FMT-泛三I算法的约束度理论

从先前提出的泛三I算法出发,面向FMT(fuzzy modus tollens)问题,提出模糊推理的FMT-泛三I约束算法。改进之前的三I约束FMT原则,给出泛三I约束解的存在条件,建立FMT-泛三I约束算法的统一形式的解。并且,针对9种具体的蕴涵算子,获得相应的泛三I约束解。最后,给出并改进FMT-三I约束算法的相关结论。     

平面分割空间问题

我们先来看三个平面的情况： 这样,我们有结论：如果三个平面两两相交于三条直线,那么这三条直线或者互相平行或者相交于一点,且三个平面最多能分割空间成8个区域．     

直三棱柱的侧截体的体积

与三棱柱各侧棱都相交的平面,是这三棱柱的侧截面．直三棱柱一底面与一侧截面间的几何体,是直三棱柱的侧截体,下面研究其体积．     

直三棱柱的侧截体的体积

与三棱柱各侧棱都相交的平面,是这三棱柱的侧截面.直三棱柱一底面与一侧截面间的几何体,是直三棱柱的侧截体,下面研究其体积.     

基于三参数区间数群决策的第三方物流服务商选择方法研究

对第三方物流服务质量评价与选择属于多属性的群决策问题.为解决传统物流服务商的选择和评价中专家主观性问题,提出了基于三参数区间数群决策的第三方物流服务商选择方法.分析了三参数区间数的概念,对三参数区间数运用偏差函数确定决策专家的权重,根据三参数区间数偏好序概率矩阵和权重,求解第三方物流服务商的排序问题.最后通过实例验证了三参数区间数群决策算法的有效性和可行性.     

县域三次产业虚拟标杆的建立及应用研究——以海南省县域为例

为了解决县域三次产业标杆不属于同一组织(市县)的问题,基于县域三次产业投入产出数据,使用超效DEA-Malmquist和面板数据模型,建立了将县域三次产业优势和谐地统一到一体的虚拟标杆.应用虚拟标杆理论实证分析了海南省县域三次产业,并以万宁市作为虚拟标杆的实施者,给出了万宁市三次产业资源配置的优化决策.结果表明,构建县域三次产业虚拟标杆对提高标杆实施者的三次产业效率具有显著的作用.     

基于一族蕴涵算子的对偶三I算法

三I算法是一种新的模糊推理方法,是传统的模糊推理方法的修改和补充. 三I表达式取最小值时的最优解算法(即对偶三I算法)是三I算法思想的延伸和完善.本文针对蕴涵算子族Ip,讨论了FMP和FMT问题的对偶三I算法,给出了相应的计算公式,从而也进一步促进了对三I算法的研究.     

基于Tucker3分解的三路数据聚类方法

从两路数据聚类分析到三路数据聚类分析实质上是由平面分析到立体分析的过程。三路数据聚类方法研究的核心之一是如何把传统的两路截面数据聚类技术向三路数据聚类扩展的问题。本文基于Tucker模型的思路,提出一种先对三路数据执行矩阵分解,而后进行聚类分析的三路数据聚类方法。这种方法不但能够通过核心矩阵反映三路数据三个模式信息联系的强度大小,而且还可以在一个分解框架下对三路数据的三个模式同时进行聚类分析。实证分析结果表明,本文提出的聚类方法不但灵活、易于理解,同时也有着良好的判别性和实用性。     

三角域上带两个形状参数的Bézier曲面的扩展

给出了三角域上带双参数λ1,λ2的类三次Bernstein基函数,它是三角域上三次Bernstein基函数的扩展.分析了该组基的性质并定义了三角域上带有两个形状参数λ1,λ2的类三次Bernstein-Bézier(B-B)参数曲面.该基函数及参数曲面分别具有与三次Bernstein基函数及三次B-B参数曲面类似的性质.当λ1,λ2取特殊的值时,可分别得到三次Bernstein基函数及三次B-B参数曲面以及参考文献中所定义的类三次Bernstein基函数及类三次B-B参数曲面.由实例可知,通过改变形状参数的取值,可以调整曲面的形状.     

三垂线定理（逆）与三角形的垂心

三垂线定理反映了空间三条直线的垂直关系,而三角形的垂心是三角形的三条高线的交点,二者的统一点是直线垂直.因此可通过三垂线定理（逆）证明三角的垂心,也可借助三角形的垂心去用三垂线定理（逆）.在证题中若注意到这点,对提高证明能力大有好处,现举例说明.     

Graphs with Branchwidth at Most Three

In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a minor. A set of four graphs is shown to be the obstruction set for the class of graphs with branchwidth at most three. Moreover, we give a safe and complete set of reduction rules for the graphs with branchwidth at most three. Using this set, a linear time algorithm is given that verifies if a given graph has branchwidth at most three, and, if so, outputs a minimum width branch decomposition.     

On the magic square and inverse

In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose inverses can be calculated easily.     

三角形的九点二次曲线

在任意三角形内,三边中点,三高的垂足,以及连接顶点与垂心的三线段的中点,都在同一圆上,此圆即为三角形九点圆.三角形的九点圆是欧氏几何中著名的优美定理,被称为欧拉圆和费尔巴哈圆.本文试图把垂心改换为平面内的任意点,相应地把三条高线改换为过每个顶点各一条的共点直线组时,则将把三角形的九点圆有趣地推广为三角形的九点二次曲线.并具体讨论在不同的区域内得到的九点二次曲线.     

求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法

利用广义投影矩阵，对求解无约束规划的三项记忆梯度算法中的参数给一条件，确定它们的取值范围，以保证得到目标函数的三项记忆梯度广义投影下降方向，建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法，并证明了算法的收敛性．同时给出了结合FR，PR，HS共轭梯度参数的三项记忆梯度广义投影算法，从而将经典的共轭梯度算法推广用于求解约束规划问题．数值例子表明算法是有效的．     

On the three diagonals of a cyclic quadrilateral

If the side lengths of a non-degenerate cyclic quadrilateral are given, but not necessarily in cyclic order, then three diagonal lengths arise in the resulting three cyclic quadrilaterals, just as three possible pairs of supplementary angles arise as opposite vertices, and where the diagonals intersect, in each of the three configurations. We obtain a formula for the sum of the lengths of the three diagonals minus the sum of the four sides which enables us to deduce the geometric inequality that the sum of the side lengths is less than the sum of the lengths of the three diagonals. We obtain another formula when these lengths are replaced by their squares, and this yields a similar inequality. A proof of both formulas is given which uses algebraic geometry, but which proceeds by analysis of degenerate situations. Two alternative proofs of the linear version of the inequality (which implies the quadratic version) are supplied which use trigonometry and Lagrange multipliers respectively. An unusual feature of these results is that they refer not to one configuration, but rather concern three possible configurations.     

Multi‐dimensional conservation laws and integrable systems

In this paper, we introduce a new property of two‐dimensional integrable hydrodynamic chains—existence of infinitely many local three‐dimensional conservation laws for pairs of integrable two‐dimensional commuting flows. Infinitely many local three‐dimensional conservation laws for the Benney commuting hydrodynamic chains are constructed. As a by‐product, we established a new method for computation of local conservation laws for three‐dimensional integrable systems. The Mikhalëv equation and the dispersionless limit of the Kadomtsev‐Petviashvili equation are investigated. All known local and infinitely many new quasilocal three‐dimensional conservation laws are presented. Also four‐dimensional conservation laws are considered for couples of three‐dimensional integrable quasilinear systems and for triplets of corresponding hydrodynamic chains.     

Invariant tori in perturbed three vortex motion

The motion of three point vortices in an ideal fluid in a plane comprises a Hamiltonian dynamical system – one that is completely integrable, so it exhibits numerous periodic orbits, and quasiperiodic orbits on invariant tori. Certain perturbations of three vortex dynamics, such as three vortex motion in a half-plane, are also Hamiltonian, but not completely integrable. Yet these perturbed systems may still have periodic trajectories and invariant tori close to those for the unperturbed dynamics. Extending recent work by the authors [4], invariant 2-tori approximating those for the unperturbed system are located and analyzed using a combination of classical analysis, asymptotics, and Hamiltonian methods. It is shown that the results and approximation methods used are applicable to several perturbations of three vortex dynamics such as three vortices in a half-plane, the restricted four vortex problem in the plane, and three coaxial vortex rings in 3-space. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hill Four-Body Problem with Oblate Bodies: An Application to the Sun–Jupiter–Hektor–Skamandrios System

We consider a restricted four-body problem, with a precise hierarchy between the bodies: two larger bodies and a smaller one, all three of oblate shape, and a fourth, infinitesimal body, in the neighborhood of the smaller of the three bodies. The three heavy bodies are assumed to move in a plane under their mutual gravity, and the fourth body to move in the three-dimensional space under the gravitational influence of the three heavy bodies, but without affecting them. We first find that the triangular central configuration of the three heavy oblate bodies is a scalene triangle (rather than an equilateral triangle as in the point mass case). Then, assuming that these three bodies are in such a central configuration, we perform a Hill approximation of the equations of motion describing the dynamics of the infinitesimal body in a neighborhood of the smaller body. Through the use of Hill’s variables and a limiting procedure, this approximation amounts to sending the two larger bodies to infinity. Finally, for the Hill approximation, we find the equilibrium points for the motion of the infinitesimal body and determine their stability. As a motivating example, we identify the three heavy bodies with the Sun, Jupiter, and the Jupiter’s Trojan asteroid Hektor, which are assumed to move in a triangular central configuration. Then, we consider the dynamics of Hektor’s moonlet Skamandrios.

     

Group divisible designs with three groups and block size four

We present new constructions and results on GDDs with three groups and block size four and also obtain new GDDs with two groups of size nine. We say a GDD with three groups is even, odd, or mixed if the sizes of the non-empty intersections of any of its blocks with any of the three groups is always even, always odd, or always mixed. We give new necessary conditions for these families of GDDs and prove that they are sufficient for these three types and for all group sizes except for the minimal case of mixed designs for group size 5t(t>1). In particular, we prove that mixed GDDs allow a maximum difference between indices. We apply the constructions given to show that the necessary conditions are sufficient for all GDDs with three groups and group sizes two, three, and five, and also for group size four with two possible exceptions, a GDD(4,3,4;5,9) and a GDD(4,3,4;7,12).     

Some minimal bimolecular mass-action systems with limit cycles

We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which is unstable for certain rate constants and then exhibits stable limit cycles, but no chaotic behaviour. For some rate constants in the Feinberg–Berner system, a stable equilibrium, an unstabe limit cycle, and a stable limit cycle coexist. All three networks are minimal in some sense.By way of homogenising these three examples, we construct bimolecular mass-conserving mass-action systems with four species that admit a stable limit cycle. The homogenised Feinberg–Berner system and the homogenised Wilhelm–Heinrich system admit the coexistence of a stable equilibrium, an unstable limit cycle, and a stable limit cycle.