We present a new method to solve general systems of equations containing complementarity conditions, with special focus on those arising in the thermodynamics multicomponent multiphase mixtures at equilibrium. Indeed, unified formulation introduced by Lauser et al. (2011) has recently emerged as promising way automatically handle appearance and disappearance phases porous media compositional fl...

0. Introduction. A. Summary. A significant problem in topology is the classification of wild arcs in S3. The first fundamental paper in this area was written by Fox and Artin in 1948 [13]. There the authors developed rigorous algebraic means for demonstrating the nontameness of arcs. Some time later (1962) Fox and Harrold [14] succeeded in completely classifying a special class of wild arcs, th...

A novel nonlinear programming (NLP) strategy is developed and applied to the optimization of diierential algebraic equation (DAE) systems. Such problems, also referred to as dynamic optimization problems, are common in chemical process engineering and remain challenging applications of nonlinear programming. These applications often consist of large, complex nonlinear models that result from di...

We are interested in the approximation of functions f ~ Lp(I), 0 < p < 1, I = [ 1 , 1], by algebraic polynomials. Such approximation has previously been studied by other authors, most notably, Storozhenko, Krotov, and Oswald [-S-K-O] and Khodak [K]. Our main departure from these previous works is that we shall prove direct estimates for the error of polynomial approximation in terms of the Ditz...

Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1, . . . , An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on th...

The integral fractional Laplacian of order $s \in (0,1)$ is a nonlocal operator. It known that solutions to the Dirichlet problem involving such an operator exhibit algebraic boundary singularity regardless domain regularity. This, in turn, deteriorates global regularity and as result convergence rate numerical solutions. For finite element discretizations, we derive local error estimates $H^s$...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

We consider sparse linear systems, where a set of “interior” degrees of freedom have been eliminated in order to reduce the problem size. This elimination is assumed to be local, so the “interior” principal submatrix is block-diagonal, and the resulting Schur complement is still sparse. For it to be beneficial, the elimination process should lead to reduced memory requirements, but equally impo...

Let $ G = \prod_{i 1}^{\mathsf r} G_i be a product of simple real algebraic groups rank one and \Gamma an Anosov subgroup with respect to minimal parabolic subgroup. For each \mathsf v in the interior positive Weyl chamber, let \mathscr R_ v\subset \Gamma\backslash denote Borel subset all points recurrent \exp (\mathbb R_+ v) $-orbits. maximal horospherical N $, we show that $-action on {\maths...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...