The manual design of addendum surfaces on common CAD platforms is very tedious which requires many trialscorrections,which will certainly a ect the construction e ciency and quality of addendum surfaces,and then a ect...The manual design of addendum surfaces on common CAD platforms is very tedious which requires many trialscorrections,which will certainly a ect the construction e ciency and quality of addendum surfaces,and then a ect the formability and quality of the workpiece in the process of sheet forming.In this paper,an automatic procedure based on parametric design method is proposed for the rapid construction of the addendum surfaces.The kernel of the parametric method is constructing boundary curves based on the shape of surfaces of workpiece and designing guide curves based on Hermite curve interpolation.By some simple parameters,the shape of the addendum surfaces could be controlled and adjusted easily.In addition,a minimum energy optimization method is employed to further optimize the constructed addendum surface.A finite element analysis for the sheet forming process is performed to evaluate the forming quality of constructed addendum surfaces.The instance illustrates that the addendum surface constructed by the proposed method could ensure both the overall smoothing of surfaces and the final forming quality,and it has a good e ect on springback after forming.This research proposes a smoothing parametric design method for addendum surfaces construction which could construct and optimize addendum surfaces rapidly.展开更多
We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves,where the supports of two variables can be arbitrary subsets in F_(p) of suitable sizes.This essentially recovers ...We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves,where the supports of two variables can be arbitrary subsets in F_(p) of suitable sizes.This essentially recovers the Polya-Vinogradov range,and also applies to symmetric powers of Kloosterman sums and Frobenius traces of elliptic curves.In the case of hyper-Kloosterman sums,we can beat the Pólya-Vinogradov barrier by combining additive combinatorics with a deep result of Kowalski,Michel and Sawin(2017) on sum-products of Kloosterman sheaves.Two Sato-Tate distributions of Kloosterman sums and Frobenius traces of elliptic curves in sparse families are also concluded.展开更多
In this paper, we prove a quantitative version of the statement that every nonempty finite subset of N＋ is a set of quadratic residues for infinitely many primes of the form [nc] with 1 〈 c 〈 243/205. Corresponding...In this paper, we prove a quantitative version of the statement that every nonempty finite subset of N＋ is a set of quadratic residues for infinitely many primes of the form [nc] with 1 〈 c 〈 243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects.展开更多
A classical problem of D. H. Lehmer suggests the study of distributions of elements of Z/pZ of opposite parity to the multiplicative inverse mod p. Zhang initiated this problem and found an asymptotic evaluation of th...A classical problem of D. H. Lehmer suggests the study of distributions of elements of Z/pZ of opposite parity to the multiplicative inverse mod p. Zhang initiated this problem and found an asymptotic evaluation of the number of such elements. In this paper, an asymptotic formula for the fourth moment of the error term of Zhang is proved,from which one may see that Zhang’s error term is optimal up to the logarithm factor.The method also applies to the case of arbitrary positive integral moments.展开更多
Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some genera...Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.61471024)National Natural Science Foundation for Young Scientists of China(Grant No.51705469).
文摘The manual design of addendum surfaces on common CAD platforms is very tedious which requires many trialscorrections,which will certainly a ect the construction e ciency and quality of addendum surfaces,and then a ect the formability and quality of the workpiece in the process of sheet forming.In this paper,an automatic procedure based on parametric design method is proposed for the rapid construction of the addendum surfaces.The kernel of the parametric method is constructing boundary curves based on the shape of surfaces of workpiece and designing guide curves based on Hermite curve interpolation.By some simple parameters,the shape of the addendum surfaces could be controlled and adjusted easily.In addition,a minimum energy optimization method is employed to further optimize the constructed addendum surface.A finite element analysis for the sheet forming process is performed to evaluate the forming quality of constructed addendum surfaces.The instance illustrates that the addendum surface constructed by the proposed method could ensure both the overall smoothing of surfaces and the final forming quality,and it has a good e ect on springback after forming.This research proposes a smoothing parametric design method for addendum surfaces construction which could construct and optimize addendum surfaces rapidly.
基金supported by National Natural Science Foundation of China (Grant Nos. 12025106 and 11971370)。
文摘We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves,where the supports of two variables can be arbitrary subsets in F_(p) of suitable sizes.This essentially recovers the Polya-Vinogradov range,and also applies to symmetric powers of Kloosterman sums and Frobenius traces of elliptic curves.In the case of hyper-Kloosterman sums,we can beat the Pólya-Vinogradov barrier by combining additive combinatorics with a deep result of Kowalski,Michel and Sawin(2017) on sum-products of Kloosterman sheaves.Two Sato-Tate distributions of Kloosterman sums and Frobenius traces of elliptic curves in sparse families are also concluded.
基金Supported by National Natural Science Foundation of China (Grant No. 11171265)the Fundamental Research Funds for the Central Universities
文摘In this paper, we prove a quantitative version of the statement that every nonempty finite subset of N＋ is a set of quadratic residues for infinitely many primes of the form [nc] with 1 〈 c 〈 243/205. Correspondingly, we can obtain a similar result for the case of quadratic non-residues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects.
基金supported by the National Natural Science Foundation of China(No.11601413)the Fundamental Research Funds for the Central Universities(No.201806078)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2017JQ1016)。
文摘A classical problem of D. H. Lehmer suggests the study of distributions of elements of Z/pZ of opposite parity to the multiplicative inverse mod p. Zhang initiated this problem and found an asymptotic evaluation of the number of such elements. In this paper, an asymptotic formula for the fourth moment of the error term of Zhang is proved,from which one may see that Zhang’s error term is optimal up to the logarithm factor.The method also applies to the case of arbitrary positive integral moments.
基金Supported by National Natural Science Foundation of China(Grant No.10601039)
文摘Let q be a sufficiently large integer and X be a Dirichlet character modulo q. In this paper, we extend the product x（-1）=-1 L（1, X） with prime q, arising from the Kummer conjecture, to the products of some general Dirichlet series, and give some meaningful estimates for them.
