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).     

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.     

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.     

Multi-element analysis by inductively coupled plasma optical emission spectrometry of airborne particulate matter collected with a low-pressure cascade impactor

A method was developed for the elemental analysis of size segregated particles ranging from 0.03 to 10 microns. Sampling and analysis problems are discussed in this paper. Particles were collected with a Dekati low-pressure cascade impactor. PTFE filters coated with oleic acid were used as substrate. Particles were microwave digested in closed vessels. The optimum digestion mixture was composed of HNO3 (1 mL), HF (50 microL) and H2O (1 mL). The optimal power setting and digestion time were studied in order to achieve an efficient digestion. A ca. 35 min microwave digestion cycle at a 650 W maximum power allowed complete digestion of the samples. Special emphasis was placed on the pressure in the closed vessels to avoid sample losses. Solution samples were analysed by inductively coupled plasma optical emission spectrometry using an ultrasonic nebuliser for 18 elements (Al, Ba, Ca, Cd, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, Pb, S, Sr, Ti, V, Zn). This procedure was tested with NIST Standard Reference Material 1648 Urban Particulate. Recoveries for certified elements ranged from 95 to 105% except for Al (90%). The influence of cascade impactor materials was investigated with 44 field samples. Strong artefacts due to contamination were shown for analysis at environmental concentrations of Al, Cr, Mn and Ni.     

Conformation and luminescence of isolated molecular semiconductor molecules

In this article, we describe, for the first time, direct comparisons of the detailed structures of two small molecule organic semiconductors, oligo(phenylenvinylene) (OPV) molecules with chains of five and six phenyl rings (5R-OC(8)H(17) and 6R-OC(8)H(17)), respectively, and their luminescence properties on a single molecule level. Our data originate from a combination of two powerful diagnostic tools in physical chemistry: ion mobility and single molecule fluorescence spectroscopy. These techniques enable us to precisely determine the shapes of isolated molecules in the gas phase and to correlate these structures to the emission from single molecules supported on bare glass substrates. The principal structural uncertainty in OPVs is the (possible) presence and location of cis-vinylene linkages (cis-defects) in the oligomer. The results show that the structures observed in the gas phase are strongly correlated to the categories of molecules observed in the single molecule polarization anisotropy measurements with nearly identical distributions for the two OPV molecules studied. Each category is also characterized by the luminescence efficiency of the molecules in each class, providing a direct correlation between the luminescence efficiency and the shape of the molecule. This combination of techniques provides a level of information far beyond that obtained via any other analytical technique.     

Production,purification, and characterization of a low-molecular-mass xylanase from Aspergillus sp. and its application in baking

An extracellular xylanase produced by a Mexican Aspergillus strain was purified and characterized. Aspergillus sp. FP-470 was able to grow and produce extracellular xylanases on birchwood xylan, oat spelt xylan, wheat straw, and corncob, with higher production observed on corncob. The strain also produced enzymes with cellulase, amylase, and pectinase activities on this substrate. A 22-kDa endoxylanase was purified 30-fold. Optimum temperature and pH were 60 degrees C and 5.5, respectively, and isoelectric point was 9.0. The enzyme has good stability from pH 5.0 to 10.0, retaining >80% of its original activity within this range. Half-lives of 150 min at 50 degrees C and 6.5 min at 60 degrees C were found. K(m) and activation energy values were 3.8 mg/mL and 26 kJ/mol, respectively, using birchwood xylan as substrate. The enzyme showed a higher affinity for 4-O-methyl-D-glucuronoxylan with a K(m) of 1.9 mg/mL. The enzyme displayed no activity toward other polysaccharides, including cellulose. Baking trials were conducted using the crude filtrate and purified enzyme. Addition of both preparations improved bread volume. However, addition of purified endoxylanase caused a 30% increase in volume over the crude extract.