几类变权强化缓冲算子的构造研究

基于最基本的缓冲算子x(k)d=(x(k)²)/(px(k)+(1-p)x(n))变形,获得了几类范围大大拓宽的适用缓冲算子的构造方法,讨论了缓冲算子的内在联系,研究了缓冲算子调节度与可变权重之间的关系,解决了传统缓冲算子作用强度过强或过弱的问题.最后通过实例验证了变权缓冲算子的有效性和优越性.     

一种新型对数弱化缓冲算子的构造及其应用

缓冲算子是灰色预测研究中的重要内容.通过对现有缓冲算子的研究,结合对数函数的性质,提出基于对数函数的新型对数弱化缓冲算子和变权对数弱化缓冲算子;从理论上证明其为弱化缓冲算子,同时研究了关于序列调节度和改变序列光滑性方向的性质.通过实例验证,所提出的对数缓冲算子能够提高预测模型的精度.     

α-因子缓冲算子的构造及其性质的研究

为了解决灰色预测模型中的随机挠动序列问题,本文在灰色系统理论以及灰色预测建模技术的基础上,通过梳理历史文献的研究结果,提出了一个具有缓冲作用强度可调整的新型缓冲算子,即α-因子缓冲算子,该算子具有强度可调整、形式统一、预测结果优良等特性.具体来说就是通过调整强度系数可以改变其缓冲作用的强度大小、形式上兼顾了弱化缓冲算子和强化缓冲算子的统一性、在一定范围内的应用中预测结果优于其他的缓冲算子.实证的结果的确显示出了这些优良性质.     

基于残差GM(1,1)模型的强(弱)化缓冲算子还原模型

残差GM(1,1)模型预测效果相对于GM(1,1)模型较好,但是其要求残差尾段符号一致的自身缺陷常常存在,在实际工作中难以运用,需要解决其自身缺陷,故本篇提出新的模型,即基于残差尾段的强(弱)化缓冲算子还原模型.在残差GM(1,1)模型的基础上,以残差尾段序列作为原始数据,判断其是否满足灰色建模条件,如满足,则直接建模;如不满足,需要对其进行序列算子强(弱)化处理,进行GM(1,1)建模,之后进行强(弱)化缓冲算子还原.以实例为证,最终结果表明强(弱)化缓冲算子还原模型的预测精度稍有提高,且解决了自身缺陷和允许序列不符合灰色建模(诱发缺陷)的情况出现.     

基于部分数据缓冲的GM(1,1)模型预测精度研究

根据灰色系统理论中新信息优先利用原理,在对缓冲算子和数据灰色序∥生成研究的基础上,借用计量经济学虚拟变量的思想,构造一类利用缓冲算子对单调数列部分数据进行灰色序列生成的新方法,有效解决了冲击扰动数据序列在建模预测过程中常常出现的定量预测结果与定性分析结论不符的问题,实例分析表明,这类新的方法能显著提高GM(1,1)模型的预测精度.     

基于变权缓冲算子的灰色G(1,1)模型在地铁能耗预测中的应用

准确预测城市轨道交通系统能源消耗量对城市轨道交通建设规划、环境保护及节能减排具有重要意义.城市轨道交通系统能源消耗量逐年上升且呈指数型变化趋势,因而适合用灰色理论G(1,1)模型描述其变化规律.为了提高模型的预测精度,采用了变权缓冲算子对历史建模数据进行预处理.实例分析表明,经遗传算法权值优化的强化缓冲算子明显增强了建模数据的指数变化特征,提高了灰色G(1,1)模型的预测精度,使预测结果更贴近实际.     

一类可靠性模型的另一个特征值

研究带无穷多个部件的,由一个可靠机器,一个不可靠机器与一个缓冲库构成的系统主算子在左半复平面中的特征值,证明2√λη1μη2-λη1-μη2是该主算子的几何重数为1的一个特征值．     

残数定理在一个可靠性模型研究中的应用

本文研究一个可靠机器、一个不可靠机器与只容纳一个部件的缓冲库构成的系统的时间依赖解的渐近行为.首先在我们已有的工作基础上指出该模型的主算子生成的C_0-半群的本质增长界小于一个负数,由此推出0是该主算子的一级极点。然后用残数定理求该系统研究中出现的投影算子的表达式.最后证明该模型的时间依赖解指数收敛于其稳态解.本文的思想和方法适用于一个可靠机器、一个不可靠机器与容纳有限个部件的缓冲库构成的系统.     

一类可靠性模型时间依赖解的渐近性质

研究了带无穷多个部件的，由一个可靠机器，一个不可靠机器与一个缓冲库构成的系统解的渐近性质．先讨论了对应于该系统的主算子的谱特征并且得到了在虚轴上除了0点外其它所有点都属于该主算子的豫解集，0是该主算子及其共轭算子几何重数为1的特征值．然后将该结果与作者以前的结果结合起来推出该系统的时间依赖解当时刻趋向于无穷时趋向于该系统的稳态解．     

一类可靠性模型解的渐近稳定性

研究一个可靠机器，一个不可靠机器和一个缓冲库构成的系统。通过研究相应算子的谱特征得到该系统解的渐近稳定性。     

Generalized random linear operators on a Hilbert space

In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained.     

Boundedness and closedness of linear relations

This paper focuses on boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships with other two important induced linear operators are established. Several characterizations for closedness, closability, bundedness, relative boundedness and boundedness from below (above) of linear relations are given in terms of their induced linear operators. In particular, the closed graph theorem for linear relations in Banach spaces is completed, and stability of closedness of linear relations under bounded and relatively bounded perturbations is studied. The results obtained in the present paper generalize the corresponding results for single-valued linear operators to multi-valued linear operators, and some improve or relax certain assumptions of the related existing results.     

Real Linear Operator Theory and its Applications

Real linear operators arise in a range of applications of mathematical physics. In this paper, basic properties of real linear operators are studied and their spectral theory is developed. Suitable extensions of classical operator theoretic concepts are introduced. Providing a concrete class, real linear multiplication operators are investigated and, motivated by the Beltrami equation, related problems of unitary approximation are addressed.     

Linear functional equations of the first, second, and third kind in L 2

Under consideration are the functional equations of the first, second, and third kind with operators in wide classes of linear continuous operators in L ₂ containing all integral operators. We propose methods for reducing these equations by linear invertible changes either to linear integral equations of the first kind with nuclear operators or to equivalent linear integral equations of the second kind with quasidegenerate Carleman kernels. Some various approximate methods of solution are applicable to the so-obtained integral equations.     

商不可分解Banach空间上线性算子的谱

This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of Co-groups are always bounded linear operators, and that generators of Co-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of Co-semigroups in quotient indecomposable spaces are not necessarily bounded.     

Certain Norm Related Quantities of Unbounded Linear Operators

Certain norm related functions of linear operators are considered in the very general setting of not necessarily continuous linear operators in normed spaces. These are shown to be closely related to the theory of precompact, strictly cosingular and a class of Φ_? type operators in addition to having applications to perturbation theory. We also obtain some basic continuity and precompactness properties of linear operators in normed spaces which are expressed in terms of the functions under consideration.     

Iterative solution of linear equations with unbounded operators

A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space, including equations with unbounded, closed, densely defined linear operators. The method is proved to be stable towards small perturbation of the data. Some abstract results are established and used in an analysis of variational regularization method for equations with unbounded linear operators. The dynamical systems method (DSM) is justified for unbounded, closed, densely defined linear operators. The stopping time is chosen by a discrepancy principle. Equations with selfadjoint operators are considered separately. Numerical examples, illustrating the efficiency of the proposed method, are given.     

Null controllability of semilinear integrodifferential systems in Banach space

Sufficient conditions for null controllability of semilinear integrodifferential systems with unbounded linear operators in Banach space are established. The results are obtained using semigroup of linear operators, fractional powers of operators, and the Schauder fixed point theorem. An application to partial integrodifferential equations is given.     

W_2~m空间中样条插值算子与线性泛函的最佳逼近

In this paper,the convergency of spline interpolation operators is obtained,these spline operators are determined by linear differential operators and constraint functionals.The errors of the interpolating spline with EHB fanctionals are estimated.The best approximation of linear functionals on W2^n spaces are investigated,which let to a useful computational method for the approximation solution of higher order linear differential equations with multipoint boundary value conditions.     

Semilinear evolution equations with nonlinear constraints and applications

This paper deals with a general class of evolution problems for semilinear equations coupled with nonlinear constraints. Those constraints may contain compositions of nonlinear operators and unbounded linear operators, and hence the associated operators are not necessarily formulated in the form of continuous perturbations of linear operators. Accordingly, a family of equivalent norms is introduced to discuss 'quasidissipativity' in a local sense of the operators and a generation theory for nonlinear semigroups is employed to construct solution operators on bounded sets. It is a feature of our treatment that the resultant solution operators are obtained as nonlinear semigroups on the whole space which are not 'quasicontractive' but locally equi-Lipschitz continuous.