Further Results for kth order Kantorovich Modification of Linking Baskakov Type Operators

In this paper we consider a non-trivial link between Baskakov type operators and their genuine Durrmeyer type modification as well as the kth order Kantorovich variant. Recursion formulas for the moments and the images of monomials are proved in order to derive asymptotic expansions. Furthermore we investigate convexity properties of the linking operators and the limiting behavior for certain function spaces.     

The phase transitions of the planar random-cluster and Potts models with $$q \ge 1$$ are sharp

We prove that random-cluster models with \(q \ge 1\) on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter \(p_c\) below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result may be extended to the Potts model via the Edwards–Sokal coupling. Our method is based on sharp threshold techniques and certain symmetries of the lattice; in particular it makes no use of self-duality. Part of the argument is not restricted to planar models and may be of some interest for the understanding of random-cluster and Potts models in higher dimensions. Due to its nature, this strategy could be useful in studying other planar models satisfying the FKG lattice condition and some additional differential inequalities.     

Voronovskaya Type Theorems in Weighted Spaces

In this article, we introduce a generalization of Gamma operators based on a function ρ having some properties and prove quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems via weighted modulus of continuity.     

Pyrolysis of polyphenylenes with PCL or/and PSt side chains

Thermal degradation characteristic of polyphenylenes is an important issue for developing a rational technology of polymer processing and applications. In this study, we discussed thermal degradation of polyphenylenes (PP) with poly(-caprolactone) (PCL) and/or PCL/polystyrene copolymers (PSt) prepared by combined controlled polymerization and cross-coupling processes via direct pyrolysis mass spectrometry. When PP-graft-PCL/PSt copolymers were considered, thermally less stabile PCL side chains decomposed in the first step. In the second stage of pyrolysis, the decomposition of the polystyrene chains has taken place. A slight increase in thermal stability of PCL chains for PP-graft-PCL/PSt copolymers was noted compared to copolymer PP-graft-PCL due to the interaction between PSt and PCL chains. This interaction was stronger when PSt chains were linked to the 2-position of the 1,4-phenylene ring.     

Synthesis and Characterization of α,ω‐Heterofunctional Poly(ethylene oxide) Macromonomers

A novel α,ω‐heterofunctional poly(ethylene oxide) (PEO) macromonomer possessing methacryloyl and thienyl end groups was prepared by ring‐opening polymerization of ethylene oxide initiated by potassium thienylethoxide and termination of the living PEO ends with methacryloyl chloride. Incorporation of methacryloyl and thienyl groups was confirmed by free‐radical and oxidative polymerization processes, respectively, and by means of ¹H NMR analysis.

     

A rheological model based on primary laboratory data of lubricants with polymers additives

The present work reports some experimental data consisting in traction behavior for lubricants with polymer additives. The rheological response of lubricants without polymer additives and with additives as a function of polymer concentration, pressure and temperature is discussed. Based on the laboratory data, the paper presents a quasi-empirical approach which predicts elastic shear modulus, limiting shear stress and characteristic shear stress of a lubricant with polymer additives.     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998