Fourier-Mukai transform and index theory

Given a submersive morphism of complex manifoldsf: X→Y, and a complex vector bundleE onX, there is a relationship between the higher direct images of ε (the sheaf of holomorphic sections ofE) and the index of the relative Dolbeault complex twisted byE. This relationship allows one to yield a global and simple proof of the equivalence between the Mukai transform of stable vector bundles on a torusT of complex dimension 2 and the Nahm transform of instantons. We also offer a proof of Mukai’s inversion theorem which circumvents the use of derived categories by introducing spectral sequences of sheaves onT (this is related to Donaldson and Kronheimer’s proof, but is automatically global and somehow simpler). The general framework developed in the first part of this paper may be applied to the study of the Mukai transform for more general varieties. Research partly supported by the Italian Ministry for University and Research through the research projects ‘Metodi geometrici e probabilistici in fisica matematica’ and ‘Geometria reale e complessa,’ and by the Spanish DGICYT through the research projects PB91-0188 and PB92-0308. This paper has been typeset by using theAMS-TEX macro package     

Use of the Szeged index and the revised Szeged index for measuring network bipartivity

We have revisited the Szeged index (Sz) and the revised Szeged index (Sz^∗), both of which represent a generalization of the Wiener number to cyclic structures. Unexpectedly we found that the quotient of the two indices offers a novel measure for characterization of the degree of bipartivity of networks, that is, offers a measure of the departure of a network, or a graph, from bipartite networks or bipartite graphs, respectively. This is because the two indices assume the same values for bipartite graphs and different values for non-bipartite graphs. We have proposed therefore the quotient Sz/Sz^∗ as a measure of bipartivity. In this note we report on some properties of the revised Szeged index and the quotient Sz/Sz^∗ illustrated on a number of smaller graphs as models of networks.     

The Banzhaf power index for political games

The Banzhaf index of a voting game is a measure of a priori power of the voters. The model on which the index is based treats the voters symmetrically, i.e. the ideology, outlook, etc., of the voters influencing their voting behavior is ignored. Here we present a nonsymmetric generalization of the Banzhaf index in which the ideology of the voters affecting their voting behavior is taken into account. A model of ideologies and issues is presented. The conditions under which our model gives the Shapley-Shubik index (another index of a priori power of the voters) are given. Finally several examples are presented and some qualitative results are given for straight majority and pure bargaining games.     

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.     

Graphs with large palette index

Given an edge-coloring of a graph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. We define the palette index of a graph as the minimum number of distinct palettes, taken over all edge-colorings, occurring among the vertices of the graph. Several results about the palette index of some specific classes of graphs are known. In this paper we propose a different approach that leads to new and more general results on the palette index. Our main theorem gives a sufficient condition for a graph to have palette index larger than its minimum degree. In the second part of the paper, by using such a result, we answer to two open problems on this topic. First, for every r odd, we construct a family of r-regular graphs with palette index reaching the maximum admissible value. After that, we construct the first known family of simple graphs whose palette index grows quadratically with respect to their maximum degree.     

Extremal Hosoya index and Merrifield-Simmons index of hexagonal spiders

For any graph G, let m(G) and i(G) be the numbers of matchings (i.e., the Hosoya index) and the number of independent sets (i.e., the Merrifield-Simmons index) of G, respectively. In this paper, we show that the linear hexagonal spider and zig-zag hexagonal spider attain the extremal values of Hosoya index and Merrifield-Simmons index, respectively.     

Scrambling index set of primitive digraphs

The scrambling index k(D)$k(D)$ of a primitive digraph D is the smallest positive integer k such that for every pair of vertices x and y, there exists a vertex v such that there exist directed walks of length k from x to v and from y to v. In this paper, we study the scrambling index set of primitive digraphs.     

Improving the accuracy of BDF methods for index 3 differential-algebraic equations

Methods for solving index 3 DAEs based on BDFs suffer a loss of accuracy when there is a change of step size or a change of order of the method. A layer of nonuniform convergence is observed in these cases, andO(1) errors may appear in the algebraic variables. From the viewpoint of error control, it is beneficial to allow smooth changes of step size, and since most codes based on BDFs are of variable order, it is also of interest to avoid the inaccuracies caused by a change of order of the method. In the case of BDFs applied to index 3 DAEs in semi-explicit form, we present algorithms that correct toO(h) the inaccurate approximations to the algebraic variables when there are changes of step size in the backward Euler method. These algorithms can be included in an existing code at a very small cost. We have also described how to obtain formulas that correct theO(1) errors in the algebraic variables appearing after a change of order.This author thanks the Centro de Estadística y Software Matemático de la Universidad Simón Bolívar (CESMa) for permitting her free use of its research facilities.     

On the Kirchhoff index of some toroidal lattices

The resistance distance is a novel distance function on a graph proposed by Klein and Randi? [D.J. Klein and M. Randi?, Resistance distance, J. Math. Chem. 12 (1993), pp. 81–85]. The Kirchhoff index of a graph G is defined as the sum of resistance distances between all pairs of vertices of G. In this article, based on the result by Gutman and Mohar [I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), pp. 982–985], we compute the Kirchhoff index of the square, 8.8.4, hexagonal and triangular lattices, respectively.     

Cyclic cocycles on deformation quantizations and higher index theorems

We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof. We give a new proof of Nest-Tsygan's algebraic higher index theorem by computing the pairing between such cyclic cocycles and the K-theory of the formal deformation quantization. Furthermore, we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold. As an application, we obtain the analytic higher index theorem of Connes-Moscovici and its extension to orbifolds.     

股价指数的记忆性特征

本文通过ARFIMA模型(分整自回归滑动平均模型)分析了上证日指数、周指数、月指数序列的记忆性特征,说明股票价格日指数具有长记忆性、周指数具有中等记忆性、月指数具有短期记忆性,这一结论说明了中国股票市场是非有效的,其本身隐含一定的政策含义。     

A mean-risk index model for uncertain capital budgeting

This paper discusses the capital budgeting problem of projects using annual cash inflows, cash outflows and initial investment outlays given by experts’ evaluations when no historical data are available. Uncertain variables are used to describe the projects’ parameters. A profit risk index and a capital risk index are proposed, and a mean-risk index model is developed for optimal project selection. In addition, the deterministic forms of the model are given and a solution algorithm is provided. For the sake of illustration, a numerical example is also presented. The results of the example show that both profit risk index and capital risk index are important in investment risk control. However, when the profit risk control requirement is strong, the selected project portfolio may be insensitive to the capital risk constraint; when the profit risk control requirement is moderate, the capital risk constraint plays an important role. The results also show the tendency that when either the tolerable profit risk level or the tolerable capital risk level becomes higher, the obtained expected net present value of the project portfolio becomes larger, which is in agreement with the investment rule that the higher the risk, the higher the return.     

The tractability index of memristive circuits: branch‐oriented and tree‐based models

The memory‐resistor or memristor is a new electrical element characterized by a nonlinear charge‐flux relation. This device poses many challenging problems, in particular from the circuit modeling point of view. In this paper, we address the index analysis of certain differential‐algebraic models of memristive circuits; specifically, our attention is focused on so‐called branch‐oriented models, which include in particular tree‐based formulations of the circuit equations. Our approach combines results coming from differential‐algebraic equation theory, matrix analysis and theory of digraphs. This framework should be useful in future studies of dynamical aspects of memristive circuits. Copyright © 2012 John Wiley & Sons, Ltd.     

On novel grey forecasting model based on non-homogeneous index sequence

To solve the problem that traditional grey models were constructed on the hypothesis that the original data sequence is in accord with homogeneous index trend rather than non-homogeneous index trend. A novel grey forecasting model based on non-homogeneous index sequence approximately (abbreviated as NDGM) is proposed. It is proved that the models based on homogeneous index sequence are all special cases that of non-homogeneous index sequence. The recursive function of the NDGM model is proposed and the forecasting precision of the model based on pure non-homogeneous index sequence is discussed and the affine properties of the model are further studied. Finally, one numerical case is used to show the effective results of the proposed model.     

智能运输系统综合效益评价指标体系及模糊综合评价

首先论述了智能运输系统 (ITS)效益综合评价的目的和意义 ,然后构建了相应的评价指标体系 .给出了综合效益评价方法和评价模型 ,运用二元比较法确定各指标的权重 ,最后进行了实例分析 .     

The Banzhaf power index for ternary bicooperative games

In this paper we analyze ternary bicooperative games, which are a refinement of the concept of a ternary voting game introduced by Felsenthal and Machover. Furthermore, majority voting rules based on the difference of votes are simple bicooperative games. First, we define the concepts of the defender and detractor swings for a player. Next, we introduce the Banzhaf power index and the normalized Banzhaf power index. The main result of the paper is an axiomatization of the Banzhaf power index for the class of ternary bicooperative games. Moreover, we study ternary bicooperative games with two lists of weights and compute the Banzhaf power index using generating functions.     

The Conley index for discontinuous vector fields

In this paper, we define the Conley index for a region of discontinuity D of a piecewise C ^k discontinuous vector field Z on an n-dimensional compact Riemannian smooth orientable manifold and prove it to be a homotopy invariant. This invariance is obtained by regularization of the discontinuous vector field. We use an adapted form of Lyapunov graph continuation to produce, in a few examples, a regularization of the discontinuous vector field with the property that the dynamics in a regularized neighborhood of D has the same Conley index as .      

The localized longitudinal index theorem for Lie groupoids and the van Est map

We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids.     

三圈图的极小广义和连通指数

图的广义和连通指数作为新提出的一类分子拓扑指数, 在QSPR/QSAR 中有很大的应用价值. 树图、单圈图和双圈图的极值问题已取得很多结果, 而三圈图相关问题的研究较为复杂. 限制 - 1\leqslant \alpha < 0, 对三圈图的广义和连通指数进行了研究. 通过对三圈图的分析, 构造了一种图的变换, 指出在三圈图中广义和连通指 数的极小值必由其中的七种类型图取得. 然后通过悬挂边的变换, 最终得到三圈图广义和连通指 数的极小值并刻画了唯一的极图.