Polynomial partitioning for a set of varieties

Polynomial and non-polynomial solutions set for wave equation with using Lie point symmetries

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

Shallow Packings, Semialgebraic Set Systems, Macbeath Regions, and Polynomial Partitioning

The packing lemma of Haussler states that given a set system (X,R) with bounded VC dimension, if every pair of sets in R have large symmetric difference, then R cannot contain too many sets. Recently it was generalized to the shallow packing lemma, applying to set systems as a function of their shallow-cell complexity. In this paper we present several new results and applications related to pac...

Partitioning a Set

an integrated temporal partitioning and mapping framework for improving performance of a reconfigurable instruction set processor

reconfigurable instruction set processors allow customization for an application domain by extending the core instruction set architecture. extracting appropriate custom instructions is an important phase for implementing an application on a reconfigurable instruction set processor. a custom instruction (ci) is usually extracted from critical portions of applications and implemented on a reconf...

Polynomial Partitioning on Varieties of Codimension Two and Point-Hypersurface Incidences in Four Dimensions

We present a polynomial partitioning theorem for finite sets of points in the real locus of a complex algebraic variety of codimension at most two. This result generalizes the polynomial partitioning theorem on the Euclidean space of Guth and Katz, and its extension to hypersurfaces by Zahl and by Kaplan, Matoušek, Sharir and Safernová. We also present a bound for the number of incidences betwe...