On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

Source point discovery through high frequency asymptotic time reversal

Given local frequency domain wave data, the Numerical Micro-Local Analysis (NMLA) method (Benamou et al., 2004) [5] and its recent improved version (Benamou et al., 2011) [4] gives a pointwise numerical approximation of the number of rays, their slowness vectors and corresponding wavefront curvatures. With time domain wave data and assuming the source wavelet is given, the method also estimates the travel-time. The paper provides a non technical presentation of the improved NMLA algorithm and presents a numerical application which can be interpreted as a high frequency asymptotic version of the classical time reversal method (Borcea et al., 2003) [7]. A detailed technical presentation of the algorithm is available in Benamou et al. (2011) [4] and more numerical experiments can be found in Collino and Marmorat (2011) [15].     

Biological activity of functionalized SiO2 thin films prepared by sol-gel method

In this work we investigated the biological properties of sol-gel films in aqueous medium. Functionalized silica films were prepared by the sol-gel process, from organically modified silicon alkoxides with amino or thiol groups. Covalent binding of proteins with different orientations according to the hydrophilic or hydrophobic character of the surface was studied. This binding occurred via a covalent coupling agent providing a very stable linkage. No denaturation was detected and a good detection of the antigen was observed. Immunoassays have demonstrated the biological activity of grafted antibodies.     

On the Structure of the Small Quantum Cohomology Rings of Projective Hypersurfaces

We give an explicit procedure which computes for degree d≤ 3 the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface X as homogeneous polynomials of degree d in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi–Yau hypersurfaces and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which express the structure constants of the quantum cohomology ring of X as weighted homogeneous polynomial functions of the constants of the Fano hypersurface with the same degree and dimension one more. We propose some conjectures about the existence and the form of the recursive laws for the structure constants of rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree four. Received: 29 November 1996 / Accepted: 15 March 1999     

Effect of molecular conformations on the adsorption behavior of gold-binding peptides

Despite extensive recent reports on combinatorially selected inorganic-binding peptides and their bionanotechnological utility as synthesizers and molecular linkers, there is still only limited knowledge about the molecular mechanisms of peptide binding to solid surfaces. There is, therefore, much work that needs to be carried out in terms of both the fundamentals of solid-binding kinetics of peptides and the effects of peptide primary and secondary structures on their recognition and binding to solid materials. Here we discuss the effects of constraints imposed on FliTrx-selected gold-binding peptide molecular structures upon their quantitative gold-binding affinity. We first selected two novel gold-binding peptide (AuBP) sequences using a FliTrx random peptide display library. These were, then, synthesized in two different forms: cyclic (c), reproducing the original FliTrx gold-binding sequence as displayed on bacterial cells, and linear (l) dodecapeptide gold-binding sequences. All four gold-binding peptides were then analyzed for their adsorption behavior using surface plasmon resonance spectroscopy. The peptides exhibit a range of binding affinities to and adsorption kinetics on gold surfaces, with the equilibrium constant, Keq, varying from 2.5x10(6) to 13.5x10(6) M(-1). Both circular dichroism and molecular mechanics/energy minimization studies reveal that each of the four peptides has various degrees of random coil and polyproline type II molecular conformations in solution. We found that AuBP1 retained its molecular conformation in both the c- and l-forms, and this is reflected in having similar adsorption behavior. On the other hand, the c- and l-forms of AuBP2 have different molecular structures, leading to differences in their gold-binding affinities.     

Expected and unexpected effects of amino acid substitutions on polypeptide-directed crystal growth

Nature's use of biomineralization polypeptides to control and modulate the growth of biogenic minerals is an important process that, if properly understood, could have significant implications for designing and creating new inorganic-based materials. Although the sequences for a number of biomineralization proteins exist, very little is known about the participation of specific amino acids in the mineral modulation process. In this letter, we investigate the impact of global Asp --> Asn and Glu --> Gln substitutions on two mollusk shell nacre polypeptides, AP7N and n16N. We find that these global substitutions, which remove all anionic Ca(II) binding sites, abolish the expected in vitro mineralization activities associated with each native polypeptide. In addition, the ability of substituted peptides to form complexes with both Ca(II) and Ca(II) metal ion analogs is also abolished. However, some unexpected effects were noted. First, the Asp --> Asn, Glu --> Gln substituted n16N polypeptide is observed to self-assemble and form biofilms or coatings that appear to mineralize in vitro. Second, both polypeptides are structurally affected by these substitutions, with Asp --> Asn substituted AP7N transforming to an alpha helix and Asp --> Asn, Glu --> Gln substituted n16N transforming to a more unfolded random-coil-like structure. We find that the participation of Asp and Glu residues is crucial to the inherent mineralization activities and conformations of AP7N and n16N polypeptides. Surprisingly, we find that the replacement of anionic residues within biomineralization polypeptides such as n16N still permits mineral modulation, but in a different form that now involves peptide self-association and biofilm formation.     

Peeling of an elastic membrane tape adhered to a substrate by a uniform cohesive traction

An analytical model is provided for the peeling of a tape from a surface to which it adheres through cohesive tractions. The tape is considered to be a membrane without bending stiffness and is initially attached everywhere to a flat rigid surface. The tape is assumed to deform in plane strain, and finite deformations in the form of elastic strains are accounted for. The cohesive tractions are taken to be uniform when the tape is within a critical interaction distance from the substrate and then to fall immediately to zero once this critical interaction distance is exceeded. When the distance between the tape and the substrate is zero, repulsive and attractive tractions balance to zero; in this segment, sliding of the tape relative to the substrate is forbidden when we pull the tape up somewhere in the middle, though we permit such sliding when the tape is peeled from one end. In the cohesive zone and where the tape is detached, the interaction of the tape with the substrate is frictionless. Results are given for the force to peel a neo-Hookean tape at any angle up to vertical when one end of it is pulled away from the substrate, as well as for scenarios when the tape is lifted somewhere in the middle to form a V shape being pulled away from the substrate.     

On the Griffiths group of the cubic sevenfold

Partially supported by Science Project Geometry of Algebraic Varieties, n. 0-198-SC1, and by fundings from M.U.R.S.T. and G.N.S.A.G.A. (C.N.R.), Italy     

A Conservative Space-time Mesh Refinement Method for the 1-D Wave Equation. Part II: Analysis

Summary. We introduced in [2] a new method for space-time refinement for the 1-D wave equation. This method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme. In this second part, we analyse the accuracy of this scheme in a detailed way by means of a plane wave analysis and numerical experiments that permit us to point out spurious numerical phenomena and explain how to control them. Mathematics Subject Classification (2000):65N12