Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

On stability of solutions to systems of convex inequalities

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Molecular Epidemiologic Typing Systems of Bacterial Pathogens: Current Issues and Perpectives

The epidemiologic typing of bacterial pathogens can be applied to answer a number of different questions: in case of outbreak, what is the extent and mode of transmission of epidemic clone(s )? In case of long-term surveillance, what is the prevalence over time and the geographic spread of epidemic and endemic clones in the population? A number of molecular typing methods can be used to classify bacteria based on genomic diversity into groups of closely-related isolates (presumed to arise from a common ancestor in the same chain of transmission) and divergent, epidemiologically-unrelated isolates (arising from independent sources of infection). Ribotyping, IS-RFLP fingerprinting, macrorestriction analysis of chromosomal DNA and PCR-fingerprinting using arbitrary sequence or repeat element primers are useful methods for outbreak investigations and regional surveillance. Library typing systems based on multilocus sequence-based analysis and strain-specific probe hybridization schemes are in development for the international surveillance of major pathogens like Mycobacterium tuberculosis. Accurate epidemiological interpretation of data obtained with molecular typing systems still requires additional research on the evolution rate of polymorphic loci in bacterial pathogens.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Hereditary completeness for systems of exponentials and reproducing kernels

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Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Male and female reproductive systems of Stolas conspersa (Germar) (Coleoptera, Chrysomelidae, Cassidinae)

Male and female reproductive systems of Stolas conspersa (Germar) (Coleoptera, Chrysomelidae, Cassidinae). The male and female reproductive systems of Stolas conspersa (Germar, 1824) are described and illustrated for the first time. The male reproductive system shows no difference from the subfamily pattern, which is a tubular well-developed median lobe; "Y", "V" or T-shaped tegmen; reduced pygidium; internal sac membranous and tubular; flagellum generally well developed needle-like structured and gastral spiculum absent. However, the female differs from the pattern proposed for Stolas in two aspects: ovary with 28 ovarioles and a reduced ampulla with indistinct velum.

New insights on the crystalline forms in binary systems of n-alkanes: Characterization of the solid ordered phases in the phase diagram tricosane + pentacosane

X-ray diffraction analyses of the pure components n-tricosane and n-pentacosane and of their binary mixed samples have enabled us to characterize the crystalline phases observed at low temperature. On the contrary to what was announced in literature on the structural behavior of mixed samples in odd-odd binary systems with D n = 2, the three domains are not all orthorhombic. This work has enabled us to show that two of the domains are, in fact, monoclinic, (Aa, Z = 4) and the other one is orthorhombic (Pca21, Z = 4). The conclusions drawn in this work can be easily transposed to other binary systems of n-alkanes.

Soil microbial biomass under different management and tillage systems of permanent intercropped cover species in an orange orchard

To mitigate soil erosion and enhance soil fertility in orange plantations, the permanent protection of the inter-rows by cover species has been suggested. The objective of this study was to evaluate alterations in the microbial biomass, due to different soil tillage systems and intercropped cover species between rows of orange trees. The soil of the experimental area previously used as pasture (Brachiaria humidicola) was an Ultisol (Typic Paleudult) originating from Caiuá sandstone in the northwestern part of the State of Paraná, Brazil. Two soil tillage systems were evaluated: conventional tillage (CT) in the entire area and strip tillage (ST) (strip width 2 m), in combination with different ground cover management systems. The citrus cultivar 'Pera' orange (Citrus sinensis) grafted onto 'Rangpur' lime rootstock was used. Soil samples were collected after five years of treatment from a depth of 0-15 cm, under the tree canopy and in the inter-row, in the following treatments: (1) CT and an annual cover crop with the leguminous species Calopogonium mucunoides; (2) CT and a perennial cover crop with the leguminous peanut Arachis pintoi; (3) CT and an evergreen cover crop with Bahiagrass Paspalum notatum; (4) CT and a cover crop with spontaneous Brachiaria humidicola grass vegetation; and (5) ST and maintenance of the remaining grass (pasture) of Brachiaria humidicola. Soil tillage and the different cover species influenced the microbial biomass, both under the tree canopy and in the inter-row. The cultivation of brachiaria increased C and N in the microbial biomass, while bahiagrass increased P in the microbial biomass. The soil microbial biomass was enriched in N and P by the presence of ground cover species and according to the soil P content. The grass species increased C, N and P in the soil microbial biomass from the inter-row more than leguminous species.

Decay of unstable states in the presence of colored noise and random initial conditions. I. Theory of nonlinear relaxation times

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

Parametric Approach to Blind Deconvolution of Nonlinear Channels

A parametric procedure for the blind inversion of nonlinear channels is proposed, based on a recent method of blind source separation in nonlinear mixtures. Experiments show that the proposed algorithms perform efficiently, even in the presence of hard distortion. The method, based on the minimization of the output mutual information, needs the knowledge of log-derivative of input distribution (the so-called score function). Each algorithm consists of three adaptive blocks: one devoted to adaptive estimation of the score function, and two other blocks estimating the inverses of the linear and nonlinear parts of the channel, (quasi-)optimally adapted using the estimated score functions. This paper is mainly concerned by the nonlinear part, for which we propose two parametric models, the first based on a polynomial model and the second on a neural network, while [14, 15] proposed non-parametric approaches.