch bulletin type without serif. Many casual observers would erroneously suggest that the simple bulletin type would be less confusing and thus more readable. Needless to say, this observation may be a phenomenon of the sample and might not similarly be observed in a replication of the study. The largest size, that which was commercially recommended (8/32 inch), did not appear necessary; the 6/32 inch elite type (primer size) was statistically equal to the larger size in four of the five grades, while in the remaining grade, the primer size actually surpassed the commercially recommended size. The three largest sizes showed approximately equal, minimal change from closer to further viewing distances. In future studies, initial measures should be made of the visual acuity of the subjects to control this possible source of variation. Additional attention also needs to be paid to the characteristics of specific letters which make them more difficult to read, regardless of size. [ABSTRACT FROM AUTHOR]