Bad news for chordal partitions

Reed and Seymour [1998] asked whether every graph has a partition into induced connected nonempty bipartite subgraphs such that the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger's Conjecture. We prove that the answer is “no.” In fact, we show that the answer is still “no” for several relaxations of the question.     

A Convenient Procedure for the Sulfation of Flavonoid Glycosides: Preparation of Rotin Nona- and Deca Sulfates

Abstract

A satisfactory procedure for the sulfation of flavonoid glycosides is described and is illustrated by the preparation of rutin nona and deca sulfates. Compounds of this type are important modulators of the complement part of the immune system.     

A neutron monitor for in-situ real-time determination of transuranics in a processed waste effluent stream

A pilot plant operation at the Savannah River Site will remove ⁹⁰Sr, ¹³⁷Cs, and transuranics from a high-level liquid waste stream prior to encapsulation in a Saltstone Facility. Monitors are required to determine the concentrations of all radionuclides, including transuranics, in real-time on this processed waste stream. A neutron counter used to measure the concentration of each actinide isotope present in the stream is described. The neutron counter assembly consists of nested annular layers of shielding, reflectors, detectors, and moderators. On-line, live-time system control and calibration is provided by a time-tagged neutron source embedded in the moderator assembly.     

Resonant hydraulic sloshing in a tank of variable depth

The forced resonant oscillations of a fluid in a tank of variable depth are considered within the hydraulic approximation. It is shown that for certain bottom topographies a continuous periodic output dominated by the first normal mode is possible. This contrasts with the case of a tank of constant depth, where hydraulic jumps are a feature of the motion. The amplitude and frequency of the output are connected by a cubic equation. The fluid response can act like that of a hard or soft spring, depending on the bottom topography. There is also a critical bottom topography that yields a higher order response amplitude.