Search results for "Separable"
showing 10 items of 91 documents
Measurable selectors and set-valued Pettis integral in non-separable Banach spaces
2009
AbstractKuratowski and Ryll-Nardzewski's theorem about the existence of measurable selectors for multi-functions is one of the keystones for the study of set-valued integration; one of the drawbacks of this result is that separability is always required for the range space. In this paper we study Pettis integrability for multi-functions and we obtain a Kuratowski and Ryll-Nardzewski's type selection theorem without the requirement of separability for the range space. Being more precise, we show that any Pettis integrable multi-function F:Ω→cwk(X) defined in a complete finite measure space (Ω,Σ,μ) with values in the family cwk(X) of all non-empty convex weakly compact subsets of a general (n…
Excited states in the three-body system
1972
Three-body excited states are calculated in a local potential model by means of the quasi-particle method. The improvement over the approach in which the local potential is approximated by a separable one is demonstrated.
Test of a separable approximation to a local soft-core potential in the three-body system
1975
Three-nucleon observables below the break-up threshold are calculated employing the pole approximation to the soft-core Malfliet-Tjon potentials. The results are compared in detail to those obtained with the local potentials and to those calculated with the usual Yamaguchi interactions.
Testing WWγ vertex in radiative muon decay
2019
Large numbers of muons will be produced at facilities developed to probe the lepton-flavor-violating process μ→eγ. We show that by constructing a suitable asymmetry, radiative muon decay μ→eγνμν̄e can also be used to test the WWγ vertex at such facilities. The process has two missing neutrinos in the final state, and upon integrating their momenta the partial differential decay rate shows no radiation-amplitude zero. However, we establish that an easily separable part of the normalized differential decay rate that is odd under the exchange of photon and electron energies does have a zero in the case of the standard model (SM). This new type of zero has hitherto not been studied in the liter…
Motor strategies and adiabatic invariants: The case of rhythmic motion in parabolic flights
2021
The role of gravity in human motor control is at the same time obvious and difficult to isolate. It can be assessed by performing experiments in variable gravity. We propose that adiabatic invariant theory may be used to reveal nearly-conserved quantities in human voluntary rhythmic motion, an individual being seen as a complex time-dependent dynamical system with bounded motion in phase-space. We study an explicit realization of our proposal: An experiment in which we asked participants to perform $\infty-$ shaped motion of their right arm during a parabolic flight, either at self-selected pace or at a metronome's given pace. Gravity varied between $0$ and $1.8$ $g$ during a parabola. We c…
Anisotropy in strain gradient elasticity: Simplified models with different forms of internal length and moduli tensors
2018
Abstract Anisotropy of centro-symmetric (first) strain gradient elastic materials is addressed and the role there played by the dual gradient directions (i.e. directions of strain gradient and of double stress lever arm) is investigated. Anisotropy manifests itself not only through the classical fourth-rank elasticity tensor C (21 independent constants) in the form of moduli anisotropy, but also through a sixth-rank elasticity tensor B (171 independent constants) in a unified non-separable form as compound internal length/moduli anisotropy. Depending on the microstructure properties, compound anisotropy may also manifest itself in a twofold separable form through a decoupled tensor B = L C …
Electric polarizability of nuclei from a longitudinal sum rule
1998
The nuclear electric polarizability is theoretically analyzed using a sum rule derived from the longitudinal part of the forward Compton amplitude. Beyond the leading dipole contribution, this approach leads to the presence of potential-dependent terms that do not show up in previous analyses. The significance of these new contributions is illustrated by performing an explicit calculation for a proton-neutron system interacting via a separable potential.
Couplings in coupled channels versus wave functions in the case of resonances: Application to the twoΛ(1405)states
2011
In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on-shell approach for the scattering matrix, commonly used, is also obtained in quantum mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also pr…
Energy-independent new physics in the flavour ratios of high-energy astrophysical neutrinos
2010
We have studied the consequences of breaking the CPT symmetry in the neutrino sector, using the expected high-energy neutrino flux from distant cosmological sources such as active galaxies. For this purpose we have assumed three different hypotheses for the neutrino production model, characterised by the flavour fluxes at production phi(0)(e) : phi(0)(mu) : phi(0)(tau) = 1 : 2 : 0, 0 : 1 : 0, and 1 : 0 : 0, and studied the theoretical and experimental expectations for the muon-neutrino flux at Earth, phi(mu), and for the flavour ratios at Earth, R = phi(mu)/phi(e) and S = phi(tau)/phi(mu). CPT violation (CPTV) has been implemented by adding an energy-independent term to the standard neutrin…
Low-energy scattering and photoproduction ofηmesons on three-body nuclei
2003
The optical potential approach for low-energy scattering of $\eta$-mesons on three-body nuclei is compared to an exact treatment of the $\eta 3N$ system using four-body scattering theory with separable interactions in s-waves only. The higher-order terms including the interaction of the struck nucleon with the surrounding nuclear medium and virtual target excitations in between successive $\eta$-scatterings are found to cause important corrections. Effects of final state interaction in $\eta$-photoproduction on $^3$H and $^3$He are also studied and sizable contributions beyond the optical model approach are found.