Mirror Principle I

We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich's stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of obstruction bundles induced by any concavex bundles -- including any direct sum of line bundles -- on $\P^n$. This includes proving the formula of Candelas-de la Ossa-Green-Parkes hence completing the program of Candelas et al, Kontesevich, Manin, and Givental, to compute rigorously the instanton prepotential function for the quintic in $\P^4$. We derive, among many other examples, the multiple cover formula for Gromov-Witten invariants of $\P^1$, computed earlier by Morrison-Aspinwall and by Manin in different approaches. We also prove a formula for enumerating Euler classes which arise in the so-called local mirror symmetry for some noncompact Calabi-Yau manifolds. At the end we interprete an infinite dimensional transformation group, called the mirror group, acting on Euler data, as a certain duality group of the linear sigma model.Comment: Typos corrected, Plain Tex 50 pages with t.o.c optio

Enhanced visibility of graphene: effect of one-dimensional photonic crystal

We investigate theoretically the light reflectance of a graphene layer prepared on the top of one-dimensional Si/SiO2 photonic crystal (1DPC). It is shown that the visibility of the graphene layers is enhanced greatly when 1DPC is added, and the visibility can be tuned by changing the incident angle and light wavelengths. This phenomenon is caused by the absorption of the graphene layer and the enhanced reflectance of the 1DPC.Comment: 4 pages, 4 figures. published, ApplPhysLett_91_18190

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called "genus two G-function". Conjecturally the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for ${\bf P}^1$-orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in certain particular cases.Comment: 37 pages, 3 figures, V2: the published versio

A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical gravitational wave with a cosmological constant. The properties of the 5D solution are briefly described.Comment: 10 pages Latex, Revtex, submitted to GR

On recent puzzles in the production of heavy quarkonia

Recently, several surprising experimental observations in the production of heavy quarkonium have been reported. In $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV, Belle Collaboration finds that $J/\psi$ mesons are predominantly produced in association with an extra $\bar{c}c$ pair, with $\sigma(e^+e^- \to J/\psi \bar{c}c) / \sigma(e^+e^- \to J/\psi X) = 0.59^{+0.15}_{-0.13}\pm 0.12$, and the BaBar collaboration reports that the produced $J/\psi$'s have mostly longitudinal polarization. In $\bar{p}p$ collisions at the Tevatron, the CDF Collaboration reported an excess of $J/\psi$ and $\psi^{\prime}$ mesons at high $p_{\perp}$ over the perturbative QCD predictions; non--perturbative approach of NRQCD can accomodate the magnitude of the production cross section but not the observed experimentally polarization of quarkonia. In this note we propose possible solutions to these puzzles, and devise further experimental tests.Comment: 3 pages, 2 figure

Assessment of China's virtual air pollution transport embodied in trade by using a consumption-based emission inventory

Substantial anthropogenic emissions from China have resulted in serious air pollution, and this has generated considerable academic and public concern. The physical transport of air pollutants in the atmosphere has been extensively investigated; however, understanding the mechanisms how the pollutant was transferred through economic and trade activities remains a challenge. For the first time, we quantified and tracked China's air pollutant emission flows embodied in interprovincial trade, using a multiregional input - output model framework. Trade relative emissions for four key air pollutants (primary fine particle matter, sulfur dioxide, nitrogen oxides and non-methane volatile organic compounds) were assessed for 2007 in each Chinese province. We found that emissions were significantly redistributed among provinces owing to interprovincial trade. Large amounts of emissions were embodied in the imports of eastern regions from northern and central regions, and these were determined by differences in regional economic status and environmental policy. It is suggested that measures should be introduced to reduce air pollution by integrating cross-regional consumers and producers within national agreements to encourage efficiency improvement in the supply chain and optimize consumption structure internationally. The consumption-based air pollutant emission inventory developed in this work can be further used to attribute pollution to various economic activities and final demand types with the aid of air quality models