Exploiting equalities in polynomial programming

We propose a novel approach for solving polynomial programs over compact domains with equality constraints. By means of a generic transformation, we show that existing solution schemes for the, typically simpler, problem without equalities can be used to address the problem with equalities.     

Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

There are infinitely many ways of representing a d.c. function as a difference of convex functions. In this paper we analyze how the computational efficiency of a d.c.optimization algorithm depends on the representation we choose for the objective function, and we address the problem of characterizing and obtaining a computationally optimal representation. We introduce some theoretical concepts which are necessary for this analysis and report some numerical experiments.      

Radial equivalence for the two basic nonlinear degenerate diffusion equations

In this paper we prove that there exists an explicit correspondence between the radially symmetric solutions of two well-known models of nonlinear diffusion, the porous medium equation and the p-Laplacian equation. We establish exact correspondence formulas between these solutions. We also study in detail the application of the results in the important case of self-similar solutions. In particular, we derive the existence of new self-similar solutions for the evolution p-Laplacian equation.     

3‐[(E)‐(3‐tert‐Butyl‐1‐phenyl‐1H‐pyrazol‐5‐yl)iminomethyl]quinolin‐2(1H)‐one: chains built by π‐stacking of hydrogen‐bonded R22(8) dimers

In the title compound, C₂₃H₂₂N₄O, there is evidence for some bond fixation in the aryl component of the quinolinone unit. Pairs of molecules related by inversion are linked into R₂²(8) dimers by almost linear N—H...O hydrogen bonds, and dimers related by inversion are linked into chains by a single aromatic π–π stacking interaction.     

Nickel and potassium co-modified β-Mo2C catalyst for CO conversion

Nickel and potassium co-medified β-Mo2C catalysts were prepared and used for CO hydrogenation reaction. The major products over β-Mo2C were C1-C4 hydrocarbons, only few alcohols were obtained. Addition of potassium resulted in remarkable selectivity shift from hydrocarbons to alcohols at the expense of CO conversion over β-Mo2C. Moreover, it was found that potassium enhanced the ability of chain propagation with a higher C2+OH production. Modified by nickel, β-Mo-2C showed a relatively high CO conversion, however, the products were similar to those of pure β-Mo2C. When co-modified by nickel and potassium,β-Mo2C exhibited high activity and selectivity towards mixed alcohols synthesis, and also the whole chain propagation to produce alcohols especially for the stage of C1OH to C2OH was remarkably enhanced. It was concluded that the Ni and K had, to some extent, synergistic effect on CO conversion.     

Butylene copolyesters based on aldaric and terephthalic acids. Synthesis and characterization

The synthesis, characterization, and some properties of new copolyesters analogous to poly(butylene terephthalate) (PBT), based on L ‐arabinaric and galactaric acids, are described. These copolyesters were obtained by polycondensation reaction in the melt of mixtures of methyl 2,3,4‐tri‐O‐methyl‐L ‐arabinarate or methyl 2,3,4,5‐tetra‐O‐methyl‐galactarate and dimethyl terephthalate with 1,4‐butanediol. Their weight‐average molecular weights ranged between 10,000 and 34,000, with polydispersities ranging from 1.4 to 2.2. The composition of all the copolymers was analyzed by NMR, and was found to have a statistical microstructure. All these copolyesters were thermally stable, with degradation temperatures well above 300 °C. The melting temperature and crystallinity decreased in both series, and the glass transition temperature increased and decreased respectively, for the PBTGa and PBTAr series with increasing amounts of aldaric units in the copolyester chain. Only PBT‐derived copolyesters containing a maximum of 30% aldaric units showed discrete scattering characteristic of crystalline material. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1168–1177, 2009