We present a general framework whereby analysis of interior-point algorithms for semidefinite programming can be extended verbatim to optimization problems over all classes of symmetric cones derivable from associative algebras. In particular, such analyses are extendible to the cone of positive semidefinite Hermitian matrices with complex and quaternion entries, and to the Lorentz cone. We pro...

We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetri...

Theoretical analyses are presented for the stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies under small perturbations in an inviscid incompressible flow at high angles of attack and sideslip. The three-dimensional problem of a pair of vortices over slender conical wings and bodies is reduced to a problem in two dimensions by using the conical flow assumpt...

Motivated by the similarities between the properties of Z-matrices on Rn + and Lyapunov and Stein transformations on the semidefinite cone S+, we introduce and study Z-transformations on proper cones. We show that many properties of Z-matrices extend to Z-transformations. We describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations. Final...

The monotonicity of the least squares mean on the Riemannian manifold of positive definite matrices, conjectured by Bhatia and Holbrook and one of key axiomatic properties of matrix geometric means, was recently established based on the Strong Law of Large Number [14, 4]. A natural question concerned with the S.L.L.N is so called the no dice conjecture. It is a problem to make a construction of...

Abstract. We show that a recent identity of Beck–Gessel–Lee–Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out their general form more...

In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (order 6 or above). For the special case of quartic forms, they collapse into the set of convex quartic homogeneous polynomial functions. We di...

1. S. GiNDiKrN, 'Analysis on homogeneous domains', Russian Math. Surveys 19 (1964) 1-89. 2. M. KOECHER, 'An elementary approach to bounded symmetric domains', Lecture Notes, Rice University, 1969. 3. O. Loos, 'Bounded symmetric domains and Jordan pairs', Lecture Notes, University of California, Irvine, 1977. 4. A. UNTERBERGER and H. UPMEIER, Pseudodifferential analysis on symmetric cones (CRC-P...