Pseudo-Taylor expansions and the Carathéodory–Fejér problem

We give a new solvability criterion for the boundary Carathéodory–Fejér problem: given a point $x\in \mathbb{R}$ and, a finite set of target values $a^0,a^1,\dots ,a^n\in \mathbb{C}$, to construct a function f in the Pick class such that the limit of $f^{(k)}(z)/k!$ as $z\to x$ nontangentially in the upper half-plane is $a^k$ for $k=0,1,\dots ,n$. The criterion is in terms of positivity of an associated Hankel matrix. The proof is based on a reduction method due to Julia and Nevanlinna.     

New approach to chemical modification of PIM-1 for gas separation membranes

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Conformational polymorphs of 22‐cyano‐N‐methyl‐5‐phenylpent‐2‐en‐4‐ynamide

Although the two polymorphic modifications, (I) and (II), of the title compound, C₁₃H₁₀N₂O, crystallize in the same space group (P2₁/c), their asymmetric units have Z′ values of 1 and 2, respectively. These are conformational polymorphs, since the mol­ecules in phases (I) and (II) adopt different rotations of the phenyl ring with respect the central 2‐cyano­carboxy­amino­prop‐2‐enyl fragment. Calculations of crystal packing using Cerius² [Molecular Simulations (1999). 9685 Scranton Road, San Diego, CA 92121, USA] have shown that (I) is more stable than (II), by 1.3 kcal mol^?1 for the crystallographically determined structures and by 1.56 kcal mol^?1 for the optimized structures (1 kcal mol^?1 = 4.184 kJ mol^?1). This difference is mainly attributed to the different strengths of the hydrogen bonding in the two forms.     

Hypercrosslinked polystyrene networks with ultimate degrees of crosslinking and their sorption activity

Hypercrosslinked networks with 43, 100, 200, 300, 400, and 500% nominal crosslinking, respectively, were prepared by crosslinking the dichloroethane-swollen styrene copolymer with 0.5% divinylbenzene by Friedel-Crafts reaction using 0.3, 0.5, 1.0, 1.5, 2.0, and 2.5 mol of a bifunctional reagent (monochlorodimethyl ether), respectively. The dependences of the free (pore) volume of networks and their equilibrium swelling in water on the degree of crosslinking are extrema with the maximum parameters 0.63 cm³/g and 1.31 ml/g corresponding to the polymer with 300% crosslinking. The apparent specific surfaces of samples with 43–400% bridges are comparable, 1300–1500 m²/g. The ability of water-swollen hypercrosslinked polymers to extract synthetic organic dyes from aqueous solutions is independent of their specific surface measured for dry samples, but depends on the volume of absorbed water.     

Copolymerization kinetics of ethylene and carbon monoxide in the presence of palladium complexes

The copolymerization kinetics of ethylene and carbon monoxide has been studied for the catalysts: Pd(C₅H₇O₂)₂-P(C₆H₅)₃-p-CH₃C₆H₄SO₃H in the medium of acetic acid (system A), and Pd(CH₃COO)₂-CF₃COOH - (C₆H₅)₂P(CH₂)_nP(C₆H₅)₂(system B), where n=1−6, in the medium of methyl alcohol. The cationic palladium(II) -diphosphine complexes: (Dppp)₂Pd(CF₃COO)₂ (I) and [(Dppp) Pd(μ-OH)₂Pd(Dppp)] (CF₃COO)₂ (II) have been synthesized and investigated by IR, electrospray mass spectrometry and elemental analysis methods. A comparative study of the copolymerization kinetics in the presence of these complexes and system B has been carried out.     

Excision in Cyclic Type Homology of Frechet Algebras

It is proved that every topologically pure extension of Fréchetalgebras 0 I A A/I 0 such that I is strongly H-unital hasthe excision property in continuous (co)homology of the followingtypes: bar, naive-Hochschild, Hochschild, cyclic, and periodiccyclic. In particular, the property holds for every extensionof Fréchet algebras such that I has a left or right boundedapproximate identity.     

Synthesis and properties of oxadiazole based V-shaped, shape persistent nematogens

A series of biaxial V-shaped, shape-persistent molecules has been synthesised by stepwise coupling of phenylene ethynylene arms to an oxadiazole bending unit. Studies of their thermotropic nematic phases point to phase biaxiality.     

Cyclic cohomology of certain nuclear Fréchet algebras and DF algebras

We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain \(\hat \otimes\)-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ?: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H ⁿ(?): H ⁿ (x) → H ⁿ (y) is automatically topological. The continuous cyclic-type homology and cohomology are described up to topological isomorphism for the following classes of biprojective \(\hat \otimes\)-algebras: the tensor algebra E \(\hat \otimes\) F generated by the duality (E,F,<·,·>) for nuclear Fréchet spaces E and F or for nuclear DF-spaces E and F; nuclear biprojective Köthe algebras λ(P) which are Fréchet spaces or DF-spaces; the algebra of distributions ε^*(G) on a compact Lie group G.