Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added. Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee     

Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

示性函数在初等概率论中的应用

示性函数在实分析等课程中很基本且应用广泛,但在初等概率论教材里应用不多.本文举例说明示性函数可以帮助学生理解初等概率论中一些基本概念、结论并精简其中一些计算.     

CCSD(T) expectation value calculations of first-order properties

An expectation value approach to calculations of first-order properties using the non-iterative, triple-excitation amplitudes in the coupled cluster wave function is exploited. Three methods are suggested and analysed using the many body perturbation theory (MBPT) expansion arguments. The first method, in which non-iterative triple-excitation amplitudes are used in the expression for the expectation values, makes the wave function accurate through the second order of MBPT. In the second method, which is an extension of the first, effects of triple-excitation amplitudes are coupled with single- and double-excitation amplitudes. The correlated density matrix equivalent through the fourth order to that obtained when CCSDT-la amplitudes are used is employed in the third method. The suggested methods are tested on dipole moment and polarizability calculations for several diatomic closed-shell molecules and are compared to other related approaches. Received: 15 May 1997 / Accepted: 5 June 1997     

非线型缩聚物的重均分子量

本文用数学期望方法研究了非线型共缩聚物的重均分子量,并推导出重均分子量表达式,将3种特例的理论曲线与实验结果相比较,两者基本相符。     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.     

连续区间数的中位算子及其灵敏度分析

研究决策信息以区间数形式给出的方案决策问题。考虑到区间数非均匀分布的特点,为避免区间极端值在区间数确定中产生较大误差,本文将中位数概念运用到区间数的确定上,提出OIP(Ordered Interval Point)有序中位算子。取单位区间单调函数(BUM函数)为二分之一所表示的值为权重,将区间数确定为一个实数,并研究算子单调性和有界性的初等运算性质。通过比较OIP算子与COWA算子对态度参数和区间长度的反应灵敏度,获得了在一定条件下OIP算子对态度参数反应更稳健,对区间长度反应更灵敏的结论。最后用算例证明该算子的可行性和有效性。     

关于保险精算函数的几点讨论

对目前精算教材中的有关保险精算函数作了较为细致的分析和比较,较为深入地讨论了均衡净保费的责任准备金计算的未来法及过去法的联系.     

Public policy structuring incorporating reciprocal expectation analysis

This paper proposes a method of structuring public policy by incorporating reciprocal expectation analysis. The proposed method is characterized by three components: identification of the problem structure perceived by stakeholders using cognitive maps, policy structuring analysis with a value–driver matrix and a reciprocal expectation matrix, and feasibility analysis of agreements among the stakeholders. The three types of relationship among stakeholders are derived from the feasibility analysis, which are “Dosho-imu”, “Isho-imu”, and “Domu”. Three tests of feasibility to reach the agreement are then proposed: “information-sharing test”, “bargaining test”, and “reframing test”. A case study is presented, applying the method to strategic transportation planning in the Kanto region of Japan. Finally, the potential functions of the proposed method in practice are discussed.     

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.