[en] Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ('acceleration equal force'), with linear and cubic forces, in N-dimensional space (N being an arbitrary positive integer, with special attention to N=2, namely, motions in a plane, and N=3, namely, motions in ordinary three-dimensional space). All the equations of motion are written in covariant form ('N-vector equal N-vector'), entailing their rotational invariance. The corresponding Hamiltonians are of normal type, with the kinetic energy quadratic in the canonical momenta, and the potential energy quadratic and quartic in the canonical coordinates

[en] Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely reviewed, and new ones introduced

[en] The π⁺π^-π⁰, K⁺K^-π⁰ and K^±K⁰π^± final states produced by p-bar p annihilation at rest at three different hydrogen target densities have been analyzed in the frame of a coupled channel analysis together with ππ and πK scattering data. Here we present the main results which concern masses, widths, ππ and KK-bar partial widths of all the involved resonances (J^P=0⁺,1^-,2⁺), the direct determination of Γ_KK-bar/Γ_ππ ratio for f₀(1370) and f₀(1500) (Γ_KK-bar/Γ_ππ=0.91±0.20 and Γ_KK-bar/Γ_ππ=0.25±0.03, respectively), the determination of a₀(1300) parameters (M=1303±16 MeV; Γ=92±16 MeV) and the observation of two different high mass ρ signals associated to ρ(1450) and ρ(1700) (M=1182±30 MeV; Γ=389±20 MeV and M=1594±20 MeV; Γ=259±20 MeV, respectively)

[en] The results of the preliminary analysis of event, from a data sample of 24 million anti pp annihilation at rest in a gaseous hydrogen target at NTP, collected with the OBELIX spectrometer at LEAR (CERN), are presented

[en] The anti pp total annihilation cross section has been measured, with the OBELIX apparatus at LEAR, at ten values of the antiproton incident momentum between 43 and 175 MeV/c. Around 50 MeV/c, a preliminary value of the cross section for the K_SK_L channel is obtained too

[en] The results of spin parity analysis on anti n p annihilation in the channels with 3 and 5 charged pions are presented. In the former case the analysis suggests the existence of two resonances with quantum numbers in the latter the presence of a broad resonance

[en] Some algebraic equations satisfied by certain matrices of rank n, constructed with the n zeros of the Hermite polynomial of order n, are given

[en] Extending the results found in a previous work, this paper shows that any member of the class of nonlinear evolution equations with x-dependent coefficients associated to the matrix Schroedinger spectral problem can be recast in a suitably generalized Lax form. The flows defined by this class are no longer isospectral, but nevertheless it is possible to determine the time-evolution of eigenvalues and eigenfunctions of the associated linear operator. (author)

[en] In this letter the explicit form of the inverse of the commutation operator is calculated for matrices of arbitrary dimensions with simple characteristic roots.(AA)

[en] Some nonlinear equations satisfied by the zeros of simple combinations of Jacobi polynomials and their derivatives are reported