LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS

Linear Estimates for solutions of Quadratic equations in Free Groups

We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by 2s for orientable equation and by 12s for non-orientable equation, where s is the sum of the lengths of the coefficients.

On the Parameterization of solutions for equations in Free Groups

Linear holonomy groups of algebraic solutions of polynomial differential equations

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Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems

We derive local error estimates for the discretization of optimal control problems governed by linear advection-diffusion partial differential equations (PDEs) using the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method. We show that if the SUPG method is used to solve optimization problems governed by an advection-dominated PDE the convergence properties of the SUPG met...

Estimates for solutions to discrete convolution equations

We study solvability of convolution equations for functions with discrete support in R, a special case being functions with support in the integer points. The more general case is of interest for several grids in Euclidean space, like the body-centred and face-centred tesselations of three-space, as well as for the non-periodic grids that appear in the study of quasicrystals. The theorem of exi...