We define an integral approximation for the modulus of the gradient | u(x)| for functions f: Ω C Rn → R by modifying a classical result due to Calderon and Zygmund. Our integral approximations are more stable ...We define an integral approximation for the modulus of the gradient | u(x)| for functions f: Ω C Rn → R by modifying a classical result due to Calderon and Zygmund. Our integral approximations are more stable than the pointwise defined derivatives when applied to numerical differentiation for discrete data. We apply our results to design and analyse neighborhood filters. These filters correspond to well-behaved nonlinear heat equations with the conductivity decreasing with respect to the modulus of gradient | u(x)|. We also show some numerical experiments and evaluate the effectiveness of our filters.展开更多
In order to enhance the interfacial adhesion of carbon fiber(CF)and polymer matrix,a multiscale gradient modulus intermediate layer with rigid-flexible(GO-PA)hierarchical structure was designed and fabricated between ...In order to enhance the interfacial adhesion of carbon fiber(CF)and polymer matrix,a multiscale gradient modulus intermediate layer with rigid-flexible(GO-PA)hierarchical structure was designed and fabricated between CFs and matrix by a facile and businesslike strategy.The polarity,roughness and wettability of CFs surface as well as the thickness of intermediate layer in composite have been significantly increased after rigid-flexible hierarchical structure was constructed.The IFSS,ILSS,compression and impact toughness manifested that the hierarchical structure could bring about a fantastic improvement(76.8%,46.4%,40.7%and 37.8%)for the interfacial and mechanical properties than other previous reports.Consequently,the establishment of CF surface with gradient modulus rigid-flexible hierarchical structure via regulation of nanoparticles and polymer array would open a new,viable and promising route to obtaining high-performance composites.展开更多
文摘We define an integral approximation for the modulus of the gradient | u(x)| for functions f: Ω C Rn → R by modifying a classical result due to Calderon and Zygmund. Our integral approximations are more stable than the pointwise defined derivatives when applied to numerical differentiation for discrete data. We apply our results to design and analyse neighborhood filters. These filters correspond to well-behaved nonlinear heat equations with the conductivity decreasing with respect to the modulus of gradient | u(x)|. We also show some numerical experiments and evaluate the effectiveness of our filters.
基金the National Natural Science Foundation of China(Nos.51803102 and 51903129)Natural Science Foundation of Shandong Province(Nos.201807070028 and 201808220020)+2 种基金the Source Innovation Project of Qingdao(No.19-6-2-75-cg)Industry and Education Cooperation Program of The Ministry of Education(Nos.201802201002,201901078008 and 201802230009)Opening Project of Shanxi Province Key Laboratory of Functional Nanocomposites,North University of China(No.NFCM202001).
文摘In order to enhance the interfacial adhesion of carbon fiber(CF)and polymer matrix,a multiscale gradient modulus intermediate layer with rigid-flexible(GO-PA)hierarchical structure was designed and fabricated between CFs and matrix by a facile and businesslike strategy.The polarity,roughness and wettability of CFs surface as well as the thickness of intermediate layer in composite have been significantly increased after rigid-flexible hierarchical structure was constructed.The IFSS,ILSS,compression and impact toughness manifested that the hierarchical structure could bring about a fantastic improvement(76.8%,46.4%,40.7%and 37.8%)for the interfacial and mechanical properties than other previous reports.Consequently,the establishment of CF surface with gradient modulus rigid-flexible hierarchical structure via regulation of nanoparticles and polymer array would open a new,viable and promising route to obtaining high-performance composites.