Solid-state structure of copper complexes of N-(2-carboxyethyl)chitosan

The sorptivity for ions of the Irving-Williams series (Zn2+, Cu2+, Co2+, Ni2+) was estimated for the chelate sorbent N-(2-carboxyethyl)chitosan cross-linked by nanosecond electron-beam irradiation. The maximum capacity reaches 3.7 mmol/g using a mixture of the appropriate sulfates at pH 4.5. The selectivity of copper sorption is 80%. The structure of the coordination sphere of the copper complexes with N-(2-carboxyethyl)chitosan was investigated by ESR spectroscopy

Amenable actions, free products and a fixed point property

We investigate the class of groups admitting an action on a set with an invariant mean. It turns out that many free products admit such an action. We give a complete characterisation of such free products in terms of a strong fixed point property.Comment: 12 page

On Alternative Supermatrix Reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated on a par. They can be unified into some kind of "sandwich" semigroups. Also we define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Comment: 22 pages, Standard LaTeX with AmS font

A sofic group away from amenable groups

We give an example of a sofic group, which is not a limit of amenable groups.Comment: 6 pages, 0 figur

Noise auto-correlation spectroscopy with coherent Raman scattering

Ultrafast lasers have become one of the most powerful tools in coherent nonlinear optical spectroscopy. Short pulses enable direct observation of fast molecular dynamics, whereas broad spectral bandwidth offers ways of controlling nonlinear optical processes by means of quantum interferences. Special care is usually taken to preserve the coherence of laser pulses as it determines the accuracy of a spectroscopic measurement. Here we present a new approach to coherent Raman spectroscopy based on deliberately introduced noise, which increases the spectral resolution, robustness and efficiency. We probe laser induced molecular vibrations using a broadband laser pulse with intentionally randomized amplitude and phase. The vibrational resonances result in and are identified through the appearance of intensity correlations in the noisy spectrum of coherently scattered photons. Spectral resolution is neither limited by the pulse bandwidth, nor sensitive to the quality of the temporal and spectral profile of the pulses. This is particularly attractive for the applications in microscopy, biological imaging and remote sensing, where dispersion and scattering properties of the medium often undermine the applicability of ultrafast lasers. The proposed method combines the efficiency and resolution of a coherent process with the robustness of incoherent light. As we demonstrate here, it can be implemented by simply destroying the coherence of a laser pulse, and without any elaborate temporal scanning or spectral shaping commonly required by the frequency-resolved spectroscopic methods with ultrashort pulses.Comment: To appear in Nature Physic

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV

Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7 $< p_{\rm{T}, assoc} < p_{\rm{T}, trig} <$ 5.0 GeV/$c$ is examined, to include correlations induced by jets originating from low momen\-tum-transfer scatterings (minijets). The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta|<0.9$. The near-side long-range pseudorapidity correlations observed in high-multiplicity p-Pb collisions are subtracted from both near-side short-range and away-side correlations in order to remove the non-jet-like components. The yields in the jet-like peaks are found to be invariant with event multiplicity with the exception of events with low multiplicity. This invariance is consistent with the particles being produced via the incoherent fragmentation of multiple parton--parton scatterings, while the yield related to the previously observed ridge structures is not jet-related. The number of uncorrelated sources of particle production is found to increase linearly with multiplicity, suggesting no saturation of the number of multi-parton interactions even in the highest multiplicity p-Pb collisions. Further, the number scales in the intermediate multiplicity region with the number of binary nucleon-nucleon collisions estimated with a Glauber Monte-Carlo simulation.Comment: 23 pages, 6 captioned figures, 1 table, authors from page 17, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/161

Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.Comment: 25 pages, 11 captioned figures, 3 tables, authors from page 20, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/87