Cotangent functors of curve singularities

Let R be a complete analytic k-algebra of dimension one, where k is a field of characteristic 0. For a Noetherian normalization , the cotangent functors T_i(R/A, R) are of finite length. It is shown that if R is smoothable, then for all j, where denotes the complementary module. This result is used to give estimates for the length of the torsion of the module of differentials _R/k.     

A note on the hilbertfunction of a one-dimensional Cohen-Macaulay ring

In this note we give examples of one-dimensional noetherian local integral domains with the property that the number of generators of the square of the maximal ideal is less than the embedding dimension. On the other hand we show that if \((R,m)\) is a local one-dimensional Cohen-Macaulay ring, then \((m^n )\) for all n such that μ \((m^n )\) < m(R). Here μ denotes the minimal number of generators of an ideal and m(R) the multiplicity of R. A similar statement was conjectured by D. Sally in [5], Our main result 2.1 generalizes Prop. 2.6. in [6].     

The hadronic cross section of electron-positron annihilation at 9.5 GeV and the ϒ and ϒ′ resonance parameters

The reaction e⁺e^?→ hadrons has been measured in the ? and ?′ region using the DASP detector at the DESY storage ring DORIS. The following final results are obtained: R_had(9.5 GeV)=3.73±0.16±0.28, Γ_ee(?)=(1.23 ± 0.08 ± 0.12) keV, B_μμ(?)=(3.2±1.3±0.3)%, $\text{Γ}{}_{\mathrm{<mtext>ee</mtext>}}\text{Γ}{}_{\mathrm{<mtext>had</mtext>}}\text{Γ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(?′)=(0.55±0.11 ±0.06)}\text{keV}$, and M(?′)?M(?)=(556 ±10) MeV.     

Numerical semigroups generated by primes

Semigroup Forum - Let $$p_1=2, p_2=3, p_3=5, \ldots$$ be the consecutive prime numbers, $$S_n$$ the numerical semigroup generated by the primes not less than $$p_n$$ and $$u_n$$ the largest...     

Correction to: Numerical semigroups generated by primes

Semigroup Forum - A correction to this paper has been published: https://doi.org/10.1007/s00233-021-10198-7     

The semileptonic decay fraction ofB-mesons in the light of interfering amplitudes

Consequences of the interference between spectator amplitudes for the lifetimes and semileptonic decay fractions ofB ⁰ andB ⁺ mesons are discussed. Extracting these amplitudes from a fit to 11 exclusive hadronicB decay fractions we finda ₁=1.05±0.03±0.10,a ₂=+0.227±0.012±0.022, an inclusive semileptonic decay fraction of (11.2±0.5±1.7)%, and a lifetime ratio (B ⁺)/(B ⁰)=0.83±0.01±0.01.Supported under DOE grant number DE-FG02-91-ER40690     

Vollständige Durchschnitte in Cohen-Macaulay-Ringen

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