A convection/reaction/switching system

We consider a spatially distributed hybrid system consisting of a convection/reaction system in which the reaction switches discontinuously in time between modes, independently at each spatial point on reaching “switching thresholds”. The model involves a novel formulation for evolution of the free boundary between the modal regions.     

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.     

Kinetic features of ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

Some remarks on the Jensen-Hadamard inequalities and applications

We provide some inequalities and integral inequalities connected to the Jensen-Hadamard inequalities for convex functions. In particular, we give some refinements to these inequalities. Some natural applications and further extensions are given.

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Sunto Forniamo alcune diseguaglianze e diseguaglianze integrali connesse alle dise-gueglianze di Jensen-Hadamard per funzioni convesse. In particolare, diamo qualche miglioramento di queste diseguaglianze. Alcune applicazioni naturali ed ulteriori estensioni sono date.

     

A study of type I intermittency of a circular differential equation under a discontinuous right-hand side

In this paper we study a circular differential equation under a discontinuous periodic input, developing a quadratic differential equations system on S¹ and a linear differential equations system in the Minkowski space M³. The symmetry groups of these two systems are, respectively, PSOo(2,1) and SOo(2,1). The Poincaré circle map is constructed exactly, and a critical value αc of the parameter is identified. Depending on α of the input amplitude the equation may exhibit periodic, subharmonic or quasiperiodic motions. When α varies from α>αc to α<αc, there undergoes an inverse tangent bifurcation; consequently, the resultant Poincaré circle map offers one route to the quasiperiodicity via a type I intermittency. In the parameter range of α<αc the orbit generated by the Poincaré circle map is either m-periodic or quasiperiodic when n/m is a rational or an irrational number.     

Transesterification of an RNA model in buffer solutions in H2O and D2O

Transesterification of a phosphodiester bond of RNA models has been studied in various buffer solutions, under neutral and slightly alkaline conditions in H₂O and D₂O. The results show that imidazole is the only buffer system where a clear buffer catalysis on the cleavage of a phosphodiester bond is observed. The rate enhancement in sulphonic acid buffers is smaller, and a sulphonate base, particularly, is inactive as a catalyst. The rate‐enhancing effect of imidazole is, however, catalytic, and the catalytic inactivity of sulphonate buffers can be attributed to their structure and/or charge. The catalysis by imidazole is a complex system which, in addition to first‐order reactions, involves a process that shows a second‐order dependence in imidazole concentration. The latter reaction becomes significant in acidic imidazole buffers (pH < pK_a), as the buffer concentration increases. The kinetic solvent deuterium isotope effect k_H/k_D, referring to first‐order catalysis by imidazole base, is 2.3 ± 0.3. That referring to second‐order catalysis is most probably much larger, but an accurate value could not be obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

AFM, SEM and GIXRD studies of thin films of red polycarbazolyldiacetylenes

In this paper we report the results of a morphological and structural investigation on film properties of a soluble polydiacetylene, the poly[1,6-bis(3,6-dihexadecyl-N-carbazolyl)-2,4-hexadiyne] (polyDCHD-HS). The red films of this polymer, prepared by standard spin-coating techniques, revealed absence of linear dichroism and birefringence in contrast with the ordered mesophases detected by powder X-ray studies. In order to interpret the optical behavior of this polymer, we performed AFM and SEM studies of polyDCHD-HS films spun on hydrophylic and hydrophobic glass substrates. We found the presence of surfaces organized in rod-like particles, more regularly oriented on the hydrophylic substrate. GIXRD studies, carried out on films sufficiently thick to allow the observation of the diffraction pattern, reveled the presence of a lamellar structure with a spacing of 3.22 nm. The low intensity of the diffraction peaks and the isotropic linear optical properties of the films show that the lamellar mesophases are not extended over large areas. These findings were compared with the data obtained from AFM and SEM studies on films of two other polydiacetylenes, the poly[1-(3,6-dihexadexyl-N-carbazolyl)-6-(N-carbazolyl)-2,4-hexadyine] (polya-DCHD) and the poly[1,6-bis(3,6-dipalmitoyl-N-carbazolyl)-2,4-hexadyine] (polyDPCHD), spun on hydrophylic glass substrate. The results confirmed the presence of nodular morphologies which seem to be a general characteristic of this class of materials. The particles organization appears instead related to the chemical nature of the substituents on the carbazolyl rings.     

Differentiators and the geometry of polynomials

In 1959, Davis introduced the concept of a differentiator of an operator on a finite-dimensional Hilbert space. We prove that every such operator possesses a differentiator. We also use the theory of differentiators to solve several problems in the geometry of polynomials. For instance, we answer in the affirmative a twenty year old unsolved conjecture of Schoenberg, a related conjecture of Katsoprinakis and a fifty year old unsolved conjecture of De Bruijn and Springer.