This study examines the issue of norm construction in al-Ghazālī’s thought focusing on grounds advanced to support his radical infallibilist position. To fulfill such end, al-Ghazālī, I explain, relies two types arguments, first one relates presumptive nature legal texts order highlight their fundamental indeterminacy and second links interpreter show impossibility fall into error. buttress the...

In this article we develop both the a priori and a posteriori error analysis of hp– version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local ...

For the low rank approximation of time-dependent data matrices and of solutions to matrix differential equations, an increment-based computational approach is proposed and analyzed. In this method, the derivative is projected onto the tangent space of the manifold of rank-r matrices at the current approximation. With an appropriate decomposition of rank-r matrices and their tangent matrices, th...

We consider a class of `0-minimization problems, which is to search for the partial sparsest solution to an underdetermined linear system with additional constraints. We introduce several concepts, including lp-induced quasi-norm (0 < p < 1), maximal scaled spark and scaled mutual coherence, to develop several new uniqueness conditions for the partial sparsest solution to this class of `0-minim...

This paper proposes a ® xed-structure technique for synthesizing controllers that are optimal with respect to various operator norms. An optimal control problem is developed for each of these operator norms, and necessary conditions for sub-optimal performance are derived. Mixed-norm optimal control problems are also formulated. A continuation algorithm using quasi-Newton corrections is used to...

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X → Y , which satisfies the inequality ||∆xf(y)− n!f(x)|| ≤ φ(x, y) for suitable control function φ, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of t 7→ f(tx) and t 7→ φ(tx, ty) imply the continuity of t 7→ M(tx).

This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with Raviart-Thomas elements on a sequence of quasi-uniform meshes of triangles and/or parallelograms. Assuming the regularity of the solution to the electric fie...

We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights w having finitely many zeros and singularities (i.e., points where w becomes infinite) on an interval and not too “rapidly changing” away from these zeros and singularities. This class of doubling weights is rather wide and, in particular, includes the classical Jacobi weights, generaliz...

This paper introduces a quasi-interpolation operator for scalarand vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces W r,p, where p ∈ [1,∞] and the smoothness index r can be arbitraril...