Spatial design matrices and associated quadratic forms: structure and properties

The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram.     

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.     

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).     

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.     

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.     

Chemical waves and pattern formation in the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/water lamellar system

The present work deals with the spatially extended oscillatory Belousov Zhabotinsky reaction-diffusion system carried out in an anisotropic environment of phosphatidylcholines/water binary system, which presents layered aqueous domains separated by lipid bilayers. We report the occurrence of stable Turing patterns, spiral waves, and other exotic structures in phospholipids bilayers that are generally used as a models for cell plasma membranes.     

Synthesis of fused purinoquinazolines. Three new heterocyclic ring systems

The Ullmann reaction of 8-aminotheophylline or 8-aminocaffeine with 2-chlorobenzoic acid and of 8-bromotheophylline with ethyl-2-aminobenzoate afforded derivatives of three new heterocyclic systems: purino[7,8-α]quinazoline-5,9,11(6H,8H,10H)-trione, purino[8,9-b]quinazoline-2,4,11(1H,3H,5H)-trione and purino[8,7-b]quinazoline-2,4,6(1H,3H,11H)-trione, respectively.     

Synthesis, characterization, and tautomerism of four novel copper(I) complexes from 3-hydroxy-3-(p-R-phenyl)-2-propenedithioic acids

The paper describes the synthesis and structural characterization of four novel copper(I) complexes [CuL(PPh(3))(2)] (L = 3-hydroxy-3-(p-R-phenyl)-2-propenedithioate). In addition, a tautomeric equilibrium in solution was found and Hammett correlations with (13)C NMR parameters were studied. The structure of one complex was fully established by X-ray diffraction analysis.