Sharp ultimate bounds of solutions to a class of second order linear evolution equations with bounded forcing term

We establish a precise estimate of the ultimate bound of solutions to some second order evolution equations with possibly unbounded linear damping and bounded forcing term.     

Hypercomplex derivative bases of polynomials in Clifford analysis

Convergence properties of hypercomplex derivative bases of special monogenic polynomials are studied. These new results extend and improve a lot of known works from the complex case to Clifford setting. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis and resolution of a new thiahexahelicene

A new thiahexahelicene bearing a methoxy group, at a selected position on the terminal aromatic ring, was prepared in a good yield through Heck coupling and photocyclization reactions. The X-ray crystal structure of the product indicates that its conformation closely resembles that of the unsubstituted hexahelicene, whose idealized symmetry is C₂. Both enantiomers of the new helically chiral hexacyclic system have been successfully separated using (R)-2-phthalimidopropanoic acid chloride as a chiral resolving agent.     

An alternative approach to 3-(diphenylphosphino)hexahelicene

3-(Diphenylphosphino)hexahelicene is synthesised in good yield and purity, via a three-step sequence involving a palladium-catalysed Mizoroki-Heck coupling reaction and classical oxidative photocyclisation. Mononuclear ruthenium and palladium complexes of 3-(diphenylphosphino)hexahelicene are prepared and characterised.     

Al–Cu intermetallic coatings processed by sequential metalorganic chemical vapour deposition and post-deposition annealing

Sequential processing of aluminum and copper followed by reactive diffusion annealing is used as a paradigm for the metalorganic chemical vapour deposition (MOCVD) of coatings containing intermetallic alloys. Dimethylethylamine alane and copper N,N′-di-isopropylacetamidinate are used as aluminum and copper precursors, respectively. Deposition is performed on steel and silica substrates at 1.33 kPa and 493–513 K. Different overall compositions in the entire range of the Al–Cu phase diagram are obtained by varying the relative thickness of the two elemental layers while maintaining the overall thickness of the coating close to 1 μm. As-deposited films present a rough morphology attributed to the difficulty of copper to nucleate on aluminum. Post-deposition annealing is monitored by in situ X-ray diffraction, and allows smoothening the microstructure and identifying conditions leading to several Al–Cu phases. Our results establish a proof of principle following which MOCVD of metallic alloys is feasible, and are expected to extend the materials pool for numerous applications, with innovative thin film processing on, and surface properties of complex in shape parts.     

Synthesis,X-Ray Analysis,and Evaluation of the Optoelectronic Properties of a New Thia[6]helicene

The synthesis and structural characterization of a new hexahelicene derivative is reported. This compound features a new type of structure bearing a bromine atom. Suitable crystals of the latter indicate that its conformation closely resembles that of the unsubstituted [6]helicene, whose idealized symmetry is C2. The optoelectronic properties of this helical hexacyclic system were determined and exhibit a very interesting behavior.     

The centroid of the zeroes of a polynomial via certain Laguerre-type operators

In this paper, we present several properties of the centroid of the zeroes of a polynomial. As an illustration, we apply these results to the d-orthogonal polynomials. Finally, we provide the relationship between different centroids of a general monic polynomial and its image under a certain Laguerre–type operator.     

Synthesis and characterization of new hexahelicene derivatives

The synthesis and structural characterization of a new hexahelicene derivative 2 is reported. This compound features a new type of structure bearing a bromine atom and a methoxy group. Suitable crystals of the latter indicate that its conformation closely resembles that of the unsubstituted [6]helicene, whose idealized symmetry is C2. This 3-bromo-14-methoxyhexahelicene was subjected to lithiation/phosphinilation and yielded the new 3-methoxy-14-(diphenylphosphino)hexahelicene 3.     

Characterization of q-Dunkl-classical symmetric orthogonal q-polynomials

The Ramanujan Journal - In this paper, we show that, up to a dilatation, the $$q^2$$ -analogue of generalized Hermite and $$q^2$$ -analogue of generalized Gegenbauer polynomials are the only...