We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension four. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real numbe...

A Boolean function f :F2 → F2 is called an affine disperser of dimension d, if f is not constant on any affine subspace of F2 of dimension at least d. Recently Ben-Sasson and Kopparty gave an explicit construction of an affine disperser for sublinear d. The main motivation for studying such functions comes from extracting randomness from structured sources of imperfect randomness. In this paper...

Let X be an integral affine or projective hypersurface over a field F of characteristic p > 0, and let F (X) denote its function field. In a recent article, Dolphin and Hoffmann obtained an explicit description of the kernel of the natural restriction homomorphism between the rings of absolute Kähler differentials of F and F (X), respectively. In this note, we examine the possibility of derivin...

Associated with the notion of the mixed Lp-affine surface area for multiple convex bodies for all real p (p 6= −n) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013), 38 pages], we define the concept of the mixed Lp-dual affine surface area for multiple star bodies for all real p (p 6= −n) and establish its monotonicity inequalities and cyclic inequalities. Besides, ...

Abstract The scope of our investigation is to study the geometric properties normalized form combination generalized Lommel–Wright function $J_{\nu ,\lambda }^{\mu ,m}$ J ? , ? ? m </mm...

Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [8] proved that there exists a unique compact set K = K(I), called the attractor of the IFS I, such that K = ⋃m j=1 φj(K). Moreover, for any given probability vector p = (p1, . . . , pm), i.e. pj > 0 for all j and ∑m j=1 pj = 1, there exists a unique compactly supported proba...

Abstract In this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under influence slip has been obtained. A coupled system partial differential equations representing equation re-written in terms fractional derivatives form by using Caputo operator. The Discrete Laplace transform method employed computing expressions ve...