3,544 research outputs found
Remarks on the geometry of coordinate projections in R^n
We study geometric properties of coordinate projections. Among other results,
we show that if a body K in R^n has an "almost extremal" volume ratio, then it
has a projection of proportional dimension which is close to the cube. We
compare type 2 and infratype 2 constant of a Banach space. This follows from a
comparison lemma for Rademacher and Gaussian averages. We also establish a
sharp estimate on the shattering dimension of the convex hull of a class of
functions in terms of the shattering dimension of the class itself.Comment: Israel Journal of Mathematics, to appea
Entropy, dimension and the Elton-Pajor Theorem
The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension
of the coordinate cube of a given size, which can be found in coordinate
projections of K. We show that the VC dimension of a convex body governs its
entropy. This has a number of consequences, including the optimal Elton's
theorem and a uniform central limit theorem in the real valued case
Welded transition joints of 9 Cr-1 Mo alloy steel/316SS for short life /100 hours maximum/ application
Welding parameters and elevated temperature aging and strength characteristics of transition joints between chromium molybdenum alloy steel and stainless stee
Geographic Variation in Bufo valliceps (Anura: Bufonidae), a Widespread Toad in the United States and Middle America
The common lowland toad Bufo valliceps has a large distribution in the southern United States, Mexico, and most of Central America; this ample distribution across diverse temperate and tropical habitats is unusual among frogs. Geographic variation in size, shape, skin texture, and color pattern among populations of this species was reviewed. Although there are great differences between extreme northern and southern populations, I did not find smooth clinal variation for any character examined. Nor is there a discrete break among these continuous morphological variables that separate the the northern and southern morphs. Variation in Biifo valliceps is characterized by a high degree of inter- and intrapopulational variation that cannot be attributed to simple trends associated with latitude, elevation, or climate. An analysis the relationship between body size and aridity, along a precipiation gradient on the Yucatan Peninsula, found no consistent covariation. Previous claims for a positive relationship between elevation and degree of development of the cranial crests were found not to be accurate. Although the several relatively distinct populations are referable to the taxa Bufo nebulifer and Bnfo valliceps wilsoni, 1 do not propose recognition of these taxa, pending further research
Systematics of the Bufo Valliceps Group (Anura: Bufonidae) of Middle America
The University of Kansas has long historical connections with Central America and the many Central
Americans who have earned graduate degrees at KU. This work is part of the Central American Theses
and Dissertations collection in KU ScholarWorks and is being made freely available with permission of the
author through the efforts of Professor Emeritus Charles Stansifer of the History department and the staff of
the Scholarly Communications program at the University of Kansas Libraries’ Center for Digital Scholarship.A phylogenetic analysis of morphological characters revealed that the species
content of the Bufo valliceps group is limited to eight species (two of them new)
occurring between the southern United States and Costa Rica. Several Middle
American species usually associated with this group are shown to be closely related,
but outside of the Bufo valliceps group. The monotypic genus Crepidophryne is
placed in the synonymy of Bufo. The taxon Bufo valliceps macrocristatus is
recognized as a species distinct from Bufo valliceps. Seven species in the Bufo
valliceps group appear to be allopatric with respect to one another and are restricted
to humid primary forest habitat on the lower slopes of the major mountain ranges of
southern Mexico, Guatemala, Honduras, and Costa Rica. The species Bufo valliceps
is widespread in humid lowland habitats from the southern United States to Costa
Rica that are either naturally more open (e.g., savanna) or disturbed secondary
growth. There are great differences in size, shape, skin texture, and color pattern
between northern and southern populations of this species; however, these differences
do not vary along a smooth cline among populations from intermediate areas. Nor is
there a discrete break among these continuous variables that separate the northern and
southern morphs. Variation in Bufo valliceps is characterized by a high degree of.
inter- and intrapopulational variation that cannot be attributed to simple trends
associated with latitude, altitude, or climate. Bufo ibarrai, long assumed to be in the
Bufo valliceps group but here shown to lie outside of the group, is reviewed and
rediagnosed with respect to other similar Central American toads. The taxon Bufo
valliceps microtis is placed in the synonymy of Bufo coccifer. Diagnostic accounts
for all species in the Bufo valliceps group and a key to the species are provided
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