On the preservation of combinatorial types for maps on trees

We study the preservation of the periodic orbits of an A-monotone tree map f:T→T in the class of all tree maps g:S→S having a cycle with the same pattern as A. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of ƒ into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved

The effect of scale in daily precipitation hazard assessment

Daily precipitation is recorded as the total amount of water collected by a rain-gauge in 24 h. Events are modelled as a Poisson process and the 24 h precipitation by a Generalised Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. Bayesian techniques are used to estimate the parameters. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimated GPD is mainly in the Fréchet DA, something incompatible with the common sense assumption of that precipitation is a bounded phenomenon. The bounded character of precipitation is then taken as a priori hypothesis. Consistency of this hypothesis with the data is checked in two cases: using the raw-data (in mm) and using log-transformed data. As expected, a Bayesian model checking clearly rejects the model in the raw-data case. However, log-transformed data seem to be consistent with the model. This fact may be due to the adequacy of the log-scale to represent positive measurements for which differences are better relative than absolute

Convenient synthesis of C75, an inhibitor of FAS and CPT1

C75 is a synthetic racemic α-methylene-γ-butyrolactone exhibiting anti-tumoral properties in vitro and in vivo as well as inducing hypophagia and weight loss in rodents. These interesting properties are thought to be a consequence of the inhibition of the key enzymes FAS and CPT1 involved in lipid metabolism. The need for larger amounts of this compound for biological evaluation prompted us to develop a convenient and reliable route to multigram quantities of C75 from easily available ethyl penta-3,4-dienoate 6. A recently described protocol for the addition of 6 to a mixture of dicyclohexylborane and nonanal followed by acidic treatment of the crude afforded lactone 8, as a mixture of cis and trans isomers, in good yield. The DBU-catalyzed isomerization of the methyl esters 9 arising from 8 gave a 10:1 trans/cis mixture from which the trans isomer was isolated and easily transformed into C75. The temporary transformation of C75 into a phenylseleno ether derivative makes its purification, manipulation and storage easier.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

Life cycle analysis and life cyle impact assessment methodologies: a state of the art

Life cycle analysis (LCA) is a comprehensive method for assessing the environmental impact of a product or an activity over its entire life cycle. The purpose of conducting LCA studies varies from one application to another. Different applications use LCA for different purposes. In general, the main aim of using LCA is to reduce the environmental impact of products through guiding the decision making process towards more sustainable solutions. The most critical phase in an LCA study is the Life Cycle Impact Assessment (LCIA) where the life cycle inventory (LCI) results of the considered substances related to the study of a certain system are transformed into understandable impact categories that represent the impact on the environment. In this research work, a general structure clarifying the steps that shall be followed ir order to conduct an LCA study effectively is presented. These steps are based on the ISO 14040 standard framework. In addition, a survey is done on the most widely used LCIA methodologies. Recommendations about possible developments and suggetions for further research work regarding the use of LCA and LCIA methodologies are discussed as well.

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips’s work devoted to monocomponent systems. Furthermore, a methodology which yields analytical expressions for the main statistical properties (mean free energies of binding and covariance matrix) of multidimensional affinity spectra is reported. Thus, the level of binding correlation between the different components can be quantified. It has to be highlighted that the reported methodology does not require the knowledge of the affinity spectrum to calculate the means, variances, and covariance of the binding energies of the different components. Nonideal competitive consistent adsorption isotherm, widely used in metal/proton competitive complexation to environmental macromolecules, and Frumkin competitive isotherms are selected to illustrate the application of the reported results. Explicit analytical expressions for the affinity spectrum as well as for the matrix correlation are obtained for the NICCA case. © 2004 American Institute of Physics.

Otolith shape analysis as a tool for population discrimination of the white grunt (Haemulon plumieri) stock in the northern coast of the Yucatan Peninsula, Mexico

In this study, the population structure of the white grunt (Haemulon plumieri) from the northern coast of the Yucatan Peninsula was determined through an otolith shape analysis based on the samples collected in three locations: Celestún (N 20°49",W 90°25"), Dzilam (N 21°23", W 88°54") and Cancún (N 21°21",W 86°52"). The otolith outline was based on the elliptic Fourier descriptors, which indicated that the H. plumieri population in the northern coast of the Yucatan Peninsula is composed of three geographically delimited units (Celestún, Dzilam, and Cancún). Significant differences were observed in mean otolith shapes among all samples (PERMANOVA; F2, 99 = 11.20, P = 0.0002), and the subsequent pairwise comparisons showed that all samples were significantly differently from each other. Samples do not belong to a unique white grunt population, and results suggest that they might represent a structured population along the northern coast of the Yucatan Peninsula

Assessment of the discrimination of animal fat by FT_Raman spectroscopy

In recent years, there has been an increased attention towards the composition of feeding fats. In the aftermath of the BSE crisis all animal by-products utilised in animal nutrition have been subjected to close scrutiny. Regulation requires that the material belongs to the category of animal by-products fit for human consumption. This implies the use of reliable techniques in order to insure the safety of products. The feasibility of using rapid and non-destructive methods, to control the composition of feedstuffs on animal fats has been studied. Fourier Transform Raman spectroscopy has been chosen for its advantage to give detailed structural information. Data were treated using chemometric methods as PCA and PLS-DA which have permitted to separate well the different classes of animal fats. The same methodology was applied on fats from various types of feedstock and production technology processes. PLS-DA model for the discrimination of animal fats from the other categories presents a sensitivity and a specificity of 0.958 and 0.914, respectively. These results encourage the use of FT-Raman spectroscopy to discriminate animal fats.

On the bicanonical map of irregular varieties

From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter ØL and ØB respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A2/L and A2/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.

Domain matched epitaxial growth of Bi1.5Zn1Nb1.5O7 thin films by pulsed laser deposition

Bi1.5Zn1Nb1.5O7 (BZN) epitaxial thin films were grown by pulsed laser deposition on Al2O3 with a double ZnO buffer layer through domain matching epitaxy (DME) mechanism. The pole figure analysis and reciprocal space mapping revealed the single crystalline nature of the thin film. The pole figure analysis also shows a 60º twinning for the (222) oriented crystals. Sharp intense spots in the SAED pattern also indicate the high crystalline nature of BZN thin film. The Fourier filtered HRTEM images of the BZN-ZnO interface confirms the domain matched epitaxy of BZN with ZnO buffer. An electric field dependent dielectric tunability of 68% was obtained for the BZN thin films with inter digital capacitors patterned over the film.

Regio- and stereoselective microwave-assisted synthesis of 5-alkyl-4-alkenyl-4-phenyl-1,3-oxazolidin-2-ones

Chiral symmetrical alk-2-yne-1,4-diols have been stereoselectively transformed into 5-alkyl-4-alkenyl-4-phenyl-1,3-oxazolidin- 2-ones, which are precursors of quaternary α-amino β-hydroxy acids. The key step was the cyclization of the bis(tosylcarbamates) of 2- phenylalk-2-yne-1,4-diols, easily obtained from the starting chiral diols. These cyclizations were accomplished with complete regioselectivity and up to 92:8 dr in the presence of catalytic amounts of Ni(0) or Pd (II) derivatives under microwave heating.

A nonparametric method for the measurement of size diversity with emphasis on data standardization

The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposedas the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where kis the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation

Experimental implementation of tightly focused beams with unpolarized transversal component at any plane

The aim of this paper is to provide a formal framework for designing highly focused fields with specific transversal features when the incoming beam is partially polarized. More specifically, we develop a field with a transversal component that remains unpolarized in the focal area. Moreover, its longitudinal component exhibits non-zero values on axis. Special attention is paid to the design of the input beam and the development of the experiment. The implementation of such fields is possible by using an interferometric setup combined with the use of digital holography techniques. Experimental results are compared with those obtained numerically.

Stable sampling and Fourier multipliers

We study the relationship between stable sampling sequences for bandlimited functions in $L^p(\R^n)$ and the Fourier multipliers in $L^p$. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship.