On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

The meson Z(+) (4430) as a tetraquark state

We test the validity of the QCD sum rules applied to the meson Z(+)(4430). by considering a diquark-antidiquark type of current with J(P) = 0(-) and with J(P) = 1(-). We find that, with the studied currents, it is possible to find an acceptable Borel window. In such a Borel window we have simultaneously a good OPE convergence and a pole contribution which is bigger than the continuum contribution. We get m(z) = (4.52 +/- 0.09) GeV and m(Z) = (4.84 +/- 0.14) GeV for the currents with J(P) = 0(-) and J(P) = 1(-), respectively. We conclude that the QCD sum rules results favors J(P) = 0(-) quantum numbers for the Z(+) (4430) meson. (C) 2008 Elsevier B.V. All rights reserved.

QCD sum rules study of the meson Z(+)(4430)

We use QCD sum rules to study the recently observed meson Z(+)(4430), considered as a D*D-1 molecule with J(P) = 0(-). We consider the contributions of condensates up to dimension eight and work at leading order in alpha(s). We get m(Z) = (4.40 +/- 0.10) GeV in a very good agreement with the experimental value. We also make predictions for the analogous mesons Z(s) and Z(bb) considered as D-s*D-1 and B*B-1 molecules, respectively. For Z(s) we predict mZ(s) = (4.70 +/- 0.06) GeV, which is above the D-s* D-1 threshold, indicating that it is probably a very broad state and, therefore, difficult to observe experimentally. For Z(bb) we predict m(Zbb) = (10.74 +/- 0.12) GeV, in agreement with quark model predictions. (c) 2008 Elsevier B.V. All rights reserved.

Quantum States Allowing Minimum Uncertainty Product of phi and L(z)

We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle phi and its canonical moment L(z). We illustrate our results with analytical examples.

Dilepton mass spectra in p plus p collisions at root s=200 GeV

PHENIX has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c(2) in p + p collisions at root s = 200 GeV. The contributions from light meson decays to e(+)e(-) pairs have been determined based on measurements of hadron production cross sections by PHENIX. Within the systematic uncertainty of similar to 20% they account for all e(+)e(-) pairs in the mass region below similar to 1 GeV/c(2). The e(+)e(-) pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 +/- 39(stat) +/- 142(syst) +/- 200(model) pb. which is consistent with QCD calculations and measurements of single leptons by PHENIX. (C) 2008 Elsevier BV. All rights reserved.

Indirect study of (11)B(p,alpha(0))(8)Be and (10)B(p,alpha)(7)Be reactions at astrophysical energies by means of the Trojan Horse Method: recent results

Nuclear (p,alpha) reactions destroying the so-called ""light-elements"" lithium, beryllium and boron have been largely studied in the past mainly because their role in understanding some astrophysical phenomena, i.e. mixing-phenomena occurring in young F-G stars [1]. Such mechanisms transport the surface material down to the region close to the nuclear destruction zone, where typical temperatures of the order of similar to 10(6) K are reached. The corresponding Gamow energy E(0)=1.22 (Z(x)(2)Z(X)(2)T(6)(2))(1/3) [2] is about similar to 10 keV if one considers the ""boron-case"" and replaces in the previous formula Z(x) = 1, Z(X) = 5 and T(6) = 5. Direct measurements of the two (11)B(p,alpha(0))(8)Be and (10)B(p,alpha)(7)Be reactions in correspondence of this energy region are difficult to perform mainly because the combined effects of Coulomb barrier penetrability and electron screening [3]. The indirect method of the Trojan Horse (THM) [4-6] allows one to extract the two-body reaction cross section of interest for astrophysics without the extrapolation-procedures. Due to the THM formalism, the extracted indirect data have to be normalized to the available direct ones at higher energies thus implying that the method is a complementary tool in solving some still open questions for both nuclear and astrophysical issues [7-12].

Indirect Study of the (2)H(d,p)(3)H and (2)H(d,n)(3)He Reactions at Astrophysical Energies via the Trojan Horse Method

The (2)H(d,p)(3)H and (2)H(d,n)(3)He reactions have been indirectly studied by means of the Trojan Horse Method applied to the quasi-free (2)H((3)He, p(3)H)(1)H (2)H((3)He, n(3)He)(1)H reaction at 18 MeV of beam energy. This is the first experiment where the spectator (here (1)H) has been detected in coincidence with the charged participant, avoiding the limitations of standard neutron detectors. The d - d relative energy has been measured from 1.5 MeV down to 2 keV, at center of mass angles from 40A degrees to 170A degrees. Indirect angular distributions are compared with the direct behaviour in the overlapping regions.

A further exploration of a nucleophilicity index based on the gas-phase ionization potentials

An empirical nucleophilicity index based on the gas-phase ionization potentials has been recently shown to be useful categorizing and settling the nucleophilicity power of a series of captodative ethylenes reacting in cycloaddition reactions (L.R. Domingo, E. Chamorro, P. Perez, Journal of Organic Chemistry 73 (2008) 4615-4624). In the present work, the applicability of such model is tested within a broader series of substituted alkenes, substituted aromatic compounds and simple nucleophilic molecules. This index obtained within a Koopman`s theorem framework has been evaluated here in both gas and solution phases for several well-known nucleophiles. These results are found to be linearly correlated. Finally, the feasibility of the predictive character of this index has been discussed in comparison to the available experimental nucleophilicities of some amines in water. These results further support and validate the usefulness of such approximation in the modeling of the global nucleophilicity. (C) 2008 Elsevier B.V. All rights reserved.

Multiple Pathways Analysis of Brain Functional Networks from EEG Signals: An Application to Real Data

In the present study, we propose a theoretical graph procedure to investigate multiple pathways in brain functional networks. By taking into account all the possible paths consisting of h links between the nodes pairs of the network, we measured the global network redundancy R (h) as the number of parallel paths and the global network permeability P (h) as the probability to get connected. We used this procedure to investigate the structural and dynamical changes in the cortical networks estimated from a dataset of high-resolution EEG signals in a group of spinal cord injured (SCI) patients during the attempt of foot movement. In the light of a statistical contrast with a healthy population, the permeability index P (h) of the SCI networks increased significantly (P < 0.01) in the Theta frequency band (3-6 Hz) for distances h ranging from 2 to 4. On the contrary, no significant differences were found between the two populations for the redundancy index R (h) . The most significant changes in the brain functional network of SCI patients occurred mainly in the lower spectral contents. These changes were related to an improved propagation of communication between the closest cortical areas rather than to a different level of redundancy. This evidence strengthens the hypothesis of the need for a higher functional interaction among the closest ROIs as a mechanism to compensate the lack of feedback from the peripheral nerves to the sensomotor areas.

Third-order nonlinearity of Er(3+)-doped lead phosphate glass

The third-order optical susceptibility and dispersion of the linear refractive index of Er(3+)-doped lead phosphate glass were measured in the wavelength range between 400 and 1940 nm by using the spectrally resolved femtosecond Maker fringes technique. The nonlinear refractive index obtained from the third-order susceptibility was found to be five times higher than that of silica, indicating that Er(3+)-doped lead phosphate glass is a potential candidate to be used as the base component for the fabrication of photonic devices. For comparison purposes, the Z-scan technique was also employed to obtain the values of the nonlinear refractive index of Er(3+)-doped lead phosphate glass at several wavelengths, and the values obtained using the two techniques agree to within 15%.

Pseudo-nonlinear and athermal lensing effects on transverse properties of Cr(3+) based solid-state lasers

Several experiments (time-resolved Z-scan experiments based on pulsed and CW pump lasers, time-resolved divergence diagnostics) have been performed to examine and clarify the question of the converging or diverging population lensing effect occurring in a Cr(3+):Al(2)O(3) ruby laser. The dynamics of the laser far-field divergence of such a laser indeed indicated initially a diverging effect while Z-scan measurements conclude to a converging one. The origin of this discrepancy is thus analysed and elucidated here by introducing the general concept of correlation collapse between the centre and the wings of a laser beam having some clipping. (C) 2010 Elsevier B.V. All rights reserved.

Measurement of the energy spectrum of cosmic rays above 10(18) eV using the Pierre Auger Observatory

We report a measurement of the flux of cosmic rays with unprecedented precision and Statistics using the Pierre Auger Observatory Based on fluorescence observations in coincidence with at least one Surface detector we derive a spectrum for energies above 10(18) eV We also update the previously published energy spectrum obtained with the surface detector array The two spectra are combined addressing the systematic uncertainties and, in particular. the influence of the energy resolution on the spectral shape The spectrum can be described by a broken power law E(-gamma) with index gamma = 3 3 below the ankle which is measured at log(10)(E(ankle)/eV) = 18 6 Above the ankle the spectrum is described by a power law with index 2 6 followed by a flux suppression, above about log(10)(E/eV) = 19 5, detected with high statistical significance (C) 2010 Elsevier B V All rights reserved

Crystal structure of the (Mg,Fe)[UO2(P,As)O-4](2) center dot 10H(2)O solid solution - A novel mineral variety of saleeite

The crystal structure of a novel variety {[(Mg0.81Fe0.19)(H2O)(6)](H2O)(4)}{(UO2)[(P0.67As0.33)O-4]}(2) of the mineral saleeite is determined using X-ray diffraction (Bruker Smart diffractometer, lambda MoK alpha, graphite monochromator, 2 theta(max) = 56.62 degrees, R = 0.0321 for 2317 reflections, T = 100 K). The main crystal data are as follows: a = 6.952(6) angstrom, b = 19.865(5) , angstrom, c = 6.969(2) angstrom, beta = 90.806(4)degrees, space group P12(l)/n1, Z = 2, and P-calcd = 3.34 g/cm(3). It is shown that the structure is formed by alternating (along the [010] direction) anionic layers, which are composed of uranium bipyramids and T(P,As) tetrahedra, and cation layers consisting of M(Mg, Fe) octahedra and water molecules, which are joined through a system of asymmetric hydrogen bonds. The hydrogen atoms are located, the scheme of hydrogen bonds is established, and their geometric characteristics are calculated.

Random walks systems with killing on Z

We study random walks systems on Z whose general description follows. At time zero, there is a number N >= 1 of particles at each vertex of N, all being inactive, except for those placed at the vertex one. Each active particle performs a simple random walk on Z and, up to the time it dies, it activates all inactive particles that it meets along its way. An active particle dies at the instant it reaches a certain fixed total of jumps (L >= 1) without activating any particle, so that its lifetime depends strongly on the past of the process. We investigate how the probability of survival of the process depends on L and on the jumping probabilities of the active particles.