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

Phonological similarity effects in Cantonese word recognition

Two lexical decision experiments in Cantonese are described in which the recognition of spoken target words as a function of phonological similarity to a preceding prime is investigated. Phonological similaritv in first syllables produced inhibition, while similarity in second syllables led to facilitation. Differences between syllables in tonal and segmental structure had generally similar effects

Anti-ferrodistortive Nanodomains in PMN Relaxor

Temperature dependent studies of the 1/2(hk0) superlattice reflections \alpha spots by synchrotron x-ray scattering measurements were performed in (PMN) and (PMN-xPT) with Ti doping x<0.32 single crystals. Separation of the \alpha spots from the underlying diffuse scattering background allowed studying them as separate entities for the first time. Structure factor calculations have shown that alpha spots constitute the presence of a new kind of anti-ferrodistortive nanoregions (AFR) in the form of fluctuations produced by anti-parallel short-range correlated Pb^2+ displacements. AFR appear to be different and unrelated to the chemical nanodomains (CND) and ferroelectric polar nanoregions (PNR). Simultaneous presence of AFR and PNR can explain relaxor behavior as a result of competition between randomly occurring ferroelectric and anti-ferroelectric fluctuations. Temperature dependence of the \alpha spots in PMN showed a direct correlation with the freezing phase transition near Tf~220 K.Comment: 10 pages, 7 figures, Conference-Fundamental Physics of Ferroelectrics 200

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

Hybrid method for understanding black-hole mergers: Inspiralling case

We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the l=2, m=±2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the superkick configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal-mode frequencies. We argue that this locking begins during the merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during the merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations

Maximal violation of Clauser-Horne-Shimony-Holt inequality for four-level systems

Clauser-Horne-Shimony-Holt inequality for bipartite systems of 4-dimension is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulae for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulae, we show that an optimal non-maximally entangled state is about 6% more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.Comment: 7 pages, three table