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FN ISI Export Format VR 1.0 PT J AU Bland, J Duchamp, T AF Bland, John Duchamp, Tom TI Anisotropic estimates for sub-elliptic operators SO SCIENCE IN CHINA SERIES A-MATHEMATICS AB In the 1970's, Folland and Stein studied a family of subelliptic scalar operators L-lambda which arise naturally in the Ob-complex. They introduced weighted Sobolev spaces as the natural spaces for this complex, and then obtained sharp estimates for partial derivative(b) in these spaces using integral kernels and approximate inverses. In the 1990's, Rumin introduced a differential complex for compact contact manifolds, showed that the Folland-Stein operators are central to the analysis for the corresponding Laplace operator, and derived the necessary estimates for the Laplacian from the Folland Stein analysis. In this paper, we give a self-contained derivation of sharp estimates in the anisotropic Folland-Stein spaces for the operators studied by Rumin using integration by parts and a modified approach to bootstrapping. C1 Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada. Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Bland, J, Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada. EM bland@math.toronto.edu PD APR PY 2008 VL 51 IS 4 BP 509 EP 522 UT ISI:000254626300003 ER PT J AU Doherty, DC AF Doherty, Davis C. TI Singularities of generic projection hypersurfaces SO PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY AB Linearly projecting smooth projective varieties provide a method of obtaining hypersurfaces birational to the original varieties. We show that in low dimension, the resulting hypersurfaces only have Du Bois singularities. Moreover, we conclude that these Du Bois singularities are in fact semi log canonical. However, we demonstrate the existence of counterexamples in high dimension - the generic linear projection of certain varieties of dimension 30 or higher is neither semi log canonical nor Du Bois. C1 Seattle Univ, Dept Math, Seattle, WA 98122 USA. Univ Washington, Dept Math, Seattle, WA 98195 USA. RP Doherty, DC, Seattle Univ, Dept Math, Seattle, WA 98122 USA. PY 2008 VL 136 IS 7 BP 2407 EP 2415 UT ISI:000254675200016 ER PT J AU Mitteroecker, P Bookstein, F AF Mitteroecker, Philipp Bookstein, Fred TI The evolutionary role of modularity and integration in the hominoid cranium SO EVOLUTION AB Patterns of morphological integration and modularity among shape features emerge from genetic and developmental factors with varying pleiotropic effects. Factors or processes affecting morphology only locally may respond to selection more easily than common factors that may lead to deleterious side effects and hence are expected to be more conserved. We briefly review evidence for such global factors in primate cranial development as well as for local factors constrained to either the face or the neurocranium. In a sample comprising 157 crania of Homo sapiens, Pan troglodytes, and Gorilla gorilla, we statistically estimated common and local factors of shape variation from Procrustes coordinates of 347 landmarks and semilandmarks. Common factors with pleiotropic effects on both the face and the neurocranium account for a large amount of shape variation, but mainly by extension or truncation of otherwise conserved developmental pathways. Local factors (modular shape characteristics) have more degrees of freedom for evolutionary change than mere ontogenetic scaling. Cranial shape is similarly integrated during development in all three species, but human evolution involves dissociation among several characteristics. The dissociation has probably been achieved by evolutionary alterations and by the novel emergence of local factors affecting characteristics that are controlled at the same time by the common factors. C1 Univ Vienna, Dept Anthropol, A-1091 Vienna, Austria. Konrad Lorenz Inst Evolut & Cognit Res, A-3422 Altenberg, Austria. Univ Vienna, Dept Theoret Biol, A-1091 Vienna, Austria. Univ Washington, Dept Stat, Seattle, WA 98195 USA. RP Mitteroecker, P, Univ Vienna, Dept Anthropol, Althanstr 14, A-1091 Vienna, Austria. EM philipp.mitteroecker@univie.ac.at PD APR PY 2008 VL 62 IS 4 BP 943 EP 958 UT ISI:000254640900018 ER PT J AU Koblitz, N Menezes, A AF Koblitz, Neal Menezes, Alfred TI Another look at generic groups SO ADVANCES IN MATHEMATICS OF COMMUNICATIONS AB Starting with houp's seminal paper [24], the generic group model has been an important tool in reductionist security arguments. After an informal explanation of this model and Shoup's theorem, we discuss the danger of flaws in proofs. We next describe an ontological difference between the generic group assumption and the random oracle model for hash functions. We then examine some criticisms that have been leveled at the generic group model and raise some questions of our own. C1 Univ Washington, Dept Math, Seattle, WA 98195 USA. Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada. RP Koblitz, N, Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA. EM koblitz@math.washington.edu ajmeneze@uwaterloo.ca PD FEB PY 2007 VL 1 IS 1 BP 13 EP 28 UT ISI:000254705300003 ER EF
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