Let K<sub>6</sub> be a real cyclic sextic number field, and K<sub>2</sub>, K<sub>3</sub> its quadratic and cubic subfield. Let h（L） denote the ideal class number of field L. Seven...Let K<sub>6</sub> be a real cyclic sextic number field, and K<sub>2</sub>, K<sub>3</sub> its quadratic and cubic subfield. Let h（L） denote the ideal class number of field L. Seven congruences for h<sup>-</sup> = h（K<sub>6</sub>）/（h（K<sub>2</sub>）h（K<sub>3</sub>）） are obtained. In particular, when the conductor f<sub>6</sub> of K<sub>6</sub> is a prime p, （mod p）, where C is an explicitly given constant, and B<sub>n</sub> is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.展开更多
Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In parti...Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, Zhang Xianke from 1948 to 1988.展开更多
In [1, 2], we get an explicit description of cubic cyclic fields by proving the following Theorem A. Let U={η∈（?）（p）|N<sub>2（p）</sub>η=1}, where p is a primitive cubic root of unity. Write G=U/U&l...In [1, 2], we get an explicit description of cubic cyclic fields by proving the following Theorem A. Let U={η∈（?）（p）|N<sub>2（p）</sub>η=1}, where p is a primitive cubic root of unity. Write G=U/U<sup>3</sup>. Suppose η∈（?）（p） such that 1, η, （?） are representative elements in a subgroup of order 3 of G. Let s=T<sub>（?）（P）</sub>.（?）η be the trace of η, and then the roots of x<sup>3</sup>-3x-s=0 define a展开更多
Klapper(1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over GF(2), but these sequences have very low linear complexities when con...Klapper(1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over GF(2), but these sequences have very low linear complexities when considered as sequences over GF(p)(p is an odd prime). This linear complexity of a binary sequence when considered as a sequence over GF(p) is called GF(p) complexity. This indicates that the binary sequences with high GF(2) linear complexities are inadequate for security in the practical application, while,their GF(p) linear complexities are also equally important, even when the only concern is with attacks using the Berlekamp-Massey algorithm [Massey, J. L., Shift-register synthesis and bch decoding, IEEE Transactions on Information Theory, 15(1), 1969, 122–127]. From this perspective, in this paper the authors study the GF(p) linear complexity of Hall's sextic residue sequences and some known cyclotomic-set-based sequences.展开更多
When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of...When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19771052).
文摘Let K<sub>6</sub> be a real cyclic sextic number field, and K<sub>2</sub>, K<sub>3</sub> its quadratic and cubic subfield. Let h（L） denote the ideal class number of field L. Seven congruences for h<sup>-</sup> = h（K<sub>6</sub>）/（h（K<sub>2</sub>）h（K<sub>3</sub>）） are obtained. In particular, when the conductor f<sub>6</sub> of K<sub>6</sub> is a prime p, （mod p）, where C is an explicitly given constant, and B<sub>n</sub> is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.
文摘Let K 6 be a real cyclic sextic number fields, and K 2, K 3 be its quadratic and cubic subfields. Let h(L) denote the ideal class number of field L. Seven congruences for h -=h(K 6)/h(K 2)h(K 3) are obtained. In particular, when conductor f\-6 of K 6 is prime p, then Ch -≡B p-16B 5(p-1)6 (mod p), where C is an explicitly given constant, and B n is the Bernoulli number. These results for real cyclic sextic fields are an extension of results for quadratic and cyclic quartic fields obtained by Ankeny_Artin_Chowla, Kiselev, Carlitz, Lu Hongwen, Zhang Xianke from 1948 to 1988.
基金Project supported by the National Natural Science Foundation of China
文摘In [1, 2], we get an explicit description of cubic cyclic fields by proving the following Theorem A. Let U={η∈（?）（p）|N<sub>2（p）</sub>η=1}, where p is a primitive cubic root of unity. Write G=U/U<sup>3</sup>. Suppose η∈（?）（p） such that 1, η, （?） are representative elements in a subgroup of order 3 of G. Let s=T<sub>（?）（P）</sub>.（?）η be the trace of η, and then the roots of x<sup>3</sup>-3x-s=0 define a
基金supported by the National Natural Science Foundation of China(Nos.61202007,U1509213)Top Priority of the Discipline(Information and Communication Engineering)Open Foundation of Zhejiang+1 种基金the Postdoctoral Science Foundation(No.2013M540323)the Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics(No.BCXJ 13-17)
文摘Klapper(1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over GF(2), but these sequences have very low linear complexities when considered as sequences over GF(p)(p is an odd prime). This linear complexity of a binary sequence when considered as a sequence over GF(p) is called GF(p) complexity. This indicates that the binary sequences with high GF(2) linear complexities are inadequate for security in the practical application, while,their GF(p) linear complexities are also equally important, even when the only concern is with attacks using the Berlekamp-Massey algorithm [Massey, J. L., Shift-register synthesis and bch decoding, IEEE Transactions on Information Theory, 15(1), 1969, 122–127]. From this perspective, in this paper the authors study the GF(p) linear complexity of Hall's sextic residue sequences and some known cyclotomic-set-based sequences.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579038 and 51490672)the National Basic Research Program of China(Grant No.2013CB036101)
文摘When ordinary Smoothed Particle Hydrodynamics （SPH） method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. I＇o deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH （SISPH） can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.
