Exact SU(2)×U(1) self-gravitating BPS global monopoles in four dimensions are constructed by dimensional reduction of eight dimensional metrics with G2 holonomy asymptotic to cones over S × S. The solutions carry two topological charges in an interesting way. They are generically axially but not spherically symmetric. This last fact is related to the isometries and asymptotic topology of the G2...

This short note extends the sparse SOS (sum of squares) and SDP (semidefinite programming) relaxation proposed by Waki, Kim, Kojima and Muramatsu for normal POPs (polynomial optimization problems) to POPs over symmetric cones, and establishes its theoretical convergence based on the recent convergence result by Lasserre on the sparse SOS and SDP relaxation for normal POPs. A numerical example i...

A novel primal-dual path-following interior-point algorithm for the Cartesian P∗(κ)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-u...

In this paper, we consider the Lidstone boundary value problem (−1)y = f(y(t)), 0 ≤ t ≤ 1, y(0) = 0 = y(1), 0 ≤ i ≤ m − 1, where f : R→ [0,∞). Growth conditions are imposed on f and inequalities involving the Green’s function for this problem are used which enable us to apply the Leggett-Williams Fixed Point Theorem for cones in ordered Banach spaces. This in turn yields the existence of at lea...

We compute the generalized triangle inequalities explicitly for all rank 3 symmetric spaces of noncompact type. For SL(4,C) there are 50 inequalities none of them redundant by [KTW]. For both Sp(6,C) and Spin(7,C) there are 135 inequalities of which 24 are trivially redundant in the sense that they follow from the inequalities defining the Weyl chamber ∆. There are 9 more redundant inequalities...

If Einstein’s equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric’s null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segré classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct r...

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-s...