Efficient group cuts for integer programs

Gomory's group relaxation for integer programs has been refined by column generation methods and dual ascent algorithms to identify a set of candidate solutions which are feasible in the relaxation but not necessarily so in the original integer program. Attempts at avoiding branch and bound procedures at this point have focussed on providing extra group constraints which eliminate all or most of the candidate solutions so that further ascent can take place. It will be shown that a single constraint usually of order 2 or 3, can eliminate all of the candidate solutions.     

The influence of substrate geometry on the emission properties of a liquid metal ion source

The effect of needle radius, cone angle and shaft diameter on the threshold voltage and angular intensity — total current relationships for a Ga liquid-metal ion source (LMIS) was investigated. The variation of threshold voltage with needle geometry could be described in terms of the Taylor theory of liquid cone formation by electrostatic fields. The beam energy spread was mainly a function of total source current and was not a sensitive function of emitter geometry. Source angular intensity at a constant total current increased linearly with threshold voltage when the latter was altered due to source geometry.     

Rate constants for the reaction of the bromomethyne radical with alkynes

Absolute rate constants were measured for the gas phase reactions of the CBr($\text{～}\text{X}$²Π) radical produced in the flash photolysis of CHBr₃ with a series of alkynes. The rate of addition to the triple bond followed the trend established for addition to double bonds and a linear correlation between log k and ionization potentials reflects the electrophilic nature of the reaction. In comparison with published data on CCl, S(³P₂) the reactivity follows the trend CBr ≈ CCl ≈ S(³P₂) > O(³P₂).     

Some properties of higher spin rest-mass zero fields in general relativity

The propagation of a zero rest-mass test field of arbitrary spins>1 through curved space-time is found to be subject to strong constraints. A null test field is shown to be possible only in a restricted class of spaces previously introduced by Kundt and Thompson. This result is in fact a simultaneous generalization of the theorems of Robinson and of Goldberg and Sachs. For test fields of spin-2 in vacuum spaces, solutions of the propagation equation are restricted, save in a few exceptional cases, to constant multiples of the Weyl spinor. The exceptional cases are discussed, and appear to be physically uninteresting.     

The pressure and composition dependence of mutual diffusion in the system helium-nitrogen at 300 K

Diffusion coefficients for the system helium-nitrogen have been measured as a function of pressure at 300 K from 1 to 12.5 atmospheres. These measurements include composition dependences at 1, 3, 5 and 7 atmospheres. The results show reasonable agreement with the Thorne-Enskog theory for moderately dense gases.