The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system. 相似文献
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems. 相似文献
The machining process is primarily used to remove material using cutting tools. Any variation in tool state affects the quality of a finished job and causes disturbances. So, a tool monitoring scheme (TMS) for categorization and supervision of failures has become the utmost priority. To respond, traditional TMS followed by the machine learning (ML) analysis is advocated in this paper. Classification in ML is supervised based learning method wherein the ML algorithm learn from the training data input fed to it and then employ this model to categorize the new datasets for precise prediction of a class and observation. In the current study, investigation on the single point cutting tool is carried out while turning a stainless steel (SS) workpeice on the manual lathe trainer. The vibrations developed during this activity are examined for failure-free and various failure states of a tool. The statistical modeling is then incorporated to trace vital signs from vibration signals. The multiple-binary-rule-based model for categorization is designed using the decision tree. Lastly, various tree-based algorithms are used for the categorization of tool conditions. The Random Forest offered the highest classification accuracy, i.e., 92.6%.
In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
A new series of azomethine-functionalized compounds was synthesized from the condensation of 2-hydroxy-1,3-propanediamine and 2-thienylcarboxaldehydes in the presence of a drying agent. The derivatives were spectroscopically characterized by NMR, LC-MS, UV/Vis, IR and elemental analysis. Variable temperature 1H-NMR (−60 to +60 °C) was performed to investigate the effect of solvent polarity; the capability of solvent to form H-bond was found to dramatically influencing the tautomerization process of the desired structures. The calculated thermochemical parameters (ΔH298, ΔG298 and ΔS298) at DFT and MP2 levels of theory explained that 3 b exists in equilibrium with two tautomers. The basis of the electronic absorptions was pursued through Time-Dependent Density-Functional Theory (TD-DFT). Analysis of the structural surfaces was inspected and the molecular electrostatic potential (MEP) demonstrated that the three functionalized compounds were relatively analogous in the electronic distributions. Furthermore, the electrophilic and nucleophilic centers lying on the molecular surfaces were probably playing a key-role in stabilizing the compounds through the nonclassical C−H⋅⋅⋅π interactions and hydrogen bonding. The impact of solvent polarity on absorption spectra were investigated via solvatochromic shifts. For instance, compound 3 c displayed a gradual shift of the maximum absorption to the red area when the solvent polarity was increased, recording a 21 nm of bathochromic shift. In contrast, no significant solvent-effect on 3 a and 3 b was observed. The solvation relation was pursued between Gutmann's donicity numbers the experimental λmax; exhibited almost positive linear performance with a minor oscillation, that ascribe to the possible weak interface between the molecules of solute and designated solvents. The bandgap energy of all products were assessed experimentally using optical absorption spectra following Tauc approach, giving −4.050 ( 3 a ), −3.900 ( 3 b ) and −3.210 ( 3 c ) eV. However, the ΔE were computationally figured out from TD-DFT simulation to be −4.258 ( 3 a ), −4.022 ( 3 b ) and −3.390 ( 3 c ) eV. 相似文献
This study aimed to investigate the chemical composition of Tribulus terrestris L. fruit (TT) extract named TT15 and its protective effect against ischemic stroke (IS) as well as corresponding mechanisms. The chemical composition of TT15 was analyzed by liquid chromatography-mass spectrometry (LC-MS), and the compound identification was conducted via searching the in-house database. The LC-MS-based multi-omics approach was applied to search the differential metabolites and differential proteins in rat brain tissue and to explore the biomarker and molecular mechanism of TT15 against middle cerebral artery occlusion (MCAO). A total of 20 compounds were identified from TT15, mainly including alkaloids, flavonoids, phenols, quinones, and esters. These 20 compounds significantly affected the metabolism of 44 metabolites and the expression of 51 proteins. Joint pathway analysis showed that these metabolites and proteins were mainly involved in the response to elevated platelet cytosolic Ca2+ and platelet activation, which inferred that TT15 may exert a protective effect against cerebral ischemic injury via regulating platelet function. This study provides useful information for further exploration of the mechanisms of TT extract against IS. 相似文献