Lanthanide Identity Governs Guest-Induced Dimerization in LnIII[15-MC N(L-pheHA)-5])3+ Metallacrowns

Series of lanthanide-containing metallic coordination complexes are frequently presented as structurally analogous, due to the similar chemical and coordinative properties of the lanthanides. In the case of chiral (Ln^III[15-MC _N(L-pheHA)-5])³⁺ metallacrowns (MCs), which are well established supramolecular hosts, the formation of dimers templated by a dicarboxylate guest (muconate) in solution of neutral pH is herein shown to have a unique dependence on the identity of the MC's central lanthanide. Calorimetric data and nuclear magnetic resonance diffusion studies demonstrate that MCs containing larger or smaller lanthanides as the central metal only form monomeric host-guest complexes whereas analogues with intermediate lanthanides (for example, Eu, Gd, Dy) participate in formation of dimeric host-guest-host compartments. The driving force for the dimerization event across the series is thought to be a competition between formation of highly stable MCs (larger lanthanides) and optimally linked bridging guests (smaller lanthanides).     

Single and two-qubit dynamics in circuit QED architectures

We use Bloch oscillations to transfer coherently many photon momenta to atoms. Then we can measure accurately the ratio h/m_Rb and deduce the fine structure constant α. The velocity variation due to the Bloch oscillations is measured thanks to Raman transitions. In a first experiment, two Raman π pulses are used to select and measure a very narrow velocity class. This method yields to a value of the fine structure constant α^-1= 137.03599884(91) with a relative uncertainty of about 6.6 ppb. More recently we use an atomic interferometer consisting in two pairs of π/2 pulses. We present here the first results obtained with this method.     

Liaison addition and the structure of a Gorenstein liaison class

We study the concept of liaison addition for codimension two subschemes of an arithmetically Gorenstein projective scheme. We show how it relates to liaison and biliaison classes of subschemes and use it to investigate the structure of Gorenstein liaison equivalence classes, extending the known theory for complete intersection liaison of codimension two subschemes. In particular, we show that on the non-singular quadric threefold in projective 4-space, every non-licci ACM curve can be obtained from a single line by successive liaison additions with lines and CI-biliaisons.     

Entangling two uncoupled flux qubits via their sequential interaction with a quantized electromagnetic field

A theoretical scheme for the generation of maximally entangled states of two superconducting flux qubits via their sequential interaction with a monochromatic quantum field is presented. The coupling of the qubits with the quantized field can be tuned on and off resonance by modulating the effective Josephson energy of each qubit via an externally applied magnetic flux. The system operates in such a way as to transfer the entanglement from a bipartite field-qubit subsystem to the two qubits. This scheme is attractive in view of the implementation of practical quantum processing systems.     

On ideals with the Rees property

A homogeneous ideal I of a polynomial ring S is said to have the Rees property if, for any homogeneous ideal ${J \subset S}$ which contains I, the number of generators of J is smaller than or equal to that of I. A homogeneous ideal ${I \subset S}$ is said to be ${\mathfrak{m}}$ -full if ${\mathfrak{m}I:y=I}$ for some ${y \in \mathfrak{m}}$ , where ${\mathfrak{m}}$ is the graded maximal ideal of ${S}$ . It was proved by one of the authors that ${\mathfrak{m}}$ -full ideals have the Rees property and that the converse holds in a polynomial ring with two variables. In this note, we give examples of ideals which have the Rees property but are not ${\mathfrak{m}}$ -full in a polynomial ring with more than two variables. To prove this result, we also show that every Artinian monomial almost complete intersection in three variables has the Sperner property.     

Resolutions of subsets of finite sets of points in projective space

Abstract

Eisenbud et al. proved a number of results regarding Gröbner bases and initial ideals of those ideals J in the free associative algebra K ?X ₁,…, X _n ? which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one weak notion of generic initial ideals in K ?X ₁,…, X _n ?, and show that generic initial ideals of ideals containing the anti-commutator ideal, or the commutator ideal, are finitely generated.     

Reduced Gorenstein codimension three subschemes of projective space

It is known, from work of Diesel, which graded Betti numbers are possible for Artinian Gorenstein height three ideals. In this paper we show that any such set of graded Betti numbers in fact occurs for a reduced set of points in , a stick figure in , or more generally, a good linear configuration in . Consequently, any Gorenstein codimension three scheme specializes to such a ``nice' configuration, preserving the graded Betti numbers in the process. This is the codimension three Gorenstein analog of a classical result of arithmetically Cohen-Macaulay codimension two schemes.

     

Oxytetracycline as environmental contaminant in arable lands

Oxytetracycline (OXY) is a broad-range antimicrobial routinely used in pig production, at doses in the range of few g/kg of medicated feed, during the weaning period. It could persist at ppm level in pig liquid manure that routinely is used for organic fertilisation. In the present work we describe a methodology to study OXY environmental fate in arable land where crops are cultivated for animal feeding purposes. A liquid-liquid extraction followed by metal chelate affinity chromatography was applied to environmental samples of manures and soils drawn within a case-control study. Extracts were then analysed by high performance liquid chromatography with UV/DAD detection, using a reverse phase column, and expressing the results as 4-epioxytetracycline epimer. Results indicate OXY is well retained at mg kg(-1) levels in soil exposed to contaminated pig manure fertilisation. Such compartment could constitute an abiotic reservoir for the systemic and/or for the external contamination of corn.