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81.
Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG()
D
. The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably. 相似文献
82.
梅家骝 《高校应用数学学报(A辑)》1989,4(4):541-549
本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。 相似文献
83.
P. Tils M. Loewenhaupt K. H. J. Buschow R. S. Eccleston 《Journal of magnetism and magnetic materials》2000,210(1-3)
Inelastic neutron scattering (INS) was used to study the magnetic excitations in the compounds Gd1−xYxFe2 and Gd2−xYxFe14B. Three inelastic magnetic lines were observed in the INS spectra of these compounds, the two smaller lines appearing as shoulders to the main line. From the concentration-dependent shift of the dominant magnetic line we have obtained experimental information of the strength of the Gd–Gd interaction in these materials and showed that the Gd–Gd contribution to the total molecular field experienced by the Gd moments is roughly an order of magnitude smaller than the contribution of the Gd–Fe interaction. Our results are compared with several earlier published results, including results of electronic band structure calculations. 相似文献
84.
首先在L-保序算子空间中引入层次ω-开集,讨论了它的一些基本性质;其次用层次ω-开集刻画了(ω_1,ω_2)-连续序同态和(ω_1,ω_2)-开序同态的一些新的特征性质. 相似文献
85.
M.A. Goberna E. González M.I. Todorov 《Journal of Mathematical Analysis and Applications》2010,364(1):209-221
Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. This paper provides five characterizations of the larger class of closed convex sets in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed in the paper. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed. 相似文献
86.
E. García-Matres J.L Martínez J. Rodríguez-Carvajal 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,24(1):59-70
A neutron diffraction study, as a function of temperature, of the title compounds is presented. The whole family (space group
Immm, a
≈ 3.8?, b
≈ 5.8?, c
≈ 11.3?) is structurally characterised by the presence of flattened NiO6 octahedra that form chains along the a-axis, giving rise to a strong Ni-O-Ni antiferromagnetic interaction. Whereas for Y-compound only strong 1D correlations exist
above 1.5 K, presenting the Haldane gap characteristic of 1D AF chain with integer spin, 3D AF ordering is established simultaneously
for both R and Ni sublattices at temperatures depending on the rare earth size and magnetic moment. The magnetic structures
of R2BaNiO5 ( R
=
Nd, Tb, Dy, Ho, Er and Tm) have been determined and refined as a function of temperature. The whole family orders with a magnetic
structure characterised by the temperature-independent propagation vector
= (1/2, 0, 1/2). At 1.5 K the directions of the magnetic moments differ because of the different anisotropy of the rare earth ions. Except
for Tm and Yb (which does not order above 1.5 K), the magnetic moment of the R3+ cations are close to the free-ion value. The magnetic moment of Ni2+ is around 1.4
, the strong reduction with respect to the free-ion value is probably due to a combination of low-dimensional quantum effects
and covalency. The thermal evolution of the magnetic structures from T
N
down to 1.5 K is studied in detail. A smooth re-orientation, governed by the magnetic anisotropy of R3+, seems to occur below and very close to T
N
in some of these compounds: the Ni moment rotates from nearly parallel to the a-axis toward the c-axis following the R moments. We demonstrate that for setting up the 3D magnetic ordering the R-R exchange interactions cannot
be neglected.
Received 19 July 2001 相似文献
87.
Arne Pfeilsticker 《Fuzzy Sets and Systems》1981,6(3):209-233
Ideas are presented to show how fuzzy mathematics can be applied in macro-economics in combination with the systems approach in order to bridge the gap between mathematical and language-oriented economists.Two reasons are given.From a mathematical point of view, fuzzy sets, fuzzy relations and fuzzy logic are not fuzzy at all. They are all well defined, but tend to be more complicated than traditional, mathematical concepts used in economics.From a language-oriented economist's point of view, fuzzy sets, etc. are used to express mathematically the type of concepts which are typical in language and most valuable in dealing with complex systems like an economy.The paper deals with economics in general terms, but examples are provided to illustrate the ideas. 相似文献
88.
Tuan-Fang Fan Churn-Jung Liau Duen-Ren Liu 《European Journal of Operational Research》2011,213(1):597-278
Attribute reduction is very important in rough set-based data analysis (RSDA) because it can be used to simplify the induced decision rules without reducing the classification accuracy. The notion of reduct plays a key role in rough set-based attribute reduction. In rough set theory, a reduct is generally defined as a minimal subset of attributes that can classify the same domain of objects as unambiguously as the original set of attributes. Nevertheless, from a relational perspective, RSDA relies on a kind of dependency principle. That is, the relationship between the class labels of a pair of objects depends on component-wise comparison of their condition attributes. The larger the number of condition attributes compared, the greater the probability that the dependency will hold. Thus, elimination of condition attributes may cause more object pairs to violate the dependency principle. Based on this observation, a reduct can be defined alternatively as a minimal subset of attributes that does not increase the number of objects violating the dependency principle. While the alternative definition coincides with the original one in ordinary RSDA, it is more easily generalized to cases of fuzzy RSDA and relational data analysis. 相似文献
89.
FAN CuiLing LEI JianGuo & SHAN XiuLing School of Sciences Nantong University Nantong China College of Mathematics Information Science Hebei Normal University Shijiazhuang 《中国科学 数学(英文版)》2011,(1)
Difference systems of sets (DSSs) are combinatorial configurations which were introduced in 1971 by Levenstein for the construction of codes for synchronization. In this paper, we present two kinds of constructions of difference systems of sets by using disjoint difference families and a special type of difference sets, respectively. As a consequence, new infinite classes of optimal DSSs are obtained. 相似文献
90.
We give the formulas of two-pion Hanbury-Brown-Twiss (HBT) correlation function for a partially coherent evolution pion-emitting source, using quantum probability amplitudes in a path-integral formalism. The multiple scattering of the particles in the source is taken into consideration based on Glauber scattering theory. Two-pion interferometry with effects of the multiple scattering and source collective expansion is examined for a partially coherent source of hadronic gas with a finite baryon density and evolving hydrodynamically. We do not find observable effect of either the multiple scattering or the source collective expansion on HBT chaotic parameter. 相似文献