A Survey of the Coupon Collector’s Problem with Random Sample Sizes

This paper surveys the coupon collector’s waiting time problem with random sample sizes and equally likely balls. Consider an urn containing m red balls. For each draw, a random number of balls are removed from the urn. The group of removed balls is painted white and returned to the urn. Several approaches to addressing this problem are discussed, including a Markov chain approach to compute the distribution and expected value of the number of draws required for the urn to contain j white balls given that it currently contains i white balls. As a special case, E[N], the expected number of draws until all the balls are white given that all are currently red is also obtained.      

Global Optimization Performance Measures for Generalized Hill Climbing Algorithms

Generalized hill climbing algorithms provide a framework for modeling several local search algorithms for hard discrete optimization problems. This paper introduces and analyzes generalized hill climbing algorithm performance measures that reflect how effectively an algorithm has performed to date in visiting a global optimum and how effectively an algorithm may pes]rform in the future in visiting such a solution. These measures are also used to obtain a necessary asymptotic convergence (in probability) condition to a global optimum, which is then used to show that a common formulation of threshold accepting does not converge. These measures assume particularly simple forms when applied to specific search strategies such as Monte Carlo search and threshold accepting.     

Precision neutron interferometric measurement of the nd coherent neutron scattering length and consequences for models of three-nucleon forces

We have performed the first high precision measurement of the coherent neutron scattering length of deuterium in a pure sample using neutron interferometry. We find b(nd)=(6.665+/-0.004) fm in agreement with the world average of previous measurements using different techniques, b(nd)=(6.6730+/-0.0045) fm. We compare the new world average for the nd coherent scattering length b(nd)=(6.669+/-0.003) fm to calculations of the doublet and quartet scattering lengths from several modern nucleon-nucleon potential models with three-nucleon force (3NF) additions and show that almost all theories are in serious disagreement with experiment. This comparison is a more stringent test of the models than past comparisons with the less precisely determined doublet scattering length of (2)a(nd)=(0.65+/-0.04) fm.     

Nanowire acting as a superconducting quantum interference device

We present the results from an experimental study of the magnetotransport of superconducting wires of amorphous indium-oxide having widths in the range 40-120 nm. We find that, below the superconducting transition temperature, the wires exhibit clear, reproducible, oscillations in their resistance as a function of magnetic field. The oscillations are reminiscent of those that underlie the operation of a superconducting quantum interference device.     

Electronic effects in transition metal porphyrins. 10. Effect of ortho substituents on the temperature dependence of the NMR spectra of a series of spin-admixed perchloratoiron(III) tetrakis(2,6- or 2,4,6-phenyl substituted)porphyrinates

The perchloratoiron(III) complexes of a series of 2,6-disubstituted tetraphenylporphyrin ligands, where the 2,6-phenyl substituents were -H, -F, -Cl, -Br, or -OMe, as well as two 2,4,6-phenyl-substituted complexes, where the substituents were -Me and -OMe, have been investigated as a function of temperature by 1H NMR spectroscopy. Curvature in the 1/T dependence was evident in most cases. Forced linear extrapolation of the temperature dependence observed over the range of the study yielded Curie plots that include negative slopes with very large positive 1/T intercepts (Cl approximately Br > Me > H) to negative slope with near zero intercept (tri-OMe) to positive slope with very large negative intercept (F, di-OMe). The NMR results were combined with EPR spectroscopic data and curve-fitting procedures based on an expanded Curie law to arrive at a consistent overview of the variety of temperature-dependence behaviors observed. This overview relies upon the premise that, in addition to the ground state observed by EPR spectroscopy, one (or more) thermally accessible excited state(s) are populated to varying degrees over the temperature range of the NMR measurements. If only one excited state is considered, the analysis is consistent with the ground state being a largely intermediate-spin state (S = 3/2) for the majority of the complexes but a largely high-spin state (S = 5/2) for ((2,6-F2)4TPP)FeOClO3 and ((2,6-(OMe)2)4TPP)FeOClO3.     

A note on Ramsey multiplicity

If G₁ and G₂ are graphs and the Ramsey number r(G₁, G₂) = p, then the fewest number of G₁ in G and G₂ in ? (G complement) that occur in a graph G on p points is called the Ramsey multiplicity and denoted R(G₁, G₂). In [2, 3] the diagonal (i.e. G₁ = G₂) Ramsey multiplicities are derived for graphs on 3 and 4 points, with the exception of K₄. In this note an upper bound is established for R(K_s, K₁). Specifically, we show that R(K₄, K₄) ? 12.     

On the Ramsey multiplicity for stars

In 1929, Ramsey proved a theorem guaranteeing that if G₁,G₂,…,G_k are graphs, then there exists an integer r so that if the edges of K_r are colored in any fashion with k colors a monochromatic G_i in color i exists for some i. Harary and Prins suggested the problem of deciding the minimum number of monochromatic G_i in any such coloring. It is the purpose of this paper to establish this minimum number in the case when G_i are stars for each i.