This paper mainly investigates the approximation of a global maximizer of the Monge–Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary.Using an approximation mechanism,the primal maximization problem can be transformed into a sequence of minimization problems.By applying the systematic canonical duality theory,one is able to derive a sequence of analytic solutions for the minimization problems.In the final analysis,the convergence of the sequence to an analytical global maximizer of the primal Monge–Kantorovich problem will be demonstrated.
Modern industrial processes are typically characterized by large-scale and intricate internal relationships.Therefore,the distributed modeling process monitoring method is effective.A novel distributed monitoring scheme utilizing the Kantorovich distance-multiblock variational autoencoder(KD-MBVAE)is introduced.Firstly,given the high consistency of relevant variables within each sub-block during the change process,the variables exhibiting analogous statistical features are grouped into identical segments according to the optimal quality transfer theory.Subsequently,the variational autoencoder(VAE)model was separately established,and corresponding T^(2)statistics were calculated.To improve fault sensitivity further,a novel statistic,derived from Kantorovich distance,is introduced by analyzing model residuals from the perspective of probability distribution.The thresholds of both statistics were determined by kernel density estimation.Finally,monitoring results for both types of statistics within all blocks are amalgamated using Bayesian inference.Additionally,a novel approach for fault diagnosis is introduced.The feasibility and efficiency of the introduced scheme are verified through two cases.
本文给出了修正q-Szász-Kantorovich算子在复空间的定义,参照Gal S G等人在文献[10]的方法,研究了当q>1时修正q-Szász-Kantorovich算子在紧圆盘对解析函数的逼近性质,获得了Voronovskaja结果,并给出其精确估计,丰富了修正q-Szász-Kantorovich算子在复空间的逼近性质.
