New or Incompletely Known Species of Feltria from North America (Acarina: Feltriidae)

The genus Feltria has a widespread Holarctic distribution. A few species (Lundblad, 1941, 1969) have also been reported from northern Burma but this latter area. as far as its water mite fauna is concerned, might better be considered part of the southern border of the Palearctic, rather than a part of the Oriental Region. Previously. thirty apparently valid species and subspecies of Feltria were known from North America. The present paper describes nine additional forms and brings the total from the Nearctic area to 39, which is nearly identical with the number known from Europe. Most North American species are found in mountainous regions, but four are known from cold streams and springs in Michigan. The majority of Nearctic species are found associated with mosses and other matted aquatic plants, but twelve (including four described in this paper) are typically residents of the interstitial water associated with stream sand and gravel deposits. For reasons to be listed along with the description of Feltria testudo n. sp., the genus Azugofeltria is reduced to the rank of subgenus. The terminology used in describing musclt: attachment plates and glandularia of the dorsum follows that of Cook (1961). In presenting measurements, those of the holotype and allotype are given first. If a series of specimens is available, the range of variation is given in parentheses following the measurements of the primary types. Holotypes and allotypes will be deposited in the Field Museum of Natural History (Chicago)

The uniform face ideals of a simplicial complex

We define the uniform face ideal of a simplicial complex with respect to an ordered proper vertex colouring of the complex. This ideal is a monomial ideal which is generally not squarefree. We show that such a monomial ideal has a linear resolution, as do all of its powers, if and only if the colouring satisfies a certain nesting property. In the case when the colouring is nested, we give a minimal cellular resolution supported on a cubical complex. From this, we give the graded Betti numbers in terms of the face-vector of the underlying simplicial complex. Moreover, we explicitly describe the Boij-S\"oderberg decompositions of both the ideal and its quotient. We also give explicit formul\ae\ for the codimension, Krull dimension, multiplicity, projective dimension, depth, and regularity. Further still, we describe the associated primes, and we show that they are persistent.Comment: 34 pages, 8 figure

North American Species of the Genus Axonopsis (Acarina: Aturidae: Axonopsinae)

(excerpt) Members of the genus Axonopsis have a broad zoogeographic distribution but are unreported from the Australian region and South America south of Colombia. Species occur in permanent standing waters and streams (including interstitial water). Representa- tives of four subgenera, Axonopsis s. s., Brachypodopsis, Paraxonopsis and Vicinaxonopsis, have been collected in North America, and a species of the closely related genus Erebaxonopsis is also known from interstitial waters in California. The only anomalous aspects of the distributional patterns are the apparent absence of Hexaxonopsis (which has a relatively widespread Palearctic range) and the stream (and interstitial) habitat of the North American species of the typical subgenus. The European species occurs only in lakes

The strong Lefschetz property in codimension two

Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of monomial ideals. Using this we classify when both bounds are sharp. Moreover, we prove that the artinian quotient of a monomial ideal in $K[x,y]$ always has the strong Lefschetz property, regardless of the characteristic of the field, exactly when the ideal is lexsegment. As a consequence we describe a family of non-monomial complete intersections that always have the strong Lefschetz property.Comment: 18 pages, 1 figure; v2: Updated history and reference