Decomposition methods in stochastic programming

Stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods, and stochastic decomposition methods for convex polyhedral multi-stage stochastic programming problems.     

Characterization of the Besov-Lipschitz and Triebel-Lizorkin spaces the caseq<1

Journal of Fourier Analysis and Applications -     

On the connectivity of graphs generated by a sum of random mappings

We consider four models of random directed multigraphs with n labeled vertices of out-degree d. First we establish formal relationships between our models with respect to exact and asymptotic (as n → ∞) probabilities of possessing a graph monotone property. We also study the asymptotic behavior of the strength of connectivity of the underlying simple graphs when d = o(n). © 1993 John Wiley & Sons, Inc.     

The program ORTOCARTAN for algebraic calculations in relativity

The program ORTOCARTAN can calculate the curvature tensors (Riemann, Ricci, Einstein and Weyl) from a given orthonormal tetrad representation of the metric tensor. It was first announced in 1981, but since then has undergone several extensions and transplants onto other computers. This article reviews the current status of the program from the point of view of a user. The following topics are discussed: the problems that the program can be applied to, the special features of the algorithms that make the program powerful, the technical requirements to run the program and two simple examples of applications.     

Analysis of the27Al(p, γ)28Si reaction at subbarrier energies in terms of the direct-semidirect model

Differential cross sections forγ-transitions to 12 states in²⁸Si following nonresonant proton capture in²⁷Al nuclei (E _p=1,625 keV) were measured and analysed in terms of the direct-semidirect model. The experimental data are reproduced only when the complex coupling constant with the GDR is enhanced for thef partial wave in the entrance channel.     

On the mixed valence of the chromium ions in the noncollinear ferrimagnetic spinels Mn1−xCuxCr2S4 (Where x = 0.85, 0.90, 0.95)

For the polycrystalline samples of Mn_1?xCu_xCr₂S₄ (x = 0.85, 0.90, 0.95) the magnetization was measured in the temperature range between 77 K and the Curie temperature, T_C, using a magnetic balance (Faraday's method) and pulsed magnetic fields up to 2.0 T. The magnetic susceptibility was measured between T_C and about 600 K. The Curie temperatures were obtained using the kink point method.In the temperature range between 4.2 and 77 K the magnetization was measured in stationary magnetic fields up to 14 T. The data indicate a noncollinear ferrimagnetic structure. The compounds under investigation can be treated as CuCr₂S₄ slightly doped with Mn, with a valence distribution Mn²⁺_1?xCu¹⁺_xCr³⁺_2?xCr⁴⁺_xS^2?₄.     

Differential cross sections for the charge exchange process π+p → π0 (π+p) at 8, 16 and 23 GeV/c

The differential cross section $\text{d}\text{σ}\text{d}\text{t′}$ for the charge-exchange process π⁺p → π⁰ (π⁺p) at 8, 16 and 23 GeV/c is presented for several regions of the π⁺p effective mass. It is found that the dip at t′ ≈ 0.6 (GeV/c)² which is observed in the Δ(1236) mass band becomes a less pronounced structure in the higher mass regions. However, while the slope of the $\text{d}\text{σ}\text{d}\text{t′}$ distributions in the near-forward direction decreases strongly with increasing π⁺p mass, there is no evidence that the observed structure moves to higher values of t′ as the π⁺p mass increases. These results are consistent with a Regge-exchange picture where the position of the dip is determined by the exchanged trajectory, but are inconsistent with a simple geometrical picture.     

Selective separation of metal ions by use of chelate-forming resins prepared by modification of conventional anion-exchangers with spadns and orange II

Anion-exchangers loaded with SPADNS or Orange II or SPADNS + Nitroso-R salt are used for selective separation of bismuth and cadmium, which are then determined by AAS.