Unconventional magnetic behavior of iron-oxide nanoparticles in polymeric matrices

We report the results of magnetization and 57Fe Mössbauer spectroscopy measurements performed in the temperature range 5-300 K on composites containing iron¿oxide nanoparticles encased in polystyrene type resins. After carrying out a suitable field treatment in order to decouple the particles from the matrix, a fraction of the particles freely rotate in response to an applied magnetic field

Collineations of a symmetric 2-covariant tensor: Ricci collineations

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra, but in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. As an application, we study the Ricci collineations of a type B warped spacetime.

Minimal analytical characterisation of engineered nanomaterials need for hazard assessment in biological matrices

The safe and responsible development of engineered nanomaterials (ENM), nanotechnology-based materials and products, together with the definition of regulatory measures and implementation of "nano"-legislation in Europe require a widely supported scientific basis and sufficient high quality data upon which to base decisions. At the very core of such a scientific basis is a general agreement on key issues related to risk assessment of ENMs which encompass the key parameters to characterise ENMs, appropriate methods of analysis and best approach to express the effect of ENMs in widely accepted dose response toxicity tests. The following major conclusions were drawn: Due to high batch variability of ENMs characteristics of commercially available and to a lesser degree laboratory made ENMs it is not possible to make general statements regarding the toxicity resulting from exposure to ENMs. 1) Concomitant with using the OECD priority list of ENMs, other criteria for selection of ENMs like relevance for mechanistic (scientific) studies or risk assessment-based studies, widespread availability (and thus high expected volumes of use) or consumer concern (route of consumer exposure depending on application) could be helpful. The OECD priority list is focussing on validity of OECD tests. Therefore source material will be first in scope for testing. However for risk assessment it is much more relevant to have toxicity data from material as present in products/matrices to which men and environment are be exposed. 2) For most, if not all characteristics of ENMs, standardized methods analytical methods, though not necessarily validated, are available. Generally these methods are only able to determine one single characteristic and some of them can be rather expensive. Practically, it is currently not feasible to fully characterise ENMs. Many techniques that are available to measure the same nanomaterial characteristic produce contrasting results (e.g. reported sizes of ENMs). It was recommended that at least two complementary techniques should be employed to determine a metric of ENMs. The first great challenge is to prioritise metrics which are relevant in the assessment of biological dose response relations and to develop analytical methods for characterising ENMs in biological matrices. It was generally agreed that one metric is not sufficient to describe fully ENMs. 3) Characterisation of ENMs in biological matrices starts with sample preparation. It was concluded that there currently is no standard approach/protocol for sample preparation to control agglomeration/aggregation and (re)dispersion. It was recommended harmonization should be initiated and that exchange of protocols should take place. The precise methods used to disperse ENMs should be specifically, yet succinctly described within the experimental section of a publication. 4) ENMs need to be characterised in the matrix as it is presented to the test system (in vitro/ in vivo). 5) Alternative approaches (e.g. biological or in silico systems) for the characterisation of ENMS are simply not possible with the current knowledge. Contributors: Iseult Lynch, Hans Marvin, Kenneth Dawson, Markus Berges, Diane Braguer, Hugh J. Byrne, Alan Casey, Gordon Chambers, Martin Clift, Giuliano Elia1, Teresa F. Fernandes, Lise Fjellsbø, Peter Hatto, Lucienne Juillerat, Christoph Klein, Wolfgang Kreyling, Carmen Nickel1, and Vicki Stone.

Minimal analytical characterization of engineered nanomaterials needed for hazard assessment in biological matrices.

Abstract This paper presents the outcomes from a workshop of the European Network on the Health and Environmental Impact of Nanomaterials (NanoImpactNet). During the workshop, 45 experts in the field of safety assessment of engineered nanomaterials addressed the need to systematically study sets of engineered nanomaterials with specific metrics to generate a data set which would allow the establishment of dose-response relations. The group concluded that international cooperation and worldwide standardization of terminology, reference materials and protocols are needed to make progress in establishing lists of essential metrics. High quality data necessitates the development of harmonized study approaches and adequate reporting of data. Priority metrics can only be based on well-characterized dose-response relations derived from the systematic study of the bio-kinetics and bio-interactions of nanomaterials at both organism and (sub)-cellular levels. In addition, increased effort is needed to develop and validate analytical methods to determine these metrics in a complex matrix.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Aplicaciones de la Teoría de Matrices en Matemática Discreta

Se describen algunas aplicaciones de la teoría de matrices a diversos temas pertenecientes alámbito de la matem\'atica discreta.

From symmetric glycerol derivatives to dissymmetric chlorohydrins

The anticipated worldwide increase in biodiesel production will result in an accumulation of glycerol for which there are insufficient conventional uses. The surplus of this by-product has increased rapidly during the last decade, prompting a search for new glycerol applications. We describe here the synthesis of dissymmetric chlorohydrin esters from symmetric 1,3-dichloro-2-propyl esters obtained from glycerol. We studied the influence of two solvents: 1,4-dioxane and 1-butanol and two bases: sodium carbonate and 1-butylimidazole, on the synthesis of dissymmetric chlorohydrin esters. In addition, we studied the influence of other bases (potassium and lithium carbonates) in the reaction using 1,4-dioxane as the solvent. The highest yield was obtained using 1,4-dioxane and sodium carbonate.

Technical Note: Dissolved organic matter fluorescence a finite mixture approach to deconvolve excitation-emission matrices

The analysis of the shape of excitation-emission matrices (EEMs) is a relevant tool for exploring the origin, transport and fate of dissolved organic matter (DOM) in aquatic ecosystems. Within this context, the decomposition of EEMs is acquiring a notable relevance. A simple mathematical algorithm that automatically deconvolves individual EEMs is described, creating new possibilities for the comparison of DOM fluorescence properties and EEMs that are very different from each other. A mixture model approach is adopted to decompose complex surfaces into sub-peaks. The laplacian operator and the Nelder-Mead optimisation algorithm are implemented to individuate and automatically locate potential peaks in the EEM landscape. The EEMs of a simple artificial mixture of fluorophores and DOM samples collected in a Mediterranean river are used to describe the model application and to illustrate a strategy that optimises the search for the optimal output.

Symmetric or asymmetric gasoline prices? A meta-analysis approach

The analysis of price asymmetries in the gasoline market is one of the most studied in the energy economics literature. Nevertheless, the great variability of results makes it very difficult to extract conclusive results on the existence or not of asymmetries. This paper shows through a meta-analysis approach how the industry segment analysed, the quality and quantity of data, the estimator and the model used may explain this heterogeneity of results.