Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...
We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer d, there is a constant such that whenever are n-element subsets of , we can find a point and subsets for every , each of size at least , suc ...
We extend the Leon verification system for Scala with support for bit-vector reasoning, thus addressing one of its fundamental soundness limitation with respect to the treatment of integers primitives. We leverage significant progresses recently achieved i ...
For positive integers w and k, two vectors A and B from Z(w) are called k-crossing if there are two coordinates i and j such that A[i] - B[i] >= k and B[j] - A[j] >= k. What is the maximum size of a family of pairwise 1-crossing and pairwise non-k-crossing ...
In an earlier work, we constructed the almost strict Morse n-category X which extends Cohen Sz Jones Sz Segal's flow category. In this article, we define two other almost strict n-categories V and W where V is based on homomorphisms between real vector spa ...
This paper defines the problem of Scalable Secure computing in a Social network: we call it the S-3 problem. In short, nodes, directly reflecting on associated users, need to compute a symmetric function f : V-n -> U of their inputs in a set of constant si ...
A Method for nuclear magnetic resonance (NMR) spectroscopy of a sample comprising the following steps: (a) excitation of long lived coherences (LLC) between the singlet state So and the central triplet state To of nuclei of the sample by initiating irradia ...
