The Brockett-Wegner diagonalizing flow Ḣt = [ Ht, [Ht, A] ] is studied. Global existence and uniqueness of solutions of this evolution equation is proved on the space B[H ] of bounded operators on a complex Hilbert space H . Local existence is proved for certain unbounded initial operators H0. Furthermore, if H0, A are Hilbert-Schmidt operators, it is demonstrated that Ht strongly converges to ...

Abstract In 1990, Romero presented a beautiful formula for the projection onto set of rectangular matrices with prescribed row and column sums. Variants Romero’s were rediscovered by Khoury Glunt, Hayden, Reams bistochastic (square) in 1998. These results have found various generalizations applications. this paper, we provide more general problem finding scaled Our approach is based on computin...

We investigate machine learning for the least square regression with data dependent hypothesis and coefficient regularization algorithms based on general kernels. We provide some estimates for the learning raters of both regression and classification when the hypothesis spaces are sample dependent. Under a weak condition on the kernels we derive learning error by estimating the rate of some K-f...

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding results mixtures polyatomic where polyatomicity modeled by discrete internal energy variable, are more recently obtained. In this work compactnes...

Regularity estimates for an integral operator with a symmetric continuous kernel on convex bounded domain are derived. The covariance of mean-square random field the is example such operator. form Hilbert--Schmidt norms and its square root, composed fractional powers elliptic equipped homogeneous boundary conditions either Dirichlet or Neumann type. These types estimates, which couple regularit...

Inspired by the computable cross norm, or realignment criterion, we present a new point of view about the characterization of the states of bipartite quantum systems. We consider the Schmidt decomposition of a bipartite density operator with respect of the HilbertSchmidt product. The corresponding Schmidt coefficients, or the associated symmetric polynomials, are discussed as functions that can...

This paper presents three results in singular value analysis of Hankel operators for nonlinear input–output systems. First, the notion of a Schmidt pair is defined for a nonlinear Hankel operator. This makes it possible to define a Hankel singular value function from a purely input–output point of view and without introducing a state space setting. However, if a state space realization is known...

In a study of articles published in the Proceedings of the National Academy of Sciences, Gunther Eysenbach discovered a significant citation advantage for those articles made freely-available upon publication (Eysenbach 2006). While the author attempted to control for confounding factors that may have explained the citation differential, the study was unable to control for characteristics of th...

The spectral problem (A+V (z))ψ = zψ is considered with A, a self-adjoint Hamiltonian of sufficiently arbitrary nature. The perturbation V (z) is assumed to depend on the energy z as resolvent of another self-adjoint operator A ′ : V (z) = −B(A ′ −z) −1 B *. It is supposed that operator B has a finite Hilbert-Schmidt norm and spectra of operators A and A ′ are separated. The conditions are form...

Motivated by physical and numerical observations of time oscillatory “galloping”, “spinning”, and “cellular” instabilities of detonation waves, we study Poincaré–Hopf bifurcation of traveling-wave solutions of viscous conservation laws. The main difficulty is the absence of a spectral gap between oscillatory modes and essential spectrum, preventing standard reduction to a finite-dimensional cen...