我国固定资产投资边际效率问题研究

将回归分析与边际效用理论有机结合,深入研究我国固定资产投资对GDP边际贡献问题.研究结果表明在整个正实数区间内高技术产业固定资产投资对GDP边际贡献高于全社会固定资产投资和城镇房地产开发固定资产投资对GDP边际贡献;在0～349578.8207亿元投资区间内,城镇房地产开发固定资产投资对GDP边际贡献高于全社会固定资产投资边际贡献平均水平;当投资额度大于349578.8207亿元时,城镇房地产开发固定资产投资对GDP边际贡献小于全社会固定资产投资边际贡献平均水平.研究结果印证了科技是第一生产力的论断,同时也与我国当前控制房地产开发投入、鼓励发展高新技术产业等宏观经济政策相吻合.     

Marginal cost analysis of single-item maintenance policies with several decision variables

The marginal cost approach for the analysis of repair/replacementmodels was introduced by Berg in 1980 and has since been appliedto many maintenance policies of various complexity. All modelshitherto analysed in the literature by the marginal cost approachhave one single decision variable only, this being, typically,the age of the current item at the time of ordering or replacement.This paper is concerned with the extension of the marginal costtechnique to maintenance policies with several decision variables.After addressing the general framework appropriate for the multi-parametercase, we exemplify the workings of the technique by analysinga two-variable maintenance model involving replacement and minimalrepair. We demonstrate that the marginal cost approach is anattractive and intuitively appealing technique also for modelswith several decision variables. Just as in the single-parametersituation, the approach is amenable to economic interpretation,a welcome feature for users of maintenance models with a primeinterest in its economic (rather than its mathematical) aspects.As an added bonus of the marginal cost approach, in our example,some otherwise necessary tools from the theory of stochasticprocesses are dispensable.     

The persistence of ideal shock waves

Local-in-time piecewise smooth solutions to hyperbolic systems of conservation laws are constructed by means of Li-Yu theory. The novelty consists in the application of this approach to shock waves for which the number of outgoing modes is at least as big as the number of incoming modes (undercompressive shocks), the motivation in a possible interpretation from the zero dissipation limit point of view.     

Micromorphic theory of turbulence

Based on the theory of micromorphic fluid dynamics (MMF), a new theory of turbulence is introduced. The law of conservation of microinertia of MMF is replaced by a balance law of microinertia, with all other laws remaining unchanged, the theory is called, “extended micromorphic fluid dynamics”. The present theory of turbulence is founded on the extended theory. Thus, a new theory of turbulence, is founded on the first principles, not using any a priori closure assumptions or semi-empirical hypothesis. Field equations are solved for the two-dimensional steady channel flow. The mean velocity turbulent shear stress and all turbulent velocities are in remarkably good agreement with the experimentally observed turbulent velocities.     

A solidarity value forn-person transferable utility games

In this paper, we introduce axiomatically a new value for cooperative TU games satisfying the efficiency, additivity, and symmetry axioms of Shapley (1953) and some new postulate connected with the average marginal contributions of the members of coalitions which can form. Our solution is referred to as the solidarity value. The reason is that its interpretation can be based on the assumption that if a coalition, sayS, forms, then the players who contribute toS more than the average marginal contribution of a member ofS support in some sense their weaker partners inS. Sometimes, it happens that the solidarity value belongs to the core of a game while the Shapley value does not.This research was supported by the KBN Grant 664/2/91 No. 211589101.     

Micromorphic theory of turbulence

Based on the theory of micromorphic fluid dynamics (MMF), a new theory of turbulence is introduced. The law of conservation of microinertia of MMF is replaced by a balance law of microinertia, with all other laws remaining unchanged, the theory is called, “extended micromorphic fluid dynamics”. The present theory of turbulence is founded on the extended theory. Thus, a new theory of turbulence, is founded on the first principles, not using any a priori closure assumptions or semi-empirical hypothesis. Field equations are solved for the two-dimensional steady channel flow. The mean velocity turbulent shear stress and all turbulent velocities are in remarkably good agreement with the experimentally observed turbulent velocities.     

考虑双参照点和Choquet积分的新型研发机构绩效评估方法及应用

针对新型研发机构绩效评估值不确定、指标间存在关联、投资主体多元且有风险偏好、指标集权重未知等绩效问题,提出基于双参照点和Choquet积分的绩效评估方法。首先,结合新型研发机构的特点,构建绩效评估指标体系;其次,基于累积前景理论设计同行-期望双参照点;然后,构建指标间直接关联矩阵,依据K-可加模糊测度和平均边际贡献Banzhaf值优化求解指标集权重,代入Choquet积分方法和参照点权重公式计算各新型研发机构的综合绩效评估值,从而实现机构排序和问题分析。该方法考虑了新型研发机构的特点、数据不确定性、指标关联性、风险偏好性、权重未知性等因素,更加符合实际情况,案例验证了方法的有效性和实用性。     

A new conservation law for linear filtering processes

A new conservation law relating basic linear filtering theory quantities is derived. The physical interpretation of the law is given and discussion of its possible uses is presented.     

On membership and marginal values

In Kleinberg and Weiss, Math Soc Sci 12:21–30 (1986b), the authors used the representation theory of the symmetric groups to characterize the space of linear and symmetric values. We call such values “membership” values, as a player’s payoff depends on the worths of the coalitions to which he belongs and not necessarily on his marginal contributions. This could mean that the player would get some share of $v(N)$ regardless of whether or not he makes a marginal contribution to the welfare of society. In this paper it is demonstrated that the set of (non-marginal) membership values include those that embody numerous widely held notions of fairness, such as partial “benefit equalization”, individual rationality and “greater rewards follow from greater contributions”, where one’s contributions are not measured marginally. We also present a very simple and revealing way of interpreting all values, including those having a marginal interpretation. Finally, we obtain a mapping which effectively embeds the space of marginal values in the space of all membership values.     

扩充偏微分方程(组)守恒律和对称的辅助方程方法及微分形式吴方法的应用

首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性.     

Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter

We show how one can construct approximate conservation laws of approximate Euler-type equations via approximate Noether-type symmetry operators associated with partial Lagrangians. The ideas of the procedure for a system of unperturbed partial differential equations are extended to a system of perturbed or approximate partial differential equations. These approximate Noether-type symmetry operators do not form a Lie algebra in general. The theory is applied to the perturbed linear and nonlinear (1+1) wave equations and the Maxwellian tails equation. We have also obtained new approximate conservation laws for these equations.     

对冯·诺意曼“量子概率论”的两点质疑

本文对于公认的量子力学数学基础—冯·诺意曼概率论提出了两点质疑。从物理上讲,它将导致“粒子的势能以一定的概率超过总能量”这种违背能量守恒原理的结论。从数学上讲,它在某些方面还不如玻恩的概率解释(即常被物理学家称为“经典概率论”的数学意义的概率论)。因此,量子力学的数学基础似乎需要进一步发展和完善。     

Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory

This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing.     

A phenomenological constitutive model for magnetostrictive materials and ferroelectric ceramics

The contribution is concerned with a thermodynamic consistent constitutive model for magnetostrictive materials and ferroelectric ceramics. It captures the nonlinear phenomenological behavior which is described by hysteresis effects. Magnetostrictive alloys and ferroelectric ceramics belong to the multifunctional materials. In recent years these materials have become widely–used in actor and sensor applications. They characterize an inherent coupling between deformation and magnetic or electric field. Due to the similarities of the coupled differential equations a uniform approach is applied for both phenomena. The presented three–dimensional material model is thermodynamically motivated. It is based on the definition of a specific free energy function and a switching criterion. Furthermore an additive split of strain and the magnetic or electric field in a reversible and an irreversible part is suggested. The irreversible quantities serve as internal variables, which is analog to plasticity theory. A one–to–one–relation between the two internal variables provides conservation of volume for the irreversible strains. The presented material model can approximate the ferromagnetic or ferroelectric hysteresis curve and the related butterfly hysteresis. Furthermore an extended approach for ferrimagnetic behavior, which occurs in magnetostrictive materials, is presented. Some numerical simulations demonstrate the capability of the presented model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A marginal contribution coefficient for sequences of nonstationary continuous Markov chains

In this work, a set of sequences of information (time series), under nonstationary regime, with continuous space state, discrete time, and a Markovian dependence, is considered. A new model that expresses the marginal transition density function of one sequence as a linear combination of the marginal transition density functions of all sequences in the set is proposed. The coefficients of this combination are denominated marginal contribution coefficients and represent how much each transition density function contributes to the calculation of a chosen transition density function. The proposed coefficient is a marginal coefficient because it can be computed instantaneously, and it may change from one time to another time since all calculations are performed before stationarity is reached. This clearly differentiates the new coefficient from well‐known measures such as the cross‐correlation and the coherence. The idea behind the model is that if a specific sequence has a high marginal contribution for the transition density function from another sequence, the first may be replaced by the latter without losing much information that means that the knowledge of few densities should be enough to recover the overall behaviour. Simulations, considering 2 chains, are presented so as to check the sensitivity of the proposed model. The methodology is also applied to a real data originated from a wire‐drawing machine whose main function is to decrease the transverse diameter of metal wires. The behaviour of the level of acceleration of each bearing in relation to the other ones is then verified.     

Incremental net effects in multiple regression

A regular problem in regression analysis is estimating the comparative importance of the predictors in the model. This work considers the ‘net effects’, or shares of the predictors in the coefficient of the multiple determination, which is a widely used characteristic of the quality of a regression model. Estimation of ;the net effects can be a difficult task because multicollinearity among the regressors can produce negative inputs to multiple determination. This paper suggests estimating the incremental net effects as subsequent marginal inputs to the coefficient of multiple determination, and it is shown that the results coincide with estimation by cooperative game theory. This approach guarantees positive and interpretable net effects, which offers a better interpretation of the regression results.     

A pathway from Bayesian statistical analysis to superstatistics

Superstatistics and Tsallis statistics in statistical mechanics are given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by Mathai’s pathway model and further both components are replaced by Mathai’s pathway models. This produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics. It is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier. Those integrals are also connected to Krätzel integrals in applied analysis, inverse Gaussian densities in stochastic processes, reaction rate integrals in the theory of nuclear astrophysics and Tsallis statistics in nonextensive statistical mechanics. The final results are obtained in terms of Fox’s H-function. Matrix variate analogue of one significant specific case is also pointed out.     

Efficiency analysis of a multisectoral economic system

The present paper is concerned with efficiency analysis applied to a single economy represented by the Leontief input–output-model extended by the constraints for primary factors. First, the efficiency frontier is generated using a multi-objective optimization model instead of having to use data from different decision making units. The solutions of the multi-objective optimization problems define efficient virtual decision making units and the efficiency of the given economy is defined as the difference between the potential of an economy and its actual performance and can be obtained as a solution of a DEA model. It can be shown that the solution of the above defined DEA model yields the same efficiency score and the same shadow prices as the models by ten Raa (Linear analysis of competitive economics, LSE handbooks in economics. Harvester Wheatsheaf, New York, 1995; The economics of input–output analysis. Cambridge University Press, Cambridge, 2005) despite the different variables used in both models. Using duality theory of linear programming the equivalence of the approaches permits a clear economic interpretation. In the second part of the paper this approach is extended to the Leontief augmented model including emissions of pollutants and abatement activities. In this way the eco-efficiency of an economy can be analyzed.

Recessions are easily recognizable from a decrease in GDP. What really should interest us, however, is the difference between the potential of an economy and its actual performance (J. Stiglitz, 2002).