On k-Strictly Convex and k-Very Smooth Banach Spaces

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A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

A new algorithm for minimizing convex functions over convex sets

Let be a convex set for which there is an oracle with the following property. Given any pointz∈ℝ ⁿ the oracle returns a “Yes” ifz∈S; whereas ifz∉S then the oracle returns a “No” together with a hyperplane that separatesz fromS. The feasibility problem is the problem of finding a point inS; the convex optimization problem is the problem of minimizing a convex function overS. We present a new algorithm for the feasibility problem. The notion of a volumetric center of a polytope and a related ellipsoid of maximum volume inscribable in the polytope are central to the algorithm. Our algorithm has a significantly better global convergence rate and time complexity than the ellipsoid algorithm. The algorithm for the feasibility problem easily adapts to the convex optimization problem.     

Nonmonotone bundle-type scheme for convex nonsmooth minimization

In this paper, we present a general scheme for bundle-type algorithms which includes a nonmonotone line search procedure and for which global convergence can be proved. Some numerical examples are reported, showing that the nonmonotonicity can be beneficial from a computational point of view.This work was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell' Universitá e della Ricerca Scientifica e Tecnologica and by ASI: Agenzia Spaziale Italiana.     

On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Unusual impurity effect on room-temperature ferromagnet Sr3YCo4O10.56

We have prepared polycrystalline samples of Sr₃YCo₄O_10.56, Sr_2.4Ca_0.6YCo₄O_10.54, and Sr₃YCo_3.76Mn_0.24O_10.59, and found that these materials show unusual impurity effects on their transport and magnetic properties. A tiny amount of impurities such as Mn or Ca suppresses room-temperature ferromagnetism of Sr₃YCo₄O_10.56. With the suppression, their resistivities and thermopowers are also dramatically changed. We propose that the unusual impurity effects are caused by the suppression of orbital ordering.     

A reinvestigation of quaternary layered bismuth oxyhalides of the Sillén X1 type

A family of layered bismuth oxyhalides, L^I_0.5Bi_1.5O₂X and L^IIBiO₂X has been reinvestigated. Formation of X1-type Sillén compounds has been established for L^I=Li, Na, L^II=Ca, Sr, Ba, and X=Cl, Br, I, but the details of their crystal structures are different. While all L^I_0.5Bi_1.5O₂X, CaBiO₂Br, and CaBiO₂I adopt the disordered tetragonal Nd₂O₂Te structure, all compounds of L^II=Sr and Ba are orthorhombic and isostructural to PbSbO₂Cl, due to L/Bi cation ordering. Crystal structures have been determined for CaBiO₂I, SrBiO₂Br, SrBiO₂I, and BaBiO₂I. We discuss the factors which determine the occurrence and type of cation ordering in the quaternary bismuth and antimony X1-type oxyhalides. We also predict that more isostructural compounds can be prepared with antimony.     

由NO分子从头计算结果和紫外光电子能谱确定NO的分子结构

对于NO分子轨道的能级次序现有两种不同的说法,不少人根据NO与O_2~+是等电子体,由O_2~+分子的能级次序确定NO分子组态。本文用NO和O_2~(+)从头计算结果以及NO的紫外光电子能谱相结合的方法说明NO的5σ轨道是弱成键轨道,5σ的轨道能稍高于1π轨道能,也就是说NO的能级次序是与N_2分子相同的;NO与O_2~+虽是等电子体,但是能级次序并不相同,因此由O_2~+的能级次序确定NO分子的电子组态是不妥的。     

Selective ordering of surfactant modified gold nanoparticles in a diblock copolymer

Ordered aggregation of thiol-passivated Au nanoparticles in a diblock copolymer polystyrene-b-poly(methyl methacrylate) has been observed. The morphology of the diblock copolymer/Au-nanocomposite was dependent on the composition of the thiol modifier. For the thiol modifier that does not preferentially interact with one of the blocks, a perpendicular (relative to the substrate) lamellar morphology is maintained. However, for a thiol with a surfactant structure similar to one of the blocks, we observed a parallel lamellar morphology and speculate that the nanoparticles have localized at the microdomain interface. These conclusions are based on transmission electron microscopy, angle-dependent X-ray photoelectron microscopy and tensiometry. These results are consistent with theoretical predictions on the hybrid systems composed of block copolymers and nanoparticles.