Using an Integer Programming Model to Determine the Price of Combination Vaccines for Childhood Immunization

The Recommended Childhood Immunization Schedule has become sufficiently crowded that the prospect of adding additional vaccines to this schedule may not be well received by either health-care providers or parents/guardians. This has encouraged vaccine manufacturers to develop combination vaccines that can permit new vaccines to be added to the schedule without requiring children to be exposed to an unacceptable number of injections during a single clinic visit. This paper develops an integer programming model to assess the economic premium that exists in having combination vaccines available. The results of this study suggest that combination vaccines provide a cost effective alternative to individual vaccines and that further developments and innovations in this area by vaccine manufacturers can provide significant economic and societal benefits.     

The Galois group of a radical extension of the rationals

The Galois group of the splitting field of an irreducible binomialx ^2e −a overQ is computed explicitly as a full subgroup of the holomorph of the cyclic group of order 2 ^e . The general casex ⁿ −a is also effectively computed.     

On graphs having domination number half their order

In this paper we present a characterization of connected graphs of order 2n with domination numbern. Using this class of graphs, we determine an infinite class of graphs with the property that the domination number of the product of any two is precisely the product of the domination numbers.     

Structure of trans-W(C0)4(CNC6H11)(CS) and a correlation of ν(cs) frequencies with CS bond distances in metal thiocarbonyl complexes

An X-ray structural investigation of $\text{trans}$-W(C0)₄(CNC₆H₁₁)(CS) shows that the Wz.bnd;C bond distances to the 3 isoelectronic ligands increase in the order: WCS(1.944Å) < WCO(2.0645Å, average) < WCNC₆H₁(2.158Å). Using data from this molecule as well as results from other thiocarbonyl complexes reported in the literature, an excellent correlation of low ν(CS) frequencies with long CS bond distances is observed, a trend which supports current bonding theories for thiocarbonyl complexes.     

A modified homogeneous algorithm for function minimization

Recently, an algorithm for function minimization was presented, based upon an homogeneous, rather than upon a quadratic, model. Numerical experiments with this algorithm indicated that it rapidly minimizes the standard test functions available in the literature. Although it was proved that the algorithm produces function values which continually descend, no proof of convergence was supplied.In this paper, the homogeneous algorithm is modified primarily by replacing the cubic interpolation routine by Armijo's step size rule. Although not quite as fast as the original version on the standard test functions, this modified form has the advantage that a proof of convergence follows from a general theorem of Polak.