Airy Equation for the Topological String Partition Function in a Scaling Limit

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.     

Simultaneous determination of low-molecular-weight organic acids and chlorinated acid herbicides in environmental water by a portable CE system with contactless conductivity detection

This report describes a method to simultaneously determine 11 low-molecular-weight (LMW) organic acids and 16 chlorinated acid herbicides within a single run by a portable CE system with contactless conductivity detection (CCD) in a poly(vinyl alcohol) (PVA)-coated capillary. Under the optimized condition, the LODs of CE-CCD ranged from 0.056 to 0.270 ppm, which were better than for indirect UV (IUV) detection of the 11 LMW organic acids or UV detection of the 16 chlorinated acid herbicides. Combined with an on-line field-amplified sample stacking (FASS) procedure, sensitivity enhancement of 632- to 1078-fold was achieved, with satisfactory reproducibility (RSDs of migration times less than 2.2%, and RSDs of peak areas less than 5.1%). The FASS-CE-CCD method was successfully applied to determine the two groups of acidic pollutants in two kinds of environmental water samples. The portable CE-CCD system shows advantages such as simplicity, cost effectiveness, and miniaturization. Therefore, the method presented in this report has great potential for onsite analysis of various pollutants at the trace level.     

Quantum Diffusion for the Anderson Model in the Scaling Limit

We consider random Schr?dinger equations on for d ≥ 3 with identically distributed random potential. Denote by λ the coupling constant and ψ_t the solution with initial data ψ₀. The space and time variables scale as with 0 < κ < κ₀(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψ_t converges weakly to a solution of a heat equation in the space variable x for arbitrary L ² initial data. The diffusion coefficient is uniquely determined by the kinetic energy associated to the momentum υ. This work is an extension to the lattice case of our previous result in the continuum [8,9]. Due to the non-convexity of the level surfaces of the dispersion relation, the estimates of several Feynman graphs are more involved. Submitted: April 18, 2006. Accepted: October 12, 2006. László Erdős: Partially supported by NSF grant DMS-0200235 and EU-IHP Network ‘Analysis and Quantum’ HPRN-CT-2002-0027. Manfred Salmhofer: Partially supported by DFG grant Sa 1362/1-1 and an ESI senior research fellowship. Horng-Tzer Yau: Partially supported by NSF grant DMS-0307295 and MacArthur Fellowship.     

Quantum Diffusion of the Random Schrödinger Evolution in the Scaling Limit II. The Recollision Diagrams

We consider random Schrödinger equations on \({\mathbb{R}^{d}}\) for d≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψ _t the solution with initial data ψ₀. The space and time variables scale as \({x\sim \lambda^{-2 -\kappa/2}, t \sim \lambda^{-2 -\kappa}}\) with 0 < κ <  κ₀(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψ _t converges weakly to the solution of a heat equation in the space variable x for arbitrary L ² initial data. The proof is based on a rigorous analysis of Feynman diagrams. In the companion paper [10] the analysis of the non-repetition diagrams was presented. In this paper we complete the proof by estimating the recollision diagrams and showing that the main terms, i.e. the ladder diagrams with renormalized propagator, converge to the heat equation.     

Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass

The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface \({\Sigma=\partial \Omega}\) and should be independent of whichever space-like region \({\Sigma}\) bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been taken by Brown-York [4,5] and Liu-Yau [16,17] (see also related works [3,6,9,12,14,15,28,32]) to define such notions using the isometric embedding theorem into the Euclidean three space. However, there exist surfaces in the Minkowski space whose quasilocal mass is strictly positive [19]. It appears that the momentum information needs to be accounted for to reconcile the difference. In order to fully capture this information, we use isometric embeddings into the Minkowski space as references. In this article, we first prove an existence and uniqueness theorem for such isometric embeddings. We then solve the boundary value problem for Jang’s [13] equation as a procedure to recognize such a surface in the Minkowski space. In doing so, we discover a new expression of quasi-local mass for a large class of “admissible” surfaces (see Theorem A and Remark 1.1). The new mass is positive when the ambient space-time satisfies the dominant energy condition and vanishes on surfaces in the Minkowski space. It also has the nice asymptotic behavior at spatial infinity and null infinity. Some of these results were announced in [29].     

Coherently Aligned Porphyrin‐Appended Polynorbornenes

You can append on me! Porphyrin‐appended polynorbornenes derived from 5,6‐endo‐fused N‐arylpyrrolidenonorbornenes have been shown to have coherently aligned pendant groups that exhibit exciton coupling and fluorescence quenching in the absorption and emission profiles (see figure).

     

Determination of senkirkine and senecionine in Tussilago farfara using microwave-assisted extraction and pressurized hot water extraction with liquid chromatography tandem mass spectrometry

Tussilago farfara (Kuan Donghua) is an important Chinese herbal medicine which has been shown to contain many bioactive compounds and widely used to relieve cough and resolve phlegm. However, besides therapeutic bioactive compounds, this herb has been found to contain toxic pyrrolizidine alkaloids (PAs), mainly senkirkine and traces of senecionine. In this report, conditions for microwave-assisted extraction (MAE) and pressurized hot water extraction (PHWE) were optimized for the extraction of the PAs. The results were compared against heating under reflux. It was found that the binary mixture of MeOH:H₂O (1:1) acidified using HCl to pH 2-3 was the optimal solvent for the extraction of the PAs in the plant materials. Liquid chromatography (LC) with ultra-violet (UV) detection and electrospray ionization mass spectrometry (ESI-MS) in the positive mode was used for the determination and quantitation of senkirkine and senecionine in the botanical extract. The proposed extraction methods with LC/MS allow for the rapid detection of the major and the minor alkaloids in T. farfara in the presence of co-eluting peaks. With LC/MS, the quantitative analysis of PAs in the extract was done using internal standard calibration and the precision was found to vary from 0.6% to 5.4% on different days. The limits of detection (LODs) and limits of quantitation (LOQs) for MAE and PHWE were found to vary from 0.26 μg/g to 1.04 μg/g and 1.32 μg/g to 5.29 μg/g, respectively. The method precision of MAE and PHWE were found to vary from 3.7% to 10.4% on different days. The results showed that major and minor alkaloids extracted using MAE and PHWE were comparable to that by heating under reflux. Our data also showed that significant ion suppression was not observed in the analysis of senkirkine and senecionine in the botanical extracts with co-eluting peaks.     

Cohomology with coefficients for operadic coalgebras

Corepresentations of a coalgebra over a quadratic operad are defined, and various characterizations of them are given. Cohomology of such an operadic coalgebra with coefficients in a corepresentation is then studied.     

Electrodeposition of Au monolayer on Pt(111) mediated by self-assembled monolayers

In-situ scanning tunneling microscopy (STM), cyclic voltammetry (CV), and infrared reflection-adsorption spectroscopy (IRRAS) have been used to examine the electrodeposition of gold onto Pt(111) electrodes modified with benzenethiol (BT) and benzene-1,2-dithiol (BDT) in 0.1 M HClO4 containing 10 microM HAuCl4. Both BT and BDT were attached to Pt(111) via one sulfur headgroup. STM and IRRAS results indicated that the other SH group of BDT was pendant in the electrolyte. Both BT and BDT formed (2 x 2) structures at the coverage of 0.25, and they were transformed into (square root(3) x square root(3))R30 degrees as the coverage was raised to 0.33. These two organic surface modifiers resulted in 3D and 2D gold islands at BT- and BDT-coated Pt(111) electrodes, respectively. The pendant SH group of BDT could interact specifically with gold adspecies to immobilize gold adatoms on the Pt(111) substrate, which yields a 2D growth of gold deposition. Molecular resolution STM revealed an ordered array of (6 x 2 square root(13)) after a full monolayer of gold was plated on the BDT/Pt(111) electrode. Since BDT was strongly adsorbed on Pt(111), gold adatoms only occupied free sites between BDT admolecules on Pt(111). This is supported by a stripping voltammetric analysis, which reveals no reductive desorption of BDT admolecules at a gold-deposited BDT/Pt(111) electrode. It seems that the BDT adlayer acted as the template for gold deposit on Pt(111). In contrast, a BT adlayer yielded 3D gold deposit on Pt(111). This study demonstrates unambiguously that organic surface modifiers could contribute greatly to the electrodeposition of metal adatoms.     

Carbon nanotube-enhanced separation of DNA fragments by a portable capillary electrophoresis system with contactless conductivity detection

It was demonstrated that separation of DNA fragments by a CE-contactless conductivity detection system (CE-CCD) could be enhanced with multiple-wall carbon nanotubes (MWCNs) as buffer additive. For HaeIII digest of PhiX174 DNA, optimized MWCN concentration was obtained when the MWCN was above its threshold concentration, at which MWCN could form a network in the buffer as pseudostationary phase to provide additional interaction sites. In the case of larger DNA, MWCN near or below its threshold concentration was enough to provide great improvement of the resolution, which was shown by the separation of the 2-Log DNA ladder. Furthermore, the buffer containing MWCN could provide a more stable baseline in the CE-CCD system, owing to less fluctuation of its conductivity. Compared with CE-UV, CE-CCD with MWCN could provide lower LODs as well as better resolution.