We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
Pythagorean-hodograph（PH） curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this pa...Pythagorean-hodograph（PH） curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs＇ constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by C1 Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.展开更多
In this study,we systematically investigate theαdecay half-lives of 263 emitters in the 52≤Z≤107region and clusters^(14)C,^(20)O,^(23)Fe,^(24,25,26)Ne,^(28,30)Mg,and^(32,34)Si in the presence of an extended form of...In this study,we systematically investigate theαdecay half-lives of 263 emitters in the 52≤Z≤107region and clusters^(14)C,^(20)O,^(23)Fe,^(24,25,26)Ne,^(28,30)Mg,and^(32,34)Si in the presence of an extended form of the Sextic potential to describe the strong nuclear interaction between the daughter nucleus and cluster in the parent nucleus using the Wentzel-Kramers-Brillouin(WKB)method.We find nuclear potential parameters that explain the decay mechanism for each variety of cluster and show that this form of double-well potential provides an excellent description of the nuclear decay phenomenon.We highlight constraints between the potential parameters and experimental data.Moreover,we emphasize the importance of the coupling parameters of the nuclear potential in the nature of the preformed cluster.The obtained results are compared with experimental and literature data.Our results are in very good agreement with the experimental data.展开更多
In this work,we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation.The Jost functions of spectral problem are derived directly,and the scattering da...In this work,we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation.The Jost functions of spectral problem are derived directly,and the scattering data with t=0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions.Then we make use of translation transformation to get the relation between potential and kernel,and recover potential according to Gel’fand-Levitan-Marchenko(GLM)integral equations.Furthermore,the time evolution of scattering data is considered,on the basis of that,the multi-soliton solutions are derived.In addition,some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis,which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.展开更多
LetK 6 be a real cyclic sextic number field, andK 2,K 3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh - =h (K 6)/(h(K 2)h(K 3)) are obtained. In particular, ...LetK 6 be a real cyclic sextic number field, andK 2,K 3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh - =h (K 6)/(h(K 2)h(K 3)) are obtained. In particular, when the conductorf 6 ofK 6 is a primep, $Ch^ - \equiv B\tfrac{{p - 1}}{6}B\tfrac{{5(p - 1)}}{6}(\bmod p)$ , whereC is an explicitly given constant, andB n 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
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
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
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the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1167106811401077+4 种基金1127106011290143)Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)the Program for Liaoning Excellent Talents in University(Grant No.LJQ2014010)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK38)
文摘Pythagorean-hodograph（PH） curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs＇ constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by C1 Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.
文摘In this study,we systematically investigate theαdecay half-lives of 263 emitters in the 52≤Z≤107region and clusters^(14)C,^(20)O,^(23)Fe,^(24,25,26)Ne,^(28,30)Mg,and^(32,34)Si in the presence of an extended form of the Sextic potential to describe the strong nuclear interaction between the daughter nucleus and cluster in the parent nucleus using the Wentzel-Kramers-Brillouin(WKB)method.We find nuclear potential parameters that explain the decay mechanism for each variety of cluster and show that this form of double-well potential provides an excellent description of the nuclear decay phenomenon.We highlight constraints between the potential parameters and experimental data.Moreover,we emphasize the importance of the coupling parameters of the nuclear potential in the nature of the preformed cluster.The obtained results are compared with experimental and literature data.Our results are in very good agreement with the experimental data.
基金supported by the National Natural Science Foundation of China(No.11975306)the Natural Science Foundation of Jiangsu Province(No.BK20181351)+3 种基金the Six Talent Peaks Project in Jiangsu Province(No.JY-059)the Fundamental Research Fund for the Central Universities(Nos.2019ZDPY07,2019QNA35)the Assistance Program for Future Outstanding Talents of China University of Mining and Technology(No.2021WLJCRCZL076)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX212139).
文摘In this work,we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation.The Jost functions of spectral problem are derived directly,and the scattering data with t=0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions.Then we make use of translation transformation to get the relation between potential and kernel,and recover potential according to Gel’fand-Levitan-Marchenko(GLM)integral equations.Furthermore,the time evolution of scattering data is considered,on the basis of that,the multi-soliton solutions are derived.In addition,some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis,which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19771052).
文摘LetK 6 be a real cyclic sextic number field, andK 2,K 3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh - =h (K 6)/(h(K 2)h(K 3)) are obtained. In particular, when the conductorf 6 ofK 6 is a primep, $Ch^ - \equiv B\tfrac{{p - 1}}{6}B\tfrac{{5(p - 1)}}{6}(\bmod p)$ , whereC is an explicitly given constant, andB n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.
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.
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.
