Antimicrobial and Cytotoxic Activity of Novel Imidazolium-Based Ionic Liquids

In this study, a series of 10 novel 1-methyl-3-octyloxymethylimidazolium derivatives carrying various anionic moieties (4-hydroxybenzenesulfonate, benzenesulfonate, carvacroloxyacetate, chloride, formate, propionate, thymoloxyacetate, vanillinoxyacetate, eugenoloxyacetate and trimethylacetate) were synthesized. Compounds were tested for their antimicrobial activity against six microbe strains (Staph-ylococcus aureus, Pseudomonas aeruginosa, Klebsiella pneumoniae, Escherichia coli, Enterococcus faecalis, and Candida albicans), cytotoxic activity against the mouse melanoma cell line (B16 F10), and surface active properties. All synthesized compounds exhibited antimicrobial activity (expressed as minimum inhibitory concentration; in range of 0.10–27.82 mM/L), especially against Gram-positive bacteria and fungi. In addition, all compounds demonstrated cytotoxicity on B16 F10 cells (IC50 values 0.0101–0.0197 mM/L). Surface properties defined as CMC values, ranged from 0.72 to 32.35 mmol L-1. The obtained results provide an insight into the promising activity of a novel group of quaternary imidazolium derivatives having ionic liquid properties. The most potent compounds, containing a thymoloxyacetate and eugenoloxyacetate moiety, could be candidates for new antimicrobial agents or surfactants.     

On the Interplay of Regularity and Decay in Case of Radial Functions II. Homogeneous Spaces

We deal with decay and boundedness properties of elements of radial subspaces of homogeneous Besov and Triebel-Lizorkin spaces. For the region of parameters which are of interest for us these homogeneous spaces are larger than the inhomogeneous counterparts. By switching from the inhomogeneous spaces to the homogeneous classes the properties of the radial elements change. Our investigations are based on the atomic decompositions for radial subspaces in the sense of Epperson and Frazier (J.?Fourier Anal Appl. 1:311?C353, 1995). Finally, we apply these results for deriving some assertions on compact embeddings on unbounded domains.     

Morrey Spaces on Domains: Different Approaches and Growth Envelopes

We deal with Morrey spaces on bounded domains \(\Omega \) obtained by different approaches. In particular, we consider three settings \(\mathcal {M}_{u,p}(\Omega )\), \(\mathbb {M}_{u,p}(\Omega )\) and \(\mathfrak {M}_{u,p}(\Omega )\), where \(0<p\le u<\infty \), commonly used in the literature, and study their connections and diversities. Moreover, we determine the growth envelopes \(\mathfrak {E}_{\mathsf {G}}(\mathcal {M}_{u,p}(\Omega ))\) as well as \(\mathfrak {E}_{\mathsf {G}}(\mathfrak {M}_{u,p}(\Omega ))\), and obtain some applications in terms of optimal embeddings. Surprisingly, it turns out that the interplay between p and u in the sense of whether \(\frac{n}{u}\ge \frac{1}{p}\) or \(\frac{n}{u} < \frac{1}{p}\) plays a decisive role when it comes to the behaviour of these spaces.     

The Triebel - Lizorkin Scale of Function Spaces for the Fourier - Helgason Transform

We define and investigate the Triebel - Lizorkin scale of function spaces F, with 1< p < ∞, 1< q ≤ ∞ for the Fourier-Helgason transform on symmetric Riemannian manifolds of the noncompact type.     

Vector-valued Fourier multipliers on symmetric spaces of the noncompact type

LetX be a Riemannian symmetric space of the noncompact type. We prove the multiplier theorem for the Helgason-Fourier transform and the vector valued function spacesL _p (X, l _q ). As a consequence we get the inequalities of the Littlewood-Paley type forL _p (X) spaces.Research supported by K.B.N. Grant 210519101 (Poland).     

Peculiarities of Λ hyperon and π−-meson production in nucleus-nucleus collisions at high energy

The analysis of the data on the production of Λ hyperons and π^- in⁴He?Li,¹²C?C,¹²C?Ne and¹⁶O?Ne at 4.5 A GeV/c and¹²C?C collisions at 4.2 A GeV/c are presented. Kinematical features of Λ's are shown to depend on the collision centrality in contrast to the stable behaviour of the pion characteristics. The correlation between the characteristics of Λ's and accompanying pions is observed. The effects seem to be incompatible with the intranuclear cascade approach. The data suggest the formation of a fully stopped and thermalized hot source in central nucleus-nucleus collisions, in which Λ hyperons are produced.     

Strangeness enhancement and strangeness suppression in nuclear collisions at 200 GeV/N

Data on yields of strange and negative hadrons in full phase space produced in proton-nucleus and central S+S collisions at 200 GeV/nucleon are reviewed. The total number of produced strange and nonstrange valence quark-antiquark pairs is determined on the basis of the hadron multiplicity at freezout. It is shown that the strangeness production factor λ _s is increased by a factor of 2 in central S+S collisions, whereas no increase is observed in proton-nucleus collisions.     

Existence of renormalized solutions to elliptic equation in Musielak–Orlicz space

We prove existence of renormalized solutions to general nonlinear elliptic equation in Musielak–Orlicz space avoiding growth restrictions. Namely, we consider

$?\mathrm{div}A(x,\mathrm{?}u)=f\in L^1(\mathrm{\Omega }),$

on a Lipschitz bounded domain in ${\mathbb{R}}^N$. The growth of the monotone vector field A is controlled by a generalized nonhomogeneous and anisotropic N-function M. The approach does not require any particular type of growth condition of M or its conjugate $M^{?}$ (neither ${\mathrm{\Delta }}_2$, nor ${\mathrm{?}}_2$). The condition we impose is log-Hölder continuity of M, which results in good approximation properties of the space. The proof of the main results uses truncation ideas, the Young measures methods and monotonicity arguments.