On extension theorems for holomorphic generalized functions

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.

Laguerre moments and generalized functions

Here we explore the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives), presenting several interesting relations. A useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so-called quasi-probabilities. One of them, the P-distribution, can be represented by a sum over Laguerre moments when the electromagnetic field is in a photon-number state. Consequently, the P-distribution can be expressed in terms of Dirac delta-function and derivatives. More specifically, we found a direct relation between P-distributions and the Laguerre factorial moments.

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integration of polyharmonic functions

The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

Growth and fatty acid composition of Octopus vulgaris fed different diets based on bogue (Boops boops) in comparison to wild individuals

[EN] Octopus vulgaris is a suitable candidate to diversify marine aquaculture (Iglesias et al., 2000; Vaz Pires et al. 2004). Actually, wild sub-adults are on-growing in floating cages showing promising results (Chapela et al., 2006; Rodríguez et al., 2006). Even though octopus industrial development is still limited, mainly associated to the dependence of wild catch individuals for ongrowing (Iglesias et al., 2007) and a lack of an appropriate formulated diet (García García and Cerezo, 2006). In addition, essential macronutrient requirements for this species are still not well known. Used of discarded bogue as single food for Octopus on-growth results in similar growth than co-fed diets with the crab (Portunus pelagic). FA content of Muscle and DG showed important ARA content, suggesting the important functions of this FA in this specie.

On the composition of Frostman Blaschke products

We construct an infinite uniform Frostman Blaschke product B such that B composed with itself is also a uniform Frostman Blaschke product. We also show that the set of uniform Frostman Blaschke products is open in the set of inner functions with the uniform norm.

Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

Knudsen effusion mass spectrometric determination of the complex vapor composition of samarium, europium, and ytterbium bromides

RATIONALE The vaporization of Sm, Eu, and Yb tri- and dibromides is accompanied by decomposition and disproportionation reactions. These result in complex vapor compositions whose analysis is an intricate problem for experimentalists. Approaches have been developed to interpret mass spectra and accurately determine the vapor composition of thermally unstable compounds. METHODS A sector type magnet instrument was used. A combined ion source allowed the study of both the molecular and ionic vapor compositions in the electron ionization (EI) and the thermionic emission (TE) modes. The methodological approaches were based on a joint analysis of the ionization efficiency functions, the temperature and time dependences of the ion currents, and special mathematical data evaluation. RESULTS The vaporization of SmBr3, YbBr3, SmBr2, EuBr2, and YbBr2 was studied in the temperature range of 850–1300 K. An initial stage of incongruent vaporization was observed in the case of the tribromides, SmBr2, and YbBr2. This eventually changed to a congruent vaporization stage. Various neutral (Ln, Br, Br2, LnBr, LnBr2, LnBr3, Ln2Br4, Ln2Br5, and Ln2Br6) and charged (Br–, LnBr3–, LnBr4–) species were detected at different vaporization stages. CONCLUSIONS The quantitative vapor composition of Sm, Eu, and Yb tri- and dibromides was determined. It was found that only EuBr2 was stable in the studied temperature range. The developed approaches can be useful in the case of other thermally unstable compounds.

Developmental Changes in the Structure and Composition of the Postsynaptic Density

The development of the brain and its underlying circuitry is dependent on the formation of trillions of chemical synapses, which are highly specialized contacts that regulate the flow of information from one neuron to the next. It is through these synaptic connections that neurons wire together into networks capable of performing specific tasks, and activity-dependent changes in their structural and physiological state is one way that the brain is thought to adapt and store information. At the ultrastructural level, developmental and activity-dependent changes in the size and shape of dendritic spines have been well documented, and it is widely believed that structural changes in spines are a hallmark sign of synapse maturation and alteration of synaptic physiology. While changes in spine structure have been studied extensively, changes in one of its most prominent components, the postsynaptic density (PSD), have largely evaded observation. The PSD is a protein-rich organelle on the cytoplasmic side of the postsynaptic membrane, where it sits in direct opposition to the presynaptic terminal. The PSD functions both to cluster neurotransmitter receptors at the cell surface as well as organize the intracellular signaling molecules responsible for transducing extracellular signals to the postsynaptic cell. Much is known about the chemical composition of the PSD, but the structural arrangement of its molecular components is not well documented. Adding to the difficulty of understanding such a complex mass of protein machinery is the fact that its protein composition is known to change in response to synaptic activity, meaning that its structure is plastic and no two PSDs are identical. Here, immuno-gold labeling and electron tomography of PSDs isolated throughout development was used to track changes in both the structure and molecular composition of the PSD. State-of-the-art cryo-electron tomography was used to study the fine structure of the PSD during development, and provides an unprecedented glimpse into its molecular architecture in an un-fixed, unstained and hydrated state. Through this analysis, large structural and compositional changes are apparent and suggest a model by which the PSD is first assembled as a mesh-like lattice of proteins that function as support for the later recruitment of various PSD components. Spatial analysis of the recruitment of proteins into the PSD demonstrated that its assembly has an underlying order.

Measurement of the flavour composition of dijet events in pp collisions at sqrts=7 TeV with the AT detector

This paper describes a measurement of the flavour composition of dijet events produced in pp collisions at root s = 7 TeV using the ATLAS detector. The measurement uses the full 2010 data sample, corresponding to an integrated luminosity of 39 pb(-1). Six possible combinations of light, charm and bottom jets are identified in the dijet events, where the jet flavour is defined by the presence of bottom, charm or solely light flavour hadrons in the jet. Kinematic variables, based on the properties of displaced decay vertices and optimised for jet flavour identification, are used in a multidimensional template fit to measure the fractions of these dijet flavour states as functions of the leading jet transverse momentum in the range 40 GeV to 500 GeV and jet rapidity vertical bar y vertical bar < 2.1. The fit results agree with the predictions of leading-and next-to-leading-order calculations, with the exception of the dijet fraction composed of bottom and light flavour jets, which is underestimated by all models at large transverse jet momenta. The ability to identify jets containing two b-hadrons, originating from e. g. gluon splitting, is demonstrated. The difference between bottom jet production rates in leading and subleading jets is consistent with the next-to-leading-order predictions.

Site characteristics, and major and trace element composition of sediment cores sampled around the Windmill Islands in 1998

To establish a natural background and its temporal and spatial variability for the area around Casey Station in the Windmill Islands, East Antarctica, the authors studied major and trace element concentrations and the distribution of organic matter in marine and lacustrine sediments. A wide range of natural variability in trace metal concentrations was identified between sites and within a time scale of 9 ka (e.g., Ni 5-37 mg/kg, Cu 20-190 mg/kg, Zn 50-300 mg/kg, Pb 4.5- 34 mg/kg). TOC concentrations are as high as 3 wt.% at the marine sites and 20 wt.% at the lacustrine sites, and indicate highly productive ecosystems. These data provide a background upon which the extent of human impact can be established, and existing data indicate negligible levels of disturbance. Geochemical and lithological data for a lacustrine sediment core from Beall Lake confirm earlier interpretation of recent climatic changes based on diatom distribution, and the onset of deglaciation in the northern part of the Windmill Islands between 8.6 and 8.0 ka BP. The results demonstrate that geochemical and lithological data can not only be used to define natural background values, but also to assess long-term climatic changes of a specific environment. Other sites, however, preserve a completely different sedimentary record. Therefore, inferred climatic record, and differences between sites, can be ascribed to differences in elevation, distance from the shore, water depth, and local catchment features. The extreme level of spatial variability seems to be a feature of Antarctic coastal areas, and demonstrates that results obtained from a specific site cannot be easily generalized to a larger area.

UNC-11, a Caenorhabditis elegans AP180 Homologue, Regulates the Size and Protein Composition of Synaptic Vesicles

The unc-11 gene of Caenorhabditis elegans encodes multiple isoforms of a protein homologous to the mammalian brain-specific clathrin-adaptor protein AP180. The UNC-11 protein is expressed at high levels in the nervous system and at lower levels in other tissues. In neurons, UNC-11 is enriched at presynaptic terminals but is also present in cell bodies. unc-11 mutants are defective in two aspects of synaptic vesicle biogenesis. First, the SNARE protein synaptobrevin is mislocalized, no longer being exclusively localized to synaptic vesicles. The reduction of synaptobrevin at synaptic vesicles is the probable cause of the reduced neurotransmitter release observed in these mutants. Second, unc-11 mutants accumulate large vesicles at synapses. We propose that the UNC-11 protein mediates two functions during synaptic vesicle biogenesis: it recruits synaptobrevin to synaptic vesicle membranes and it regulates the size of the budded vesicle during clathrin coat assembly.

ELPA (European Leaf Physiognomic Approach): Grid data set of the leaf physiognomic composition of the extant European hardwood vegetation

Physiognomic traits of plant leaves such as size, shape or margin are decisively affected by the prevailing environmental conditions of the plant habitat. On the other hand, if a relationship between environment and leaf physiognomy can be shown to exist, vegetation represents a proxy for environmental conditions. This study investigates the relationship between physiognomic traits of leaves from European hardwood vegetation and environmental parameters in order to create a calibration dataset based on high resolution grid cell data. The leaf data are obtained from synthetic chorologic floras, the environmental data comprise climatic and ecologic data. The high resolution of the data allows for a detailed analysis of the spatial dependencies between the investigated parameters. The comparison of environmental parameters and leaf physiognomic characters reveals a clear correlation between temperature related parameters (e.g. mean annual temperature or ground frost frequency) and the expression of leaf characters (e.g. the type of leaf margin or the base of the lamina). Precipitation related parameters (e.g. mean annual precipitation), however, show no correlation with the leaf physiognomic composition of the vegetation. On the basis of these results, transfer functions for several environmental parameters are calculated from the leaf physiognomic composition of the extant vegetation. In a next step, a cluster analysis is applied to the dataset in order to identify "leaf physiognomic communities". Several of these are distinguished, characterised and subsequently used for vegetation classification. Concerning the leaf physiognomic diversity there are precise differences between each of these "leaf physiognomic classes". There is a clear increase of leaf physiognomic diversity with increasing variability of the environmental parameters: Northern vegetation types are characterised by a more or less homogeneous leaf physiognomic composition whereas southern vegetation types like the Mediterranean vegetation show a considerable higher leaf physiognomic diversity. Finally, the transfer functions are used to estimate palaeo-environmental parameters of three fossil European leaf assemblages from Late Oligocene and Middle Miocene. The results are compared with results obtained from other palaeo-environmental reconstructing methods. The estimates based on a direct linear ordination seem to be the most realistic ones, as they are highly consistent with the Coexistence Approach.