Constrained best approximation in Hilbert space III. Applications ton-convex functions

This paper continues the study of best approximation in a Hilbert spaceX from a subsetK which is the intersection of a closed convex coneC and a closed linear variety, with special emphasis on application to then-convex functions. A subtle separation theorem is utilized to significantly extend the results in [4] and to obtain new results even for the “classical” cone of nonnegative functions. It was shown in [4] that finding best approximations inK to anyf inX can be reduced to the (generally much simpler) problem of finding best approximations to a certain perturbation off from either the coneC or a certain subconeC _F. We will show how to determine this subconeC _F, give the precise condition characterizing whenC _F=C, and apply and strengthen these general results in the practically important case whenC is the cone ofn-convex functions inL ₂ (a,b),     

Optimal assignment of NOP due-dates and sequencing in a single machine shop

We consider the problem of optimal assignment of NOP due-dates ton jobs and sequencing them on a single machine to minimize a penalty function depending on the values of assigned constant waiting allowance and maximum job tardiness. It is shown that the earliest due date (EDD) order is an optimal sequence. For finding optimal constant waiting allowance, we reduce the problem to a multiple objective piecewise linear programming with single variable. An efficient algorithm for optimal solution of the problem is given.     

Sums over positive integers with few prime factors

The author has presented estimates for sums of multiplicative functions, satisfying certain conditions, extended over positive integers n such that n is less than or equal to x^t, the greatest prime factor of n is at most equal to x, and n is relatively prime to a natural number k. These estimates are uniform in t, x, and k.     

Cold and hot binary and ternary fission yields in the spontaneous fission of 252Cf

The spontaneous fission (SF) of ²⁵²Cf has been studied via γ-γ-γ coincidence and light charged particle—γ-γ coincidence with Gammasphere. The yields of correlated Mo-Ba pairs in binary fission with 0–10 neutron emission have been remeasured with an uncompressed cube. The previous hot fission mode with 8–10 neutron emission seen in the Mo-Ba split is found to be smaller than earlier results but still present. New 0n binary SF yields are reported. By gating on the light charged particles detected in ΔE-E detectors and γ-γ coincidence with Gammasphere, the relative yields of correlated pairs in alpha ternary fission with zero to 6n emission are observed for the first time. The peak occurs around the α2n channel. A number of correlated pairs are identified in ternary fission with ¹⁰Be as the light charged particle. We observed only cold, 0n ¹⁰Be and little, if any, hot, xn ¹⁰Be channels.     

Vibrational relaxation of the C-X stretching mode in halobenzenes

The Raman linewidths of the carbon-halogen stretching mode in several halobenzenes were measured as a function of temperature and in dilute cyclohexane solution. It was found that, as in an earlier investigation on haloalkanes, the vibrational relaxation efficiencies, τ^?1_iso, vary in the order Cl > Br > I. The temperature dependence of τ_iso, together with the results in dilute solution, provide evidence that dipolar interactions play a significant role in vibrational relaxation in these systems.