1. An O(mm(n) log(n)) = O(nω+ ) algorithm which finds the shortest distance matrix for a graph G by recursively finding the shortest distance matrix for the graph G2. 2. The problem of determining the successor matrix for tripartite graphs. 3. O(nω) time algorithm for finding successor matrix in in a simple tripartite graph when there is a unique successor for any 2 vertices. 4. An O(mm(n) log(...

We determine the center of a localization of Uq(nω) ⊆ U q (g) by the covariant elements (non-mutable elements). Here, g is any finite-dimensional complex Lie algebra and ω is any element in the Weyl group W. The non-zero complex parameter q is assumed not to be a root of unity. The center is determined by the null space of 1 + ω. Another family of quadratic algebras is also considered.

A series of Nω-nitro-Nω'-substituted guanidines has been prepared as potential inhibitors of the human Nitric Oxide Synthase (NOS) isoforms. The reported utility of aminoguanidine and nitroarginine in iNOS inhibition points to a potential similar utility for analogs of nitro-guanidine. The compound library was tested against the three isoforms of Nitric Oxide Synthase (eNOS, iNOS and nNOS). Sev...

We prove that for k ≪ 4 √n regular resolution requires length nΩ(k ) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a k-clique. This lower bound is optimal up to the multiplicative constant in the exponent, and also implies unconditional nΩ(k ) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.

The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O(NΓ log NΓ) is almost linear in NΓ – the number of de...

We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ǫ > 0 produces an output XA with (1−ǫ)per(A) ≤ XA ≤ (1+ǫ)per(A) for almost all (0-1) matrices A. For any positive constant ǫ > 0, and almost all (0-1) matrices the algorithm runs in time O(nω), i.e., almost linear in the size of the matrix, where ω = ω(n) is any function satisfying ω(n) → ∞ as n ...

We present new algorithms for finding induced four-node subgraphs in a given graph, which run in time roughly that of detecting a clique on three nodes (i.e., a triangle). • The best known algorithms for triangle finding in an nnode graph take O(nω ) time, where ω < 2.373 is the matrix multiplication exponent. We give a general randomized technique for finding any induced four-node subgraph, ex...

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number nω of benzene rings along the ribbon width is odd. A series of numerical...