SELF-DUAL PERMUTATION CODES OVER FORMAL POWER SERIES RINGS AND FINITE PRINCIPAL IDEAL RINGS

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.

Self-Dual Permutation Codes over Finite Chain Rings

Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a T-group, and the group action is transitive, the sufficient and necessary condition of the existence of permutation codes is given.

The Self-dual Codes over Formal Power Series Rings

The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we study self-dual codes over R_∞by means of self-dual codes over Ri,and give some characterizations of self-dual codes over R_∞.

Self-dual Codes Defined on Factor Graphs

A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.

ON SELF-DUAL PERMUTATION CODES

Permutation codes over finite fields are introduced, some conditions for existence or non-existence of self-dual permutation codes are obtained.

New MDS Euclidean and Hermitian Self-Dual Codes over Finite Fields

In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes.

Self-dual Codes with Symplectic Inner Product

In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.

Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N−m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N−1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation.

Fractional Breaking Soliton Equation Reduced from a Linear Spectral Problem Associated with Fractional Self-Dual Yang-Mills Equations

Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fractional breaking soliton equation is derived from the reduction of the linear spectral problem associated with the local fractional non-isospectral self-dual Yang-Mills equations.More specifically,the employed linear spectral problem is first reduced to the(2+1)-dimensional local fractional zero-curvature equation through variable transformations.Based on the reduced local fractional zero-curvature equation,the fractional breaking soliton equation is then constructed by the method of undetermined coefficients.This paper shows that some other local fractional models can be obtained by generalizing the existing methods of generating nonlinear partial differential equations with integer orders.

On Study of Solutions of Kac-van Moerbeke Lattice and Self-dual Network Equations

Kac 货车 Moerbeke 格子和 self-dualnetwork 方程的答案的关上的形式被基于 Riccati 方程建议转变考虑，用符号的计算。与微分差别方程的旅行波浪解决方案的数字计算相对照，我们的方法获得有物理关联的准确答案。

Self-dual Vortices in Schrdinger-Chern-Simons Model

By making use of the U(1) gauge potential decomposition theory and the φ-mapping topological currenttheory,we investigate the Schrdinger-Chern-Simons model in the thin-film superconductor system and obtain anexact Bogomolny self-dual equation with a topological term.It is revealed that there exist self-dual vortices in thesystem.We study the inner topological structure of the self-dual vortices and show that their topological charges aretopologically quantized and labeled by Hopf indices and Brouwer degrees.Furthermore,the vortices are found generatingor annihilating at the limit points and encountering,splitting or merging at the bifurcation points of the vector field φ.

Deformation of Rigid Conjugate Self-dual Galois Representations

In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called rigid.Second,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.

规范场论中自对偶磁单极子解的存在唯一性

Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity.

职教师资队伍建设的自组织逻辑及变革路向

高素质专业化的职教师资队伍建设是新时代职业教育发展的迫切要求。基于自组织视角,我国职教师资队伍建设还面临组织困境,诸如职教师资队伍来源相对单一、组织的开放性不够,职教师资队伍建设模式相对固化、组织的发展动力不强,职教师资的制度建设相对滞后、组织的发展保障不足等问题。职教师资的跨界属性必然要求突出职教师资队伍自身开放性,构建多元参与的治理体系;注重与环境关系的非平衡性,增强职教师资队伍的发展动力;优化发展的非线性,加强职教师资队伍建设的制度保障。

时间感知的双塔型自注意力序列推荐模型

用户的偏好具有聚合性和漂移性。现有推荐算法在序列建模框架中融合了交互时间相关性的建模,取得了很大的性能改善,但它们在建模时仅考虑了交互的时间间隔,使得它们在捕捉用户偏好的时间动态方面存在局限性。首先,提出了一种新的时间感知的位置嵌入方法,将时间信息与位置嵌入相结合,帮助模型学习时间层面的项目相关性。随后,在时间感知位置嵌入基础上,提出了时间感知的双塔自注意力序列推荐模型(TiDSA)。TiDSA包含项目级和特征级的自注意力模块,分别从项目和特征两个角度对用户偏好随时间变化的过程进行分析,实现了对时间、项目和特征的统一建模,并且在特征级自注意力模块,设计了多维度的自注意力权重计算方式,从特征维度、项目维度和项目与特征交叉维度充分学习特征之间的相关性。最后,TiDSA将项目级与特征级的信息相融合得到最终的用户偏好表示,并根据该表示为用户提供可靠的推荐结果。四个真实推荐数据集的实验结果表明,TiDSA的性能优于许多先进的基线模型。

基于2个不相交子集的MDS自对偶码构造

最大距离可分(maximum distance separable, MDS)自对偶码是一类最优线性码,在通信、数据存储和区组设计等领域有着广泛的应用,构造MDS自对偶码是当前编码理论研究的一个热点问题。文章基于有限域及其乘法群的2个不相交子集,利用广义Reed-Solomon(RS)码构造了几类新的MDS自对偶码;得到的MDS自对偶码具有灵活的长度。

Cyclic Code and Self-Dual Code over F2 ＋ uF2 ＋ u^2F2

We give the structures of a cyclic code over ringR = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.

Self-Dual Weak Hopf Algebras

In this paper, we define the notion of self-dual graded weak Hopf algebra and self-dual semilattice graded weak Hopf algebra. We give characterization of finite-dimensional such algebras when they are in structually simple forms in the sense of E. L. Green and E. N. Morcos. We also give the definition of self-dual weak Hopf quiver and apply these types of quivers to classify the finite- dimensional self-dual semilattice graded weak Hopf algebras. Finally, we prove partially the conjecture given by N. Andruskiewitsch and H.-J. Schneider in the case of finite-dimensional pointed semilattice graded weak Hopf algebra H when grH is self-dual.