A distribution D on a set S ⊂ Zp -fools polynomials of degree at most d in N variables over Zp if for any such polynomial P , the distribution of P (x) when x is chosen according to D differs from the distribution when x is chosen uniformly by at most in the `1 norm. Distributions of this type generalize the notion of -biased spaces and have been studied in several recent papers. We establish t...

Recently, a distance function was defined on the face-centered cubic and body-centered cubic grids by combining weights and neighbourhood sequences. These distances share many properties with traditional path-based distance functions, such as the city-block distance, but are less rotational dependent. We present conditions for metricity and algorithms to compute the distances.

In this paper, a new affine projection sign algorithm with a variable step-size, robust in impulsive noise environments, is proposed. For that purpose, l1-norm of the a posteriori error vector is minimized under a box constraint on the step-size. Since the proposed l1-norm minimization problem is non-differentiable convex one, an efficient numerical procedure is developed for the affine project...

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation ut = −(uuxxx)x , modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u0(x) ∈ H 1(IR), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L1-norm of the strong...

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the 1-norm minimization problem 2011 . The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving 1-norm minimization problems. Under mild conditions, we show that the proposed algorit...

Model equations are derived from what we call the strain-vorticity dynamics of the incompressible viscous uid motion. The global existence and blow-up are examined for them and we see that the L 1 norm of the vorticity plays an important role. Blow-up solutions are obtained as self-similar solutions.

This paper addresses the 1-center location problem on a 2-dimensional plane having arbitrarily shaped barriers and using Manhattan metric distances. Barriers commonly occur in practical location and layout problems and are regions where neither travel through nor location of the new facility is permitted. Along the lines of Larson and Sadiq (1983) we divide the feasible location region into cel...

Velocity-stack inversion is the process of creating a model in velocity space that can correctly reconstruct the measured data. This is usually implemented by minimizing the L2 norm of the data misfit and the L2 norm of the model. Superior velocity space images, with a better separation of primaries and multiples, can be created by minimizing a different norm of the data misfit and a different ...

In the last lecture we defined metric spaces, normed spaces, and considered the distortion resulting from certain embeddings. In particular, we proved that l1 norms cannot always be embedded isometrically into l2 by considering a specific four-point l1 norm and showing that it requires at least √ 2 distortion. Today’s lecture further explores the 1 norm. We see a couple of interesting examples ...