From rr-Spin Intersection Numbers to Hodge Integrals

Generalized Kontsevich Matrix Model (GKMM) with a certain given potential is the partition function of $r$-spin intersection numbers. We represent this GKMM in terms of fermions and expand it in terms of the Schur polynomials by boson-fermion correspondence, and link it with a Hurwitz partition function and a Hodge partition by operators in a $\widehat{GL}(\infty)$ group. Then, from a $W_{1+\infty}$ constraint of the partition function of $r$-spin intersection numbers, we get a $W_{1+\infty}$ constraint for the Hodge partition function. The $W_{1+\infty}$ constraint completely determines the Schur polynomials expansion of the Hodge partition function.Comment: 51 pages, 1 figur

Application of RQMC for CDO Pricing with Stochastic Correlations under Nonhomogeneous Assumptions

In consideration of that the correlation between any two assets of the asset pool is always stochastic in the actual market and that collateralized debt obligation (CDO) pricing models under nonhomogeneous assumptions have no semianalytic solutions, we designed a numerical algorithm based on randomized quasi-Monte Carlo (RQMC) simulation method for CDO pricing with stochastic correlations under nonhomogeneous assumptions and took Gaussian factor copula model as an example to conduct experiments. The simulation results of RQMC and Monte Carlo (MC) method were compared from the perspective of variance changes. The results showed that this numerical algorithm was feasible, efficient, and stable for CDO pricing with stochastic correlation under nonhomogeneous assumptions. This numerical algorithm is expected to be extended to other factor Copula models for CDO pricing with stochastic correlations under nonhomogeneous assumptions

Design of Halogenated Donors for Efficient All-Small-Molecular Organic Solar Cells

Precise adjustment of the nanoscale morphology within the active layers is crucial for optimizing the photovoltaic performance of all-small-molecule organic solar cells (ASM-OSCs), and the halogen substituent strategy for photovoltaic materials plays a vital role in the development of the morphology evolution. In this work, we systematically study a series of acceptor–donor–acceptor (A-D-A) type small-molecule donors by incorporating halogenation at the thienyl benzo[1,2-b:4,5-b′]dithiophene (BDT-T) donor core unit named BSTR-F, BSTR-Cl, and BSTR-Br. Such halogenation is demonstrated to induce a significant increase in the ionization potential, i.e., deeper HOMO, and more ordered packing property. Using N3 as the acceptor, the BSTR-F-based devices achieve a power conversion efficiency (PCE) up to 15.93%, compared with the control nonhalogenated donor BSTR-H-based devices of 13.80%, indicating that the suitable halogenation strategy could effectively promote the high performance of ASM-OSCs