Explicit birational geometry of 3-folds of general type, I

Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V):=\text{dim} H^0(V, 12K_V)>0$ and $P_{m_0}(V)>1$ for some positive integer $m_0\leq 24$. A direct consequence is the birationality of the pluricanonical map $\varphi_m$ for all $m\geq 126$. Besides, the canonical volume $\text{Vol}(V)$ has a universal lower bound $\nu(3)\geq \frac{1}{63\cdot 126^2}$.Comment: 29 pages, Ann Sci Ecole Norm Sup (to appear

Explicit birational geometry of threefolds of general type

Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V)>0$ and $P_{24}(V)>1$ (which answers an open problem of J. Kollar and S. Mori). We also prove that the canonical volume has an universal lower bound $\text{Vol}(V) \geq 1/2660$ and that the pluri-canonical map $\Phi_m$ is birational onto its image for all $m\geq 77$. As an application of our method, we prove Fletcher's conjecture on weighted hyper-surface 3-folds with terminal quotient singularities. Another featured result is the optimal lower bound $\text{Vol}(V)\geq {1/420}$ among all those 3-folds $V$ with $\chi({\mathcal O}_V)\leq 1$.Comment: (updated version on October 15, 2007) 55 pages, a couple of missing P_2 terms in Section 5 added and slight rearrangements to the contex

Frustrated double ionization in two-electron triatomic molecules

Using a semi-classical model, we investigate frustrated double ionization (FDI) in $\mathrm{D_3^+}$, a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We compute the kinetic energy release of the nuclei and find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a feature that can potentially be observed experimentally and is a signature of only one of the two pathways of FDI.Comment: 5 pages, 4 figure

On the theory of the CO+OH reaction, including H and C kinetic isotope effects

The effect of pressure, temperature, H/D isotopes, and C isotopes on the kinetics of the OH+CO reaction are investigated using Rice-Ramsperger-Kassel-Marcus theory. Pressure effects are treated with a step-ladder plus steady-state model and tunneling effects are included. New features include a treatment of the C isotope effect and a proposed nonstatistical effect in the reaction. The latter was prompted by existing kinetic results and molecular-beam data of Simons and co-workers [J. Phys. Chem. A 102, 9559 (1998); J. Chem. Phys. 112, 4557 (2000); 113, 3173 (2000)] on incomplete intramolecular energy transfer to the highest vibrational frequency mode in HOCO*. In treating the many kinetic properties two small customary vertical adjustments of the barriers of the two transition states were made. The resulting calculations show reasonable agreement with the experimental data on (1) the pressure and temperature dependence of the H/D effect, (2) the pressure-dependent 12C/13C isotope effect, (3) the strong non-Arrhenius behavior observed at low temperatures, (4) the high-temperature data, and (5) the pressure dependence of rate constants in various bath gases. The kinetic carbon isotopic effect is usually less than 10 per mil. A striking consequence of the nonstatistical assumption is the removal of a major discrepancy in a plot of the kOH+CO/kOD+CO ratio versus pressure. A prediction is made for the temperature dependence of the OD+CO reaction in the low-pressure limit at low temperatures

On a notion of maps between orbifolds, II. homotopy and CW-complex

This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set of algebraic invariants -- the homotopy groups, and (2) an analog of CW-complex theory. As a corollary of this machinery, the classical Whitehead theorem which asserts that a weak homotopy equivalence is a homotopy equivalence is extended to the orbifold category.Comment: 51 pages, Communications in Contemporary Mathematics, to appea

On the theory of the reaction rate of vibrationally excited CO molecules with OH radicals

The dependence of the rate of the reaction CO+OH-->H+CO2 on the CO-vibrational excitation is treated here theoretically. Both the Rice-Ramsperger-Kassel-Marcus (RRKM) rate constant kRRKM and a nonstatistical modification knon [W.-C. Chen and R. A. Marcus, J. Chem. Phys. 123, 094307 (2005).] are used in the analysis. The experimentally measured rate constant shows an apparent (large error bars) decrease with increasing CO-vibrational temperature Tv over the range of Tv's studied, 298–1800 K. Both kRRKM(Tv) and knon(Tv) show the same trend over the Tv-range studied, but the knon(Tv) vs Tv plot shows a larger effect. The various trends can be understood in simple terms. The calculated rate constant kv decreases with increasing CO vibrational quantum number v, on going from v=0 to v=1, by factors of 1.5 and 3 in the RRKM and nonstatistical calculations, respectively. It then increases when v is increased further. These results can be regarded as a prediction when v state-selected rate constants become available

Longevity impact on life insurers in low interest rate environment

This paper aims at shedding some light on the interplay between two key risk factors affecting most life insurance products, namely biometric and investment risk. We enhance the pioneering model by Briys and de Varenne, featuring a stylized participating life insurance company by explicitly tying benefits to the survivorship of a cohort of policyholders. In particular, we allow for the two main components of biometric risk, that is systematic (longevity) risk and diversifiable (process) risk