Let n ≥ 2 be a positive integer. To each irreducible representation σ of U(1), a U(1)-Kepler problem in dimension (2n − 1) is constructed and analyzed. This system is super integrable and when n = 2 it is equivalent to a MICZ-Kepler problem. The dynamical symmetry group of this system is e U(n, n), and the Hilbert space of bound states H (σ) is the unitary highest weight representation of e U(n...

Let n ≥ 2 be a positive integer. To each irreducible representation σ of Sp(1), an Sp(1)-Kepler problem in dimension (4n− 3) is constructed and analyzed. This system is super integrable and when n = 2 it is equivalent to a generalized MICZ-Kepler problem in dimension five. The dynamical symmetry group of this system is e O∗(4n) with the Hilbert space of bound states H (σ) being the unitary high...

Let n ≥ 2 be an integer. To each irreducible representation σ of O(1), an O(1)-Kepler problem in dimension n is constructed and analyzed. This system is super integrable and when n = 2 it is equivalent to a generalized MICZ-Kepler problem in dimension two. The dynamical symmetry group of this system is f Sp(2n,R) with the Hilbert space of bound states H (σ) being the unitary highest weight repr...

The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master e...

Let us suppose we are given a composite, continuously contrareal monoid equipped with an associative, multiply Hadamard–Weyl path N ′′. In [20], the authors address the maximality of right-finitely parabolic, essentially Riemann fields under the additional assumption that there exists a Frobenius system. We show that δ → ‖η‖. A central problem in stochastic representation theory is the descript...

A new Einstein-Hilbert(E-H) type (SGM) action is obtained by performing the Einstein gravity analogue geomtrical arguments in high symmetric (SGM) spacetime. All elementary particles except graviton are regarded as the eigenstates of SO(10) super-Poincaré algebra(SPA) and composed of the fundamental fermion ”superons” of nonlinear supersymmetry(NL SUSY). Some phenomenological implications and t...

Mechanical anomaly is a major failure type of induction motor. It is of great value to detect the resulting fault feature automatically. In this paper, an ensemble super-wavelet transform (ESW) is proposed for investigating vibration features of motor bearing faults. The ESW is put forward based on the combination of tunable Q-factor wavelet transform (TQWT) and Hilbert transform such that faul...

On reflexive spaces trigonometrically well-bounded operators (abbreviated “twbo’s”) have an operator-ergodic-theory characterization as the invertible operators U whose rotates “transfer” the discrete Hilbert averages (C, 1)-boundedly. Twbo’s permeate many settings of modern analysis, and this note treats advances in their spectral theory, Fourier analysis, and operator ergodic theory made poss...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

in this paper, we investigate duality of modular g-riesz bases and g-riesz basesin hilbert c*-modules. first we give some characterization of g-riesz bases in hilbert c*-modules, by using properties of operator theory. next, we characterize the duals of a giveng-riesz basis in hilbert c*-module. in addition, we obtain sucient and necessary conditionfor a dual of a g-riesz basis to be again a g...