Frobenius splitting of Hilbert schemes of points on surfaces

Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. In this note we show that if X is Frobenius split then so is the Hilbert scheme Hilb of n points inX. In particular, we get the higher cohomology vanishing for ample line bundles on Hilb when X is projective and Frobenius split. Received November 2, 1999 / Published online March 12, 2001     

Regioselective alkanoylation of cyclodextrins

The regioselective transesterification of native α- and β-Cyclodextrins (CDs) with vinyl acetate and vinyl laurate is presented in this paper. The reactions were carried out in dimethyl sulfoxide by using low molecular weight salts (Na₂HPO₄ and NaCl, respectively). MALDI-TOF mass spectrometry and NMR analysis were applied to investigate the chemical structure and the degree of the modification of the final products. Results show that these salts catalyze regioselective transesterification between β-CDs and vinyl laurate aiming for the secondary C-2 hydroxyl group. The synthesis and separation of β-CD-laurate derivatives leads to a mixture of mono-2-O-dodecanoyl-β-CD and native β-CDs. Unreacted β-CDs could be selectively removed enzymatically by cyclodextrin glucosyl-transferase (CGTase) and β-amylase.     

Equivariant Euler characteristics of unitary buildings

Journal of Algebraic Combinatorics - The (p-primary) equivariant Euler characteristics of the buildings for the general unitary groups over finite fields are determined.     

Transition from the Compact to the Dense Phase of Two-Dimensional Polymers

We present a unifying picture of the compact, dense, and dilute phases of two-dimensional polymers. The lattice dependence of the scaling exponents for compact polymers is reconciled with their universality in the dense and dilute cases. In particular, we show that violations of the fully packing constraint in the compact phase can be interpreted as magnetic screening in the associated Coulomb gas, which induces a flow to either the dense or the dilute phase. When more than one flavor of polymers is present the flow away from the compact phase leads to a decoupling of the flavors, and the central charge decreases by an integer. If charge asymmetry develops, the polymer flavors may independently flow to either of the two noncompact phases.     

Bioorthogonal Click of Colloidal Gold Nanoparticles to Antibodies In vivo

Combining nanotechnology and bioorthogonal chemistry for theranostic strategies offers the possibility to develop next generation nanomedicines. These materials are thought to increase therapeutic outcome and improve current cancer management. Due to their size, nanomedicines target tumors passively. Thus, they can be used for drug delivery purposes. Bioorthogonal chemistry allows for a pretargeting approach. Higher target-to-background drug accumulation ratios can be achieved. Pretargeting can also be used to induce internalization processes or trigger controlled drug release. Colloidal gold nanoparticles (AuNPs) have attracted widespread interest as drug delivery vectors within the last decades. Here, we demonstrate for the first time the possibility to successfully ligate AuNPs in vivo to pretargeted monoclonal antibodies. We believe that this possibility will facilitate the development of AuNPs for clinical use and ultimately, improve state-of-the-art patient care.     

Quantum holonomy theory and hilbert space representations

We present a new formulation of quantum holonomy theory, which is a candidate for a non‐perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the algebra, which is generated by holonomy‐diffeomorphisms on a 3‐dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy‐diffeomorphisms form a non‐commutative ‐algebra. A proof that the state that generates the representation exist is left for later publications.