Broad angle phase matching in subdiffractive photonic crystals

We show that photonic crystals made of materials with normal dispersion allow broad angular range phase matching in nonlinear wave mixing processes if tuned to the subdiffractive (or equivalently self-collimated) beam propagation regimes for the frequencies of both interacting waves. This allows efficient parametric mixing of narrow beams. We demonstrate this idea by numerical simulation of the second harmonic generation in two-dimensional photonic crystal in particular nonlinear material (AlGaAs) in planar waveguide geometry.     

Observability of continuous Petri nets with infinite server semantics

Timed continuous Petri net (contPN) systems with infinite server semantics are nonlinear systems, particularly a subclass of piecewise linear (PWL) systems. This paper addresses several problems regarding the state observability of these systems. We assume that the initial marking/state is not known and by measuring the marking of some places we want to estimate all the others. First, a study of the different linear systems corresponding to a continuous Petri net system is performed. It is shown that in some cases, some of them are redundant, and so can be disregarded. The notion of distinguishable modes is introduced which helps us in giving a necessary and sufficient criterion for the observability in infinitesimal time. Structural observability, i.e., observability for all possible values of firing rates of transitions, is studied and it is proved that in some cases it can be reduced to a linear problem, even if the system is nonlinear. Using results from linear structured systems, the concept of weak structural or generic observability is considered.     

Double electron capture cross-sections by protons in collisions with He

Double electron capture (DEC) by protons from He was studied in collisions at energies in the keV regime, theoretically and experimentally. Theoretical cross-sections were calculated using the electron nuclear dynamic approach and a binomial distribution method in the energy range 1–100 keV. Experimental cross-sections were measured by means of the grow-rate method in the energy range of 4–10 keV. The cross-sections measured are consistent with those of the previous data at the high energies of the measured interval and show a different trend for the low energy. This behavior is consistent with those of other DEC cross-sections measured by protons from He-like targets. With the two collision models, it is proven that the reference data for this system are consistent only with the assumption of uncorrelated electrons and with independent target-projectile nuclei dynamics.     

Abelian class groups of reductive group schemes

We introduce the abelian class group C _ab (G) of a reductive group scheme G over a ring A of arithmetical interest and study some of its basic properties. For example, we show that if the fraction field of A is a global field without real primes, then there exists a surjection C(G) ? C _ab (G), where C(G) is the class set of G.     

Hypoellipticity for infinitely degenerate quasilinear equations and the dirichlet problem

In [10], we considered a class of infinitely degenerate quasilinear equations of the form div $A(x,w)\nabla w + \overrightarrow r (x,w) \cdot \nabla w + f(x,w) = 0$ and derived a priori bounds for high order derivatives D ^a w of their solutions in terms of w and ?w. We now show that it is possible to obtain bounds in terms of just w for a further subclass of such equations, and we apply the resulting estimates to prove that continuous weak solutions are necessarily smooth. We also obtain existence, uniqueness, and interior ${\varrho ^\infty }$ -regularity of solutions for the corresponding Dirichlet problem with continuous boundary data.     

Globally generated vector bundles on with

One classifies the globally generated vector bundles on with the first Chern class c₁ = 3. The case c₁ = 1 is very easy, the case c₁ = 2 was done in [42], the case c₁ = 3, rank =2 was settled in [21] and the case c₁ ≤ 5, rank = 2 in [10]. Our work is based on Serre's theorem relating vector bundles of rank = 2 with codimension 2 lci subschemes and its generalization for higher ranks, considered firstly by Vogelaar in [48].     

Fatty Acid Ethyl Esters (FAEE): A New,Green and Renewable Solvent for the Extraction of Carotenoids from Tomato Waste Products

Currently there is a drive towards the minimisation and reclamation of valuable materials from the waste products of the food and beverage industry. This can be achieved through the extraction of residual nutraceuticals from such materials. Tomato pomace contains carotenoids and other chemicals which can be extracted directly into edible oils to improve the health-giving properties of such oils. We report here a novel green solvent, fatty acid ethyl esters (FAEE), which is significantly more effective than sunflower oil and hexane for the extraction of lycopene and beta-carotene from tomato skin waste. FAEE are a non-toxic renewable resource that is environmentally friendly and to our knowledge has never been used as a vegetal extraction fluid. The efficiency of FAEE extraction was significantly improved relative to both sunflower oil and hexane under ultrasound-assisted extraction (UAE) conditions. In addition, FAEE have the additional and significant advantage that once enriched with the extracted nutraceuticals can be used directly as a food additive.     

Study of the Cost Functional for Free Material Design Problems

We study properties of the cost functional arising in free material optimization problems, with special emphasis on semicontinuity and its relation to convexity.     

Semi‐heterogeneous Dual Nickel/Photocatalysis using Carbon Nitrides: Esterification of Carboxylic Acids with Aryl Halides

Cross‐coupling reactions mediated by dual nickel/photocatalysis are synthetically attractive but rely mainly on expensive, non‐recyclable noble‐metal complexes as photocatalysts. Heterogeneous semiconductors, which are commonly used for artificial photosynthesis and wastewater treatment, are a sustainable alternative. Graphitic carbon nitrides, a class of metal‐free polymers that can be easily prepared from bulk chemicals, are heterogeneous semiconductors with high potential for photocatalytic organic transformations. Here, we demonstrate that graphitic carbon nitrides in combination with nickel catalysis can induce selective C?O cross‐couplings of carboxylic acids with aryl halides, yielding the respective aryl esters in excellent yield and selectivity. The heterogeneous organic photocatalyst exhibits a broad substrate scope, is able to harvest green light, and can be recycled multiple times. In situ FTIR was used to track the reaction progress to study this transformation at different irradiation wavelengths and reaction scales.