This note deals with the existence and uniqueness of a minimiser of the following Grtzsch-type problem inf f ∈F∫∫_(Q_1)φ(K(z,f))λ(x)dxdyunder some mild conditions,where F denotes the set of all homeomorphims f wi...This note deals with the existence and uniqueness of a minimiser of the following Grtzsch-type problem inf f ∈F∫∫_(Q_1)φ(K(z,f))λ(x)dxdyunder some mild conditions,where F denotes the set of all homeomorphims f with finite linear distortion K(z,f)between two rectangles Q_1 and Q_2 taking vertices into vertices,φ is a positive,increasing and convex function,and λ is a positive weight function.A similar problem of Nitsche-type,which concerns the minimiser of some weighted functional for mappings between two annuli,is also discussed.As by-products,our discussion gives a unified approach to some known results in the literature concerning the weighted Grtzsch and Nitsche problems.展开更多
Distortion often appears at the corners of heavy turbine blade castings during heat treatment processes, so a great machining allowance is generally set in production which directly results in cost increase. In this p...Distortion often appears at the corners of heavy turbine blade castings during heat treatment processes, so a great machining allowance is generally set in production which directly results in cost increase. In this paper, a novel real-time measuring technology is developed for non-contact measuring the deformation behavior of heavy steel castings in heat treatment process. It was employed to measure the distortion and the temperature field of a batch of heavy turbine blade castings at cooling stage in normalizing process. Three inflection points appear in the distortion-time curves, and the residual distortion is affected by the regional area of not finished martensite transformation when the second inflection point appears. When the mean air temperature falls into the range of 10℃-20℃, the residual distortion is small; when it is lower than 10℃, positive distortion appears; when it is higher than 20℃, negative distortion appears. The distortion varies with seasonal temperature, which is directly responsible for the great machining allowance given in production.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11371268 and 11171080)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123201110002)the Natural Science Foundation of Jiangsu Province(Grant No.BK20141189)
文摘This note deals with the existence and uniqueness of a minimiser of the following Grtzsch-type problem inf f ∈F∫∫_(Q_1)φ(K(z,f))λ(x)dxdyunder some mild conditions,where F denotes the set of all homeomorphims f with finite linear distortion K(z,f)between two rectangles Q_1 and Q_2 taking vertices into vertices,φ is a positive,increasing and convex function,and λ is a positive weight function.A similar problem of Nitsche-type,which concerns the minimiser of some weighted functional for mappings between two annuli,is also discussed.As by-products,our discussion gives a unified approach to some known results in the literature concerning the weighted Grtzsch and Nitsche problems.
基金supported by the National Eleventh Five-Year Science and Technology Support Program of China (Grant No.2007BAF02B02)the Major Projects of Ministry of Science of China (Grant No.2009ZX04014-082)
文摘Distortion often appears at the corners of heavy turbine blade castings during heat treatment processes, so a great machining allowance is generally set in production which directly results in cost increase. In this paper, a novel real-time measuring technology is developed for non-contact measuring the deformation behavior of heavy steel castings in heat treatment process. It was employed to measure the distortion and the temperature field of a batch of heavy turbine blade castings at cooling stage in normalizing process. Three inflection points appear in the distortion-time curves, and the residual distortion is affected by the regional area of not finished martensite transformation when the second inflection point appears. When the mean air temperature falls into the range of 10℃-20℃, the residual distortion is small; when it is lower than 10℃, positive distortion appears; when it is higher than 20℃, negative distortion appears. The distortion varies with seasonal temperature, which is directly responsible for the great machining allowance given in production.
