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Hua’s theorem on five squares of primes
《Frontiers of Mathematics in China》2020年第4期835-850,共16页Wenjia ZHAO 
We give an alternative proof of Hua’s theorem that each large N≡5(mod 24)can be written as a sum of five squares of primes.The proof depends on an estimate of exponential sums involving the Mobius function.
关键词：Exponential sums Hua's theorem Mobius function 
High-order sum-of-squares structured tensors:theory and applications
《Frontiers of Mathematics in China》2020年第2期255-284,共30页Haibin CHEN Yiju WANG Guanglu ZHOU 
This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11601261,11671228);the Natural Science Foundation of Shandong Province(No.ZR2019MA022).
Tensor decomposition is an important research area with numerous applications in data mining and computational neuroscience.An important class of tensor decomposition is sum-of-squares(SOS)tensor decomposition.SOS ten...
关键词：Sum-of-squares(SOS)tensor positive semi-definite(PSD)tensor H-eigenvalue structured tensor 
Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes
《Frontiers of Mathematics in China》2019年第5期1017-1035,共19页Rui ZHANG 
The author would like to express the most sincere gratitude to Prof.Zhixin Liu for his valuable advice and constant encouragement;This work was supported by the National Natural Science Foundation of China(Grant No.11871367).
We prove that,with at most O(N17/192+ε)exceptions,all even positive integers up to N are expressible in the form P1^2+P2^2+P3^3+P5^4+P6^4,where Pi,P2,……,P6 are prime numbers.This gives large improvement of a recent...
关键词：Waring-Goldbach problem circle method exceptional set 
On Diophantine approximation with one prime and three squares of primes
《Frontiers of Mathematics in China》2019年第4期761-779,共19页Wenxu GE Feng ZHAO Tianqin WANG 
The authors thank the referees for their time and comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871193, 11471112);the Key Research Project of Henan Province Higher Education (No. 17A110009).
Let λ1,λ2,λ3,λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2,λ1/λ3 are irrational and algebraic. Then there are infinitely many solutions in primes pj, j = 1, 2,3,4...
关键词：DIOPHANTINE inequalities PRIMES Davenport-Heilbronn met HOD SIEVE methods 
On computing minimal H-eigenvalue of sign-structured tensors被引量：5
《Frontiers of Mathematics in China》2017年第6期1289-1302,共14页Haibin CHEN Yiju WANG 
This work was done during the first authors＇ postdoctoral period in Qufu Normal University. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11601261, 11671228） and the Natural Science Foundation of Shandong Province （No. ZR2016AQ12）.
Finding the minimal H-eigenvalue of tensors is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a sum-of-squares （SOS） algorithm for computing the minimal H-eigenv...
关键词：Extended essentially nonnegative tensor （EEN-tensor） positive semi-definiteness H-eigenvalue sum-of-squares （SOS） polynomial 
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