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. 相似文献
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. 相似文献
We consider random Schr?dinger equations on
for d ≥ 3 with identically distributed random potential. Denote by λ the coupling constant and ψt 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 ψt converges weakly to a solution of a heat equation in the space variable x for arbitrary L2 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. 相似文献
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 ψt 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 ψt converges weakly to the solution of a heat equation in the space variable x for arbitrary L2 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. 相似文献
Preconditionings have proved to be a powerful technique for accelerating the rate of convergence of an iterative method. This paper, which is concerned with the conjugate gradient algorithm for large matrix computations, investigates an approximate polynomial preconditioning strategy. The method is particularly attractive for implementation on vector computers. 相似文献
We consider for j=?, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field.
The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the
form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordstr?m solutions. In other words,
the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-?-particles to a black hole,
our result indicates that the Dirac particles must eventually disappear inside the event horizon.
Received: 2 November 1998 / Accepted: 23 February 1999 相似文献
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]. 相似文献
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).