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.     

Electrical conductivity and chemical diffusion coefficient measurements in single crystalline nickel oxide at high temperatures

Electrical conductivity measurements on nickel oxide have been performed at high temperatures (1273 K<T< 1673 K) and in partial pressures of oxygen ranging from Po₂ = 1.89 × 10^?4 atm to Po₂ = 1 atm. The $\text{po}{}_2{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}$ dependence of the conductivity decreases from about $\text{1}\text{4}$ for Po₂ = 1 atm to smaller values for lower partial pressures of oxygen. The activation enthalpy for conduction increases for decreasing oxygen partial pressures (from 22.5 kcal mol^?1 at Po₂ = 1 atm to 26.0 kcal mol^?1 for Po₂ = 1.89 × 10^?4 atm). This behaviour can be explained by the simultaneous presence of singly and doubly ionized nickel vacancies, with different energies of formation.Furthermore, chemical diffusion coefficient measurements have been performed in the same temperature range, using the conductivity technique, and leading to the result:

$\text{D}\text{?}\text{= 0.244 exp (?}\text{36,600}\text{RT}\text{) cm}{}^2\text{s}{}^{\mathrm{?1}}$

.     

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.     

Une approche polynomiale du théorème de Faltings

We present here an elementary proof of a quantitatively improved version of the Mordell's Conjecture which is now Faltings's Theorem. For the count of the ‘large points’ of $C(K)$ (see below for the notations) we use Vojta's method which was simplified by Bombieri and then by T. de Diego, G. Rémond. To count the points of small heights of $C(K)$, we use a result of S. David and P. Philippon, allowing to us estimate the number of points of small height of the bigger set $C(\overline{K})\cap J(K)$. To cite this article: B. Farhi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

The ep -->e'p eta reaction at and above the S11(1535) baryon resonance

New cross sections for the reaction e p-->e p eta are reported for total center of mass energy W = 1.5--1.86 GeV and invariant momentum transfer Q2 = 0.25--1.5 (GeV/c)(2). This large kinematic range allows extraction of important new information about response functions, photocouplings, and eta N coupling strengths of baryon resonances. Newly observed structure at W approximately 1.65 GeV is shown to come from interference between S and P waves and can be interpreted with known resonances. Improved values are derived for the photon coupling amplitude for the S11(1535) resonance.