Refinement of Lower Bounds of the Chromatic Number of a Space with Forbidden One-Color Triangles

Mathematical Notes - The present paper deals with estimates of the chromatic number of a space with forbidden one-color triangles. New lower bounds for the quantity under study, which are sharper...     

Short communication controlling LC-SPE-NMR systems

There are several stages of the LC-SPE-NMR process that should be monitored closely to ensure an efficient isolation and concentration of the target analyte, for instance analyte break-through and compound transfer from the LC-SPE to the NMR probe. In this study, analyte break-through monitoring was performed with a UV detector and a mass spectrometer placed after the SPE unit. Easy break-through was a problem when attempting multiple trapping of various compounds using C18 SPE cartridges with the original commercial system. However, on lowering the flow rate over the SPE system and using SPE cartridges packed with porous carbon, the number of trappings possible increased five-fold. To increase control over the on-line SPE-NMR transfer, a gradient pump-UV system was used to elute compounds trapped on an SPE to an NMR probe. The analyte band was placed in the active volume of the probe by a stop-flow mechanism. The modified LC-SPE system was also coupled with off-line NMR analysis for determination of a degradation product of the insecticide monuron, present in the low ppm range.     

On the number of edges in a uniform hypergraph with a range of permitted intersections

The paper studies the quantity p(n, k, t ₁, t ₂) equal to the maximum number of edges in a k-uniform hypergraph with the property that the size of the intersection of any two edges lies in the interval [t ₁, t ₂]. Previously known upper and lower bounds are given. New bounds for p(n, k, t ₁, t ₂) are obtained, and the relationship between these bounds and known estimates is studied. For some parameter values, the exact values of p(n, k, t ₁, t ₂) are explicitly calculated.     

On chromatic numbers of nearly Kneser distance graphs

A family of distance graphs whose structure is close to that of Kneser graphs is studied. New lower and upper bounds for the chromatic numbers of such graphs are obtained, and relations between these numbers are considered. The structure of certain important independent sets of the family of graphs under consideration is described, and the cardinalities of these sets are explicitly calculated.     

A Generalization of Kneser Graphs

Mathematical Notes - Graphs which are analogs of Kneser graphs are studied. The problem of determining the chromatic numbers of these graphs is considered. It is shown that their structure is...