Integrable Rosochatius Deformations for an Integrable Couplings of CKdV Equation Hierarchy

We propose a method to construct the integrable Rosochatius deformations for an integrable couplings equations hierarchy. As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy with self-consistent sources and its Lax representation are presented.     

Elementary inductive dichotomy: Separation of open and clopen determinacies with infinite alternatives

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy.     

基于正交试验法和AHP的PNN焊接螺母质量评估

为满足人工神经网络对样本数据的要求,通过正交试验法采集样本数据,利用层次分析法确定影响产品质量各因素的权重,以得到的权重值处理样本数据,以此训练概率神经网络.结果表明,概率神经网络的模式识别能力得到显著提高.     

基于层次分析法的战时气象资料质量评估

采用层次分析法(Analytic Hierarchy Process,AHP),以战时气象资料的及时性、准确性、可用性、全面性、相关性和连续性等6项指标建立战时气象资料质量评估层次结构模型,构造出两两判断矩阵,并以3个气象台提供的不同气象资料为例,通过进行层次单排序及一致性检验、层次总排序及一致性检验,最终得出质量最佳的气象资料.通过气象资料质量的综合评估,为气象台及时、全面地发现组织气象观探测、预报保障、装备性能与维护、信息传输网络等方面的问题,以及为针对问题采取相应的对策提供指导,也为战时气象资料质量的提高程度的评价提供量化依据.     

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.     

Algebro-geometric Constructions of Quasi Periodic Flows of the Discrete Self-dual Network Hierarchy and Applicationsℰ

In this paper we obtain the discrete integrable self-dual network hierarchy associated with a discrete spectral problem. On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the discrete self-dual network hierarchy are straightened using the Abel-Jacobi coordinates. The meromorphic function and the Baker-Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the discrete self-dual network hierarchy are constructed with the help of the asymptotic properties and the algebra-geometric characters of the meromorphic function, the Baker-Akhiezer function and the hyperelliptic curve.     

The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy

In this paper, the compatibility between the gauge transformations and the additional symmetry of the constrained discrete Kadomtsev-Petviashvili hierarchy is given, which preserves the form of the additional symmetry of the cdKP hierarchy, up to shifting of the corresponding additional flows by ordinary time flows.     

Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy

The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the （1, 2）- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of （N, 1）-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of （N, 1）-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation （a useful ecological competition model） are given.