Search results for "Separable space"
showing 10 items of 67 documents
Six Matrix Adjustment Problems Solved by Some Fundamental Theorems on Biproportion
2011
After defining biproportion (or RAS) rigorously, we recall two fundamental theorems: unicity of biproportion (any biproportional algorithm leads to the same solution than biproportion, which turns biproportion into a mathematical tool as indisputable than proportion), ineffectiveness of separability (premultiplying or post multiplying the initial matrix by a diagonal matrix does not change the biproportional solution) and its corollary (it is equivalent to do a separable modification of the initial matrix or to do a proportional change of each biproportional factors). We then apply these theorems to show immediately that: i) no difficulties are encountered when solving the biproportional pr…
Structure of transactinide nuclei with relativistic energy density functionals
2013
A microscopic theoretical framework based on relativistic energy density functionals (REDFs) is applied to studies of shape evolution, excitation spectra, and decay properties of transactinide nuclei. Axially symmetric and triaxial relativistic Hartree-Bogoliubov (RHB) calculations, based on the functional DD-PC1 and with a separable pairing interaction, are performed for the even-even isotopic chains between Fm and Fl. The occurrence of a deformed shell gap at neutron number $N=162$ and its role on the stability of nuclei in the region around $Z=108$ is investigated. A quadrupole collective Hamiltonian, with parameters determined by self-consistent constrained triaxial RHB calculations, is…
Solution of universal nonrelativistic nuclear DFT equations in the Cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h) : a new version …
2021
We describe the new version (v3.06h) of the code HFODD that solves the universal nonrelativistic nuclear DFT Hartree-Fock or Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we implemented the following new features: (i) zero-range three- and four-body central terms, (ii) zero-range three-body gradient terms, (iii) zero-range tensor terms, (iv) zero-range isospin-breaking terms, (v) finite-range higher-order regularized terms, (vi) finite-range separable terms, (vii) zero-range two-body pairing terms, (viii) multi-quasiparticle blocking, (ix) Pfaffian overlaps, (x) particle-number and parity symmetry restoration, (xi) axializatio…
Relations among Henstock, McShane and Pettis integrals for multifunctions with compact convex values
2013
Fremlin (Ill J Math 38:471–479, 1994) proved that a Banach space valued function is McShane integrable if and only if it is Henstock and Pettis integrable. In this paper we prove that the result remains valid also in case of multifunctions with compact convex values being subsets of an arbitrary Banach space (see Theorem 3.4). Di Piazza and Musial (Monatsh Math 148:119–126, 2006) proved that if \(X\) is a separable Banach space, then each Henstock integrable multifunction which takes as its values convex compact subsets of \(X\) is a sum of a McShane integrable multifunction and a Henstock integrable function. Here we show that such a decomposition is true also in case of an arbitrary Banac…
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 …