On the Generation of Certain Bundles of the Projective Space

Extending a result of Manivel, we prove the following: THEOREM. Suppose $\sum\limits_i {b_i \geqslant } \sum\limits_i {a_i } + n$ and $$\sum\limits_i {b_i } [n + d_i d_i - 1] \geqslant \sum\limits_i {a_i } [n + l_i l_i - 1] + n.$$ Then the kernel E(d) of the general morphism: $$\mathop \oplus \limits_{i = 1}^v (Bi \otimes O_{P^n } (d_i )) \to \mathop \oplus \limits_{j = 1}^v (A_j \otimes O_{P^n } (l_i ))$$ (l ₁>...>l _s>d ₁>...>d _v) is a globally generated vector bundle, except for at most finitely many sets $\left\{ {b_i ,a_i } \right\}$ .     

Enantiopure α-imino glyoxylate: a versatile substrate for the spontaneous asymmetric synthesis of unnatural hydroxyaryl glycinates

A novel synthesis of useful enantiomerically pure arylglycinates via spontaneous reaction between phenol or naphthol derivatives and enantiopure α-imino glyoxylate in the absence of an acid catalyst is reported. A library of enantiopure substituted phenol or naphthol glycinates was obtained in good yields and high diastereoselectivities. Diastereoisomerically pure aryl glycinates were obtained by direct flash chromatography separation of the crude reaction mixture. The free OH moiety of the phenols or naphthols contributed to the activation of the imino group to form an intermolecular hydrogen bond and promoted the reaction in the absence of an acid catalyst, as shown in the transition state reported. The diastereoselectivity is due to thermodynamic control in the addition step.     

Combinatorial analysis of Tetris-like games

We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion.     

Markovian approximation in foreign exchange markets

In this paper, using the exit-time statistic, we study the structure of the price variations for the high-frequency data set of the bid–ask Deutschemark/US dollar exchange rate quotes registered by the inter-bank Reuters network over the period October 1, 1992 to September 30, 1993. Having rejected random-walk models for the returns, we propose a Markovian model which reproduce the available information of the financial series. Besides the usual correlation analysis we have verified the validity of this model by means of other tools all inspired by information theory. These techniques are not only severe tests of the approximation but also evidence of some aspects of the data series which have a clear financial relevance.     

State-specific reactions and autoionization dynamics of Ar produced by synchrotron radiation

The long-lived excited states of doubly charged rare gases can markedly affect their reactivity. In this paper we demonstrate the presence of strong state-specific effects in the charge exchange of Ar²⁺ (³P, ¹D and ¹S) with several neutral targets (He, Ne, Kr, Xe, D₂, and CH₄). State sensitive measurements have been performed by producing the different Ar²⁺ electronic states via tunable synchrotron radiation (Elettra-Trieste, Italy and SuperACO-Orsay, France). From the product ion yield data of charge transfer, state-selected total cross-sections have been deduced. Using the state-specific reactivity of Ar²⁺ towards different neutral targets, it has been possible to extract the photon-energy-dependent production branching of the three doubly charged states and to investigate the autoionization dynamics of neutral or singly charged Ar in the vicinity of the double ionization threshold.     

Yield criteria for quasibrittle and frictional materials: A generalization to surfaces with corners

Convexity of a yield function (or phase-transformation function) and its relations to convexity of the corresponding yield surface (or phase-transformation surface) is essential to the invention, definition and comparison with experiments of new yield (or phase-transformation) criteria. This issue was previously addressed only under the hypothesis of smoothness of the surface, but yield surfaces with corners (for instance, the Hill, Tresca or Coulomb–Mohr yield criteria) are known to be of fundamental importance in plasticity theory. The generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase-transformation surfaces is provided in this paper, together with the (necessary to the proof) extension of a theorem on nonsmooth elastic potential functions. While the former of these generalizations is crucial for yield and phase-transformation functions, the latter may find applications for potential energy functions describing phase-transforming materials, or materials with discontinuous locking in tension, or contact of a body with a discrete elastic/frictional support.     

Rationality in families of threefolds

We prove that in a family of projective threefolds defined over an algebraically closed field, the locus of rational fibers is a countable union of closed subsets of the locus of separably rationally connected fibers. When the ground field has characteristic zero, this implies that the locus of rational fibers in a smooth family of projective threefolds is the union of at most countably many closed subfamilies.     

CAESAR models for developmental toxicity

Background

The new REACH legislation requires assessment of a large number of chemicals in the European market for several endpoints. Developmental toxicity is one of the most difficult endpoints to assess, on account of the complexity, length and costs of experiments. Following the encouragement of QSAR (in silico) methods provided in the REACH itself, the CAESAR project has developed several models.

Results

Two QSAR models for developmental toxicity have been developed, using different statistical/mathematical methods. Both models performed well. The first makes a classification based on a random forest algorithm, while the second is based on an adaptive fuzzy partition algorithm. The first model has been implemented and inserted into the CAESAR on-line application, which is java-based software that allows everyone to freely use the models.

Conclusions

The CAESAR QSAR models have been developed with the aim to minimize false negatives in order to make them more usable for REACH. The CAESAR on-line application ensures that both industry and regulators can easily access and use the developmental toxicity model (as well as the models for the other four endpoints).