Quotients of fake projective planes

Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to \bbZ/3\bbZ, \bbZ/7\bbZ, $7:3$, or (\bbZ/3\bbZ)^2, where $7:3$ is the unique non-abelian group of order 21. Let $G$ be a group of automorphisms of a fake projective plane $X$. In this paper we classify all possible structures of the quotient surface $X/G$ and its minimal resolution.Comment: 16 pages, with minor change of the expositio

Enhancing the Efficiency of Organic Photovoltaics by a Photoactive Molecular Mediator

High boiling-point solvent additives, such as 1,8-diiodooctane, have been widely used to tune nanoscale phase morphology for increased efficiency in bulk heterojunction organic solar cells. However, liquid-state solvent additives remain in the active films for extended times and later migrate or evaporate from the films, leading to unstable device performance. Here, a solid-state photoactive molecular mediator, namely N(BAI)3, is reported that could be employed to replace the commonly used solvent additives to tune the morphology of bulk heterojunction films for improved device performance. The N(BAI)3 mediator not only resides in the active films locally to fine tune the phase morphology, but also contributes to the additional absorption of the active films, leading to ∼11% enhancement of power conversion efficiency of P3HT:PC60BM devices. Comparative studies are carried out to probe the nanoscale morphologies using grazing incidence wide-angle X-ray scattering and complementary neutron reflectometry. The use of 1 wt% N(BAI)3 is found to effectively tune the packing of P3HT, presumably through balanced π-interactions endowed by its large conjugated π surface, and to promote the formation of a PC60BM-rich top interfacial layer. These findings open up a new way to effectively tailor the phase morphology by photoactive molecular mediators in organic photovoltaics

Algebraic Montgomery-Yang problem and smooth obstructions

Let $S$ be a rational homology complex projective plane with quotient singularities. The algebraic Montgomery-Yang problem conjectures that the number of singular points of $S$ is at most three if its smooth locus is simply-connected. In this paper, we leverage results from the study of smooth 4-manifolds, including the Donaldson diagonalization theorem and Heegaard Floer correction terms, to establish additional conditions for $S$. As a result, we eliminate the possibility of a rational homology complex projective plane of specific types with four singularities. Moreover, we identify large families encompassing infinitely many types of singularities that satisfy the orbifold BMY inequality, a key property in algebraic geometry, yet are obstructed from being a rational homology complex projective plane due to smooth conditions. Additionally, we discuss computational results related to this problem, offering new insights into the algebraic Montgomery-Yang problem.Comment: 26 pages, 14 figures, minor revisions for the purpose of correcting typos and refining the languag

Analysis of Supersymmetric Effects on B -> phi K Decays in the PQCD Approach

We study the effects of the MSSM contribution on B -> phi K decays using the perturbative QCD approach. In this approach, strong phases can be calculated, so that we can predict the values of CP asymmetries with the MSSM contribution. We predict a large relative strong phase between the penguin amplitude and the chromomagnetic penguin amplitude. If there is a new CP violating phase in the chromomagnetic penguin amplitude, then the CP asymmetries may change significantly from the SM prediction. We parametrize the new physics contributions that appear in the Wilson coefficients. We maximize the new physics parameters up to the point where it is limited by experimental constraints. In the case of the LR insertion, we find that the direct CP asymmetries can reach about 85% and the indirect CP asymmetry can reach about -30%.Comment: 18 pages, 9 figures, REVTeX, Minor changes, Version to appear in Phys. Rev.