Significant improvements to the Ford-Johnson algorithm for sorting

For almost twenty years, the Ford-Johnson algorithm for sortingt items using comparisons was believed to be optimal. Recently, Manacher was able to show that the Ford-Johnson algorithm is not optimal for certain ranges of values oft. In this paper, we present some new algorithms which achieve much stronger results compared to Manacher's algorithms.     

The functional equation for Poincaré series of trace rings of generic 2×2 matrices

In this note we give a rational expression for the Poincaré series of Π_m,2, the trace ring ofm generic 2×2 matrices. This result extends the computations of E. Formanek form⩽4. As a consequence, we prove that the Poincaré series satisfies the functional equation(II_m,2;1/t)=-t^4m.P(II_m,2,t) (m>2) supporting the conjecture that Π_m,2 is a Gorenstein ring. Work supported by an NFWO/FNRS grant.     

Nuclear moments and charge radius changes in platinum isotopes

Isotope shift (IS) and hyperfine structure (HFS) measurements have been performed for^{185, 187, 189, 191, 195}Pt using the PILIS (Post ISOCELE Laser Isobar Separator) apparatus installed at the ISOCELE facility. Magnetic and quadrupole moments have been deduced from the HFS results. The charge radius changes determined for these odd nuclei from the IS results, added to the σ<r²> values of the even-A nuclei are compared to the results of lattice Hartree-Fock+BCS calculations for asymmetric solutions:¹⁸⁵Pt is confirmed to be prolate shaped whereas^{187, 189, 191}Pt are likely triaxial in their ground states.     

亚纯函数的零点和极点的分布与充满圆

本文主要结果的含意是:设f(z)为ρ(0<ρ<∞)级亚纯函数,且在角域D上以0和∞为Borel例外值,若在D内一列趋于∞的弧段上,f^(l)(z)(l≥0)充分接近于一有穷非零复数,则在这列弧段附近,f^(l)(z)不存在ρ级充满圆。这个结果可用以估计亚纯函数及其各级导数的亏值数目。     

Addition d'hydrazone aux oléfines en milieu acide: cycloaddition polaire cationique [3+ + 2]

The stereospecificity and the orientation observed for the addition reaction of acetaldehyde hydrazone with (E)- and (Z)-alkenes in acidic media are compatible with a concerted process of the polar [3⁺ + 2] cycloaddition type.