Modelling of diffractive structures in photorefractive Er/Yb–co-doped glass waveguides

The photorefractive properties of Ge-doped glasses are routinely exploited for the production of Bragg gratings in optical fibres. Today, the most common fabrication procedure relies on the phase-mask technique, which allows to produce (through UV irradiation) a periodical refractive index variation in Ge-doped fibre cores. The same methodology can be applied to integrated optical components in photorefractive glass planar substrates. If rare earth ions (such as erbium and ytterbium) are included in the glass matrix, both active and photorefractive properties can be combined in the same material. This fact allows for the possibility of realizing complex integrated optical components, such as Bragg-reflection lasers and amplifiers. In this work, a numerical analysis of a waveguide Bragg reflector is presented based on a homemade modelling technique.     

Mathematics standards and curricula in the Netherlands

This paper addresses the question of what mathematics Dutch students should learn according to the standards as established by the Dutch Ministry of Education. The focus is on primary school and the foundation phase of secondary school. This means that the paper covers the range from kindergarten to grade 8 (4~14 years olds). Apart from giving an overview of the standards, we also discuss the standards' nature and history Furthermore, we look at textbooks and examination programs that in the Netherlands both have a key role in determining the intended mathematics curriculum. In addition to addressing the mathematical content, we also pay attention to the way mathematics is taught. The domain-specific education theory that forms the basis for the Dutch approach to teaching mathematics is called “Realistic Mathematics Education” Achievement scores of Dutch students from national and international tests complete this paper. These scores reveal what the standards bring us in terms of students' mathematical understanding. In addition to informing an international audience about the Dutch standards and curricula, we include some critical reflections on them.     

Existence of equilibria via Ekeland's principle

In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland's theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland's variational principle for equilibrium problems. Via the existence of ε-solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.     

The sum of the Betti numbers of smooth Hilbert schemes

Journal of Algebraic Combinatorics - Recently, Skjelnes and Smith classified which Hilbert schemes on projective space are smooth in terms of integer partitions $$\lambda = (\lambda _1,\ldots...     

Recovery of bioactive molecules from chestnut (Castanea sativa Mill.) by-products through extraction by different solvents

The underutilised forest and industrial biomass of Castanea sativa (Mill.) is generally discarded during post-harvest and food processing, with high impact on environmental quality. The searching on alternative sources of natural antioxidants from low-cost supplies, by methods involving environment-friendly techniques, has become a major goal of numerous researches in recent times. The aim of the present study was the set-up of a biomolecules extraction procedure from chestnut leaves, burs and shells and the assessing of their potential antioxidant activity. Boiling water was the best extraction solvent referring to polyphenols from chestnut shells and burs, whereas the most efficient for leaves resulted 60% ethanol at room temperature. Greatest polyphenol contents were 90.35, 60.01 and 17.68 mg gallic acid equivalents g^?1 in leaves, burs and shells, respectively. Moreover, flavonoids, tannins and antioxidant activity were assessed on the best extract obtained from each chestnut by-product.     

Two new clerodane-type diterpenoids from Bornean liverwort Gottschelia schizopleura and their cytotoxic activity

The Bornean liverwort Gottschelia schizopleura was investigated phytochemically for the first time. Two new and four previously known clerodane-type diterpenoids were isolated from the MeOH extract of G. schizopleura through a series of chromatographic techniques. The structures of the new metabolites were established by analyses of their spectroscopic data (1D NMR, 2D NMR, HRESIMS and IR). All the isolated compounds 1–6 were tested against human promyelocytic leukaemia (HL-60), human colon adenocarcinoma (HT-29) and Mus musculus skin melanoma (B16-F10). Compound 1 and 2 showed active inhibition against HL-60 and B16-F10 cells.     

Minimax theorems for set-valued maps without continuity assumptions

We introduce several classes of set-valued maps with new generalized convexity properties. We also obtain minimax theorems for set-valued maps which satisfy these convexity assumptions and which are not continuous. Our method consists of the use of a fixed point theorem for weakly naturally quasiconcave set-valued maps, defined on a simplex in a topological vector space, or of a constant selection of quasiconvex set-valued maps.     

Analyzing slowly exchanging protein conformations by ion mobility mass spectrometry: study of the dynamic equilibrium of prolyl oligopeptidase

Ion mobility mass spectrometry (IMMS) is a biophysical technique that allows the separation of isobaric species on the basis of their size and shape. The high separation capacity, sensitivity and relatively fast time scale measurements confer IMMS great potential for the study of proteins in slow (µs–ms) conformational equilibrium in solution. However, the use of this technique for examining dynamic proteins is still not generalized. One of the major limitations is the instability of protein ions in the gas phase, which raises the question as to what extent the structures detected reflect those in solution. Here, we addressed this issue by analyzing the conformational landscape of prolyl oligopeptidase (POP) – a model of a large dynamic enzyme in the µs–ms range – by native IMMS and compared the results obtained in the gas phase with those obtained in solution. In order to interpret the experimental results, we used theoretical simulations. In addition, the stability of POP gaseous ions was explored by charge reduction and collision‐induced unfolding experiments. Our experiments disclosed two species of POP in the gas phase, which correlated well with the open and closed conformations in equilibrium in solution; moreover, a gas‐phase collapsed form of POP was also detected. Therefore, our findings not only support the potential of IMMS for the study of multiple co‐existing conformations of large proteins in slow dynamic equilibrium in solution but also stress the need for careful data analysis to avoid artifacts. Copyright © 2016 John Wiley & Sons, Ltd.     

Organosulfate Formation through the Heterogeneous Reaction of Sulfur Dioxide with Unsaturated Fatty Acids and Long‐Chain Alkenes

The heterogeneous reaction between SO₂ and unsaturated compounds results in the efficient production of organosulfates for several fatty acids and long‐chain alkenes. The presence of an acid group, the physical state of the reactants (solid or liquid), the nature of the double bond (cis, trans, terminal), and the use of light irradiation all have an impact on the reaction rate. The reaction was investigated using different set‐ups (coated flow tube, aerosol flow tube, and diffuse reflectance infrared Fourier transform cell). The reaction products were identified by high‐resolution mass spectrometry and the impact of this reaction on organosulfate formation in the atmosphere is discussed.