On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

On the scales of computability potentials of finite algebras: Results and problems

We give a review of general known results on problems concerning the structure of scales of computability potentials of n-element algebras. We also formulate a number of natural open problems. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 145–164, 2003.     

双奇核188Au的准粒子带结构研究

利用在束γ谱学实验技术, 通过¹⁷³Yb(¹⁹F,4nγ)反应 布居了¹⁸⁸Au的高自旋态, 并对其准粒子带结构进行了研究. 基于实验测量结果, 对原有的双奇核¹⁸⁸Au能级纲图做了较大的修改. 通过系统性比较, 对15⁺以上的能级结构进行了讨论.     

Sorption and Catalytic Activity of Adsorbent-Catalyst Based on Montmorillonite Modified with Cr(III) and Cu(II) Mixed Oxides

The sorption properties of mixed adsorbent-catalyst based on high-silica zeolite and montmorillonite modified with mixed oxides of Cr(III) and Cu(II) with respect to organic compounds of various classes were studied, and the optimal dynamic conditions of its operation were determined.     

Writhing instabilities of twisted rods: from infinite to finite length

We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable through out. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behavior. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood.     

Plasticity field adjacent to faces of asperities on a rotating roll after initial indentation into a half-space

The plastic deformation field near the horizontal surface of a half space of perfectly plastic material associated with an indenting rotating rigid tooth is studied using slip line theory. The tooth is one of many on a roll surface and indents first into the half-space material and then rotates about the roll center. A slip line field is proposed for the deforming plastic region and a solution scheme is outlined. The emphasis is on determining the shape of the deforming region, especially that of the free surface. The study has a potential application in roughness transfer in metal forming processing.     

Synthesis and crystal structure of bis(di-n-butyldithiocarbamato)(1,10-phenanthroline)cadmium(II)

A new mixed-ligand complex, Cd(S₂CN(C₄H₉)₂)₂Phen, is synthesized and investigated by thermal, element, and IR analyses and by diffractometry of polycrystals (DRON-3M, CuK_α radiation, Ni filter). The crystal structure was determined on a CAD-4 Enraf-Nonius automatic diffractometer (MoK_α radiation, θ from 1.5 to 25?, 2325 nonzero independent reflections, 190 refined parameters, R = 0.036 for I > 2Σ(I)). Crystal data for C₃₀H₄₄CdN₄S₄ : a = 15.592(3), b = 22.724(5), c = 9.922(2) å, space group Pbcn, V = 3515.5(12) å₃, Z = 4, M = 701.33, d_calc = 1.325 g/cm³. The structure involves monomeric molecules in which the cadmium atom has a distorted octahedral environment.