Renormalized loop expansion to compute finite size effects of the constraint effective potential

In latticeφ ⁴ close to the critical line, finite size effects can be computed by renormalized loop expansions. In order to do so, the constraint effective potential is computed to two loop order. Using this expression, we are able to extract results for renormalized masses and coupling constants from Multigrid Monte Carlo data of Mack and Meyer for the constraint effective potential close to the critical line, and compare them with the analytical results ofLüscher and Weisz. Perfect agreement is found.     

Approximation of stochastic equations driven by predictable processes

Summary A theory of stochastic differential equations driven by predictable processes in Stratonovich sense is developed. These driving processes include a large class of discontinuous semimartingales. The theory of stochastic differential equations driven by continuous semimartingales in Stratonovich sense is extended without involving Lebesgue-Stieltjes integrals as done by Meyer. Moreover, a change of variables formula without extra terms involving the jumps of the processes holds for this theory. Results on approximation of driving processes are preserved.Research partially supported by the Institute for Mathematics and its Applications at the University of Minnesota, Minneapolis, USA; by the AFOSR under contract #AFOSR-85-0315, the ARO under contract #DAAG 29-84-K-0082, and #DAAL 03-86-K-0171.     

Degrevlex Gröbner bases of generic complete intersections

In this paper, we study the Hilbert–Samuel function of a generic standard graded K-algebra

K[X₁,…,X_n]/(g₁,…,g_m)

when refined by an (ℓ)-adic filtration, ℓ being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gröbner) bases for this order; in particular, we consider an “orderly filling up” conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases.     

Optimal Domains for <Emphasis Type="Italic">L</Emphasis><Superscript>0</Superscript>-valued Operators Via Stochastic Measures

We study extension of operators T: E→ L⁰([0, 1]), where E is an F–function space and L⁰([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic measures and the corresponding spaces of integrable functions. Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain).     

Magneto-volume effects in Fe–Cu solid solutions

The magnetic properties of Fe–Cu metastable solid solutions have been investigated by means of neutron diffraction and magnetisation measurements. These compounds exhibit ferromagnetic order with Curie temperatures above room temperature for concentrations beyond 40 at% in Fe. The magnetic moment at 5 K can reach values over 2 μ_B, while the high field susceptibility is similar to that found in FCC–FeNi Invar alloys. These features together with the low values for the linear coefficient for thermal expansion in the ferromagnetic region suggest that magneto-volume anomalies, including Invar behaviour, play a major role in the magnetic properties of this system when the crystal structure is face centred cubic. Such behaviour could be explained using theoretical total-band energy calculations.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

Structure,Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, I _h , D _2h , T). Our results demonstrate that it is possible to create two new families of nested chiral icosahedral (I) fullerenes namely C₂₆₀@C₅₆₀@C₉₈₀@C₁₅₂₀@, ...,and C₁₄₀@C₃₈₀@C₇₄₀@C₁₂₂₀@ ..., which exhibit interlayer separations of ca. 3.4 Å. These chiral fullerenes are thought to possess metalliclike conduction properties. We discuss in detail the transformation of polyhedral graphitic particles into quasispherical nested giant fullerenes by reorganization of carbon atoms, which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed under extreme conditions, such as those produced by high-energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.     

Reaction of 2H-azirine phosphine oxide and -phosphonates with nucleophiles. Stereoselective Synthesis of functionalized aziridines and alpha- and beta-aminophosphorus derivatives

[reaction: see text] A simple and efficient stereoselective synthesis of aziridine-2-phosphonate 3, and -phosphine oxide 5 by diastereoselective addition of Grignard reagents to 2H-azirine phosphonate 1 and -phosphine oxide 4 is reported. Similarly, the addition of heterocyclic amines and benzenethiol to aziridines 1 and 4 yielded functionalized aziridines 10, 11, and 18. These aziridines are used as intermediates for the regioselective synthesis of beta-aminophosphine oxides 6 and beta-aminophosphonates 7, as well as alpha- aminophosphonates 8. Phenylsulfenyl-substituted alpha-aminophosphorus derivatives 15 and 19 are obtained directly from benzenethiol and 2H-azirine phosphonates 1 and -phosphine oxides 4.     

Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C(3))- or four (T(d), tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by F?rster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.     

Synthesis of novel 2,5-dihydro-1,5,2-diazaphosphinines from primary enamine phosphonates and from alkyl phosphonates

A simple method for the preparation of phosphorus-containing pyrimidine analogues such as 2,5-dihydro-2-ethoxy-1,5,2-diazaphosphinine 2-oxides 9, 12-15 and adducts 3, 10 is described. Dihydrophosphinines 9, 12-15 are prepared from primary enamine phosphonates and nitriles or from phosphonates and nitriles in the presence of base, while highly stable hydrogen-bonded amine-dihydro-diazaphosphinine adducts 3, 10 are obtained by the addition of amine to dihydrophosphinines 9 or by reaction of alkylphosphonates with nitriles in the presence of LDA.