自然界和工程技术领域存在大量的非线性问题,它们通常需要用非线性微分方程来描述.守恒量在微分方程的求解、约化和定性分析方面发挥重要作用.因此,研究非线性动力学方程的近似守恒量具有重要意义.文章利用Noether对称性方法研究弱非线...自然界和工程技术领域存在大量的非线性问题,它们通常需要用非线性微分方程来描述.守恒量在微分方程的求解、约化和定性分析方面发挥重要作用.因此,研究非线性动力学方程的近似守恒量具有重要意义.文章利用Noether对称性方法研究弱非线性动力学方程的近似守恒量.首先,将弱非线性动力学方程化为一般完整系统的Lagrange方程,在Lagrange框架下建立Noether准对称性的定义和广义Noether等式,给出近似Noether守恒量.其次,将弱非线性动力学方程化为相空间中一般完整系统的Hamilton方程,在Hamilton框架下建立Noether准对称性的定义和广义Noether等式,给出近似Noether守恒量.再次,将弱非线性动力学方程化为广义Birkhoff方程,在Birkhoff框架下建立Noether准对称性的定义和广义Noether等式,给出近似Noether守恒量.最后,以著名的van der Pol方程,Duffing方程以及弱非线性耦合振子为例,分析三个不同框架下弱非线性系统的Noether准对称性与近似Noether守恒量的计算.结果表明:同一弱非线性动力学方程可以化为不同的一般完整系统或不同的广义Birkhoff系统;Hamilton框架下的结果是Birkhoff框架的特例,而Lagrange框架下的结果与Hamilton框架的等价.利用Noether对称性方法寻找弱非线性动力学方程的近似守恒量不仅方便有效,而且具有较大的灵活性.展开更多
We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with ...We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent展开更多
We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in L...We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.展开更多
In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied...In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied.The quasi-fractional dynamics model here refers to the variational problem based on the definition of RiemannLiouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL).First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained.Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved.The Pfaff-Birkhoff principles,Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article.Finally,some examples are given.展开更多
The structures of Ωω states with spin-parity JP= 5/2^-, 3/2^-, and 1/2^- are dynamically studied in both the chlral SU（3） quark model and the extended chiral SU（3） quark model by solving a resonating group meth...The structures of Ωω states with spin-parity JP= 5/2^-, 3/2^-, and 1/2^- are dynamically studied in both the chlral SU（3） quark model and the extended chiral SU（3） quark model by solving a resonating group method （RGM） equation. The model parameters are taken from our previous work, which gave a satisfactory description of the energies of the baryon ground states, the binding energy of the deuteron, the nucleon-nucleon （NN） scattering phase shifts, and the hyperon-nucleon （YN） cross sections. The calculated results show that the Ωω state has an attractive interaction, and in the extended chiral SU（3） quark model such attraction can make for a Ωω quasi-bound state with spin-parity JP = 3/2^- or 5/2^- and the binding energy of about several MeV.展开更多
It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape f...It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini＇s element＇s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.展开更多
In this paper, we propose a new lightweight block cipher named RECTANGLE. The main idea of the design of RECTANGLE is to allow lightweight and fast implementations using bit-slice techniques. RECTANGLE uses an SP-netw...In this paper, we propose a new lightweight block cipher named RECTANGLE. The main idea of the design of RECTANGLE is to allow lightweight and fast implementations using bit-slice techniques. RECTANGLE uses an SP-network. The substitution layer consists of 16 4 × 4 S-boxes in parallel. The permutation layer is composed of 3 rotations. As shown in this paper, RECTANGLE offers great performance in both hardware and software environment, which provides enough flexibility for different application scenario. The following are3 main advantages of RECTANGLE. First, RECTANGLE is extremely hardware-friendly. For the 80-bit key version, a one-cycle-per-round parallel implementation only needs 1600 gates for a throughput of 246 Kbits/s at100 k Hz clock and an energy efficiency of 3.0 p J/bit. Second, RECTANGLE achieves a very competitive software speed among the existing lightweight block ciphers due to its bit-slice style. Using 128-bit SSE instructions,a bit-slice implementation of RECTANGLE reaches an average encryption speed of about 3.9 cycles/byte for messages around 3000 bytes. Last but not least, we propose new design criteria for the RECTANGLE S-box.Due to our careful selection of the S-box and the asymmetric design of the permutation layer, RECTANGLE achieves a very good security-performance tradeoff. Our extensive and deep security analysis shows that the highest number of rounds that we can attack, is 18(out of 25).展开更多
文摘自然界和工程技术领域存在大量的非线性问题,它们通常需要用非线性微分方程来描述.守恒量在微分方程的求解、约化和定性分析方面发挥重要作用.因此,研究非线性动力学方程的近似守恒量具有重要意义.文章利用Noether对称性方法研究弱非线性动力学方程的近似守恒量.首先,将弱非线性动力学方程化为一般完整系统的Lagrange方程,在Lagrange框架下建立Noether准对称性的定义和广义Noether等式,给出近似Noether守恒量.其次,将弱非线性动力学方程化为相空间中一般完整系统的Hamilton方程,在Hamilton框架下建立Noether准对称性的定义和广义Noether等式,给出近似Noether守恒量.再次,将弱非线性动力学方程化为广义Birkhoff方程,在Birkhoff框架下建立Noether准对称性的定义和广义Noether等式,给出近似Noether守恒量.最后,以著名的van der Pol方程,Duffing方程以及弱非线性耦合振子为例,分析三个不同框架下弱非线性系统的Noether准对称性与近似Noether守恒量的计算.结果表明:同一弱非线性动力学方程可以化为不同的一般完整系统或不同的广义Birkhoff系统;Hamilton框架下的结果是Birkhoff框架的特例,而Lagrange框架下的结果与Hamilton框架的等价.利用Noether对称性方法寻找弱非线性动力学方程的近似守恒量不仅方便有效,而且具有较大的灵活性.
基金supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028the Natural Science Foundation of Fujian Province under Grant No.2008J0199
文摘We firstly propose two kinds of new multi-component BKP （mcBKP） hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable （1＋1）-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of hi-directional SK equations with self-consistent
文摘We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.
基金supported by the National Natural Science Foundation of China (Nos.11972241,11572212 and 11272227)the Natural Science Foundation of Jiangsu Province(No. BK20191454)。
文摘In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied.The quasi-fractional dynamics model here refers to the variational problem based on the definition of RiemannLiouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL).First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained.Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved.The Pfaff-Birkhoff principles,Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article.Finally,some examples are given.
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10475087
文摘The structures of Ωω states with spin-parity JP= 5/2^-, 3/2^-, and 1/2^- are dynamically studied in both the chlral SU（3） quark model and the extended chiral SU（3） quark model by solving a resonating group method （RGM） equation. The model parameters are taken from our previous work, which gave a satisfactory description of the energies of the baryon ground states, the binding energy of the deuteron, the nucleon-nucleon （NN） scattering phase shifts, and the hyperon-nucleon （YN） cross sections. The calculated results show that the Ωω state has an attractive interaction, and in the extended chiral SU（3） quark model such attraction can make for a Ωω quasi-bound state with spin-parity JP = 3/2^- or 5/2^- and the binding energy of about several MeV.
文摘It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini＇s element＇s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.
基金supported by National Natural Science Foundation of China(Grant No.61379138)Research Fund KU Leuven(OT/13/071)+1 种基金"Strategic Priority Research Program"of the Chinese Academy of Sciences(Grant No.XDA06010701)National High-tech R&D Program of China(863 Program)(Grant No.2013AA014002)
文摘In this paper, we propose a new lightweight block cipher named RECTANGLE. The main idea of the design of RECTANGLE is to allow lightweight and fast implementations using bit-slice techniques. RECTANGLE uses an SP-network. The substitution layer consists of 16 4 × 4 S-boxes in parallel. The permutation layer is composed of 3 rotations. As shown in this paper, RECTANGLE offers great performance in both hardware and software environment, which provides enough flexibility for different application scenario. The following are3 main advantages of RECTANGLE. First, RECTANGLE is extremely hardware-friendly. For the 80-bit key version, a one-cycle-per-round parallel implementation only needs 1600 gates for a throughput of 246 Kbits/s at100 k Hz clock and an energy efficiency of 3.0 p J/bit. Second, RECTANGLE achieves a very competitive software speed among the existing lightweight block ciphers due to its bit-slice style. Using 128-bit SSE instructions,a bit-slice implementation of RECTANGLE reaches an average encryption speed of about 3.9 cycles/byte for messages around 3000 bytes. Last but not least, we propose new design criteria for the RECTANGLE S-box.Due to our careful selection of the S-box and the asymmetric design of the permutation layer, RECTANGLE achieves a very good security-performance tradeoff. Our extensive and deep security analysis shows that the highest number of rounds that we can attack, is 18(out of 25).
