International Press of Boston - publishers of scholarly mathematical and scientific journals and books

Purpose: The purpose of this paper is to present a novel method for minor fabric defects detection.Design/methodology/approach: This paper proposes a PETM-CNN algorithm. PETM-CNN is designed based on self-similar estimation algorithm and Convolutional Neural Network. The PE (Patches Extractor) algorithm extracts patches that are possible to be defective patches to preprocess the fabric image. Then a TM-CNN (Triplet Metric CNN) method is designed to predict labels of the patches and the final label of the image. The TM-CNN can perform better than normal CNN.Findings: This algorithm is superior to other algorithms on the data set of fabric images with minor defects. The proposed method achieves accurate classification of fabric images whether it has minor defects or not. The experimental results show that the approach is effective.Originality/value: Traditional fabric defects detection is not effective as minor defects detection, so this paper develops a method of minor fabric images classification based on self-similar estimation and CNN. This paper offers the first investigation of minor fabric defects.

Thermodynamics of charged and slowly rotating black holes in 4D Gauss–Bonnet gravity has attracted a great deal of attention due to its intrinsic complications and rich phase structures. In this paper, we revisit the thermodynamics of charged and slowly rotating black holes and provide the correct thermodynamic volume and entropy. Thermodynamic geometries are a powerful tool to study the microstructure of black holes. Based on the Hessian matrix of the black hole mass, we introduce thermodynamic geometric methods and give its scalar curvature (Ruppeiner and Weinhold). Furthermore, we investigate the Joule–Thomson expansion of slowly rotating black hole in 4D Gauss–Bonnet gravity in this research study. Interestingly, we explicitly state that the expression of the Joule–Thomson coefficient is obtained from the basic formulas of enthalpy and temperature. Then, we obtain the isenthalpic curve in the T − P graph and demonstrate the cooling–heating region by the inversion curve. The inversion temperature and inversion curves are obtained, and we investigate the similarities and differences between van der Waals fluids and charged fluids.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books

In this paper, we study the limiting behavior of solutions to a 1D two-point boundary value problem for viscous conservation laws with genuinely-nonlinear fluxes as $\varepsilon$ goes to zero. We here discuss different types of non-characteristic boundary layers occurring on both sides. We first construct formally the three-term approximate solutions by using the method of matched asymptotic expansions. Next, by energy method we prove that the boundary layers are nonlinearly stable and thus it is proved the boundary layer effects are just localized near both boundaries. Consequently, the viscous solutions converge to the smooth inviscid solution uniformly away from the boundaries. The rate of convergence in viscosity is optimal.