Control of complex ecological-economic systems

The paper is devoted to developing methods for control of ecological-economic systems consisting of three hierarchically subordinate subjects of control. In describing the dynamics of a system state, equations in partial derivatives that are solved numerically according to a semi-implicit scheme of the finite-difference method are used. To achieve its main goal (maintenance of an ecological subsystem in stable state), the subject of control of the upper level applies different control methods. Methods of hierarchical control (motivation, enforcement, and persuasion) that differ in the direction of action (on the objective function or domain of admissible controls) are proposed; examples of their use are represented and a comparative analysis of the obtained results is made.     

Minimum of power consumption in the problem of oscillation damping

Consideration was given to minimization of the L ¹-norm of control of the linear oscillatory system. For consumption of the energy resources required to damp oscillations, bilateral estimates were obtained.     

利用客户端脚本实现复合查询的新思路

本文主要针对目前网站上常用的查询系统所存在的某些常见问题而提出了一种新的查询设计思路,这种新的设计思路主要是在客户端利用JavaScript脚本语言对用户设置的查询条件进行预处理,让用户设置的条件以两种形式出现在系统中,一种形式方便方便用户阅读和理解,另一种形式用于真正的数据查询;此外,通过脚本语言将用户设置的查询条件保存于页面上列表中,用户可以随意组合现有的条件形成更为复杂的查询条件;同时用户也可以在列表中随意选择某个条件执行数据查询。     

Specific optimal estimation of special Markov jump processes

A solution to the filtering problem of states of special Markov jump processes that is optimal in the mean-square sense at the class of polynomial observation functions is presented. A comparison of the proposed estimates with the known estimates of optimal linear and nonlinear filtering is given.     

Form,interpretation, and the uniqueness of content: Response to Morris

In response to Michael Morris, I attempt to refute the crucial second premise of the argument, which states that the formality condition cannot be satisfied non-stipulatively in computational systems. I defend the view of representation urged in Meaning and Mental Representation against the charge that it makes content stipulative and therefore irrelevant to the explanation of cognition. Some other reservations are expressed.     

基于心态指标的区间灰数关联度模型

针对已有的灰色关联度模型仅适用于实数序列而不能应用于区间灰数序列的情况,通过引入决策者心态指标,将区间灰数序列转化为决策者心态指标序列,并且当决策者的心态指标确定时,心态指标序列就转化为实数序列,于是通过对体现决策者心态的实数序列建立灰色关联度模型,得到了反映出决策者心态的灰色关联度,从而构建了基于心态指标的区间灰数关联度模型。决策者处于不同心态时,可以通过调整其心态计算灰关联度,从而使建立的关联度模型更加符合实际。最后,通过计算实例说明了模型的可行性。     

On local convergence of a Newton-type method in Banach space

In this study we are concerned with the local convergence of a Newton-type method introduced by us [I.K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear equations in Banach spaces, Appl. Math. Lett. 5 (1992), pp. 7–9.] for approximating a solution of a nonlinear equation in a Banach space setting. This method has also been studied by Homeier [H.H.H. Homeier, A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math. 157 (2003), pp. 227–230.] and Özban [A.Y. Özban, Some new variants of Newton's method, Appl. Math. Lett. 17 (2004), pp. 677–682.] in real or complex space. The benefits of using this method over other methods using the same information have been explained in [I.K. Argyros, Computational theory of iterative methods, in Studies in Computational Mathematics, Vol. 15, C.K. Chui and L. Wuytack, eds., Elsevier Science Inc., New York, USA, 2007.; I.K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear equations in Banach spaces, Appl. Math. Lett. 5 (1992), pp. 7–9.; H.H.H. Homeier, A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math. 157 (2003), pp. 227–230.; A.Y. Özban, Some new variants of Newton's method, Appl. Math. Lett. 17 (2004), pp. 677–682.]. Here, we give the convergence radii for this method under a type of weak Lipschitz conditions proven to be fruitful by Wang in the case of Newton's method [X. Wang, Convergence of Newton's method and inverse function in Banach space, Math. Comput. 68 (1999), pp. 169–186 and X. Wang, Convergence of Newton's method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000), pp. 123–134.]. Numerical examples are also provided.     

High-accuracy quadrature methods for solving boundary integral equations of steady-state anisotropic heat conduction problems with Dirichlet conditions

This paper presents the mechanical quadrature methods (MQMs) for solving the boundary integral equations of steady-state anisotropic heat conduction equation on the smooth domains and polygons, respectively. The costless and high-accurate Sidi–Israeli quadrature formula are applied to deal with the integrals in which the kernels have a logarithmic singularity. Especially, the Sidi transformation is used for the polygon cases in order to obtain a rapid convergence by degrading the singularity at the corners on the boundary. The convergence and stability of the MQMs solution are proved based on Anselone's collective compact theory. In addition, asymptotic error expansion of the MQMs shows that the approximation order is of O(h³), where h is the partition size of the boundary. Finally, numerical examples are tested and results verify the theoretical analysis.