In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming ...In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.展开更多
The intelligent development of machines,as one of the essential research components of smart manufacturing,is urgently needed to improve the intelligent production of product manufacturing processes within product fam...The intelligent development of machines,as one of the essential research components of smart manufacturing,is urgently needed to improve the intelligent production of product manufacturing processes within product families.The uncertainty of the process requirements within a product family and the time-varying nature of the processing performance of machines pose significant challenges for intelligent manufacturing.Digital twins(DTs)have proven to be very effective architectures for intelligent manufacturing;DTs support dynamic modeling capabilities in time and space and can provide effective technical support for manufacturing intelligence under multi-variety production.Therefore,a process autonomous digital twin(PADT)framework driven by characterization,prediction,and evaluation-based multi-models(CPEM)associated with process information is constructed to realize intelligent production.First,the multidimensional information contained in the machining process is analyzed to accurately locate the features of machining precision,and a machine performance characterization model is built.Second,a machine capacity prediction model based on time-scale information fusion is established to predict the processing capacities of machines under different production demands.Finally,a product distribution evaluation model based on the 3σ rule is established,which provides an effective evaluation index for the optimization of processing parameters.The application of CPEM-driven PADT in a commutator machining machine provides predictive manufacturing intelligence within a product family.展开更多
基金support by the Louisiana State Board of Regents grant LEQSF(2005-2007)-ENH-TR-21
文摘In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.
基金supported by the National Key R&D Program of China(Grant No.2022YFB3304100)the Key Research and Development Program of Hubei Province(Grant Nos.2022BAA055 and 2023BAB086)。
文摘The intelligent development of machines,as one of the essential research components of smart manufacturing,is urgently needed to improve the intelligent production of product manufacturing processes within product families.The uncertainty of the process requirements within a product family and the time-varying nature of the processing performance of machines pose significant challenges for intelligent manufacturing.Digital twins(DTs)have proven to be very effective architectures for intelligent manufacturing;DTs support dynamic modeling capabilities in time and space and can provide effective technical support for manufacturing intelligence under multi-variety production.Therefore,a process autonomous digital twin(PADT)framework driven by characterization,prediction,and evaluation-based multi-models(CPEM)associated with process information is constructed to realize intelligent production.First,the multidimensional information contained in the machining process is analyzed to accurately locate the features of machining precision,and a machine performance characterization model is built.Second,a machine capacity prediction model based on time-scale information fusion is established to predict the processing capacities of machines under different production demands.Finally,a product distribution evaluation model based on the 3σ rule is established,which provides an effective evaluation index for the optimization of processing parameters.The application of CPEM-driven PADT in a commutator machining machine provides predictive manufacturing intelligence within a product family.
