Browsing by Department "Charles University"

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  • Cation-sensitive compartmentalization in metallacarborane containing polymer nanoparticles
    (2016) Dordovic, Vladimir; Uchman, Mariusz; Reza, Mehedi; Ruokolainen, Janne; Zhigunov, Alexander; Ivankov, Olexandr I.; Matějíček, Pavel
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    Alkaline cations (Li+, Na+ and K+) are introduced as agents suitable to control compartmentalization in metallacarborane-rich nanoparticles of double-hydrophilic block copolymer poly(ethylene oxide)-block-poly(2-alkyloxazoline), PEO-POX. Interaction of the metallacarborane (cobalt bis(dicarbollide) anion) with PEO-POX is based mainly on dihydrogen bonding between metallacarborane boron clusters and the polymer backbone resulting in compact nanoparticles. However, the cations are a crucial factor as to whether interaction with PEO or POX segments is preferred. Changes in the bulk concentration of alkaline cations can thus provoke changes in the inner structure of polymeric nanoparticles, which is accompanied by exchange of boron clusters and alkaline cations like Li+. Because of the biomedical importance of metallacarboranes, their conjugates and also lithium salts, the hybrid nanoparticles can act as stimuli-responsive systems for drug delivery.
  • On quadratic Waring’s problem in totally real number fields
    (2023-04-01) Krásenský, Jakub; Yatsyna, Pavlo
     A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
    We improve the bound of the g-invariant of the ring of integers of a totally real number field, where the g-invariant g(r) is the smallest number of squares of linear forms in r variables that is required to represent all the quadratic forms of rank r that are representable by the sum of squares. Specifically, we prove that the gOK(r) of the ring of integers OK of a totally real number field K is at most gZ([K : Q]r). Moreover, it can also be bounded by gOF ([K : F]r + 1) for any subfield F of K. This yields a subexponential upper bound for g(r) of each ring of integers (even if the class number is not 1). Further, we obtain a more general inequality for the lattice version G(r) of the invariant and apply it to determine the value of G(2) for all but one real quadratic field.