49,461 research outputs found
Bounded perturbation resilience of projected scaled gradient methods
We investigate projected scaled gradient (PSG) methods for convex
minimization problems. These methods perform a descent step along a diagonally
scaled gradient direction followed by a feasibility regaining step via
orthogonal projection onto the constraint set. This constitutes a generalized
algorithmic structure that encompasses as special cases the gradient projection
method, the projected Newton method, the projected Landweber-type methods and
the generalized Expectation-Maximization (EM)-type methods. We prove the
convergence of the PSG methods in the presence of bounded perturbations. This
resilience to bounded perturbations is relevant to the ability to apply the
recently developed superiorization methodology to PSG methods, in particular to
the EM algorithm.Comment: Computational Optimization and Applications, accepted for publicatio
Relativistic Harmonic Oscillator
We study the semirelativistic Hamiltonian operator composed of the
relativistic kinetic energy and a static harmonic-oscillator potential in three
spatial dimensions and construct, for bound states with vanishing orbital
angular momentum, its eigenfunctions in compact form, i. e., as power series,
with expansion coefficients determined by an explicitly given recurrence
relation. The corresponding eigenvalues are fixed by the requirement of
normalizability of the solutions.Comment: 14 pages, extended discussion of result
Common Space of Spin and Spacetime
Given Lorentz invariance in Minkowski spacetime, we investigate a common
space of spin and spacetime. To obtain a finite spinor representation of the
non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an
indefinite inner product space (IIPS) with a normalized positive probability.
In this IIPS, the common momentum and common variable of a massive fermion turn
out to be ``doubly strict plus-operators''. Due to this nice property, it is
straightforward to show an uncertainty relation between fermion mass and proper
time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint,
and the fermion field equations are derivable from the Lagrangians. Finally,
the nonlinear QED equations and Lagrangians are presented as an example.Comment: 17 pages, a reference corrected, final version published on
Foundations of Physics Letters in June of 2005, as a personal tribute to
Einstein and Dira
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