Modular Forms and Special Cubic Fourfolds

We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (2, 20).Comment: 13 page

Massive Quiescent Cores in Orion: VI. The Internal Structures and a Candidate of Transiting Core in NGC 2024 Filament

We present a multi-wavelength observational study of the NGC 2024 filament using infrared to sub-millimeter continuum and the NH$_3$ $(1,1)$ and $(2,2)$ inversion transitions centered on FIR-3, the most massive core therein. FIR-3 is found to have no significant infrared point sources in the Spitzer/IRAC bands. But the NH$_3$ kinetic temperature map shows a peak value at the core center with $T_{\rm k}=25$ K which is significantly higher than the surrounding level ($T_{\rm k}=15-19$ K). Such internal heating signature without an infrared source suggests an ongoing core collapse possibly at a transition stage from first hydrostatic core (FHSC) to protostar. The eight dense cores in the filament have dust temperatures between 17.5 and 22 K. They are much cooler than the hot ridge ($T_{\rm d}=55$ K) around the central heating star IRS-2b. Comparison with a dust heating model suggests that the filament should have a distance of $3-5$ pc from IRS-2b. This value is much larger than the spatial extent of the hot ridge, suggesting that the filament is spatially separated from the hot region along the line of sight.Comment: 20 pages, 7 figures, 6 tables. Accepted to Ap

Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model, for example, the orders of the fractional derivative or the source term, are often unknown, which requires one to discuss inverse problems to identify these physical quantities from some additional information that can be observed or measured practically. This chapter investigates several kinds of inverse coefficient problems for the fractional diffusion equation

Exports, Productivity, and Credit Constraints : A Firmâ€ÂLevel Empirical Investigation of China

Recent Melitz-type (2003) intra-industry heterogonous trade models argue that a firm's productivity has significant effects on the firm's exports. This paper examines how a firms credit constraints as well as its productivity affect its export decisions. We imbed the firm's credit constraints into a Melitz-type general-equilibrium model by endogenizing the probability of the success of firm-specific projects. We show that, all else equal, it is easier for firms to enter the export market if (1) the probability of the success of their project is higher and consequently they have easier access to external finance from financial intermediaries; or (2) they have alternative sources, other than from financial intermediaries, to obtain funds. We test these theoretical hypotheses using firm-level data from Chinese manufacturing industries and find strong evidence supporting the predictions of the model.Credit Constraints, Heterogeneous Firms, productivity, trade