Strongly polynomial-time approximation for a class of bicriteria problems

Consider the following problem: given a ground set and two minimization objectives of the same type find a subset from a given subset-class that minimizes the first objective subject to a budget constraint on the second objective. Using Megiddo's parametric method we improve an earlier weakly polynomial time algorithm.     

Separation of potential flavoring compounds by high-performance liquid chromatography

High-performance liquid chromatography separated successively and quantitatively the food flavoring agents pyrimidines, purines and nucleosides, followed by nucleotides, then by polyphenols and finally by pyrazines with a reversed-phase octadecylsilica (μBondapak C₁₈) column and various proportions of methanol, water, acetic acid and tetrabutylammonium phosphate (PIC A). The polar solvent (solvent A) was water—acetic acid—PIC A (97.5:1.5:1.0) and the relatively non-polar solvent (solvent B) was methanol—acetic acid—PIC A (97.5:1.5:1.0). Purines, pyrimidines, and nucleosides were eluted with solvent A. Nucleotides were eluted with a mixture of solvents A and B (9:1). Polyphenols were separated with a gradient starting at 10% solvent B and finishing at 25% solvent B, and finally the pyrazines were removed successively from the column with a gradient starting at 25% solvent B and finishing at 45% solvent B. The resolution and reproducibility were excellent for more than 50 compounds. By this method beverages could be analyzed directly, without solvent extraction, for flavoring compounds.     

Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

Unnatural parity levels populated in the 16O(6Li,d)20Ne reaction

The ¹⁶O(⁶Li, d)²⁰Ne reaction to the 2^?, 4.97 MeV, 3^?, 5.63 MeV, and 4^?, 7.01 MeV members of the K^π = 2^? band has been studied. Angular distributions were measured at 32 MeV from 7.5° to 145° (lab). Excitation functions were measured at 15° (lab) and 145° (lab) from 31 to 33 MeV and 31.75 to 32.5 MeV, respectively. Results of multi-step and compound nuclear calculations are compared to the data. At this incident energy, both mechanisms appear to contribute to the population of the unnatural parity levels.