相关论文: Lambert function methods for laser dynamics with t…

We give simple proofs of some simple statements concerning the Lambert problem. We first restate and reprove the known existence and uniqueness results for the Keplerian arc. We also prove in some cases that the elapsed time is a convex…

A linear regression algorithm is applied to a digital-supermode distributed Bragg reflector laser to optimise wavelength switching times. The algorithm uses the output of a digital coherent receiver as feedback to update the pre-emphasis…

Reward learning typically relies on a single feedback type or combines multiple feedback types using manually weighted loss terms. Currently, it remains unclear how to jointly learn reward functions from heterogeneous feedback types such as…

In this work, a new relationship is established between the solutions of higher fractional differential equations and a Wright-type transformation. Solutions could be interpreted as expected values of functions in a random time process. As…

Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…

Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small…

Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…

Microscopic many-body theory coupled to Maxwell's equation is used to investigate dual-wavelength operation in vertical external-cavity surface-emitting lasers. The intrinsically dynamic nature of coexisting emission wavelengths in…

In these notes, using the method of differential constraints, novel exact kink-like solutions are obtained for certain classes of complex Ginzburg--Landau equations with cubic-quintic nonlinearity. The foregoing solutions are presented in…

This is the third part of four series papers, aiming at the delay compensation for the abstract linear system (A,B,C). Both the input delay and output delay are investigated. We first propose a full state feedback control to stabilize the…

We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…

We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a…

A shift-invariant system is a collection of functions $\{g_{m,n}\}$ of the form $g_{m,n}(k) = g_m(k-an)$. Such systems play an important role in time-frequency analysis and digital signal processing. A principal problem is to find a dual…

In this paper we introduce the $p$-adic analogue of the Lambert $W$ function, and study its main properties.

Temporal alignment of multiple signals through time warping is crucial in many fields, such as classification within speech recognition or robot motion learning. Almost all related works are limited to data in Euclidean space. Although an…

Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…

The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by…

The phase synchronization of two semiconductor DFB lasers submitted to both frequency-shifted cross-injection and self-feedback is investigated, both numerically and experimentally. A dedicated setup based on monolithic DFB lasers permits…

We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical and path…

Employing the Lagrange inverting series, a solution of the transcendental equation $(x-a)(x-b)=le^{x}$, that can be considered a quadratic generalization of the equation defining Lambert $W$ function, has been found in terms of Bessel…