Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Importance of nuclear effects in the measurement of neutrino oscillation parameters

We investigate how models for neutrino–nucleus cross sections based on different assumptions for the nuclear dynamics affect the forecasted sensitivities to neutrino oscillation parameters at future neutrino facilities. We limit ourselves to the quasi-elastic regime, where the neutrino cross sections can be evaluated with less uncertainties, and discuss the sensitivity reach to θ₁₃${\theta }_{13}$ and δ at a prototype low-γ β-beam, mostly sensitive to the quasi-elastic regime.     

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.     

Almost everywhere convex functions on R n and weak derivatives

The classical subdifferential calculus is a useful tool in order to establish characterizations of convex functions and optimality conditions; but it becomes useless when one thinks to study almost everywhere convex functions. In this paper by using Sobolev space theory we give some characterizations of this class of functions.     

Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces

In this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a “classical” framework, as the problem of computation of Stokes matrices and monodromy of differential equations with regular and irregular singularities. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups. Received: 24 October 1998 / Accepted: 27 April 1999     

Studies on pyrrolidinones. Synthesis of 1,2,3,5,11,11a-hexahydroindolizino[7,6-b]indole-3,11-dione

Condensation of N-trimethylsilylindole with methyl N-trimethylsilyloxymethylpyroglutamate is the best method to obtain methyl N-indolylmethylpyroglutamate. Friedel-Crafts cyclization of the corresponding acid yields a new ketone (1,2,3,5,11,11a-hexahydroindolizino[7,6-b] indole-3,11-dione).     

Automated preparation of carbon-11 ethanol and carbon-11 butanol for human studies using positron emission tomography

An automated continuous flow process has been developed for the synthesis of¹¹C-ethanol and¹¹C-butanol. These alcohols were synthesized via the same route. The reaction of¹¹CO₂ with methylmagnesium bromide or with n-propylmagnesium chloride, followed by a lithium aluminum hydride reduction and hydrolysis produced respectively¹¹C-ethanol and¹¹C-butanol. Preparation can be completed in 25 min. In each case the radiochemical purity, as determined by high pressure liquid chromatography /HPLC/ was greater than 98%. Biological quality control shows that the products are suitable for human use. The process has been completely automated to limit radiation exposure to personnel, reduce preparation time, and increase reproducibility.     

Global wellposedness for quasi-linear symmetric hyperbolic systems with regularized coefficients

Following the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasi-linear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a regularizing function. In the case of unbounded regularized coefficients, local existence of classical solutions is proved, as well as uniqueness and regularity of (not necessarily existing) global weak solutions with initial value in a Sobolev space. As the regularizing function tends to Dirac's δ, local-in-time convergence to the classical solution of the non-regularized problem is proved.