模糊逼近集与模糊逼近泛函映射

本文通过对模糊逼近集与模糊逼近泛函映射的建立和研究，为时间序列预测工作开辟新的途径，建立新的方法·     

分形集的逼近算法

1引 言 设(X,d)是一个完备的距离空间,给定了X上的压缩映射组f_1,f_2,…,f_m记S={f_1,f_2,…,f_m},A是X的一个非空子集,如果具有性质A=∪f_i(A),则称A关于S是     

集值Superpramart的上鞅逼近

文中讨论了可积随机集条件期望的若干性质,在此基础上给出了集值Ｓｕｐｅｒｐｒａｍａｒｔ的上鞅逼近,同时,证明了集值Ｓｕｐｅｒｐｒａｍａｒｔ 在Ｋｕｒａｔｏｗｓｋｉ－Ｍｏｓｃｏ意义下的收敛定理。     

密度泛函核估计的Bootstrap逼近

设Ｘ１，．．．，Ｘｎ是从分布密度函数为ｆ的总中抽取的ｉｉｄ样本，μ＝ＥＸ１本文研究了密度泛函θ＝ｆ（μ）的核型估计，ｆｎ（ｘ）为通常的Ｒｏｓｅｎｂｌａｔｔ－Ｐａｒｚｅｎ核估计。     

集值Pramart的一类鞅逼近

在X^＊可分的条件下,首先讨论了集值Pramart有关支撑函数和距离函数的性质,利用支撑函数和距离函数研究了集值Pramart鞅逼近,在此基础上,给出了集值Pramart的一类鞅分解.     

关于上密度无限制的缺项多项式加权逼近

令Ca为由在实轴R上连续且满足f(t)exp(-a(t))→0的函数f组成的Banach空间,其中a(t)为非负连续函数.在本文中,我们得到缺项的多项式在Ca中不完备的充分条件.本文的要点在于我们不要求上密度是有限的.     

集值Subpramart的另一类Riesz逼近

假定(X,‖.‖)为可分的Banach空间,X*为其对偶空间,X*可分。设(Ω,Φ,P)为完备的概率空间,{Φn,n≥1}为Φ的上升子σ-域族,且Φ=∨Φn本文首先讨论了集值Subpramart若干性质,在此基础上,给出了集值Subpramart的一类Riesz鞅逼近。     

条件密度近邻—核估计的逼近速度

本文首先了条件密度函数近邻一核估计的误差分布的正态逼近精度,然后利用随机加权法构造了近邻－核估计的随机加权统计量,获得了随机加权逼近精度。     

集值上鞅的轨道正则性

本文证明了在有限维Ｂａｎａｃｈ空间中，任一闭凸集值鞅（在ｋ－收敛意义下）存在右连左极修正．     

The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis

We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.     

An approximation of feasible sets in semi-infinite optimization

The paper deals with the feasible setM of a semi-infinite optimization problem, i.e.M is a subset of the finite-dimensional Euclidean space and is basically defined by infinitely many inequality constraints. Assuming that the extended Mangasarian-Fromovitz constraint qualification holds at all points fromM, it is shown that the quadratic distance function with respect toM is continuously differentiable on an open neighborhood ofM. If, in addition,M is compact, then the set , which is described by this quadratic distance function, is shown to be an appropriate approximation ofM and the setsM and can be topologically identified via a homeomorphism.     

A linear time approximation algorithm for multiprocessor scheduling

Givenn jobs andm identical processors anO(n) approximation algorithm is presented which tries to determine a nonpreemptive schedule with minimum finish time. Ifr is the number of jobs placed onto the processor with maximum finish time, then the worst case ratio of the new algorithm's finish time to the optimal solution is shown to be less thanrm/(rm–m+1). Extensive empirical results show that the new algorithm is competitive with the LPT algorithm in terms of quality of solution and faster in terms of computing time.     

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Closed convex sets and their best simultaneous approximation properties with applications

We develop a theory of best simultaneous approximation for closed convex sets in a conditionally complete lattice Banach space X with a strong unit. We study best simultaneous approximation in X by elements of closed convex sets, and give necessary and sufficient conditions for the uniqueness of best simultaneous approximation. We give a characterization of simultaneous pseudo-Chebyshev and quasi-Chebyshev closed convex sets in X. Also, we present various characterizations of best simultaneous approximation of elements by closed convex sets in terms of the extremal points of the closed unit ball B _X* of X*.     

On mean approximation by polynomials with gaps on Caratheodory sets

The paper presents some new results on the possibility of approximation by polynomials with gaps. The approximations are done in the norm of the space L _p , 1 ≤ p < + ∞, on the Caratheodory sets in the complex plane. The lacunary versions of some results by Farell—Markushevich, S. Sinanian, A. L. Shahinian are obtained (Theorems 1, 3, 5). Similar approximations by the real parts of lacunary polynomials are given (Theorems 2, 4, 6). Dedicated to the memory of academician S. N. Mergelyan     

On the approximation of continuous time threshold ARMA processes

Threshold autoregressive (AR) and autoregressive moving average (ARMA) processes with continuous time parameter have been discussed in several recent papers by Brockwellet al. (1991,Statist. Sinica,1, 401–410), Tong and Yeung (1991,Statist. Sinica,1, 411–430), Brockwell and Hyndman (1992,International Journal Forecasting,8, 157–173) and Brockwell (1994,J. Statist. Plann. Inference,39, 291–304). A threshold ARMA process with boundary width 2>0 is easy to define in terms of the unique strong solution of a stochastic differential equation whose coefficients are piecewise linear and Lipschitz. The positive boundary-width is a convenient mathematical device to smooth out the coefficient changes at the boundary and hence to ensure the existence and uniqueness of the strong solution of the stochastic differential equation from which the process is derived. In this paper we give a direct definition of a threshold ARMA processes with =0 in the important case when only the autoregressive coefficients change with the level of the process. (This of course includes all threshold AR processes with constant scale parameter.) The idea is to express the distributions of the process in terms of the weak solution of a certain stochastic differential equation. It is shown that the joint distributions of this solution with =0 are the weak limits as 0 of the distributions of the solution with >0. The sense in which the approximating sequence of processes used by Brockwell and Hyndman (1992,International Journal Forecasting,8, 157–173) converges to this weak solution is also investigated. Some numerical examples illustrate the value of the latter approximation in comparison with the more direct representation of the process obtained from the Cameron-Martin-Girsanov formula. It is used in particular to fit continuous-time threshold models to the sunspot and Canadian lynx series.Research partially supported by National Science Foundation Research Grants DMS 9105745 and 9243648.     

Universal meromorphic approximation on Vitushkin sets

The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ _n } ? ?, there exists a function ?, meromorphic on ?, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n _k } of ? such that $ \left\{ {\varphi \left( {z + \lambda _{n_k } } \right)} \right\} The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ _n } ⊂ ℂ, there exists a function ϕ, meromorphic on ℂ, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n _k } of ℕ such that converges to f(z) uniformly on K. A similar result is obtained for arbitrary domains G ≠ ℂ. Moreover, in case {λ _n }={n} the function ϕ is frequently universal in terms of Bayart/Grivaux [3]. Original Russian Text ? W.Luh, T.Meyrath, M.Niess, 2008, published in Izvestiya NAN Armenii. Matematika, 2008, No. 6, pp. 66–75.     

Polynomial time approximation schemes for dense instances of minimum constraint satisfaction

It is known that large fragments of the class of dense Minimum Constraint Satisfaction (MIN‐CSP) problems do not have polynomial time approximation schemes (PTASs) contrary to their Maximum Constraint Satisfaction analogs. In this paper we prove, somewhat surprisingly, that the minimum satisfaction of dense instances of kSAT ‐formulas, and linear equations mod 2, Ek‐LIN2, do have PTASs for any k. The MIN‐Ek‐LIN2 problems are equivalent to the k‐ary versions of the Nearest Codeword problem, the problem which is known to be exceedingly hard to approximate on general instances. The method of solution of the above problems depends on the development of a new density sampling technique for k‐uniform hypergraphs which could be of independent interest. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 73–91, 2003