Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

The system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.

A PSO-CVX Algorithm of Sum and Difference Beam Patterns for Time-Modulated Antenna Array

An integrated optimization of sum and difference beam for time-modulated linear antenna array is studied in this paper. The goal of sum and difference beam synthesis is to generate sum beam in the main band and difference beams in the first-order sideband with low side-lobe level through timing switches. The turn-on times of antenna array are achieved by solving a quadratic constraint linear programming; meanwhile, the opening times are optimized by particle swarm optimization algorithm. The results of linear array show that the sum and difference beam can be scanned within ± 40 degrees, with lower peak side-lobe level.

Robust MFC anti-windup scheme for LTI systems with norm-bounded uncertainty

On the basic of the fact that all signals in the practical system are always bounded, this paper proposes a 4-degree-of-freedom (DoF) anti-windup scheme for saturated systems with parametric uncertainty. A fairly straightforward tuning rule is introduced to the robust stability analysis for the proposed anti-windup structure under the framework of IQC (Integral Quadratic Constraint). And the sufficient stability conditions are derived to check the reasonable definiteness of the related transfer function. Moreover, the control design for disturbance response and set-point tracking response are two separate part in this proposed scheme. Numerical example demonstrates the effectiveness and the considerable performance improvement of the anti-windup compensator that is designed by the proposed technique.

Stability of 1-Bit Compressed Sensing in Sparse Data Reconstruction

1-bit compressing sensing (CS) is an important class of sparse optimization problems. This paper focuses on the stability theory for 1-bit CS with quadratic constraint. The model is rebuilt by reformulating sign measurements by linear equality and inequality constraints, and the quadratic constraint with noise is approximated by polytopes to any level of accuracy. A new concept called restricted weak RSP of a transposed sensing matrix with respect to the measurement vector is introduced. Our results show that this concept is a sufficient and necessary condition for the stability of 1-bit CS without noise and is a sufficient condition if the noise is available.