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Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription
Canzani, Yaiza,Gover, Rod,Jakobson, Dmitry,Ponge, Raphaë,l Oxford University Press 2014 International mathematics research notices Vol.2014 No.9
<P>In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant’s Nodal Domain Theorem. We also show that on any manifold of dimension <I>n</I>≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension <I>n</I>≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the <I>Q</I>-curvature prescription problems for noncritical <I>Q</I>-curvatures.</P>
Wesley G,Jennings,Angela R,Gover,Alex R,Piquero 한국공안행정학회 2015 한국공안행정학회보 Vol.24 No.3
Macro-level research evidencing the relationship between communities and crime dates date back to the early ecological work of Park and Burgess and later further developed by Shaw and McKay into what is commonly referred to as social disorganization theory. In contrast, micro-level theories such as Sampson and Laub’s theory argues that individual pathways of offending can be altered by life transitions such as marriage and employment. Comparatively, Moffitt’s taxonomy asserts that there are two theoretically distinct groups of offenders, where one group displays an adolescent-limited type of offending and the other group are considered to be life-course-persistent or chronic offenders. Results from this study, relying on official data from two large U.S.-based birth cohorts, yielded varying levels of support for all of the theoretical frameworks mentioned above. Yet, once multinomial logistic regression models were estimated incorporating the individual-level and neighborhood-level effects there was evidence of mediation. Implications and directions for future research are also discussed
COMPLEX ANALYSIS AND THE FUNK TRANSFORM
Bailey, T.N.,Eastwood, M.G.,Gover, A.R.,Mason, L.J. Korean Mathematical Society 2003 대한수학회지 Vol.40 No.4
The Funk transform is defined by integrating a function on the two-sphere over its great circles. We use complex analysis to invert this transform.
Wesley G. Jennings,Angela R. Gover,Alex R. Piquero 한국공안행정학회 2015 한국공안행정학회보 Vol.24 No.3
Macro-level research evidencing the relationship between communities and crime dates date back to the early ecological work of Park and Burgess and later further developed by Shaw and McKay into what is commonly referred to as social disorganization theory. In contrast, micro-level theories such as Sampson and Laub’s theory argues that individual pathways of offending can be altered by life transitions such as marriage and employment. Comparatively, Moffitt’s taxonomy asserts that there are two theoretically distinct groups of offenders, where one group displays an adolescent-limited type of offending and the other group are considered to be life-course-persistent or chronic offenders. Results from this study, relying on official data from two large U.S.-based birth cohorts, yielded varying levels of support for all of the theoretical frameworks mentioned above. Yet, once multinomial logistic regression models were estimated incorporating the individual-level and neighborhood-level effects there was evidence of mediation. Implications and directions for future research are also discussed.
Complex analysis and the Funk transform
T. N. Bailey,M. G. Eastwood,A. R. Gover,L. J. Mason 대한수학회 2003 대한수학회지 Vol.40 No.4
The Funk transform is defined by integrating a function on thetwo-sphere over its great circles. We use complex analysis toinvert this transform.