Search results for "Polynomials"
showing 10 items of 144 documents
Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations
2020
In this study, an improved matrix method based on collocation points is developed to obtain the approximate solutions of systems of high-order pantograph type delay differential equations with variable coefficients. These kinds of systems described by the existence of linear functional argument play a critical role in defining many different phenomena and particularly, arise in industrial applications and in studies based on biology, economy, electrodynamics, physics and chemistry. The technique we have used reduces the mentioned delay system solution with the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Thereby, the approximate solution is…
Stability analysis of an electromagnetically levitated sphere
2006
We present a combined numerical and analytical approach to analyze the static and dynamic stabilities of an electromagnetically levitated spherical body depending on the ac frequency and the configuration of a three-dimensional (3D) coil made of thin winding which is modeled by linear current filaments. First, we calculate numerically the magnetic vector potential in grid points on the surface of the sphere and then use Legendre and fast Fourier transforms to find the expansion of the magnetic field in terms of spherical harmonics. Second, we employ a previously developed gauge transformation to solve analytically the 3D electromagnetic problem in terms of the numerically obtained expansion…
Experimental study of $\eta$ meson photoproduction reaction at MAMI
2015
New data for the differential cross sections, polarization observables $T$, $F$, and $E$ in the reaction of $\eta$ photoproduction on proton from the threshold up to a center-of-mass energy of W=1.9 GeV are presented. The data were obtained with the Crystal-Ball/TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The polarization measurements were made using a frozen-spin butanol target and circularly polarized photon beam. The results are compared to existing experimental data and different PWA predictions. The data solve a long-standing problem related the angular dependence of older $T$ data close to threshold. The unexpected relative phase motion betwe…
Nonlinear inverse bremsstrahlung and highly anisotropic electron distributions
1996
A procedure is proposed to deal with the approximate solution of the kinetic equation for the velocity distribution function of electrons in a fully ionized plasma in the presence of strong, high frequency radiation. The Legendre polynomial expansion is applied after the kinetic equation has been written in an oscillating frame, where some directions are appropriately scaled, with the aim of making approximately isotropic, on the average, distributions that are otherwise anisotropic. The equations are derived for the isotropic part of the electron distribution in the scaled frame and for the scaling factor. The procedure is meant to display its potential in cases where the electron distribu…
Multipole strength inC12from the (e,e’α) reaction for momentum transfers up to 0.61fm−1
1995
We have excited the giant resonance region in $^{12}\mathrm{C}$ via inelastic electron scattering, and have measured the first complete angular correlations for charged particle emission for this reaction for four values of momentum transfer ranging from 0.24 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ to 0.61 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. By analyzing the \ensuremath{\alpha}-emission channels via the Legendre and resonance formalisms, we unambiguously determined the multipole contributions to the total cross section for \ensuremath{\alpha} emission to the ground state of $^{8}\mathrm{Be}$, and have set limits on these contributions for \ensuremath{\alpha} emission to the first…
Search for theZ(4430)−atBABAR
2009
We report the results of a search for Z(4430)^- decay to J/Ψ π^- or Ψ(2S)π^- in B(^-.0)→ J/Ψ π^-K^(0.+) and B^(-.0) → Ψ(2S)π^-K^(0.+) decays. The data were collected with the BABAR detector at the SLAC PEP-II asymmetric-energy e^+e^- collider operating at center-of-mass energy 10.58 GeV, and the sample corresponds to an integrated luminosity of 413 fb^(-1). Each K π^- mass distribution exhibits clear K^*(892) and K_2^*(1430) signals, and the efficiency-corrected spectrum is well described by a superposition of the associated Breit-Wigner intensity distributions, together with an S-wave contribution obtained from the LASS I=1/2 K π^- scattering amplitude measurements. Each K π^- angular dist…
B meson decay constants f B c $$ {f}_{B_c} $$ , f B s $$ {f}_{B_s} $$ and f B from QCD sum rules
2014
Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant f B c $$ {f}_{B_c} $$ , and revisit f B and f B s $$ {f}_{B_s} $$ . Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are f B c $$ {f}_{B_c} $$ = 528 ± 19 MeV, f B = 186 ± 14 MeV, and f B s $$ {f}_{B_s} $$ = 222 ± 12 MeV.
General formulae for polarization observables in two-body break-up of deuteron photodisintegration
1988
The formal expressions of all possible polarization observables ind(γ,N)N with polarized photons and oriented deuterons are derived in terms of thet-matrix elements. Furthermore, using the multipole expansion of thet-matrix, all observables are expanded in terms of Legendre polynomials or associated functions, the coefficients of which are given as bilinear forms of the multipole moments and allow a model independent analysis of experimental data.
How to perform QCD analysis of DIS in Analytic Perturbation Theory
2015
We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic scattering up to the next leading order and compare the results with ones obtained within the standard perturbation QCD. Based on a popular parameterization of the corresponding parton distribution we perform the analysis within the Jacobi Polynomial formalism and under the control of the numerical inverse Mellin transform. To reveal the main features of the FAPT two-loop approach, we consider a wide range of momentum transfer from high $Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach still works.
Finite Energy Sum Rules with Legendre Polynomial Kernels
2016
Abstract In this note we report about a method to deal with finite energy sum rules. With a reasonable knowledge of the main resonances of the spectrum, the method guarantees that we can find a nice duality matching between the low energy hadronic data and asymptotic QCD at high energies.