长沙建设国家中心城市的对策研究

建设国家中心城市是长沙市近年的奋斗目标.长沙市怎样建设国家中心城市,可以从与国内其他国家中心城市的全面比照当中得到建设方案.一是从经济实力、产业结构、科教实力、金融行业发展、对外开放等代表城市综合实力的5个方面,二是从引领和辐射功能、集聚功能、物流枢纽功能等代表城市功能的3个方面,对长沙与国内5个国家中心城市(天津、重庆、成都、武汉、郑州)进行对比研究.通过对比,从国内5个国家中心城市的城市功能差别当中找准长沙的城市功能定位,从长沙市城市综合实力的差距和优劣势当中发现长沙建设国家中心城市所要解决的问题,为此提出长沙建设国家中心城市的建设对策.     

Central Points of the Complete Quadrangle

Generalizing the classical geometry of the triangle in the Euclidean plane E, we define a central point of an n-gon as a symmetric function E ⁿ → E which commutes with all similarities. We first review various geometrical characterizations of some well-known central points of the quadrangle (n = 4) and show how a look at their mutual positions produces a morphologic classification (cyclic, trapezoidal, orthogonal etc.). From a basis of four central points, full information on the quadrangle can be retrieved. This generalizes a problem first faced by Euler for the triangle. Reconstructing a quadrangle from its central points is a geometric analogue of solving an algebraic equation of degree 4: here the diagonal triangle plays the role of a Lagrange resolvent and the determination of loci for the central points replaces the examination of discriminants for real roots.

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Received: March 2007     

A probabilistic analysis of a measure of combinatorial complexity for the central curve

We investigate certain combinatorial properties of the central curve associated with interior point methods for linear optimization. We define a measure of complexity for the curve in terms of the number of turns, or changes of direction, that it makes in a geometric sense, and then perform an average case analysis of this measure for P-matrix linear complementarity problems. We show that the expected number of nondegenerate turns taken by the central curve is bounded by n ²-n, where the expectation is taken with respect to a sign-invariant probability distribution on the problem data. As an alternative measure of complexity, we also consider the number of times the central curve intersects with a wide class of algebraic hypersurfaces, including such objects as spheres and boxes. As an example of the results obtained, we show that the primal and dual variables in each coordinate of the central curve cross each other at most once, on average. As a further example, we show that the central curve intersects any sphere centered at the origin at most twice, on average. Received May 28, 1998 / Revised version received October 12, 1999?Published online December 15, 1999     

On the Log-exponential Trajectory of Linear Programming

Development in interior point methods has suggested various solution trajectories, also called central paths, for linear programming. In this paper we define a new central path through a log-exponential perturbation to the complementarity equation in the Karush-Kuhn-Tucker system. The behavior of this central path is investigated and an algorithm is proposed. The algorithm can compute an -optimal solution at a superlinear rate of convergence.     

中央环保督察背景下地方政府环境管制行为研究

中央环保督察对环境的改善效果备受肯定,但是这种改善效果的持续性却受到质疑。基于演化博弈理论,本文构建了地方政府和污染企业的动态复制系统,探究中央环保督察压力下空气质量改善的途径。研究结果表明:中央环保督察过程中,空气质量的改善可能来自于地方政府无差别的关停污染企业;中央政府一味地加大对地方政府环保失职的惩罚,可能会导致地方政府采取一刀切式的“懒政”、“怠政”行为;辖区的初始污染水平、管制成本均影响地方政府的行为选择。地方政府一刀切行为是多因素驱动的结果,中央政府应协调各方力量,理性决策,推动中央环保督察的良性运行。     

Visibility of the higher-dimensional central projection into the projective sphere

We can describe higher-dimensional classical spaces by analytical projective geometry, if we embed the d-dimensional real space onto a d + 1-dimensional real projective metric vector space. This method allows an approach to Euclidean, hyperbolic, spherical and other geometries uniformly [8]. To visualize d-dimensional solids, it is customary to make axonometric projection of them. In our opinion the central projection gives more information about these objects, and it contains the axonometric projection as well, if the central figure is an ideal point or an s-dimensional subspace at infinity. We suggest a general method which can project solids into any picture plane (space) from any central figure, complementary to the projection plane (space). Opposite to most of the other algorithms in the literature, our algorithm projects higher-dimensional solids directly into the two-dimensional picture plane (especially into the computer screen), it does not use the three-dimensional space for intermediate step. Our algorithm provides a general, so-called lexicographic visibility criterion in Definition and Theorem 3.4, so it determines an extended visibility of the d-dimensional solids by describing the edge framework of the two-dimensional surface in front of us. In addition we can move the central figure and the image plane of the projection, so we can simulate the moving position of the observer at fixed objects on the computer screen (see first our figures in reverse order). Supported by DAAD 2008 Multimedia Technology for Mathematics and Computer Science Education.     

Linear groups with rank restrictions on the subgroups of infinite central dimension

The authors study linear groups of infinite central dimension and of infinite p-rank all of whose proper subgroups of infinite p-rank are of finite central dimension.     

A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

The main goals of this paper are to: i) relate two iteration-complexity bounds derived for the Mizuno-Todd-Ye predictor-corrector (MTY P-C) algorithm for linear programming (LP), and; ii) study the geometrical structure of the LP central path. The first iteration-complexity bound for the MTY P-C algorithm considered in this paper is expressed in terms of the integral of a certain curvature function over the traversed portion of the central path. The second iteration-complexity bound, derived recently by the authors using the notion of crossover events introduced by Vavasis and Ye, is expressed in terms of a scale-invariant condition number associated with m × n constraint matrix of the LP. In this paper, we establish a relationship between these bounds by showing that the first one can be majorized by the second one. We also establish a geometric result about the central path which gives a rigorous justification based on the curvature of the central path of a claim made by Vavasis and Ye, in view of the behavior of their layered least squares path following LP method, that the central path consists of long but straight continuous parts while the remaining curved part is relatively “short”. R. D. C. Monteiro was supported in part by NSF Grants CCR-0203113 and CCF-0430644 and ONR grant N00014-05-1-0183. T. Tsuchiya was supported in part by Japan-US Joint Research Projects of Japan Society for the Promotion of Science “Algorithms for linear programs over symmetric cones” and the Grants-in-Aid for Scientific Research (C) 15510144 of Japan Society for the Promotion of Science.     

On the limiting distribution of sample central moments

We investigate the limiting behavior of sample central moments, examining the special cases where the limiting (as the sample size tends to infinity) distribution is degenerate. Parent (non-degenerate) distributions with this property are called singular, and we show in this article that the singular distributions contain at most three supporting points. Moreover, using the delta-method, we show that the (second-order) limiting distribution of sample central moments from a singular distribution is either a multiple, or a difference of two multiples of independent Chi-square random variables with one degree of freedom. Finally, we present a new characterization of normality through the asymptotic independence of the sample mean and all sample central moments.

     

Central simple superalgebras with anti-automorphisms of order two of the first kind

By a theorem of Albert's, a central simple associative algebra has an involution of the first kind if and only if it is of order 2 in the Brauer group. Our main purpose is to develop the theory of existence of anti-automorphisms of order 2 of the first kind on finite dimensional central simple associative superalgebras over K, where K is a field of arbitrary characteristic. First we need to generalize the Skolem–Noether Theorem to the superalgebra case. Then we show which kind of finite dimensional central simple superalgebras have an anti-automorphism of order 2 of the first kind.     

Refinement of the gravitational energy definition

We analyze the error arising in the well-known “energy” method for calculating the central density of a white dwarf with maximum possible mass in the framework of the theory of tetrad energy-momentum complexes of the gravitational field. We choose the preferable complex by comparing the central density calculated using each of the three complexes under study with its value obtained by numerically integrating the Einstein equations.     

Solvable infinite-dimensional linear groups with restrictions on the nonabelian subgroups of infinite rank

Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class.     

Some properties of the Schröder numbers

In the paper, the authors present some properties, including convexity, complete monotonicity, product inequalities, and determinantal inequalities, of the large Schröder numbers and find three relations between the Schröder numbers and central Delannoy numbers. Moreover, the authors sketch generalizing the Schröder numbers and central Delannoy numbers and their generating functions.     

New central polynomials for the matrix algebra

Forn≥3 we find a central polynomial of degree (n−1)²+4 for then×n matrix algebra over a field of characteristic 0. Forn=3,4 our polynomial coincides with the known central polynomials of minimal degree and forn>4 the result gives new central polynomials. Until now, forn>4 the minimal degree of the known central polynomials wasn ². Partially supported by the Alexander von Humboldt Foundation in Germany and by Grant MM2/91 of the Ministry of Education and Science in Bulgaria.     

Weighted Estimates for Commutators of Hausdorff Operators on the Heisenberg Group

The aim of this paper is to give some sufficient conditions for the boundedness of commutators of Hausdorff operators with symbols in weighted central BMO type spaces on the Herz spaces, central Morrey spaces and Morrey-Herz spaces associated with both power weights and Muckenhoupt weights on the Heisenberg group.

     

The derivation algebra and the universal central extension of the q-analog of the virasoro-like algebra *

In this paper, the derivation algebra and the universal central extension of the q-analog of the Virasoro-like algebra are given.     

Nonvanishing of Hecke <Emphasis Type="Italic">L</Emphasis>-functions and the Bloch–Kato conjecture

In this paper we study the central values of L-functions associated to a large class of algebraic Hecke characters of imaginary quadratic fields. When these central values are nonzero, the Bloch–Kato conjecture predicts an exact formula for the algebraic parts of the central values in terms of periods and arithmetic data, most notably the Selmer groups corresponding to the Hecke characters. We investigate the nonvanishing of these central values, and prove the p-part of the Bloch–Kato conjecture in these cases for primes p which split in K.     

On the self-intersections of curves deep in the lower central series of a surface group

We give various estimates of the minimal number of self-intersections of a nontrivial element of the kth term of the lower central series and derived series of the fundamental group of a surface. As an application, we obtain a new topological proof of the fact that free groups and fundamental groups of closed surfaces are residually nilpotent. Along the way, we prove that a nontrivial element of the kth term of the lower central series of a nonabelian free group has to have word length at least k in a free generating set.     

George Dantzig in the development of economic analysis

The role of optimization is central to economic analysis, particularly in its “neoclassical” phase, since about 1870, and is therefore highly compatible with the impulse behind linear programming (LP), as developed by Dantzig. LP’s stress on alternative activities fits very well with modern economic analysis. The concept of economic equilibrium, properly understood, required the central notion of complementary slackness. so central in LP.

LP was seen as a tool for actual implementation of neoclassical principles precisely at a time when the market was under attack from several directions. The economists Koopmans and Hurwicz played an important role both in stimulating the crucial development of the simplex method and in relating LP to the world of economics.

LP became widely used in national economic planning, particularly for developing countries, and for the study of individual industries, especially the energy sector. The works of Chenery and of Manne are central in these fields.

As respect for the usefulness of the market increased, the emphasis on national planning diminished and was replaced by an emphasis on equilibrium analysis, in which LP still plays a large part in the study of individual sectors, particularly energy.     

The lower central series of the free partially commutative group

This paper is devoted to the study of the lower central series of the free partially commutative groupF(A, ?) in connection with the associated free partially commutative Lie algebra. Using a convenient Magnus transformation, we show that the quotients of the lower central series ofF(A, ?) are free abelian groups and thatF(A, ?) can be fully ordered.