Hinged dissection of polyominoes and polyforms

A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edge-to-edge gluings of n congruent copies of a polygon P that join corresponding edges of P. This construction uses kn pieces, where k is the number of vertices of P. When P is a regular polygon, we show how to reduce the number of pieces to k/2(n−1). In particular, we consider polyominoes (made up of unit squares), polyiamonds (made up of equilateral triangles), and polyhexes (made up of regular hexagons). We also give a hinged dissection of all polyabolos (made up of right isosceles triangles), which do not fall under the general result mentioned above. Finally, we show that if P can be hinged into Q, then any edge-to-edge gluing of n congruent copies of P can be hinged into any edge-to-edge gluing of n congruent copies of Q.     

矩阵特征值的一类新的存在性区域

用盖尔斯果林圆盘定理估计矩阵特征值是一个经典的方法，后人对此定理虽有许多改进，例如用卵形区域代替盖氏圆盘，但都显得粗糙，本文的研究得出了一类新的特征值存在区域，它们与盖氏圆盘等方法结合结合能提高估计的精确度。     

Nielsen numbers of mappings of surfaces

With each continuous map f of a compact polyhedron into itself there is associated a certain natural number, its Nielsen number N(f). The Nielsen number N(f) is bounded below by the number of fixed points of any map homotopic to f. The question of the sharpness of this estimate is classical: can one find for a given map f a map homotopic to it having exactly N(f) fixed points? It is known that this estimate is not sharp in general and that it is sharp for maps of compact polyhedra, which do not have locally separating points and which are not surfaces. The main result of the paper shows that this estimate is sharp for homotopy self-equivalence of compact surfaces. Its proof is based on Thurston's theory of diffeomorphisms of surfaces. In addition examples of maps of compact surfaces into themselves are discussed in the paper for which it seems that this estimate is not sharp.     

Majorization, 4G Theorem and Schrödinger perturbations

Schrödinger perturbations of transition densities by singular potentials may fail to be comparable with the original transition density. For instance, this is so for the transition density of a subordinator perturbed by any time-independent unbounded potential. In order to estimate such perturbations, it is convenient to use an auxiliary transition density as a majorant and the 4G inequality for the original transition density and the majorant. We prove the 4G inequality for the 1/2-stable and inverse Gaussian subordinators, discuss the corresponding class of admissible potentials and indicate estimates for the resulting transition densities of Schrödinger operators. The connection of the transition densities to their generators is made via the weak-type notion of fundamental solution.     

On the stability of a class of splitting methods for integro-differential equations

The classical convection–diffusion–reaction equation has the unphysical property that if a sudden change in the dependent variable is made at any point, it will be felt instantly everywhere. This phenomena violate the principle of causality. Over the years, several authors have proposed modifications in an effort to overcome the propagation speed defect. The purpose of this paper is to study, from analytical and numerical point of view a modification to the classical model that take into account the memory effects. Besides the finite speed of propagation, we establish an energy estimate to the exact solution. We also present a numerical method which has the same qualitative property of the exact solution. Finally we illustrate the theoretical results with some numerical simulations.     

Convergence of a Simulated Annealing Algorithm for Continuous Global Optimization

In this paper a simulated annealing algorithm for continuous global optimization will be considered. The algorithm, in which a cooling schedule based on the distance between the function value in the current point and an estimate of the global optimum value is employed, has been first introduced in Bohachevsky, Johnson and Stein (1986) [2], but without any proof of convergence. Here it will be proved that, under suitable assumptions, the algorithm is convergent     

单相关回归模型的效率及其模拟分析

本文研究一类单相关回归模型的效率及其应用,证明了对单相关回归模型的任一可估函数ｃ′β＝ｃ′（Ｘ′Ｘ）－Ｘ′Ｙ的最小二乘估计（ＬＳ）都是最佳线性一致无偏估计（ＢＬＵ）,给出了这类模型的均方误差比效率的下确界（ｉｎｆρＭＳＥＲ）．同时研究了用最小二乘估计代替最佳线性一致无偏估计时应注意的问题     

基于灰色理论的未观测经济规模估测——理论探讨及实证分析

一国未观测经济的规模大小,直接影响着政府统计的质量,其规模的衡量指标之一就是隐性就业规模.传统的CD函数模型估测隐性就业规模,一般采用回归分析法去估测参数.但是,回归分析法亦有其自身的缺陷.相比于传统方法,灰色理论是一种比较新颖的动态测算方法,它可以较准确地测算各个不同时期的CD函数待估系数.本文应用灰色理论的方法测算我国1982—2003年间的隐性就业规模,并基于测算结果进行了分析.     

A Successive Projection Algorithm for Solving the Multiple-Sets Split Feasibility Problem

The multiple-sets split feasibility problem (MSFP) arises in many areas and it can be unified as a model for many inverse problems where the constraints are required on the solutions in the domain of a linear operator as well as in the operator's range. Some existing algorithms, in order to get the suitable step size, need to compute the largest eigenvalue of the related matrix, estimate the Lipschitz constant, or use some step-size search scheme, which usually requires many inner iterations. In this article, we introduce a successive projection algorithm for solving the multiple-sets split feasibility problem. In each iteration of this algorithm, the step size is directly computed, which is not needed to compute the largest eigenvalue of the matrix or estimate the Lipschitz constant. It also does not need any step-size search scheme. Its theoretical convergence results are also given.     

Dominance and dependence in input-output analysis: the nonlinear (network) approach

In this paper, the network approach is applied to estimate the relative importance of sectors in a macro economy for which estimates of technical coefficients were originally derived using the Analytic Hierarchy Process. The proposed approach suggestes a plausible alternative, since the presence of nonlinear structural relations of an economic system involving intersectoral feedbacks cannot be examined within the framework of the standard input-output model.     

A comparison of kriging with nonparametric regression methods

“Kriging” is the name of a parametric regression method used by hydrologists and mining engineers, among others. Features of the kriging approach are that it also provides an error estimate and that it can conveniently be employed also to estimate the integral of the regression function. In the present work, the kriging method is described and some of its statistical characteristics are explored. Also, some extensions of the nonparametric regression approach are made so that it too displays the kriging features. In particular, a “data driven” estimator of the expected square error is derived. Theoretical and computational comparisons of the kriging and nonparametric regressors are offered.     

Social Interactions within a Dynamic Competitive Economy

This paper considers social interactions and investigates how far the properties of moderate social influence and of diminishing returns foster the uniqueness and stability of a dynamic competitive economy. In particular, in contrast to the static framework, it is shown that moderate social influence can neither ensure unique long run outcomes nor rule out other kinds of complexities such as indeterminacy; also, the assumption of diminishing returns for the aggregate economy does not eliminate any of these complexities. Instead, the (derived) property of moderate dynamic social influence, which accounts explicitly for intertemporal spillovers, provides the proper criterion for the (saddlepoint) stable evolution of a competitive economy.     

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the nean square errors criterion,where the model matrix need not have full rank and the dispersion matrix can be singular.Our results show that any one of both estimates cannot be always superior to the other.Some sufficient criteria for any one of them to be better than the other are established.Some interesting relations between these two estimates are also given.     

一类重尾风险因子的模拟及其投资高风险值和置信区间的估计

由于金融市场中的日周期或短周期对数回报率的样本数据多数呈现胖尾分布，于是现有的正态或对数正态分布模型都在不同程度上失效，为了准确模拟这种胖尾分布和提高投资风险估计及金融管理，本文引进了一种可根据实际金融市场数据作出调正的蒙特卡洛模拟方法．这个方法可以有效地复制金融产品价格的日周期对数回报率数据的胖尾分布．结合非参数估计方法，利用该模拟方法还得到投资高风险值以及高风险置信区间的准确估计。     

On conditions for estimating the precision of solutions of inverse problems

Examples exist of inverse problems for which no uniqueness theorem is known, yet the error in an approximate solution that has been obtained can be estimated. In the present paper we give conditions that make it possible to estimate the error of an approximate solution without using any corresponding uniqueness theorem. Bibliography: 10 titles. Translated fromProblemy Matematischeskoi Fiziki, 1998, pp. 141–150.     

Bounded influence regression using high breakdown scatter matrices

In this paper we estimate the parameters of a regression model using S-estimators of multivariate location and scatter. The approach is proven to be Fisher-consistent, and the influence functions are derived. The corresponding asymptotic variances are obtained and it is shown how they can be estimated in practice. A comparison with other recently proposed robust regression estimators is made.     

A bayesian approach to inference for monotone failure rates

In reliability theory, the notion of monotone failure rates plays a central role. When prior information indicates that such monotonicity is meaningful, it must be incorporated into the prior distribution whenever inference about the failure rates needs to be made. In this paper we show how this can be done in a straightforward and intuitively pleasing manner. The time interval is partitioned into subintervals of equal width and the number of failures and censoring in each interval is recorded. By defining a Dirichlet as the joint prior distribution for the forward or the backward differences of the conditional probabilities of survival in each interval, we find that the monotonicity is presenved in the posterior estimate of the failure rates. A posterior estimate of the survival function can also be obtained. We illustrate our method by applying it to some real life medical data.     

A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect

In observational cohort mortality studies with prolonged periods of exposure to the agent under study, it is not uncommon for risk factors for death to be determinants of subsequent exposure. For instance, in occupational mortality studies date of termination of employment is both a determinant of future exposure (since terminated individuals receive no further exposure) and an independent risk factor for death (since disabled individuals tend to leave employment). When current risk factor status determines subsequent exposure and is determined by previous exposure, standard analyses that estimate age-specific mortality rates as a function of cumulative exposure may underestimate the true effect of exposure on mortality whether or not one adjusts for the risk factor in the analysis. This observation raises the question, which if any population parameters can be given a causal interpretation in observational mortality studies?In answer, we offer a graphical approach to the identification and computation of causal parameters in mortality studies with sustained exposure periods. This approach is shown to be equivalent to an approach in which the observational study is identified with a hypothetical double-blind randomized trial in which data on each subject's assigned treatment protocol has been erased from the data file. Causal inferences can then be made by comparing mortality as a function of treatment protocol, since, in a double-blind randomized trial missing data on treatment protocol, the association of mortality with treatment protocol can still be estimated.We reanalyze the mortality experience of a cohort of arsenic-exposed copper smelter workers with our method and compare our results with those obtained using standard methods. We find an adverse effect of arsenic exposure on all-cause and lung cancer mortality which standard methods fail to detect.     

Asymptotics of resolvent integrals: The suppression of crossings for analytic lattice dispersion relations

We study the so-called crossing estimate for analytic dispersion relations of periodic lattice systems in dimensions three and higher. Under a certain regularity assumption on the behaviour of the dispersion relation near its critical values, we prove that an analytic dispersion relation suppresses crossings if and only if it is not a constant on any affine hyperplane. In particular, this applies to any dispersion relation which is an analytic Morse function. We also provide two examples of simple lattice systems whose dispersion relations do not suppress crossings in the present sense.