THE LINEAR DISCREPANCY OF 3 × 3 × 3

Linear Sphericity Testing of 3-Connected Single Source Digraphs

It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Lecture 3 : Constructive Bounds on Discrepancy

In previous lectures we saw a constructive proof of the Lovasz Local Lemma and an application to a variant of the max-min allocations problem. In this lecture we will continue the topic of algorithmic versions of existential theorems with a recent result due to Bansal [Ban10] that makes Spencer’s [Spe85] and Srinavasan’s [Sri97] bounds on discrepancy of set systems constructive. What makes Bans...

Preparation and Characterization of Smcl3(THF)3 and Sm(BH4)3(THF)3 Complexes

The synthesis of SmCl3(THF)3 from SmCl3.6H2O is described. The reaction of SmCl3(THF)3 with NaBH4 in dry THF gave white microcrystalline tris (tetrahydroborato) tris (tetrahydrofuran) samarium (III), Sm(BH4)3(THF)3. The vibrational and magnetic properties of Sm(BH4)3...

2-recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph

Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that $ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups $B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and by the set of orders of maximal abelian subgroups are ...