On noninferior performance index vectors

The noninferior vector index problem of optimal control theory is investigated in an effort to establish some basic properties of the noninferior index surface in the generalN-dimensional index problem. The vector performance index problem is first converted to a family of scalar index problems by forming an auxiliary scalar index as a function of the vector index and a vector of weighting parameters. The functional relationship between noninferior vectors and the weighting vectors of the auxiliary index problem is investigated for the particular case in which the auxiliary index is a weighted sum of the vector index elements. Special attention is devoted to the noninferior index problem for whichN = 2.     

A generalized Malmquist productivity index

In 1953 Sten Malmquist, a Swedish economist and statistician, published inTrabajos de Estadística the foundations of a productivity index which now bears his name. In this paper we generalize the Malmquist productivity index. We show that (i) the generalized Malmquist productivity index can be expressed as the product of a Malmquist productivity index and a Malmquist scale index; (ii) the generalized Malmquist productivity index can also be expressed as the ratio of a Malmquist output quantity index to a Malmquist input quantity index; (iii) the geometric mean of a pair of Malmquist scale indexes is equal to the reciprocal of the Törnqvist scale index, which implies that (iv) the geometric mean of a pair of generalized Malmquist productivity indexes is equal to a Törnqvist productivity index.     

The mathematical description of uniformity and related theorems

Uniform index is a conception that can describe the uniformity of a finite point set in a polyhedron, and is closely related to chaos. In order to study uniform index, the concept of contained uniform index is defined, which is similar to uniform index and has good mathematical properties. In this paper, we prove the convergence of the contained uniform index, and develop the base of proving the convergence of uniform index.     

一类综合评价指数编制路径及案例

综合评价指数是一种广义上的统计指数,在讨论了综合评价指数与一般统计指数不同的基础上,引述了综合评价指数一般编制步骤并详细分析研究了综合评价指数编制过程中的权重确定,提出了基于等权设计思想的加权修正综合评价指数编制方法,最后以甘肃省装备制造产业为例进行了展示.     

A fixed point index theory for symmetric product mappings

In this paper we develop a fixed point index theory for symmetric product mappings of ENR-spaces. For such mappings we show that an index can be defined which is an extension of the usual integer-valued fixed point index. Further, we show that the classical properties of the index hold in this setting: The index is additive, multiplicative and commutative, the index is preserving under homotopy, and finally, the index is equal to the Lefschetz number as defined by Maxwell [9].     

A global cost Malmquist productivity index using data envelopment analysis

This paper proposes a global cost Malmquist productivity index, new cost Malmquist productivity index, that is circular and that gives a single measure of productivity change. The index is inspired by the global Malmquist productivity index as extended to productivity measurement. Decomposition of the proposed cost Malmquist productivity index is presented. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.     

Cobordism invariance of the index of Callias-type operators

We introduce a notion of cobordism of Callias-type operators overcomplete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application, we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a sum of indexes of Callias-type operators on two noncompact but topologically simpler manifolds. As another application, we give a new proof of the relative index theorem for Callias-type operators, which also leads to a new proof of the Callias index theorem.     

房屋销售价格指数与地产指数关系的协整分析

对房屋销售价格指数和深交所地产指数的协整关系进行实证分析,并做了Granger因果检验,结果显示:在所考虑的数据区间房屋销售价格指数与地产指数确实存在协整关系,地产指数是引起房屋销售价格指数变化的原因,最后给出了一些相关的建议.     

测算具有方向技术效率的DEA方法

本文总结了现有技术效率的主要测算方法，借鉴定向技术距离函数思想，结合DEA思路，提出了一种新的用于技术效率指数测算的模型，并进一步探讨了如何识别决策单元的技术有效性和如何改进非技术有效决策单元的问题．着重分析了该技术效率指数模型与L型技术效率指数的关系，指出该模型是L型技术效率指数模型的一般形式．     

A new index of poverty

This paper introduces a new index of poverty. The index satisfies all the axioms for ‘a good index of poverty’.     

A decisiveness index for simple games

The decisiveness index introduced in this paper is designed to provide a normalized measure of the agility of all simple games, primarily viewed as collective decision-making mechanisms. We study the mathematical properties of the index and derive different axiomatic characterizations for it. Moreover, a close relationship is shown to the Banzhaf index of power––for which twice the decisiveness index plays the role of potential function––that gives rise to an effective computational procedure. Some real-world examples illustrate the usefulness of the decisiveness index, together with the Banzhaf power index, in applications to political science.     

Banzhaf index for multiple voting systems. An application to the European Union

Multi-criteria simple games constitute an extension of the basic framework of voting systems and collective decision-making. The study of power index plays an important role in the theory of multi-criteria simple games. Thus, in this paper, we propose the extended Banzhaf index for these games, as the natural generalization of this index in conventional simple games. This approach allows us to compare various criteria simultaneously. An axiomatic characterization of this power index is established. The Banzhaf index is computed by taking into account the minimal winning coalitions of each class. Since this index depends on the number of ways in which each player can effect a swing, one of the main difficulties for finding this index is that it involves a large number of computations. We propose a combinatorial procedure, based on generating functions, to obtain the Banzhaf index more efficiently for weighted multi-criteria simple games. As an application, the distribution of voting power in the European Union is calculated.     

Partitioning a non-symmetric measure of association for three-way contingency tables

The Goodman-Kruskal tau index is a popular measure of asymmetry for two-way contingency tables where there is a one-way relationship between the variables. Numerous extensions of this index for multi-way tables have been considered in the statistical literature. These include the Gray-Williams measures, Simonetti's delta index and the Marcotorchino index.This paper looks at the partition of the Marcotorchino index for a three-way contingency table with one, two and three ordered categorical variables. Such a partition makes use of orthogonal polynomials and identifies two-way measures of asymmetry (akin to the Goodman-Kruskal tau index) and three-way measures generalisation. These partitions provide information about the structure of the asymmetric relationship between the categories in terms of location, dispersion and higher order moments.     

Why indexing works

We develop a simple stock selection model to explain why active equity managers tend to underperform a benchmark index. We motivate our model with the empirical observation that the best performing stocks in a broad market index often perform much better than the other stocks in the index. Randomly selecting a subset of securities from the index may dramatically increase the chance of underperforming the index. The relative likelihood of underperformance by investors choosing active management likely is much more important than the loss those same investors take due to the higher fees of active management relative to passive index investing. Thus, active management may be even more challenging than previously believed, and the stakes for finding the best active managers may be larger than previously assumed.     

A mixed 0–1 LP for index tracking problem with CVaR risk constraints

Index tracking problems are concerned in this paper. A CVaR risk constraint is introduced into general index tracking model to control the downside risk of tracking portfolios that consist of a subset of component stocks in given index. Resulting problem is a mixed 0?C1 and non-differentiable linear programming problem, and can be converted into a mixed 0?C1 linear program so that some existing optimization software such as CPLEX can be used to solve the problem. It is shown that adding the CVaR constraint will have no impact on the optimal tracking portfolio when the index has good (return increasing) performance, but can limit the downside risk of the optimal tracking portfolio when index has bad (return decreasing) performance. Numerical tests on Hang Seng index tracking and FTSE 100 index tracking show that the proposed index tracking model is effective in controlling the downside risk of the optimal tracking portfolio.     

k-分支星状树的第二几何算术指标

数学化学中,第二几何算术指标是新近提出的一个图的拓扑指标,它与Szeged指标和点PI指标具有紧密关系.如果树的一个顶点υ的度大于等于3,则称顶点υ是其一个分支点.通过树的第二几何算术指标的一个增加或减少的变换,刻画了k-分支星状树的第二几何算术指标的最值,同时确定了相应的极图.     

On the covering index of convex bodies

Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the covering parameter of a convex body as a means of quantifying its covering properties. In this paper, we introduce two relatives of the covering parameter called covering index and weak covering index, which upper bound well-studied quantities like the illumination number, the illumination parameter and the covering parameter of a convex body. Intuitively, the two indices measure how well a convex body can be covered by a relatively small number of homothets having the same relatively small homothety ratio. We show that the covering index is a lower semicontinuous functional on the Banach-Mazur space of convex bodies. We further show that the affine d-cubes minimize the covering index in any dimension d, while circular disks maximize it in the plane. Furthermore, the covering index satisfies a nice compatibility with the operations of direct vector sum and vector sum. In fact, we obtain an exact formula for the covering index of a direct vector sum of convex bodies that works in infinitely many instances. This together with a minimization property can be used to determine the covering index of infinitely many convex bodies. As the name suggests, the weak covering index loses some of the important properties of the covering index. Finally, we obtain upper bounds on the covering and weak covering index.     

On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths

Using the ideas of Keller, Maslov introduced in the mid-1960's an index for Lagrangian loops, whose definition was clarified by Arnold. Leray extended Arnold results by defining an index depending on two paths of Lagrangian planes with transversal endpoints. We show that the combinatorial and topological properties of Leray's index suffice to recover all Lagrangian and symplectic intersection indices commonly used in symplectic geometry and its applications to Hamiltonian and quantum mechanics. As a by-product we obtain a new simple formula for the Hörmander index, and a definition of the Conley–Zehnder index for symplectic paths with arbitrary endpoints. Our definition leads to a formula for the Conley–Zehnder index of a product of two paths.     

基于混合高斯模型的指标优化方法

借鉴混合高斯模型的方法,提出了基于混合高斯模型的非参数检验法用于评价指标体系的构建.首先运用混合高斯模型对现有指标体系进行聚类分析,然后运用非参数检验的秩相关系数对分类后的指标体系进行筛选,最终确定评价指标体系的构成,保证指标体系的全面性和代表性.实例结果表明,方法分类精度高、简便、实用,在指标优化中具有应用价值.     

On the rigidity of the coisotropic Maslov index on certain rational symplectic manifolds

We revisit the definition of the Maslov index of loops in coisotropic submanifolds tangent to the characteristic foliation of this submanifold. This Maslov index is given by the mean index of a certain symplectic path which is a lift of the holonomy along the loop. We prove a Maslov index rigidity result for stable coisotropic submanifolds in a broad class of ambient symplectic manifolds. Furthermore, we establish a nearby existence theorem for the same class of ambient manifolds.