ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.

MULTIPLE BOUNDARY LAYER PHENOMENA OF THE SOLUTION OF NONLINEAR HIGHER ORDER ELLIPTIC EQUATIONS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.

Infrared Fault Detection Method for Dense Electrolytic Bath Polar Plate Based on YOLOv5s

Electrolysis tanks are used to smeltmetals based on electrochemical principles,and the short-circuiting of the pole plates in the tanks in the production process will lead to high temperatures,thus affecting normal production.Aiming at the problems of time-consuming and poor accuracy of existing infrared methods for high-temperature detection of dense pole plates in electrolysis tanks,an infrared dense pole plate anomalous target detection network YOLOv5-RMF based on You Only Look Once version 5(YOLOv5)is proposed.Firstly,we modified the Real-Time Enhanced Super-Resolution Generative Adversarial Network(Real-ESRGAN)by changing the U-shaped network(U-Net)to Attention U-Net,to preprocess the images;secondly,we propose a new Focus module that introduces the Marr operator,which can provide more boundary information for the network;again,because Complete Intersection over Union(CIOU)cannot accommodate target borders that are increasing and decreasing,replace CIOU with Extended Intersection over Union(EIOU),while the loss function is changed to Focal and Efficient IOU(Focal-EIOU)due to the different difficulty of sample detection.On the homemade dataset,the precision of our method is 94%,the recall is 70.8%,and the map@.5 is 83.6%,which is an improvement of 1.3%in precision,9.7%in recall,and 7%in map@.5 over the original network.The algorithm can meet the needs of electrolysis tank pole plate abnormal temperature detection,which can lay a technical foundation for improving production efficiency and reducing production waste.

A Generalized Discrete Morse-Floer Theory

Forman has developed a version of discrete Morse theory that can be understood in terms of arrow patterns on a(simplicial,polyhedral or cellular)complex without closed orbits,where each cell may either have no arrows,receive a single arrow from one of its facets,or conversely,send a single arrow into a cell of which it is a facet.By following arrows,one can then construct a natural Floer-type boundary operator.Here,we develop such a construction for arrow patterns where each cell may support several outgoing or incoming arrows(but not both),again in the absence of closed orbits.Our main technical achievement is the construction of a boundary operator that squares to 0 and therefore recovers the homology of the underlying complex.

FAST SPECTRAL GALERKIN METHOD FOR LOGARITHMIC SINGULAR EQUATIONS ON A SEGMENT＊

We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Conver- gence rates of several orders are obtained for fractional Sobolev spaces H^-1/2 （or H00^-l/2）. Main tools are the approximation properties of the discretization basis, the construction of a suitable Hilbert scale for weighted L2-spaces and local regularity estimates. Numerical experiments are provided to validate our claims,

Advanced Geometric Modeler with Hybrid Representation

An advanced geometric modeler GEMS4.0 has been developed, in whichfeature representation is used at the highest level abstraction of a productmodel. Boundary representation is used at the bottom level, while CSG modelis adopted at the median level. A BRep data structure capable of modelingnon-manifold is adopted. NURBS representation is used for all curved surfaces.Quadric surfaces have dual representations consisting of their geometric datasuch as radius, center point, and center tals. Boundary representation of freeform surfaces is easily built by sweeping and skinning method with NURBSgeometry Set operations on curved solids with boundary representation areperformed by an evaluation process consisting of four steps. A file exchangefacility is provided for the conversion between product data described by STEPand product information generated by GEMS4.0