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101.
G. Z. Chelidze 《Mathematical Notes》2000,68(2):263-269
To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a
certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this
parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced,
and the relation between the two parameters is examined.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000. 相似文献
102.
In this note, we point out that the conclusion of Theorem 2.1 of Ref. 1 applies to any decomposable linear subspace of L
p
(T, E). 相似文献
103.
Received May 29, 2000 / Published online June 1, 2001 相似文献
104.
Kazutoshi Maegawa 《Proceedings of the American Mathematical Society》2008,136(8):2875-2879
For a dominant algebraically stable rational self-map of the complex projective plane of degree at least 2, we will consider three different definitions of the Fatou set and show the equivalence of them (Ascoli-Arzelà type theorem). As a corollary, it follows that all Fatou components are Stein. This is an improvement of an early result by Fornæss and Sibony.
105.
106.
107.
The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well. 相似文献
108.
Dobrila Petrovic Ying Xie Keith Burnham Radivoj Petrovic 《European Journal of Operational Research》2008
This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems. 相似文献
109.
H. Kawasaki 《Journal of Optimization Theory and Applications》2008,137(1):1-10
In some nonlinear diffusive phenomena, the systems have three or more stable states. Sternberg and Zeimer established the
existence of minimal solutions for the problem of partitioning a certain domain Ω⊂ℝ2 into three subdomains having least interfacial area. Ikota and Yanagida investigated stability and instability for stationary
curves with one triple junction and for stationary binary-tree type interfaces. In this paper, we introduce a new concept
of separation of three convex sets by a triangle, define a dual problem to the three-phase partition problem, and present
a duality theorem.
The author thanks Professor F. Giannessi for valuable comments, especially on Gale and Klee-type separation theorems.
This research was partially supported by Kyushu University 21st Century COE Program (Development of Dynamic Mathematics with
High Functionality) and by the Grant-in-Aid for General Scientific Research from the Japan Society for the Promotion of Science
14340037. 相似文献
110.
Self-Affine Sets and Graph-Directed Systems 总被引:1,自引:0,他引:1
Abstract. A self-affine set in R
n
is a compact set T with A(T)= ∪
d∈ D
(T+d) where A is an expanding n× n matrix with integer entries and D
={d
1
, d
2
,···, d
N
} ⊂ Z
n
is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the
case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in
wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether
such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T
o
≠ ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer. 相似文献