An Improvement of the Rational Representation for High-Dimensional Systems

Journal of Systems Science and Complexity - Based on the rational univariate representation of zero-dimensional polynomial systems, Tan and Zhang proposed the rational representation theory for...     

Rational general solutions of higher order algebraic odes

This paper generalizes the method of Ngô and Winkler (2010, 2011) for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation (AODE) to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.     

Rational Solutions of High-Order Algebraic Ordinary Differential Equations

This paper considers algebraic ordinary differential equations(AODEs) and study their polynomial and rational solutions. The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE. An AODE satisfying this condition is called noncritical. Then the authors prove that some common classes of low-order AODEs are noncritical. For rational solutions, the authors determine a class of AODEs, which are called maximally comparable, such that the possible poles of any rational solutions are recognizable from their coefficients. This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient. Finally, the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs, which is applicable to 78.54% of the AODEs in Kamke's collection of standard differential equations.     

Determination and (re)parametrization of rational developable surfaces

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, the authors focus on the rational developable surfaces. For a given algebraic surface, the authors ?rst determine whether it is developable by geometric inspection, and then give a rational proper parametrization in the affrmative case. For a rational parametric surface, the authors also determine the developability and give a proper reparametrization for the developable surface.     

Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments. The authors first transform the problem into a parameterized polynomial optimization problem, and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming (SDP). A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function, and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs. At last, the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.     

The Invertibility of Rational Univariate Representations

In this paper, the so-called invertibility is introduced for rational univariate representations, and a characterization of the invertibility is given. It is shown that the rational univariate representations, obtained by both Rouillier’s approach and Wu’s method, are invertible. Moreover, the ideal created by a given rational univariate representation is defined. Some results on invertible rational univariate representations and created ideals are established. Based on these results, a new appr...     

Optimal Multimodel Representation by Laguerre Filters Applied to a Communicating Two Tank System

This paper presents the development of a new nonlinear representation by exploiting the multimodel approach and the new linear representation ARX-Laguerre for each operating region. The resulting multimodel, entitled ARX-Laguerre multimodel, is characterized by the parameter number reduction with a recursive representation. However, a significant reduction of this multimodel is subject to an optimal choice of Laguerre poles characterizing each local linear model ARX-Laguerre. Therefore, the authors propose an optimization algorithm to estimate, from input/output measurements, the optimal values of Laguerre poles. The ARX-Laguerre multimodel as well as the proposed optimization algorithm are tested on a continuous stirred tank reactor system (CSTR). Moreover, the authors take into account a practical validation on an experimental communicating two tank system (CTTS).     

The Fitzpatrick-Neville-Type Algorithm for Multivariate Vector-Valued Osculatory Rational Interpolation

In this paper,the authors first apply the Fitzpatrick algorithm to multivariate vectorvalued osculatory rational interpolation.Then based on the Fitzpatrick algorithm and the properties of an Hermite interpolation basis,the authors present a Fitzpatrick-Neville-type algorithm for multivariate vector-valued osculatory rational interpolation.It may be used to compute the values of multivariate vector-valued osculatory rational interpolants at some points directly without computing the interpolation function explicitly.     

The sufficient and necessary condition of the major stochastic preference rule in group decision making

Group decision making problem with stochastic preference is investigated.The authors present four rational conditions for testing group stochastic preference rule,and prove that the combination of these four rational conditions is the sufficient and necessary condition of major stochastic preference rule for group stochastic preference rule.     

Hypergames and bayesian games: A theoretical comparison of the models of games with incomplete information

The present study discusses the relationships between two independently developed models of games with incomplete information,hypergames(Bennett,1977) and Bayesian games(Harsanyi, 1967).The authors first show that any hypergame can naturally be reformulated in terms of Bayesian games in an unified way.The transformation procedure is called Bayesian representation of hypergame. The authors then prove that some equilibrium concepts defined for hypergames are in a sense equivalent to those for Bayesian games.Furthermore,the authors discuss carefully based on the proposed analysis how each model should be used according to the analyzer’s purpose.     

A Survey of the Representations of Rational Ruled Surfaces

The rational ruled surface is a typical modeling surface in computer aided geometric design. A rational ruled surface may have different representations with respective advantages and disadvantages. In this paper, the authors revisit the representations of ruled surfaces including the parametric form, algebraic form, homogenous form and Plücker form. Moreover, the transformations between these representations are proposed such as parametrization for an algebraic form, implicitization for a parametric form, proper reparametrization of an improper one and standardized reparametrization for a general parametrization. Based on these transformation algorithms, one can give a complete interchange graph for the different representations of a rational ruled surface. For rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces, the characterization methods are recalled to identify the ruled surfaces from them.

     

资源约束下的时间-费用交换问题研究

传统的活动网络时间 -费用交换问题着重研究如何通过增加费用压缩活动工期以实现项目费用最小 ,而没有考虑资源的约束 .考虑资源可用量限制情况下 ,建立了资源约束下的时间 -费用交换问题模型 .采用特殊编码方式为该模型设计了启发式遗传算法并编写了 VC++5 .0程序 ,用数值实例说明了该模型的合理性和程序的有效性 .该模型对项目业主和承包商之间的合同谈判决策具有借鉴意义 .     

因素空间理论与知识表示的数学框架（续）——DFE决策与因素状态的合成

本文是文〔１,２,３,４〕的继续,该文及后续论文仍将系统地研究因素空间理论及其在知识表示中的应用。首先介绍最大隶属原则,然后讨论基于反馈外延的决策,即ＤＦＥ决策,最后研究因素状态的合成方法。指出在很多情况下使用加权求和公式是不合理的,比如模糊控制中清晰化环节使用的加权求和公式或重心法就是不合理的。     

战略决策专家系统中的一种新知识表示方法

介绍了战略决策专家系统中一种新的知识表示方法“分解－综合”知识表示法，给出了“分解－综合”表示法的应用实例，指出了“分解－综合”表示法的优点.     

Heterogeneity,nonlinearity and endogenous market volatility

This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. An exogenous noise is introduced to the model with the assumption of IID normal innovations of the fundamental value in order to investigate how noisy dynamics interacts with deterministic process. The market is composed of two typical trader types: the rational fundamentalists and the boundedly rational traders governed by greed and fear. The interaction between noise and deterministic element determines the evolution process of the system as key parameters are changed. The authors find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S&P500 index, such as volatility clustering, fat tails (leptokurtosis), autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. The authors also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.     

森林分类经营条件下的生态补偿机制

对森林实施分类经营进行了分析,阐述了森林生态效益补偿的必要性,提出从森林合理分类、森林生态资产评估、森林生态健康经营成本、森林生态补偿系统的边界等方面来确定补偿机制标准。针对森林灾后的恢复和重建,提出了森林生态保险。参14。     

Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry

This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.     

Hierarchical hypergames and Bayesian games: A generalization of the theoretical comparison of hypergames and Bayesian games considering hierarchy of perceptions

This paper discusses the relationship of two independently developed models of games with incomplete information, hierarchical hypergames and Bayesian games. It can be considered as a generalization of the previous study on the theoretical comparison of simple hypergames and Bayesian games (Sasaki and Kijima, 2012) by taking into account hierarchy of perceptions, i.e., an agent’s perception about the other agents’ perceptions, and so on. The authors first introduce the general way of transformation of any hierarchical hypergames into corresponding Bayesian games, which was called as the Bayesian representation of hierarchical hypergames. The authors then show that some equilibrium concepts for hierarchical hypergames can be associated with those for Bayesian games and discuss implications of the results.     

论施肥系统工程

施肥是作物增产的重要手段。尤其是化肥施用,已成为现代农业生产中一项重要的技术措施。据联合国粮农组织以及各国专家的估计,粮食增产量中,30％～60％应归功于化肥的施用。中国农科院土壤肥料研究所张夫道等统计分析了我国解放后三十年农作物产量后指出,我国粮棉总产水平与化肥氮磷钾施用水平呈极显著的正相关。但另一方面,随着化肥等商品能投入的增加,使农业对外界的依赖性越来越大。1987年我国化肥施用量已达8377万吨,比1980年增加57.5％。化肥投入要占农作物生产物     

Hidden Markov Models: Inverse Filtering,Belief Estimation and Privacy Protection

A hidden Markov model(HMM) comprises a state with Markovian dynamics that can only be observed via noisy sensors. This paper considers three problems connected to HMMs, namely,inverse filtering, belief estimation from actions, and privacy enforcement in such a context. First, the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter. Next, the authors consider a rational decision-maker that forms a private belief(posterior distribution) on the state of the world by filtering private information. The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent. In the setting of adversarial systems, the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions. Applications range from financial portfolio investments to life science decision systems.