关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

Exact Solutions to Space-Time Fractional Fokas-Lenells Equations With Parameters北大核心CSCD

利用多项式完全判别系统法求得非线性光学中带参数时空分数阶Fokas-Lenells方程在一般情况下的精确解,包括有理函数解、周期解、孤波解、Jacobi椭圆函数解和双曲函数解等,绘制了精确解的相关图像,并由此分析了参数对解的结构的影响。     

一类广义Zakharov方程的精确行波解

本文研究了一类广义Zakharov方程的精确解行波解的问题.利用改进的G/G展开方法,借助于计算机代数系统Mathematica,获得了具有重要物理背景的广义Zakharov方程一系列新的含有多个参数的精确行波解,这些解包括孤立波解,双曲函数解,三角函数解,以及有理函数解.     

Riccati展开法求非线性Konno-Oono耦合方程的新精确解

应用Riccati展开法,给出了非线性Konno-Oono方程的一系列新精确解.这些解的形式包括三角函数解、双曲函数解、有理函数解.最后,对特殊函数下的精确解进行数值模拟,给出这些精确解的直观表示.     

非预解形式线性微分方程的解

通过几个实例给出解非预解形式线性微分方程的一般方法,并讨论了预解形式的线性微分方程与非预解形式的线性微分方程解集的差别.     

向量均衡问题的超有效性的对偶形式

在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式.     

应用辅助方程法求Zakharov方程的精确解

应用辅助方程法求得Zakharov方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明:辅助方程法在非线性光学、量子光学、激光物理和等离子体物理等领域具有广泛的应用.     

一类推广的KdV方程的新行波解

本文研究了一类推广的Kd V方程的行波解求解的问题.利用新的G展开法,并借助Mathematica计算软件,获得了该方程的含有多个任意参数的新的行波解,分别为三角函数解、双曲函数解、有理函数解和指数函数解,扩大了该类方程的解的范围.     

广义浅水波方程新的行波解

通过利用新的G展开法,并借助Mathematica计算软件,研究了广义浅水波方程的精确解,获得了该方程的含有多个任意参数的新的显式行波解,分别为三角函数解、双曲函数解、有理函数解和指数函数解,扩大了该类方程的解的范围.     

应用改进的简单方程法求非线性数学物理方程的精确解

应用改进的简单方程法求得Cahn-Allen方程和Jimbo-Miwa方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可以得到了孤立波解.当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,简单方程法对于研究非线性数学物理方程具有非常广泛的应用意义.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

白骨化尸体死亡时间的推断

本文分析了15具白骨化尸体标本的股骨汞(Hg),铅(Pb),镉(Cd)元素含量数据,在三年的时间内采集了3次,一共收集到45个数据。首先将这组数据看着纵向数据,利用线性随机效应混合模型、Cox随机混合效应模型进行分析,结果显示,如果对每个白骨化尸体标本建立线性模型,可以精确预测出死亡时间,而且不需要采集铅元素含量数据。混合效应模型的预测效果也很好,最大误差不会超过1个月。其次我们对数据不作任何假设,利用机器学习中随机森林方法分析数据,并利用5折交叉验证方法来判断结果的可靠性,训练集和测试集的NMSE分别为0.1205944,0.5604286,因此可以用训练出的模型来预测死亡时间。     

Applications of Parameterizations of Oblique Duals of a Frame Sequence

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.     

Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients

In spaces of functions square summable on finite intervals we study the simple completeness of the system of eigen- and associated functions for the pencil of ordinary differential operators generated by a differential expression with constant coefficients (we assume that the roots of the corresponding characteristic equation lie on one and the same ray) and specific semisplitting homogeneous boundary value conditions.     

高超声速飞行器纵向动力系统平衡态集的拓扑结构研究

以高超声速飞行器纵向运动的空气动力学模型和结构动力学模型为依据,采用数值分析的方法,研究了高超声速飞行器动力系统平衡点集的拓扑结构.首先根据高超声速飞行器在巡航阶段的飞行边界的限制条件得到在给定的飞行高度和马赫数下的平衡点集,由此近似估算出了高超声速飞行器的飞行包线.然后根据得到的平衡点集,分别研究了高超声速飞行器的迎角、升降舵偏角和发动机的燃料当量比与飞行马赫数和高度的关系,并进行了数值拟合,在此基础上分别描绘了以上三个拟合关系式的曲面关系图。     

Location of courts of justice: The making of the new judiciary map of Portugal

Location modeling techniques have been applied to an extremely wide variety of public facilities. However, their application to one of the most ubiquitous public facilities – courts of justice – has been very rare. In this paper, we describe a study promoted by the Ministry of Justice of Portugal to define a proposal for the country's new judiciary map – that is, the spatial organization of the judicial system. The new map aims to promote the efficiency and specialization of the justice system (leading to better and faster court decisions) and to provide a good level of accessibility to courts. We developed two optimization models addressing those goals – a districting model, to determine the borders of new, large judicial districts; and a court location model, to determine the location, type, size, and coverage area of the courts included in each new district. Both models are discrete facility location models and consider hierarchical facilities – generic courts and specialized courts of multiple types. Our study was publicly acknowledged by the Portuguese government as having contributed to the new judiciary map that has since been approved and implemented.     

Groups of Automorphisms of Tournaments

By the Holland Representation Theorem, every lattice ordered group (l-group) is isomorphic to a subalgebra of the l-group of automorphisms of a chain. Since weakly associative lattice groups (wal-groups) and tournaments are non-transitive generalizations of l-groups and chains, respectively, the problem concerning the possibility of representation of wal-groups by automorphisms of tournaments arises. In the paper we describe the class of wal-groups isomorphic to wal-groups of automorphisms of tournament and show some of its properties.