17,813 research outputs found
Elliptic genera from multi-centers
I show how elliptic genera for various Calabi-Yau threefolds may be
understood from supergravity localization using the quantization of the phase
space of certain multi-center configurations. I present a simple procedure that
allows for the enumeration of all multi-center configurations contributing to
the polar sector of the elliptic genera\textemdash explicitly verifying this in
the cases of the quintic in , the sextic in
, the octic in and the
dectic in . With an input of the corresponding
`single-center' indices (Donaldson-Thomas invariants), the polar terms have
been known to determine the elliptic genera completely. I argue that this
multi-center approach to the low-lying spectrum of the elliptic genera is a
stepping stone towards an understanding of the exact microscopic states that
contribute to supersymmetric single center black hole entropy in
supergravity.Comment: 30+1 pages, Published Versio
Extremal families of cubic Thue equations
We exactly determine the integral solutions to a previously untreated
infinite family of cubic Thue equations of the form with at least
such solutions. Our approach combines elementary arguments, with lower
bounds for linear forms in logarithms and lattice-basis reduction
Lines Tangent to 2n-2 spheres in R^n
We show that there are 3 \cdot 2^(n-1) complex common tangent lines to 2n-2
general spheres in R^n and that there is a choice of spheres with all common
tangents real.Comment: Minor revisions. Trans. AMer. Math. Soc., to appear. 15 pages, 3 .eps
figures; also a web page with computer code verifying the computations in the
paper and with additional picture
Solution intervals for variables in spatial RCRCR linkages
© 2019. ElsevierAn analytic method to compute the solution intervals for the input variables of spatial RCRCR linkages and their inversions is presented. The input-output equation is formulated as the intersection of a single ellipse with a parameterized family of ellipses, both related with the possible values that certain dual angles determined by the configuration of the mechanism can take. Bounds for the angles of the input pairs of the RCRCR and RRCRC inversions are found by imposing the tangency of two ellipses, what reduces to analyzing the discriminant of a fourth degree polynomial. The bounds for the input pair of the RCRRC inversion is found as the intersection of a single ellipse with the envelope of the parameterized family of ellipses. The method provides the bounds of each of the assembly modes of the mechanism as well as the local extrema that may exist for the input variablePeer ReviewedPostprint (author's final draft
- …