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.     

Three-dimensional in vivo scanning microscopy with inertia-free focus control

The acquisition of high-resolution images in three dimensions is of utmost importance for the morphological and functional investigation of biological tissues. Here, we present a laser scanning two-photon microscope with remote and motionless control of the focus position. The movement of the excitation spot along the propagation direction is achieved by shaping the laser wavefront with a spatial light modulator. Depending on the optical properties of the objective in use, this approach allows z movements in a range of tens to hundreds of micrometers with small changes of the point spread function. We applied this technique for the three-dimensional (3D) imaging of fluorescent cells in the mouse neocortex in vivo. The presented system bypasses the limitations of microscopes based on moving objectives, enabling high-resolution inertia-free 3D imaging.     

A note on congruences of semilattices with sectionally finite height

We present a bijective correspondence between congruences of semilattices with sectionally finite height (i.e., meet-semilattices whose principal downsets have finite length) and certain special subsets of their universes. We characterize these subsets from a purely order-theoretic point of view and prove that the bijection coincides with the Leibniz operator of abstract algebraic logic.     

Organic room-temperature phosphorescence from halogen-bonded organic frameworks: hidden electronic effects in rigidified chromophores

Development of purely organic materials displaying room-temperature phosphorescence (RTP) will expand the toolbox of inorganic phosphors for imaging, sensing or display applications. While molecular solids were found to suppress non-radiative energy dissipation and make the RTP process kinetically favourable, such an effect should be enhanced by the presence of multivalent directional non-covalent interactions. Here we report phosphorescence of a series of fast triplet-forming tetraethyl naphthalene-1,4,5,8-tetracarboxylates. Various numbers of bromo substituents were introduced to modulate intermolecular halogen-bonding interactions. Bright RTP with quantum yields up to 20% was observed when the molecule is surrounded by a Br⋯O halogen-bonded network. Spectroscopic and computational analyses revealed that judicious heavy-atom positioning suppresses non-radiative relaxation and enhances intersystem crossing at the same time. The latter effect was found to be facilitated by the orbital angular momentum change, in addition to the conventional heavy-atom effect. Our results suggest the potential of multivalent non-covalent interactions for excited-state conformation and electronic control.

The number and position of halogen substituents in purely organic π–π* chromophores critically affect the efficiency of phosphorescence.     

Determination of elemental compositions by gas chromatography/time‐of‐flight mass spectrometry using chemical and electron ionization

Many metabolomic applications use gas chromatography/mass spectrometry (GC/MS) under standard 70 eV electron ionization (EI) parameters. However, the abundance of molecular ions is often extremely low, impeding the calculation of elemental compositions for the identification of unknown compounds. On changing the beam‐steering voltage of the ion source, the relative abundances of molecular ions at 70 eV EI were increased up to ten‐fold for alkanes, fatty acid methyl esters and trimethylsilylated metabolites, concomitant with 2‐fold absolute increases in ion intensities. We have compared the abundance, mass accuracy and isotope ratio accuracy of molecular species in EI with those in chemical ionization (CI) with methane as reagent gas under high‐mass tuning. Thirty‐three peaks of a diverse set of trimethylsilylated metabolites were analyzed in triplicate, resulting in 342 ion species ([M+H]⁺, [M–CH₃]⁺ for CI and [M]^{+ .} , [M–CH₃]^{+ .} for EI). On average, CI yielded 8‐fold more intense molecular species than EI. Using internal recalibration, average mass errors of 1.8 ± 1.6 mm/z units and isotope ratio errors of 2.3 ± 2.0% (A+1/A ratio) and 1.7 ± 1.8% (A+2/A ratio) were obtained. When constraining lists of calculated elemental compositions by chemical and heuristic rules using the Seven Golden Rules algorithm and PubChem queries, the correct formula was retrieved as top hit in 60% of the cases and within the top‐3 hits in 80% of the cases. Copyright © 2010 John Wiley & Sons, Ltd.     

Entropy principle for the moment systems of degree $\alpha$ associated to the Boltzmann equation. Critical derivatives and non controllable boundary data

m moments and of degree . For such theories the entropy principle is still valid only, if the non equilibrium field variables and their derivatives are sufficiently small with respect to the required approximation order. In this paper we prove through simple examples of stationary problems that the entropy principle fails in general, if all the non-equilibrium variables are of the same order of magnitude. This is due to the fact that there exist some derivatives of non equilibrium variables (critical derivatives) that are not small along all the solutions. This property can be used to fix the non controllable boundary data in such a manner that the critical derivatives are kept small for the solution that we may choose. Thus, for the stationary unidimensional case we propose the requirement that the critical derivatives vanish on the boundary, eventually with some successive derivatives. This is a sufficient condition for the validity of the entropy principle at least in a neighborhood of the boundary and makes it possible to assign the non controllable data in a simple manner when the number of moments is greater than 13. We have tested this procedure in several cases of theories, showing that the criterion implies continuity with respect to the change of the moment number and to the truncation order. In particular for the planar unidimensional heat conduction problem we have obtained a behavior for the temperature that is always the same as the one predicted by the classical Fourier law. This result is in evident contrast with the minimax principle expectation. However we have qualitative differences between the temperature behavior described by Extended Thermodynamics and the one by Fourier-Navier-Stokes theory for heat conduction in radial symmetry. Received June 25, 2001 / Published online February 28, 2002     

Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions

We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2 ^N −2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases. (Accepted October 6, 1995)