Linear systems of arbitrary genus

Kalman's theory is extended to a complete, smooth, and irreducible algebraic curve of arbitrary genus.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006     

Pyrroloindoles. 16. Some electrophilic substitution reactions of 2,7-dicarbethoxy-1H,6H-pyrrolo[2,3-e]indoles

Electrophilic substitutions of 2,7-dicarbethoy-1H,6H-pyrrolo[2,3-e]indole (Friedel-Crafts acylation, nitration, bromination) take place both at position 3 of the indole ring and at positions 5 and 8 in the benzene ring.For communication 15 see [1].Iv. Dzhavakhishvili State University, Tbilisi 380028. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1197–1201, September, 1994. Original article submitted July 5, 1994.     

A chitosan-based chemomechanical polymer triggered by stacking effects with aromatic effectors including aminoacid derivatives

Chitosan with a covalently attached anthrylunit is used as chemomechanical polymer, in which stacking and cation-π interactions allow aromatic effector compounds with positively charged nitrogen centers to trigger macroscopic motions in aqueous surrounding. Thus, only protonated heterocycles such as imidazole or histamine lead at pH 5 to expansion, in contrast to toluenesulfonic acid, or pyrazole and pyrimidine. Inorganic salts and pH influence the polymer swelling, and must be taken into account for the calculation of net effects induced by organic effectors. Reversible volume expansions on the top of the swelling effect of water alone are observed as function of different effector structures, showing, for example, 45% net effect with imidazole and 66% with benzimidazole. Aminoacids, for solubility reasons measured in the form of their methylesters, yield smaller expansions, showing, however, a regular and selective increase with the lipophilicity of the residues. The kinetics of effector uptake, which relates to the velocity of expansion, are measured with histamine and follow first order, with t_1/2=2.7 min for 50% absorption.     

Dramatic selectivity differences in the association of DNA and RNA models with new ethylene- and propylene diamine derivatives and their copper complexes

The affinities of polyamines consisting of ethylenediamine units equipped with either one or two terminal naphthyl-, anthryl-, or acridyl units towards PolyA.PolyU as an RNA model, and Poly(dA).Poly(dT) as a DNA model are screened by measuring the melting point changes (DeltaT(m)) of the double strands, and also partially by a fluorimetric binding assay using ethidium bromide. The larger aromatic moieties with long spacers between them allow bisintercalation; this leads to an increased preference for DNA in comparison to RNA, where ion pairing of the ammonium centers with the major RNA groove phosphates dominates. Allosteric affinity control by metalation is achieved e.g. with Cu(2+) ions, which induce conformational distortions within the chains. With anthryl- in contrast to naphthyl derivatives intercalation can be so strong that distortion of the ethylenediamine chain by metalation is not powerful enough. A particularly high concentration of positive charges is accessible with tripodal derivatives built up from ethylenediamine and propylenediamine units; in the absence of aryl parts, which interfere with the RNA groove preference, one observes the highest affinity difference known until today, reflected in a melting point ratio of DeltaT(m(RNA))/DeltaT(m(DNA)) = 40, whereas other synthetic ligands reach only a DeltaT(m(RNA))/DeltaT(m(DNA)) ratio of about 3.     

Summation of Singular Series Corresponding to Representations of Numbers by Some Quadratic Forms in Twelve Variables

Formulas for calculating the sum of singular series corresponding to the number of representations of integers by some quadratic forms in 12 variables with integral coefficient are derived.