Semiconductor laser systems excited by multiplicative Ornstein-Uhlenbeck noise and additive sine-Wiener noise in relation to real and imaginary parts.

In this paper we study a semiconductor laser system excited by multiplicative Ornstein-Uhlenbeck (OU) noise and additive sine-Wiener (SW) noise with a related real part and imaginary part. The two-dimensional Langevin equation (LE) with cross-correlating complex OU noise and complex SW noise is equivalent to the six-dimensional LE. Based on functional methods and spatial dimension extension methods, the six-dimensional Fokker-Planck equation (FPE) is achieved. Through Taylor expansion approximation and linear transformation, the dimensionality of FPE is reduced, and the exact expression of the probability distribution (SPD) in steady state is obtained. The impacts of noise parameters on laser intensity on SPD are further analyzed. Moreover, based on the reduced FPE, the information entropy of the system is obtained. This calculation is useful for us to understand further the influence of system parameters and noise correlation coefficient on the system. The main work lies in obtaining an alternative method for deriving a FPE corresponding to the two-dimensional stochastic semiconductor laser model, which is more applicable than methods in previous literature. An equivalent expression for cross-correlated OU noise and cross-correlated SW noise as well as a method for approximate solutions of a high-dimensional FPE are also provided.

Waste-to-energy incineration site selection framework based on heterogeneous fuzzy regret-PROMETHEE model considering life-cycle carbon emissions.

Waste incineration technology has received extensive attention for its advantages of being harmless, reducing, and recycling. However, the waste-to-energy incineration project confronts significant "not-in-my-backyard (NIMBY) concerns," and irrational location choices will have negative effects on the project's economy and sustainability; it is also a great challenge to the credibility of the government. To this end, a multi-criteria decision-making framework is constructed for the site selection of waste-to-energy incineration projects. To begin with, a site selection criteria system is established including 16 sub-criteria from four aspects, where probabilistic linguistic term sets are introduced to depict the qualitative sub-criteria and probabilistic hesitant fuzzy sets are employed to express the uncertainty of quantitative sub-criteria. An optimization model is then built to determine the weights of criteria based on the Pearson correlation coefficient and least square method. Furthermore, a regret-preference ranking organization methods for enrichment evaluations (PROMETHEE) model is presented to rank alternatives in a heterogeneous decision environment. Finally, a case study in China is conducted to validate the applicability of the proposed framework; the result of the site selection demonstrates that alternative A2 located in Miyun, Beijing, is the most optimal option. This work provides investors with scientific decision reference and also extends the methods in the decision-making field.