Equidistribution of negative statistics and quotients of Coxeter groups of type B and D

We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Schützenberger, Gessel, and Roselle on various distributions of statistics, like inversion number, major index, and descent number. In order to show our results we provide explicit characterizations of the systems of minimal coset representatives of Coxeter groups of type B and D.     

Gas-chromatography–mass spectrometry analysis of dimethyl fumarate in consumer products

Two methods for the analysis of dimethyl fumarate (DMF) on silica gel, leather and other similar products are presented. The methods are based on solvent extraction or head space solid phase microextraction coupled with gas-chromatography–mass spectrometry. The methods are developed in order to satisfy the mandatory requirements of the European Community and with the aim to have easy and reliable methods to provide rapid responses.     

A heterodyne interferometric polarimeter for the detection of jones and stokes polarization vectors

A heterodyne interferometric polarimeter for detection of the Jones components and Stokes parameters is demonstrated. The measurement of both sets of quantities for various polarization states is achieved with excellent precision. The details of the corresponding Lissajous picture (ellipse) can be visualized in real time. Finally, the polarization data collected at the output of a highly birefringent fiber have been used for submillimetric beat-Length measurements.     

Supersolvable LL-lattices of binary trees

Some posets of binary leaf-labeled trees are shown to be supersolvable lattices and explicit EL-labelings are given. Their characteristic polynomials are computed, recovering their known factorization in a different way.     

Assessment of Cardiorespiratory Interactions during Apneic Events in Sleep via Fuzzy Kernel Measures of Information Dynamics

Apnea and other breathing-related disorders have been linked to the development of hypertension or impairments of the cardiovascular, cognitive or metabolic systems. The combined assessment of multiple physiological signals acquired during sleep is of fundamental importance for providing additional insights about breathing disorder events and the associated impairments. In this work, we apply information-theoretic measures to describe the joint dynamics of cardiorespiratory physiological processes in a large group of patients reporting repeated episodes of hypopneas, apneas (central, obstructive, mixed) and respiratory effort related arousals (RERAs). We analyze the heart period as the target process and the airflow amplitude as the driver, computing the predictive information, the information storage, the information transfer, the internal information and the cross information, using a fuzzy kernel entropy estimator. The analyses were performed comparing the information measures among segments during, immediately before and after the respiratory event and with control segments. Results highlight a general tendency to decrease of predictive information and information storage of heart period, as well as of cross information and information transfer from respiration to heart period, during the breathing disordered events. The information-theoretic measures also vary according to the breathing disorder, and significant changes of information transfer can be detected during RERAs, suggesting that the latter could represent a risk factor for developing cardiovascular diseases. These findings reflect the impact of different sleep breathing disorders on respiratory sinus arrhythmia, suggesting overall higher complexity of the cardiac dynamics and weaker cardiorespiratory interactions which may have physiological and clinical relevance.     

A moving boundary hyperbolic problem for a stress impact in a bar of rate-type material

In this paper we present some results obtained by studying the mathematical model describing a moving boundary hyperbolic problem related to a time dependent stress impact in a bar of Maxwell-like material. Due to the impact a shock front propagates with a finite speed. Here our interest is to underline the influence of the dissipative term on the propagation of the shock front.

In the framework of the similarity analysis we are able to reduce the moving boundary hyperbolic problem to a free boundary value problem for an ordinary differential system. It is then possible, by applying two numerical transformation methods, to solve the free boundary value problem numerically. The influence of the dissipative term is evident: the free boundary (that defines the shock front propagation) is an increasing function of the dissipative coefficient.     

Solid-state (15)N CPMAS NMR and computational analysis of ligand hapticity in rhodium(η-diene) poly(pyrazolyl)borate complexes

Novel [Rh(η-diene)Tp(x)] complexes of sterically encumbered Tp(x) ligands (Tp(x) = Tp(4Bo), diene = cod, 1; nbd, 2; Tp(x) = Tp(4Bo,5Me), diene = cod, 3; nbd, 4; Tp(x) = Tp(a,3Me), diene = cod, 5; nbd, 6; Tp(x) = Tp(a*,3Me), diene = cod, 7; nbd, 8) have been prepared by treatment of [Rh(η-diene)(μ-Cl)](2) with TlTp(x) (Tp(x) in general, in detail: Tp(4Bo) = hydrotris(indazol-1-yl)borate, Tp(4Bo,5Me) = hydrotris(5-methyl-indazol-1-yl)borate, Tp(a,3Me) = hydrotris(3-methyl-2H-benz[g]-4,5-dihydroindazol-2-y1)borate, Tp(a*,3Me) = hydrotris(3-methyl-2H-benz[g]indazol-2-yl)borate), and characterized by analytical and spectral data (IR, (1)H, (11)B, and (13)C NMR solution). The structures adopted by [Rh(nbd)Tp(4Bo)] 2, [Rh(cod)Tp(4Bo,5Me)] 3, [Rh(nbd)Tp(a,3Me)] 6, [Rh(nbd)Tp(a*,3Me)] 8, and [Rh(nbd)Tp(a*,3Me*)] 8* (incorporating a borotropomeric ligand), have been investigated. Low steric hindrance between the ligands in 2 and 3 permits κ(3) coordination of the pyrazolylborate while the high steric encumbrance present in 6, 8, and 8* results in κ(2) ligands. The coordination modes of the ligands to the metal have also been established by (15)N CPMAS studies of selected ligands and their corresponding Rh complexes. These spectroscopic data are in agreement with the (15)N chemical shifts obtained by using quantum-chemical methods to assist reliable assignments of the experimental values, affording new insights into the extraction of structural information concerning the hapticity (κ(2) or κ(3)) of the poly(pyrazolyl)borate ligands to the Rh metal.     

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.     

Pseudo-Goldstino in field theory

We consider two SUSY-breaking hidden sectors which decouple when their respective couplings to the visible particles are switched off. In such a scenario one expects to find two light fermions: the Goldstino and the pseudo-Goldstino. While the former remains massless in the rigid limit, the latter becomes massive due to radiative effects which we analyze from several different points of view. This analysis is greatly facilitated by a version of the Goldberger-Treiman relation, which allows us to write a universal nonperturbative formula for the mass. We carry out the analysis in detail in the context of gauge mediation, where we find that the pseudo-Goldstino mass is at least around the GeV scale and can be easily at the electroweak range, even in low scale models. This leads to interesting and unconventional possibilities in collider physics and it also has potential applications in cosmology.     

Numerical analysis of space charge effects in electron bunches at laser-driven plasma accelerators

Laser-driven Plasma Accelerators (LPA) have successfully generated high energy, high charge electron bunches which can reach many kA peak current, over short distances. Space charge issues, even in transport lines as simple as a drift section, have to be carefully taken into account since they can degrade the beam quality, preventing any further application of such electron beams. We analyse the space charge effects within an electron bunch with numerical simulations in order to assess their effect on the beam. We use LPA beam parameters published in previous experimental studies. These studies can give an indication of the working point where space charge can dominate the beam dynamics and has to be taken into account in the application of such beams.