The standard a priori error analysis of discontinuous Galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the Galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm. In this paper, a new error analysis of discontinuous Galerkin methods is developed using only ...

In this paper we develop with considerable details a theory of multivector functions of a p-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these multivector functions are introduced, as e.g., the A-directional derivative (where A is a p-vector) and the generalized concepts of curl, divergence and gradie...

Let f be a Lipschitz mapping of a separable Banach space X to a Banach space Y. We observe that the set of points at which f is diierentiable in a spanning set of directions but not G^ ateaux diierentiable is-directionally porous. Since Borel-directionally porous sets, in addition to being rst category sets, are null in Aronszajn's (or, equivalently, in Gaussian) sense, we obtain an alternative...

Non-trivial deformations result in local contractions and expansions. These naturally capture object scalings but can have a negative side effect, namely making object features disappear or inflate. For this reason we want the deformation fields to have zero acceleration in the direction perpendicular to image features; this guarantees that the features are only ‘transported’. This requirement ...

We solve, by separation of variables, the problem of three anyons with a harmonic oscillator potential. The anyonic symmetry conditions from cyclic permutations are separable in our coordinates. The conditions from two-particle transpositions are not separable, but can be expressed as reflection symmetry conditions on the wave function and its normal derivative on the boundary of a circle. Thus...

We study the set disjointness problem in the most powerful model of bounded-error communication, the k-party randomized number-on-the-forehead model. We show that set disjointness requires Ω( √ n/2kk) bits of communication, where n is the size of the universe. Our lower bound generalizes to quantum communication, where it is essentially optimal. Proving this bound was a longstanding open proble...

In this paper, we introduce the notion of a second-order coneconvex function involving second-order directional derivative. Also, second-order cone-pseudoconvex, second-order cone-quasiconvex and other related functions are defined. Second-order optimality and Mond-Weir type duality results are derived for a vector optimization problem over cones using the introduced classes of functions.

In this paper, we introduce the magnitude, orientation, and anisotropic ratio for the higher order derivative ∇k+1u (with k ≥ 1) of a function u to characterize its anisotropic behavior. The magnitude is equivalent to its usual Euclidean norm. The orientation is the direction along which the absolute value of the k + 1-th directional derivative is about the smallest, while along its perpendicul...

This paper presents a novel approach of fingerprint image enhancement that relies on detecting the fingerprint ridges as image regions where the second directional derivative of the digital image is positive. A facet model is used in order to approximate the derivatives at each image pixel based on the intensity values of pixels located in a certain neighborhood.We note that the size of this ne...

In this paper we study the controllability of an artificial advection-diffusion system through the boundary. Suitable Carleman estimates give us the observability on the adjoint system in the one dimensional case. We also study some basic properties of our problem such as backward uniqueness and we get an intuitive result on the control cost for vanishing viscosity. Introduction Artificial adve...