In this paper, we give an exact expression for Clarke generalized Jacobian of the projection onto symmetric cones, which is linked to rank-1 matrices. As an application, we employ the projection operator to design a semismooth Newton algorithm for solving nonlinear symmetric cone programs. The algorithm is proved to be locally quadratically convergent without assuming strict complementarity of ...

We give a description of the tropical Severi variety of univariate polynomials of degree n having two double roots. We show that, as a set, it is given as the union of three explicit types of cones of maximal dimension n − 1, where only cones of two of these types are cones of the secondary fan of {0, . . . , n}. Through Kapranov’s theorem, this goal is achieved by a careful study of the possib...

We present a series of models three-dimensional rotation-symmetric fragile topological insulators in class AI (time-reversal symmetric and spin-orbit-free systems), which have gapless surface states protected by time-reversal ($T$) $n$-fold rotation ($C_n$) symmetries ($n=2,4,6$). Our are generalizations Fu's model spinless crystalline insulator, orbital degrees freedom play the role pseudo-spi...

Interior point methods can be extended to a number of cones (self-dual homogeneous cones) • Rn (linear programming) • vectorized symmetric matrices over real numbers (semidefinite programming) • vectorized Hermitian matrices over complex numbers • vectorized Hermitian matrices over quaternions • vectorized Hermitian 3×3 matrices over octonions Grötschel, Lovász and Schrijver [3]: semidefinite p...

In this article, we study minimal graded free resolutions of Cohen-Macaulay tangent cones some monomial curves associated to 4-generated pseudo symmetric numerical semigroups. We explicitly give the matrices in these resolutions.

In this article I show that every special Lagrangian cone in C 3 determines, and is determined by, a primitive harmonic surface in the 6-symmetric space SU3/SO2. For cones over tori, this allows us to use the classification theory of harmonic tori to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the ex...

The Berry curvature (BC) - a quantity encoding the geometric properties of electronic wavefunctions in solid is at heart different Hall-like transport phenomena, including anomalous Hall and non-linear Nernst effects. In non-magnetic quantum materials with acentric crystalline arrangements, local concentrations BC are generally linked to single-particle that superposition electron hole excitati...