A holomorphic and background independent partition function for matrix models and topological strings

We study various properties of a nonperturbative partition function which can be associated with any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix integrals over all possible filling fractions, and includes all the multi-instanton corrections to the perturbative 1/N$1/N$ expansion. We show that the nonperturbative partition function, which is manifestly holomorphic, is also modular and background independent: it transforms as the partition function of a twisted fermion on the spectral curve. Therefore, modularity is restored by nonperturbative corrections. We also show that this nonperturbative partition function obeys the Hirota equation and provides a natural nonperturbative completion for topological string theory on local Calabi–Yau 3-folds.     

L 2-Harmonic 1-Forms on Submanifolds with Finite Total Curvature

Let $x:M^{m}\to\bar{M}$ , m≥3, be an isometric immersion of a complete noncompact manifold M in a complete simply connected manifold $\bar{M}$ with sectional curvature satisfying $-k^{2}\leq K_{\bar{M}}\leq0$ , for some constant k. Assume that the immersion has finite total curvature in the sense that the traceless second fundamental form has finite L ^m -norm. If $K_{\bar{M}}\not\equiv0$ , assume further that the first eigenvalue of the Laplacian of M is bounded from below by a suitable constant. We prove that the space of the L ² harmonic 1-forms on M has finite dimension. Moreover, there exists a constant Λ>0, explicitly computed, such that if the total curvature is bounded from above by Λ then there are no nontrivial L ²-harmonic 1-forms on M.     

Fatty Acid Carboxylate‐ and Anionic Surfactant‐Controlled Delivery Systems That Use Mesoporous Silica Supports

We report the preparation of a MCM‐41 mesoporous material that contains the dye [Ru(bipy)₃]Cl₂ (bipy=bipyridine) inside the mesopores and functionalised with suitable binding groups at the entrance of the pores. Solids S1 – S3 were obtained by the reaction of the mesoporous material with N‐methyl‐N′‐propyltrimethoxysilylimidazolium chloride, N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]thiourea, or N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]urea, respectively. A study of the dye delivery of these systems in buffered water (pH 7.0, 2‐[4‐(2‐hydroxyethyl)piperazin‐1‐yl]ethanesulfonic acid (HEPES), 10^?3 mol dm^?3) in the presence of a family of carboxylate ions was carried out. In the interaction of the anions with the surface of the solids, the response depends on the characteristics of the binding groups (i.e., imidazolium, urea and thiourea) at the pore outlets and their specific interaction with the corresponding anion. The interaction of long‐chain carboxylate ions with the binding sites at the surface of the solids resulted in a remarkable inhibition of the delivery of the dye. This inhibition was observed clearly for the dodecanoate anion, whereas the octanoate, decanoate, cholate, deoxycholate, glycodeoxycholate and taurocholate anions induced a certain pore blockage that varied according to the solid studied. The interaction of smaller anions, such as acetate, butanoate, hexanoate and octanoate, with the solids had no effect on the dye release process. The possible use of the gating system for the chromo‐fluorogenic detection of anionic surfactants through selective dye delivery inhibition was also explored. Molecular dynamic simulations that use force‐field methods have been made to theoretically study the capping carboxylate mechanism. The calculations are in agreement with the experimental results, thus allowing a representation of the dye delivery inhibition in the presence of long‐chain carboxylate ions.     

On Cullen numbers which are both Riesel and Sierpiński numbers

We describe an algorithm to determine whether or not a given system of congruences is satisfied by Cullen numbers. We use this algorithm to prove that there are infinitely many Cullen numbers which are both Riesel and Sierpiński. (Such numbers should be discarded if you are searching prime numbers with Proth?s theorem.)     

On positive solutions for a class of quasilinear elliptic systems

We investigate the existence and properties of solutions for a class of systems of Dirichlet problems involving the perturbed phi-Laplace operators. We apply variational methods associated with the Fenchel conjugate. Our results cover both sublinear and superlinear cases of nonlinearities.     

On the stability of metal–aminoacid complexes in water based on water–ligand exchange reactions and electronic properties: Detailed study on iron–glycine hexacoordinated complexes

Thermodynamic stability of metal–aminoacid complexes in water is discussed in terms of the Gibbs free energy of water–ligand exchange processes, and the electronic stabilizing factors thoroughly investigated by means of 1‐electron and 2‐electron density properties. Hexacoordinated complexes formed between iron cations and glycine molecules acting as monodentate or bidentate ligands have been chosen as targets for the current study. Results agree with experimental findings, and complexes formed with bidentate ligands are found to be more stable than those formed with monodentate ones. The larger the number of the coordinated glycine molecules the more stable is the complex. Fe(III) complexes are more stable than Fe(II) ones, but differences are small and the Fe³⁺/Fe²⁺ exchange process appears to be energetically feasible for these complexes. Formation of the second glycine–iron interaction involving the amino nitrogen in the bidentate ligands is enthalpycally unfavorable but takes place due to the large entropy rise of the process. The larger stability of Fe(III) complexes is due however to the balance between energetic and solvation terms, which is favorable to these complexes. Electron density properties account satisfactorily for the electronic energy changes along the complex formation in terms of ligand–metal electron transfer and covalent bond orders. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010