Delay-dependent stability criterion for delayed Hopfield neural networks

In this paper, a new Lyapunov–Krasovskii functional is constructed for delayed Hopfield neural networks, and several free-weighting matrices and S-procedure are employed to derive the delay-dependent stability criterion. The derived criterion is formulated in terms of linear matrix inequality (LMI). A numerical example is given to demonstrate the effectiveness and less conservativeness of the presented criterion.     

Criteria for the strong regularity of J-inner functions and γ-generating matrices

The class of left and right strongly regular J-inner mvf's plays an important role in bitangential interpolation problems and in bitangential direct and inverse problems for canonical systems of integral and differential equations. A new criterion for membership in this class is presented in terms of the matricial Muckenhoupt condition (A₂) that was introduced for other purposes by Treil and Volberg. Analogous results are also obtained for the class of γ-generating functions that intervene in the Nehari problem. The new criterion is simpler than the criterion that we presented earlier. A determinental criterion is also presented.     

A new development for the Tikhonov Theorem in nonlinear singular perturbation systems

This paper deals with the exponential stability of nonlinear perturbation systems under a new condition. A novel criterion of exponential stability of nonlinear systems is firstly given in a general form. In this criterion, a new kind of characteristic value is introduced, which makes the exponential stability measurable. Based on this criterion, a new development for the Tikhonov Theorem in nonlinear singular perturbation systems is presented.     

A scheme of adaptive control

A new scheme of adaptive control is proposed. This scheme does not require a priori knowledge of the structure of the plant to be controlled. The principal part of the scheme is a procedure which decides the order of the model of the plant. A criterion for the order determination is developed. Using this criterion, we can decide whether to keep the current controller or to adopt a new controller based on the information gathered during the operation of the system. The effectiveness of the scheme is illustrated by a numerical example. The Institute of Statistical Mathematics     

Strength of glass-reinforced plastics in the complex stress state

A new criterion of strength is proposed for anisotropic materials of the glass-reinforced plastic type. This criterion takes into account not only the different ultimate strengths in tension and compression in each direction but also the dependence of the ultimate shear strengths on the sign (direction) of the shear stresses. The criterion is given in tensor invariant form, so that it can be rewritten for any direction of the glass fibers. The criteria proposed by other authors, in particular, R. Hill's condition of plasticity [1], follow from the new generalized criterion as special cases. The results of experiments conducted both by the authors of the present article and by other investigators provide good confirmation of the proposed criterion.Mekhanika Polimerov, Vol. 1, No. 2, pp. 70–78, 1965     

Limit-Point Criteria For Not Necessarily Symmetric Ordinary Differential Expressions

A limit-point criterion for not necessarily symmetric differential expressions L of arbitrary order is proved by applying a known limit-point criterion for symmetric even-order differential expressions to (L⁺L)^p for some positive integer p where L⁺ denotes the formal adjoint of L. For certain differential expressions the results obtained from the new criterion are stronger than those obtained from the original one and can even be improved by increasing p.     

Recurrence properties of hypercyclic operators

We generalize the notions of hypercyclic operators, \(\mathfrak {U}\)-frequently hypercyclic operators and frequently hypercyclic operators by introducing a new concept in linear dynamics, namely \(\mathcal {A}\)-hypercyclicity. We then state an \(\mathcal {A}\)-hypercyclicity criterion, inspired by the hypercyclicity criterion and the frequent hypercyclicity criterion, and we show that this criterion characterizes the \(\mathcal {A}\)-hypercyclicity for weighted shifts. We also investigate which density properties can the sets \({N(x, U)=\{n\in \mathbb {N}\ ; \ T^nx\in U\}}\) have for a given hypercyclic operator, and we study the new notion of reiteratively hypercyclic operators.     

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.     

Involutive divisions for effective involutive algorithms

Properties of involutive divisions on monomials are studied. A new method of involutive graphs is developed. The concept of complete global involutive division is introduced. A criterion of Noetherianity of involutive divisions, a property of graphs of global involutive division, a test for completeness of global involutive division, and a criterion of global involutive division are considered. A new series of involutive divisions is obtained by the process of completion. The properties of the divisions contained in the constructed series are studied. It is shown that the divisions from the series are better than the classical involutive divisions for involutive algorithms. A problem stated by Gao is solved: another series of involutive divisions is obtained. It is proved that all divisions of this series are continuous. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 237–253, 2003.     

A note on rank-additivity

A new criterion is given for rank additivity of a collection of m × n complex matrices.     

On the Schur-Cohn problem

A new criterion (in terms of determinant inequalities) is obtained for all the roots of a real polynomial to lie inside the unit circle, i.e., a criterion of stability of periodic motions. In contrast to the Schur-Cohn criterion, the number of determinants used by us is by four times smaller.     

Inequality for a trace on a unital <Emphasis Type="Italic">C</Emphasis>*-algebra

A new inequality for a trace on a unital C*-algebra is established. It is shown that the inequality obtained characterizes the traces in the class of all positive functionals on a unital C*-algebra. A new criterion for the commutativity of unital C*-algebras is proved.     

Practical criteria for positive-definite matrix,M-matrix and Hurwitz matrix

All the conventional criterions to verify if a matrix is positive definite, Hurwitz or an M-matrix, such as Sylvester condition and Hurwitz theorem, require us to compute n determinants. This paper develops a new and simple criterion, based on a new type of Gaussian elimination process. In contrast to the traditional criterions, the new criterion only computes one determinate. Thus, the computing cost is greatly reduced. An illustrative example is given to show the application of the new criterion in the stability analysis of Hopfied-type neural networks with time delays.     

Criteria of algebraic independence with multiplicities and interpolation determinants

We generalize Gel'fond's criterion of algebraic independence by taking into account the values of the derivatives of the polynomials, and show how the new criterion applies to proving results of algebraic independence using interpolation determinants. We also establish a new result of approximation of a transcendental number by algebraic numbers of bounded degree and size. It contains an earlier result of E. Wirsing and also a result announced by A. Durand.

     

Fatigue Life Estimation for Layered Composites Under a Plane Stress State with the Use of a Nonlinear Fatigue Damage Accumulation Model

Mechanics of Composite Materials - A new fatigue failure criterion to predict the fatigue life of layered composites under a plane stress state is presented. The criterion is based on a nonlinear...     

The additivity criterion for finite metric spaces and minimal fillings

A new additivity criterion for finite metric spaces is obtained. The criterion is based on properties of minimal fillings in the sense of M. Gromov     

Finding the Number of Normal Groups in Model-Based Clustering via Constrained Likelihoods

Deciding the number of clusters k is one of the most difficult problems in cluster analysis. For this purpose, complexity-penalized likelihood approaches have been introduced in model-based clustering, such as the well-known Bayesian information criterion and integrated complete likelihood criteria. However, the classification/mixture likelihoods considered in these approaches are unbounded without any constraint on the cluster scatter matrices. Constraints also prevent traditional EM and CEM algorithms from being trapped in (spurious) local maxima. Controlling the maximal ratio between the eigenvalues of the scatter matrices to be smaller than a fixed constant c ? 1 is a sensible idea for setting such constraints. A new penalized likelihood criterion which takes into account the higher model complexity that a higher value of c entails is proposed. Based on this criterion, a novel and fully automated procedure, leading to a small ranked list of optimal (k, c) couples is provided. A new plot called “car-bike,” which provides a concise summary of the solutions, is introduced. The performance of the procedure is assessed both in empirical examples and through a simulation study as a function of cluster overlap. Supplementary materials for the article are available online.     

A new approach to filtering and adaptive control: stability results

A new approach to adaptive control is proposed. The principal distinguishing feature is the direct estimation and updating of the criterion function by means of a filtering operation on a vector of transitional pseudo-return functions. The data storage and computational problems often associated with explicit probability distribution updating via Bayes' rule are thus avoided. Convergence properties are established for a simple linear criterion function filter designed for a class of adaptive control problems typified by a well-known two-armed bandit problem. Optimality properties are established for the filter in a companion paper.     

A note on the selection of Benders’ cuts

A new cut selection criterion for Benders’ cuts is proposed and computationally analyzed. The results show that the new criterion is more robust—and often considerably faster—than the standard ones.     

自适应稀疏伪谱逼近新方法

自适应稀疏伪谱逼近法是广义混沌多项式类方法的最新进展,相对于其它方法具有计算精度高、速度快的优点.但它仍存在如下缺点：1）终止判据对逼近误差的估计精度偏低;2）只适用于单输出问题.本文提出了适用于多输出问题且具有更高逼近精度的自适应稀疏伪谱逼近新方法.本文首先提出了新型终止判据及基于此新型终止判据的自适应稀疏伪谱逼近新方法,并以命题的形式证明了新型终止判据相比于现有终止判据具有更高的估计精度,从而使基于此的逼近函数精度更接近于预期精度;进而,本文基于指标集的统一策略和新型终止判据,提出了适用于多输出问题的自适应稀疏伪谱逼近新方法,该方法因能充分利用各输出变量的抽样结果,具有比将单输出方法直接推广到多输出问题更高的计算效率.多个算例验证了本文所提出新方法的有效性和正确性.