Key Word Index of Volume 38 – 2003

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Key Word Index of Volume 38 – 2003     

Poisson integrals and Riesz transforms for Hermite function expansions with weights

We consider expansions with respect to the multi-dimensional Hermite functions which are eigenfunctions of the harmonic oscillator L=−Δ+|x|². For the heat-diffusion and Poisson semigroups corresponding to a self-adjoint extension of L we investigate their boundary behaviour and mapping properties. All this is done for functions from L^p(w), 1?p<∞, w∈A_p. Then Riesz transforms and conjugate Poisson integrals are considered. The Riesz transforms occur to be Calderón-Zygmund operators hence their mapping properties follow by using results from a general theory.     

On odd points and the volume of lattice polyhedra

Denote by _n ³ ,n 2, the lattice consisting of all pointsx in ³ such thatnx belongs to the fundamental lattice ³ of points with integer coordinates. Letl _n be the subset of _n ³ consisting of all points whose coordinates are odd multiples of 1/n. The purpose of this paper is to give several new Pick-type formulae for the volume of three-dimensional lattice polyhedra, that is, polyhedra with vertices in ³. Our formulae are in terms of numbers of only thel _n-points belonging to a lattice polyhedronP in contrast to already known formulae which employ numbers of all the _n ³ -points inP. On our way to establishing the formulae we show that the number of points froml _n belonging to a three-dimensional lattice polyhedronP has some polynomiality properties similar to those of the well-known Ehrhart polynomial expressing the number of points of _n ³ inP. The paper contains also some comments on a problem of finding a volume formula which would employ only the setsl _n and which would be applicable to lattice polyhedra in arbitrary dimensions.Research partially supported by KBN Grant 2 P03A 008 10.     

Photochemical molecular imprinting of cholesterol

Cinnamoylated photocrosslinkable cyclodextrin derivatives (BCC) were synthesized by the substitution of β-cyclodextrin (β-CD) with cinnamoyl chloride (CC) and crosslinked with either hexamethylenediisocyanate (HMDI) or toluenediisocyanate (TDI). Cyclodextrin rings were substituted with one or two cinnamoyl moieties, as found from mass spectrometry. The polymeric matrix with cholesterol molecular imprint was obtained on irradiation of molecular assembly formed by the cinnamoyl-functionalized β-cyclodextrin-cholesterol with light at 275 nm, absorbed exclusively by the cinnamoyl chromophores. Irradiation induced crosslinking due to the photodimerization of the cinnamoyl moieties. To determine the adsorption properties of the produced material imprinting was performed in the presence of tritiated cholesterol and the intensity of β radiation from the material was measured. The materials obtained by the adsorption of tritiated cholesterol by nonirradiated polymer were used as controls. It was found that the polymer photocrosslinked in the presence of cholesterol have shown a considerable higher adsorption capacity for cholesterol than the control materials. This confirmed successful formation of molecularly imprinted polymer (MIP) by photochemical crosslinking. The selectivity of imprinting was also confirmed using compounds of similar structures, i.e. ergosterol, dehydroergosterol, and Vitamin D.     

Injectable poloxamer/graphene oxide hydrogels with well‐controlled mechanical and rheological properties

Although significant progress has been made in the design and application of injectable hydrogels for biomedical applications, concurrent control of rheological and mechanical properties of injectable hydrogels has remained as an open challenge to the researchers. In this work, we introduce and put into practice a photo‐curable poloxamer (also known as Pluronic)/graphene oxide (Plu/GO) injectable hydrogel with well‐controlled rheological and mechanical properties. Acrylate group was anchored to hydrogel structure to endow photo‐crosslinking ability through decelerating degradation rate of poloxamer hydrogels after injection. It was found that the modified Plu remains stable in biological media for a long‐term period without significant weight loss. Rheological properties of hydrogels were also carried out as essential prerequisite for an ideal injectability via frequency sweep, flow curve, recovery, and yield stress before and after modification, signifying shear‐thinning behavior of Plu/GO hydrogels with high recoverability. The viscosity of shear‐thinning‐like hydrogels dropped at higher shear stress, which facilitated injection process. Moreover, mechanical behavior of Plu was optimized by manipulating the content of Plu, degree of modification with reactive precursor, curing, and particularly incorporation of GO without deteriorating effects on rheological behavior of Plu.     

Recent Advances in Polyurethane/POSS Hybrids for Biomedical Applications

Advanced organic-inorganic materials-composites, nanocomposites, and hybrids with various compositions offer unique properties required for biomedical applications. One of the most promising inorganic (nano)additives are polyhedral oligomeric silsesquioxanes (POSS); their biocompatibility, non-toxicity, and phase separation ability that modifies the material porosity are fundamental properties required in modern biomedical applications. When incorporated, chemically or physically, into polyurethane matrices, they substantially change polymer properties, including mechanical properties, surface characteristics, and bioactivity. Hence, this review is dedicated to POSS-PU composites that have recently been developed for applications in the biomedical field. First, different modes of POSS incorporation into PU structure have been presented, then recent developments of PU/POSS hybrids as bio-active composites for scaffolds, cardiovascular stents, valves, and membranes, as well as in bio-imaging and cancer treatment, have been described. Finally, characterization and methods of modification routes of polyurethane-based materials with silsesquioxanes were presented.     

Toward Transition-Metal-Templated Construction of Arylated B4 Chains by Dihydroborane Dehydrocoupling

The reactivity of a diruthenium tetrahydride complex towards three selected dihydroboranes was investigated. The use of [DurBH₂] (Dur=2,3,5,6-Me₄C₆H) and [(Me₃Si)₂NBH₂] led to the formation of bridging borylene complexes of the form [(Cp*RuH)₂BR] (Cp*=C₅Me₅; 1 a : R=Dur; 1 b : R=N(SiMe₃)₂) through oxidative addition of the B−H bonds with concomitant hydrogen liberation. Employing the more electron-deficient dihydroborane [3,5-(CF₃)₂-C₆H₃BH₂] led to the formation of an anionic complex bearing a tetraarylated chain of four boron atoms, namely Li(THF)₄[(Cp*Ru)₂B₄H₅(3,5-(CF₃)₂C₆H₃)₄] ( 4 ), through an unusual, incomplete threefold dehydrocoupling process. A comparative theoretical investigation of the bonding in a simplified model of 4 and the analogous complex nido-[1,2(Cp*Ru)₂(μ-H)B₄H₉] ( I ) indicates that there appear to be no classical σ-bonds between the boron atoms in complex I , whereas in the case of 4 the B₄ chain better resembles a network of three B−B σ bonds, the central bond being significantly weaker than the other two.     

X-ray diffraction and solid-state NMR studies of a germanium binuclear complex

A compound formulated as (C4H12N2)[Ge2(pmida)2(OH)2] x 4 H2O (where pmida(4-) = N-(phosphonomethyl)iminodiacetate and C4H12N2(2+) = piperazinedium cation), containing the anionic [Ge2(pmida)2(OH)2]2- complex, has been synthesised by the hydrothermal approach and its structure determined by single-crystal X-ray diffraction analysis. Several high-resolution solid-state magic-angle spinning (MAS) NMR techniques, in particular two-dimensional 1H-X(13C,31P) heteronuclear correlation (HETCOR) and 1H-1H homonuclear correlation (HOMCOR) experiments incorporating a frequency-switched Lee-Goldburg (FS-LG) decoupling scheme, have been employed for the first time in such a material. Using these tools in tandem affords an excellent general approach to study the structure of other inorganic-organic hybrids. We assigned the NMR resonances with the help of C...H and P...H internuclear distances obtained through systematic statistical analyses of the crystallographic data. The compound was further characterised by powder X-ray diffraction techniques, IR and Raman spectroscopy, and by elemental and thermal analyses (thermogravimetric analysis and differential scanning calorimetry).     

Biodegradable PEO/cellulose‐based solid–solid phase change materials

A series of poly(ethylene oxide) (PEO) blends with cellulose (CEL) or cellulose derivatives—carboxymethyl cellulose (CMC), cellulose acetate (CAC), and cellulose ether (CET)—has been investigated as phase change materials for thermal energy storage. For PEO/CEL blends solid–solid phase transition has been observed in the whole concentration's range; for PEO/CMC and PEO/CET blends solid–solid phase transition has been found for PEO content 25 or 50 and 25 wt%, respectively. Otherwise, solid–liquid phase transition takes place. MTDSC investigations revealed that for PEO/CEL and PEO/CMC blends transition the strongest recrystallization effect (as evidenced by exothermic effect in reversing heat flow) as melting process occurred. FTIR analysis shows a shift of the stretching vibration bands of both the proton‐donor O? H groups from CEL and PEO due to intermolecular hydrogen interactions between the blends' components. Copyright © 2010 John Wiley & Sons, Ltd.