Abstract Let $G$ be a connected semisimple real algebraic group and $\Gamma < G$ Zariski dense Anosov subgroup with respect to minimal parabolic subgroup. We prove local mixing of the one-parameter diagonal flow $\{\exp (t\mathsf {v}): t \in {\mathbb {R}}\}$ on \backslash for any interior direction $\mathsf {v}$ limit cone $ Bowen–Margulis–Sullivan measure associated {v}$. More generally...

A. We construct optimal order multilevel preconditioners for interior-penalty discontinuous Galerkin (DG) finite element discretizations of three-dimensional (3D) anisotropic elliptic boundary-value problems. In this paper we extend the analysis of our approach, introduced earlier for 2D problems [20], to cover 3D problems. A specific assembling process is proposed which allows us to cha...

We give an effective upper bound on the h-polynomial of a lattice polytope in terms of its degree and leading coefficient, confirming a conjecture of Batyrev. We deduce this bound as a consequence of a strong Cayley decomposition theorem which says, roughly speaking, that any lattice polytope with a large multiple that has no interior lattice points has a nontrivial decomposition as a Cayley su...

Introduction. Since the time of Riemann, there has been a close interplay between the study of the geometry of complex algebraic curves (or, equivalently, compact Riemann surfaces) and the topology of 2-manifolds. These connections arise from the uniformization theorem, which asserts that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the plane, o...

Self{scaled barrier functions are fundamental objects in the theory of interior{point methods for linear optimization over symmetric cones, of which linear and semideenite programming are special cases. We are classifying all self{scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with ...

In this paper, we employ the regularized meshless method to solve antiplane shear problems with multiple inclusions. The solution is represented by a distribution of double-layer potentials. The singularities of kernels are regularized by using a subtracting and adding-back technique. Therefore, the troublesome singularity in the method of fundamental solutions (MFS) is avoided and the diagonal...

The classical control theory and methods (such as root locus) that we have been using in class to date are based on a simple input-output description of the plant, usually expressed as a transfer function. These methods do not use any knowledge of the interior structure of the plant, and limit us to single-input single-output (SISO) systems, and as we have seen allows only limited control of th...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...