We construct commuting families in fraction fields of symmetric powers of algebras. The classical limit of this construction gives Poisson commuting families associated with linear systems. In the case of a K3 surface S, they correspond to lagrangian fibrations introduced by Beauville. When S is the canonical cone of an algebraic curve C, we construct commuting families of differential operator...

We prove, under a certain representation theoretic assumption, that the set of real symmetric matrices, whose eigenvalues satisfy linear matrix inequality, is itself spectrahedron. The main application derivative relaxations positive semidefinite cone are spectrahedra. From this we further deduce statements on their Wronskians. These imply Newton's inequalities, as well strengthening correlatio...

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is √ log , where ...

We show that the feasibility of a system of m linear inequalities over the cone of symmetric positive semide nite matrices of order n can be tested in mnO(minfm;n2g) arithmetic operations with lnO(minfm;n2g)-bit numbers, where l is the maximum binary size of the input coe cients. We also show that any feasible system of dimension (m;n) has a solution X such that log kXk lnO(minfm;n2g).

We will analyze mixed-0/1 second-order cone programs where the continuous and binary variables are solely coupled via the conic constraints. We devise a cutting-plane framework based on an implicit Sherali-Adams reformulation. The resulting cuts are very effective as symmetric solutions are automatically cut off and each equivalence class of 0/1 solutions is visited at most once. Further, we pr...

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

There recently has been much interest in non-interior continuation/smoothingmethods for solving linear/nonlinear complementarity problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric positive semidefinite real matrices. These extensions involve the ChenMangasarian class of smoothing functions and the smoothed Fischer-Burme...

The P -property of the following two Z-transformations with respect to the positive semidefinite cone is characterized: (i) I − S, where S : S → S is a nilpotent linear transformation, (ii) I − L A , where LA is the Lyapunov transformation defined on S n×n by LA(X) = AX + XA . (Here S denotes the space of all symmetric n×n matrices and I is the identity transformation.)

This paper is devoted to the study of the following nonlocal p -Laplacian functional differential equation −φp(x′(t)) )′ = λ f (t,x(t),x ′ (t)) (∫ 1 0 f (s,x(s),x′ (s))ds )n , 0 < t < 1, subject to multi point boundary conditions. We obtain some results on the existence of at least one (when n ∈ Z+ ) or triple (when n = 0) pseudo-symmetric positive solutions by using fixedpoint theory in cone. ...