Coincidence of the upper Kuratowski topology with the co-compact topology on compact sets, and the Prohorov property

For a Hausdorff space X, let F be the hyperspace of all closed subsets of X and H a sublattice of F. Following Nogura and Shakhmatov, X is said to be H-trivial if the upper Kuratowski topology and the co-compact topology coincide on H. F-trivial spaces are the consonant spaces first introduced and studied by Dolecki, Greco and Lechicki. In this paper, we deal with K-trivial spaces and Fin-trivial space, where K and Fin are respectively the lattices of compact and of finite subsets of X. It is proved that if C_k(X) is a Baire space or more generally if X has ‘the moving off property’ of Gruenhage and Ma, then X is K-trivial. If X is countable, then C_p(X) is Baire if and only if X is Fin-trivial and all compact subsets of X are finite. As for consonant spaces, it turns out that every regular K-trivial space is a Prohorov space. This result remains true for any regular Fin-trivial space in which all compact subsets are scattered. It follows that every regular first countable space without isolated points, all compact subsets of which are countable, is Fin-nontrivial. Examples of K-trivial non-consonant spaces, of Fin-trivial K-nontrivial spaces and of countably compact Prohorov Fin-nontrivial spaces, are given. In particular, we show that all (generalized) Fréchet–Urysohn fans are K-trivial, answering a question by Nogura and Shakhmatov. Finally, we describe an example of a continuous open compact-covering mapping f :X→Y, where X is Prohorov and Y is not Prohorov, answering a long-standing question by Topsøe.     

Approximation by modified Szasz—Mirakjan operators on weighted spaces

The theorems on weighted approximation and the order of approximation of continuous functions by modified Szasz—Mirakjan operators on all positive semi-axis are established.     

One-Dimensional P-Algorithm with Convergence Rate O(n−3+δ) for Smooth Functions

Algorithms based on statistical models compete favorably with other global optimization algorithms as shown by extensive testing results. A theoretical inadequacy of previously used statistical models for smooth objective functions was eliminated by the authors who, in a recent paper, have constructed a P-algorithm for a statistical model for smooth functions. In the present paper, a modification of that P-algorithm with an improved convergence rate is described.     

概率约束随机规划的一种近似方法及其它的有效解模式

根据最小风险的投资最优问题，我们给出了一个统一的概率约束随机规划模型。随后我们提出了求解这类概率约束随机规划的一种近似算法，并在一定的条件下证明了算法的收敛性。此外，提出了这种具有概率约束多目标随机规划问题的一种有效解模型。     

Globally Convergent Broyden-Like Methods for Semismooth Equations and Applications to VIP, NCP and MCP

In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complementarity fails to hold. We pay particular attention to semismooth equations arising from nonlinear complementarity problems, mixed complementarity problems and variational inequality problems. We show that under certain conditions, the related methods based on the perturbed Fischer–Burmeister function, Chen–Harker–Kanzow–Smale smoothing function and the Gabriel–Moré class of smoothing functions converge globally and superlinearly.     

A note on an algorithm for generalized fractional programs

We present a modification of an algorithm recently suggested by the same authors in this journal (Ref. 1). The speed of convergence is improved for the same complexity of computation.The research of S. Schaible was supported by Grants A4534 and A5408 from NSERC.     

A successive quadratic programming algorithm with global and superlinear convergence properties

This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.     

UPWIND SPLITTING SCHEME FOR CONVECTION-DIFFUSION EQUATIONS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｖｅｃｔｉｏｎ ｄｉｆｆｕｓｉｏｎｅｑｕａｔｉｏｎｉｓａｆｕｎｄａｍｅｎｔａｌｅｑｕａｔｉｏｎｄｅｓｃｒｉｂｉｎｇｔｈｅｐｒｏｃｅｓｓｏｆｆｌｕｉｄｔｒａｎｓ ｆｅｒ,ｆｏｒｅｘａｍｐｌｅ ,ｕｎｄｅｒｇｒｏｕｎｄｗａｔｅｒｃｏｎｔａｍｉｎａｔｉｏｎ ,ｄｉｓｐｌａｃｅｍｅｎｔｉｎｐｏｒｏｕｓｍｅｄｉａ[1,2 ] ,ａｎｄｓｏｏｎ .Ｆｏｒｏｖｅｒｃｏｍｉｎｇｔｈｅｎｕｍｅｒｉｃａｌｉｎｓｔａｂｉｌｉｔｙｏｆｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄｏｒｆｉｎｉｔｅｅｌｅｍｅ…     

NOTES ON ERDOS' CONJECTURE

Let Xn,n 1,be a sequence of independent random variables satisfying P(Xn = O) = 1 － P(Xn = an) = 1 － 1/pn,where an,n 1,is a sequence of real numbers,andpn isthenthprime,setFN(x)=P(N∑Xnn=1 x).The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent,it is both sufficient and necessary that there exist three numbers x0 and x1 ＜ x2 such that limsup(FN(x2) －FN(x1)) ＞ 0 holds,and Lo =N→∞ lim FN(x0) exists.Moreover,the authors point ont that they can also obtain the same N→∞ result in the weakened case of liminfP(Xn = 0) ＞ 0.n→∞