基于毕达哥拉斯犹豫模糊距离测度的灰关联双向投影决策法

为解决多属性决策单方向偏差难题所提出的灰关联投影法尚存在适用性差的技术不足。为此,在借鉴双向投影技术要点的基础上联合新型灰关联系数,并引入毕达哥拉斯犹豫模糊集的表达优势,提出基于毕达哥拉斯犹豫模糊距离测度的灰关联双向投影决策方法。新方法能够有效解决毕达哥拉斯犹豫模糊多属性决策问题,具有较高的分辨度。通过算例应用分析,直接验证了毕达哥拉斯犹豫模糊灰关联双向投影方法的实用性,间接验证了毕达哥拉斯犹豫模糊距离测度和灰关联双向投影法的有效性。     

Improving weighted information criterion by using optimization

Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results.     

Bayesian Nonparametric Inference for the Power Likelihood

The aim in this article is to provide a means to undertake Bayesian inference for mixture models when the likelihood function is raised to a power between 0 and 1. The main purpose for doing this is to guarantee a strongly consistent model and hence, make it possible to compare the consistent posterior with the correct posterior, looking for signs of discrepancy. This will be explained in detail in the article. Another purpose would be for simulated annealing algorithms. In particular, for the widely used mixture of Dirichlet process model, it is far from obvious how to undertake inference via Markov chain Monte Carlo methods when the likelihood is raised to a power other than 1. In this article, we demonstrate how posterior sampling can be carried out when using a power likelihood. Matlab code to implement the algorithm is available as supplementary material.     

An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle

We present "one-dimensional" Fourier theory on commutative groups T hH , 0 h h < X , 0< H h X within the framework of the so-called calculus on measure chains (or time scales). Depending on certain values of the graininess h and length H of the group the four classical types of Fourier transform are covered: Fourier integral ( T 0 X = R ), Fourier series ( T 1 X = Z ), Fourier analysis of periodic functions ( T 0,2 ~ = S 1 (0) unit circle) and discrete Fourier transform ( T 1 N = Z N ). We will present Fourier theory on these groups in a unified manner. This also allows to closely track the roles of the graininess h and length H of the group--especially for h M 0 and H M X . In the final part of the paper, we investigate the solution of a fundamental equation on T hH , which can be considered as a generalization of the Gauss function. It finally leads to a version of the Heisenberg uncertainty principle, which extends the classical one, valid for T 0 X = R , to the case T hH , where either h >0 or H < X .     

On First Order Impulsive Dynamic Equations on Time Scales

In this paper, the nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first order impulsive dynamic equations on time scales.     

A Finite-difference Solution of the Ginzburg–Landau Equation

Two finite-difference methods, which differ only in the way that they approximate the derivative boundary conditions, are developed for solving a particular form of the complex Ginzburg–Landau equation of superconductivity. The non-linear term in this equation is linearized in a way familiar to readers of Professor Mickens' work, and the numerical solution is obtained at each time step by solving a linear algebraic system. Consistency and stability are discussed and some numerical results are reported.     

具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性

本文研究具有Hille-Yosida算子的非线性随机脉冲泛函微分包含的可控性.假设多值非线性和脉冲函数满足由非紧性测度表示的正则性条件,利用非紧性测度理论和多值凝聚不动点定理,得到这类微分包含的可控性的充分条件.     

On the System of Hamilton–Jacobi and Transport Equations Arising in Geometrical Optics

Abstract

In the present article, we study the system of eikonal and transport equations arising in geometrical optics. The mathematical analysis is performed by using the suitable notion of solution, i.e., the viscosity solution for the Hamilton–Jacobi equation and the measure solution for the transport equation defined via the generalized Filippov characteristics. We study the stability as well as the geometry of the solution to the system.     

Instrumental Variable Estimation for Linear Stochastic Differential Equations Driven by Fractional Brownian Motion

Abstract

We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by fractional Brownian motion.