Search results for "moment"
showing 10 items of 3027 documents
Application of the star-product method to the angular momentum quantization
1992
We define a *-product on ℝ3 and solve the polarization equation f*C=0 where C is the Casimir of the coadjoint representation of SO(3). We compute the action of SO(3) on the space of solutions. We then examine the case of non-zero eigenvalues of C, in order to find finite-dimensional representations of SO(3). Finally, we compute \(\sqrt C *\sqrt C \) as an asymptotic series of C. This gives an explanation of the use of the star square root of C in a paper by Bayen et al. instead of its natural square root.
Causality and the Coulomb sum rule in nuclei.
1989
The spectral function in the Jost-Lehmann-Dyson representation of causal commutators is determined for the nonrelativistic limit of inclusive lepton scattering from nuclei. From this an extrapolation of the Coulomb sum rule to higher-momentum transfers is performed which is consistent with the requirement of causality.
Theoretical study on travelling web dynamics and instability under non-homogeneous tension
2013
Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibration…
Validity and reliability of Veloflex to measure active cervical range of motion in asymptomatic and symptomatic subjects
2021
Background Neck pain has a high annual incidence and decreases the cervical active range of motion (ROM). Clinicians use various methods to evaluate cervical range of motion (CROM) that some of them have also been proposed to give instant feedback. Accordingly, this study aimed to examine the validity and reliability of Veloflex (VF) to measure the CROM by comparison with the cervical range of motion (CROM) device, and to examine their test-retest reliability. Methods Thirty-eight healthy and 20 symptomatic participants were evaluated. Cervical flexion-extension, side bending, and rotations were tested in two sessions, first by the CROM and VF and in the second only with the VF. To evaluat…
Is there an absolutely continuous random variable with equal probability density and cumulative distribution functions in its support? Is it unique? …
2014
This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal.
On the use of fractional calculus for the probabilistic characterization of random variables
2009
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
Production of Λ and KS0 in jets in p–Pb collisions at √sNN = 5.02 TeV and pp collisions at √s = 7 TeV
2022
The production of Λ baryons and KS0 mesons (V0 particles) was measured in p–Pb collisions at √sNN=5.02 TeV and pp collisions at √s=7 TeV with ALICE at the LHC. The production of these strange particles is studied separately for particles associated with hard scatterings and the underlying event to shed light on the baryon-to-meson ratio enhancement observed at intermediate transverse momentum (pT) in high multiplicity pp and p–Pb collisions. Hard scatterings are selected on an event-by-event basis with jets reconstructed with the anti-kT algorithm using charged particles. The production of strange particles associated with jets pT,jetch>10 and pT,jetch>20 GeV/c in p–Pb collisions, and with …
The chemical bonds in CuH, Cu2, NiH, and Ni2 studied with multiconfigurational second order perturbation theory
1994
The performance of multiconfigurational second order perturbation theory has been analyzed for the description of the bonding in CuH, Cu2, NiH, and Ni2. Large basis sets based on atomic natural orbitals (ANOS) were employed. The effects of enlarging the active space and including the core‐valence correlation contributions have also been analyzed. Spectroscopic constants have been computed for the corresponding ground state. The Ni2 molecule has been found to have a 0+g ground state with a computed dissociation energy of 2.10 eV, exp. 2.09 eV, and a bond distance of 2.23 Å. The dipole moments of NiH and CuH are computed to be 2.34 (exp. 2.4±0.1) and 2.66 D, respectively. pou@uv.es ; merchan@…
Coupled-cluster theory for atoms and molecules in strong magnetic fields
2015
An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the depende…