On Quadratic Integral Polynomials with only Finitely Many Roots in any Commutative Finite-Dimensional Algebra

The monic quadratic polynomials f with integer coefficients such that each commutative finite-dimensional algebra over a field contains only finitely many roots of f are determined as the polynomials of the form f = X ² + (2m + 1)X + m ² + m, where ${m \in \mathbb{Z}}$ .     

A characterization of going-down-ring pairs of commutative rings

SoientA ⊆B des anneaux (commutaifs et unitaires). On dit que (A,B) est une paire d’anneaux de going-down siD est un anneau de going-down pour tout anneauD tel queA ⊆D ⊆B. On preuve que (A,B) est une paire d’anneaux de going-down si et seulement siA[b ₁,b ₂] est un anneau de going-down pour toutb ₁,b ₂ εB.     

Reaction of zirconium hydrocarbyls with carbon monoxide

Carbon monoxide reacts with tetrahydrocarbylzirconium compounds, (RCH₂)₄Zr, where R = phenyl or vinyl to give a polymeric species containing ZrOC bonds, which on hydrolysis yields products consistent with successive insertion of CO and ZrC(O)CH₂R into the ZrC bonds.     

The synthesis and development of 2,5-disubstituted tetrahydrofurans as potential scaffolds for diversity-oriented synthesis

The synthesis of 2,5-disubstituted tetrahydrofurans from donor silylmethylcyclopropanes (without bearing an acceptor function) is described. Their further elaboration via a wide range of synthetic transformations is presented to highlight the potential of this method and the resulting THFs as potential scaffolds for diversity-oriented synthesis.     

Lattice-free sets,multi-branch split disjunctions,and mixed-integer programming

In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (Discret Optim 5:724–734, 2008). By analyzing $n$ -dimensional lattice-free sets, we prove that for every integer $n$ there exists a positive integer $t$ such that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with $n$ integer variables is a $t$ -branch split cut. We use this result to give a finite cutting-plane algorithm to solve mixed-integer programs. We also show that the minimum value $t$ , for which all facets of polyhedral mixed-integer sets with $n$ integer variables can be generated as $t$ -branch split cuts, grows exponentially with $n$ . In particular, when $n=3$ , we observe that not all facet-defining inequalities are 6-branch split cuts.     

Observation of the h(c)(1P) Using e+ e- collisions above the DD threshold

Using 586 pb(-1) of e+ e- collision data at E(c.m.) = 4170 MeV, produced at the Cornell Electron Storage Ring collider and collected with the CLEO-c detector, we observe the process e+ e- → π+ π- h(c)(1P). We measure its cross section to be 15.6±2.3±1.9±3.0 pb, where the third error is due to the external uncertainty on the branching fraction of ψ(2S) → π0 h(c)(1P), which we use for normalization. We also find evidence for e+ e- → ηh(c)(1P) at 4170 MeV at the 3σ level and see hints of a rise in the e+ e- → π+ π- h(c)(1P) cross section at 4260 MeV.