Self-dual, not self-polar

The smallest number of points of an incidence structure which is self-dual but not self-polar is 7. For non-binary structures (where a “point” may occur more than once in a “block”) the number is 6.     

Quasi-symmetric designs related to the triangular graph

LetT _m be the adjacency matrix of the triangular graph. We will give conditions for a linear combination ofT _m, I andJ to be decomposable. This leads to Bruck-Ryser-Chowla like conditions for, what we call, triangular designs. These are quasi-symmetric designs whose block graph is the complement of the triangular graph. For these designs our conditions turn out to be stronger than the known non-existence results for quasi-symmetric designs.     

Quinolone antibacterials. 1. 7-(2-substituted-4-thiazolyl and thiazolidinyl)quinolones

A series of 7-(2-substituted-4-thiazolyl and thiazolidinyl)-1-ethyl-1,4-dihydro-4-oxoquinoline-3-carboxylic acids and their 6-fluoro analogues were synthesized. The Hantzsch method was used for the preparation of the thiazolylquinolones. The thiazolidinylquinolones were synthesized by quaternization of the corresponding thiazolyl analogues, followed by reduction of the obtained thiazolium salts with sodium borohydride in aqueous solution. Antibacterial activity was tested in vitro. Most of the compounds were inactive against Gram-negative bacteria but some of them showed however good activity against Gram-positive bacteria and mycobacteria. This activity pattern is rarely found among the quinolone antibacterials.     

2-designs having an intersection number k − n

In this paper we examine 2-designs having an intersection number k ? n. This intersection number gives rise to an equivalence relation on the blocks of the design. Conditions on the sizes of these equivalence classes and some properties of any further intersection numbers are obtained. If such a design has at most three intersection numbers then it gives rise to a strongly regular graph. This leads to a result on the embedding of quasi-residual designs. As as example a quasi-residual 2-(56, 12, 3) design is constructed and embedded in a symmetric 2-(71, 15, 3) design.     

Thiazolopyridine analogs of naldixic acid. 1. Thiazolo[5,4-b]pyridines

A series of 2-substituted-7-alkyl-4,7-dihydro-4-oxothiazolo[5,4-b]pyridine-5-carboxylic acids were synthesized. Antibacterial activity was tested in vitro. None of the new compounds prepared showed any antibacterial activity in vitro against the strains tested.     

Deza graphs: A generalization of strongly regular graph

We consider the following generalization of strongly regular graphs. A graph G is a Deza graph if it is regular and the number of common neighbors of two distinct vertices takes on one of two values (not necessarily depending on the adjacency of the two vertices). We introduce several ways to construct Deza graphs, and develop some basic theory. We also list all diameter two Deza graphs which are not strongly regular and have at most 13 vertices.     

Spectral symmetry in conference matrices

Designs, Codes and Cryptography - A conference matrix of order n is an $$n\times n$$ matrix C with diagonal entries 0 and off-diagonal entries $$\pm 1$$ satisfying $$CC^\top =(n-1)I$$ . If C is...