New explicit critical criterion of Hopf–Hopf bifurcation in a general discrete time system

Hopf–Hopf bifurcation is one of typical codimension-two bifurcations, which requires some rigid bifurcation conditions and occurs only in high-dimension systems. In this paper, a new critical criterion of this bifurcation is presented for a general discrete time system. Unlike the corresponding classical critical criterion (or the bifurcation definition), the new criterion is composed of a series of algebraic conditions explicitly expressed by the coefficients of the characteristic polynomial, which does not depend on eigenvalue computations of Jacobian matrix. This characteristic gives the advantage of the proposed criterion which is more convenient and efficient for detecting the existence of this type of codimension-two bifurcation or exploring the parameter mechanism of the bifurcation than the corresponding classical criterion. The equivalence between the proposed criterion and the corresponding classical criterion is rigorously proved. The bifurcation design problem of a three-degree-of-freedom vibro-impact system is used as example to show the effectiveness of the proposed criterion.     

Convexification for data fitting

The main results reported in this paper are two theorems concerning the use of a newtype of risk-averting error criterion for data fitting. The first states that the convexity region of the risk-averting error criterion expands monotonically as its risk-sensitivity index increases. The risk-averting error criterion is easily seen to converge to the mean squared error criterion as its risk-sensitivity index goes to zero. Therefore, the risk-averting error criterion can be used to convexify the mean squared error criterion to avoid local minima. The second main theorem shows that as the risk-sensitivity index increases to infinity, the risk-averting error criterion approaches the minimax error criterion, which is widely used for robustifying system controllers and filters.     

2-D digital filter realization without overflow oscillations

A novel criterion for the elimination of overflow oscillations in 2-D state-space digital filters described by the Roesser model employing two’s complement overflow arithmetic is presented. The criterion takes the form of linear matrix inequality (LMI) and, hence, is computationally tractable. The criterion is a generalization and improvement over an earlier criterion. An example shows the effectiveness of the new criterion.     

识别准则及其应用

针对模糊综合评判中使用最大属性准则可能得到不合理的结论 ,提出置信度准则作为新的识别准则 ,实例说明其更加合理 .并引入评分准则作为推广 .     

Elimination of limit cycles in a class of digital filters using single saturation nonlinearity

Using Lyapunov's direct method, a novel frequency-domain criterion for the elimination of limit cycles in a class of digital filters using single saturation nonlinearity is derived. The criterion turns out to be a generalization and improvement over an earlier criterion due to Kar and Singh. An example showing the effectiveness of the criterion is given. A graphical interpretation of a simplified version (involving one free parameter) of the criterion is discussed.     

Novel criterion for stability of discrete-time systems in a state-space realization utilizing saturation nonlinearities

A new criterion for the global asymptotic stability of discrete-time systems in a state-space realization utilizing saturation nonlinearities is presented. The form of the criterion is unconventional in that it offers the flexibility of using even an unsymmetric Lyapunov matrix P. A recently reported criterion is shown to be a special case of the present criterion. An example shows the effectiveness of the new criterion.     

Choice of weights in FMA estimators under general parametric models

The choice of weights in frequentist model average estimators is an important but difficult problem. Liang et al. (2011) suggested a criterion for the choice of weight under a general parametric framework which is termed as the generalized OPT (GOPT) criterion in the present paper. However, no properties and applications of the criterion have been studied. This paper is devoted to the further investigation of the GOPT criterion. We show that how to use this criterion for comparison of some existing weights such as the smoothed AIC-based and BIC-based weights and for the choice between model averaging and model selection. Its connection to the Mallows and ordinary OPT criteria is built. The asymptotic optimality on the criterion in the case of non-random weights is also obtained. Finite sample performance of the GOPT criterion is assessed by simulations. Application to the analysis of two real data sets is presented as well.     

JOINT MODEL AND CRITERION OPTIMAL EXPERIMENT DESIGN

In this paper,a new optimal design criterion--joint model and criterion optimal de-sign criterioon is put forward. The design that is subject to this criterion satisfies many kinds of lin-ear optimal criterion and D-optimal criterion on several experiment models at the same time. Theequivalent condition of this optimal design is given. Its iterative algorithm and the algorithm cover-genee are stated.     

Generalized criterion of the long-term strength of viscoelastic materials

A long-term strength condition of the same type as the Il'yushin [2] or Moskvitin [1] nonlinear criterion is proposed. A method is suggested for determining the stress and time functions forming part of the proposed criterion from the long-term strength diagrams and from the data of pulsed or stepped loading tests. It is shown, on the basis of the experimental data, that the proposed criterion, which in a particular case is identical with the Moskovitin criterion, describes the experimental results better than the Bailey criterion.     

Comments on: A comparative analysis for determining optimal price and order quantity when a sale increases demand

Although the net present value (NPV) criterion is theoretically the correct approach to developing optimal inventory policies, in the classical EOQ case, the average profit criterion generates solutions that are practically identical to those resulting from the NPV criterion. Nevertheless, a recent paper suggests that, when the demand for a product is price-elastic and a wholesaler offers a one-time-only price discount, use of the average profit criterion may obtain policies that are drastically suboptimal compared to the policies obtained by using the NPV criterion. We show that this suggestion is based on inaccurate models and inconsistent comparisons. Although in cases of large one-time-only discounts, there may be significant differences in the policies and consequences resulting from the two criteria, such large discounts are unrealistic. Furthermore, the larger the discount, the less practicable are the optimal order quantities based on either one of these criteria. Thus, in most real-life situations, the use of the average profit criterion does not result in serious suboptimization. In these situations, what may be important is not whether a retailer uses the NPV criterion or the average profit criterion, but whether the retailer can and does implement the optimal decisions resulting from the use of either criterion.     

预测复合材料开裂方向的比应变能密度准则

本文提出预测复合材料中裂纹方向的比应变能密度准则,并将Tsai-Hill与Norris准则扩展来预测复合材料中的开裂方向.用这三个准则预测了具有各种不同纤维方向的单向纤维复合材料的裂纹扩展方向,预测结果与现有的比正应力准则和应变能密度准则进行了对比.     

Comparison of criteria on the direction of crack extension

There are three famous criteria for the prediction on the direction of crack extension: maximum energy release rate criterion, local symmetric criterion and maximum stress criterion. It has already been proved that these criteria are different. In this paper, we show how to measure the difference between maximum energy release rate criterion and maximum stress criterion. The results in this paper and special solutions in Amestoy and Leblond (Internat. J. Solids Struct. 29 (1992) 465) indicate that it is enough to use the maximum stress criterion for the numerical prediction of crack path, if the stress intensity factor of the shearing mode is not too big.     

复合型脆断的周向应力应变乘积判据

本文提出一个新的复合型脆断判据,即周向应力应变乘积判据,该判据与实验数据非常一致.     

An information criterion for model selection with missing data via complete-data divergence

We derive an information criterion to select a parametric model of complete-data distribution when only incomplete or partially observed data are available. Compared with AIC, our new criterion has an additional penalty term for missing data, which is expressed by the Fisher information matrices of complete data and incomplete data. We prove that our criterion is an asymptotically unbiased estimator of complete-data divergence, namely the expected Kullback–Leibler divergence between the true distribution and the estimated distribution for complete data, whereas AIC is that for the incomplete data. The additional penalty term of our criterion for missing data turns out to be only half the value of that in previously proposed information criteria PDIO and AICcd. The difference in the penalty term is attributed to the fact that our criterion is derived under a weaker assumption. A simulation study with the weaker assumption shows that our criterion is unbiased while the other two criteria are biased. In addition, we review the geometrical view of alternating minimizations of the EM algorithm. This geometrical view plays an important role in deriving our new criterion.     

Bias correction of cross-validation criterion based on Kullback-Leibler information under a general condition

This paper deals with the bias correction of the cross-validation (CV) criterion to estimate the predictive Kullback-Leibler information. A bias-corrected CV criterion is proposed by replacing the ordinary maximum likelihood estimator with the maximizer of the adjusted log-likelihood function. The adjustment is just slight and simple, but the improvement of the bias is remarkable. The bias of the ordinary CV criterion is O(n^-1), but that of the bias-corrected CV criterion is O(n^-2). We verify that our criterion has smaller bias than the AIC, TIC, EIC and the ordinary CV criterion by numerical experiments.     

Improved global robust stability criterion for delayed neural networks

A criterion for the uniqueness and global robust stability of the equilibrium point of interval Hopfield-type delayed neural networks is presented. The criterion is a marked improvement over a recent criterion due to Cao, Huang and Qu.     

Analysis of crack formation in bonded lap joints using finite fracture mechanics on the basis of linear elasticity solutions.

In this work, crack formation and the corresponding failure load of bonded lap joints is analyzed. The analysis is based on linear elasticity solutions for bonded lap joints and makes use of the finite fracture mechanics. A hybrid criterion is applied that states the spontaneous formation of a crack of finite size if a stress and an energy criterion are fulfilled simultaneously. The stress distribution of a linear elasticity solution is used for the stress criterion and for the calculation of the incremental energy release rate which is necessary for definition of the energy criterion. The resulting fracture criterion is compared to literature results and shows a good agreement. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Further analysis on uniform stability of impulsive infinite delay differential equations

A criterion for the uniform stability of impulsive functional differential equations with infinite delays is presented by using Lyapunov functions and the Razumikhin technique. The criterion is more general than several recent works. An example showing the effectiveness and advantage of the present criterion is given.     

确定聚类数目的一个准则

Aiming to provide an appropriate number K of clusters, in this paper, we propose a new criterion function - H criterion function, whose three properties have also been proved. We validate the performance of the H criterion function on one artificial dataset and three real-world datasets, and the results are almostly consistent with a previous method. The nonparametric criterion we proposed is intuitive, simple and the computational cost is acceptable.     

The Condorcet criterion and committee selection

Recent studies have evaluated election procedures on their propensity to select committees that meet a Condorcet criterion. The Condorcet criterion has been defined to use majority agreement from voters' preferences to compare the selected committee to all other committees. This study uses a different definition of the Condorcet criterion as defined on committees. The focus of the new definition is on candidates. That is, we consider majority agreement on each candidate in the selected committee as compared to each candidate not in the selected committee.This new definition of the Condorcet criterion allows for the existence of majority cycles on candidates within the selected committee. However, no candidate in the non-selected group is able to defeat any candidate in the selected committee by majority rule. Of particular interest is the likelihood that a committee meeting this Condorcet criterion exists. Attention is also given to the likelihood that various simple voting procedures will select a committee meeting this Condorcet criterion when one does exist.