We investigate the universal nonequilibrium dynamics of superradiant phase transition in anisotropic quantum Rabi model. By introducing position and momentum operators, we find generators displaced operators to diagonalize Hamiltonian, then obtain ground states their excitation gaps. According Kibble-Zurek mechanism, that gap near critical point vanishes as $\ensuremath{\omega}\ensuremath{\sim}...

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...

The problem of finding a minimizer of the sum of two convex functions — or, more generally, that of finding a zero of the sum of two maximally monotone operators — is of central importance in variational analysis. Perhaps the most popular method of solving this problem is the Douglas–Rachford splitting method. Surprisingly, little is known about the range of the Douglas–Rachford operator. In th...

PURPOSE To establish a practical method that uses concurrent b0 images to standardize the display conditions for diffusion-weighted images (DWI) that vary among institutions and interpreters. METHOD Using identical parameters, we obtained DWI for 12 healthy volunteers at 4 institutions using 4 MRI scanners from 3 vendors. Three operators manually set the window width for the images equal to t...

Abstract DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite-dimensional Banach spaces. We analyze and prove estimates on the resulting approximation generalization errors. In particular, we extend universal property of to include measurable mappings in non-compact By decomposition error into encoding, reconstruction errors, both lower ...

We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. We next show that this result is best possible by including a result of N.J. Kalton: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two...

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

We consider estimating a random vector from its measurements in a fusion frame, in presence of noise and subspace erasures. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first consider the linear minimum mean-squared error (LMMSE) estimation of the random...