We extend the narrowband Weyl symbol (WS) and the wideband P0-Weyl symbol (P0WS) for dispersive time–frequency (TF) analysis of nonstationary random processes and time-varying systems. We obtain the new TF symbols using unitary transformations on the WS and the P0WS. For example, whereas the WS is matched to systems with constant or linear TF characteristics, the new symbols are better matched ...

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for c...

We study the Hankel determinant generated by Laguerre weight with jump discontinuities at $t_k, k=1,\cdots,m$. By employing ladder operator approach to establish Riccati equations, we show that $\sigma_n(t_1,\cdots,t_m)$, logarithmic derivative of $n$-dimensional determinant, satisfies a generalization $\sigma$-from Painlev\'{e} V equation. Through investigating Riemann-Hilbert problem for asso...

We present a method of treating the interaction of a single threelevel ion with two laser beams. The idea is to apply a unitary transformation such that the exact transformed Hamiltonian has one of the three levels decoupled for all values of the detunings. When one takes into account damping, the evolution of the system is governed by a master equation usually obtained via adiabatic approximat...

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establis...

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...

We show how Bell observables on a bipartite quantum system can be obtained by local observables via a controlled-unitary transformation. For continuous variables this result holds for the Bell observable corresponding to the non-conventional heterodyne measurement on two radiation modes, which is connected through a 50-50 beam-splitter to two local observables given by single-mode homodyne meas...