On Convolutions and Linear Combinations of Pseudo-Isotropic Distributions

Let E be a Banach space, and let E* be its dual. For understanding the main results of this paper it is enough to consider E= ⁿ . A symmetric random vector X taking values in E is called pseudo-isotropic if all its one-dimensional projections have identical distributions up to a scale parameter, i.e., for every E* there exists a positive constant c() such that (, X) has the same distribution as c() X ₀, where X ₀ is a fixed nondegenerate symmetric random variable. The function c defines a quasi-norm on E*. Symmetric Gaussian random vectors and symmetric stable random vectors are the best known examples of pseudo-isotropic vectors. Another well known example is a family of elliptically contoured vectors which are defined as pseudo-isotropic with the quasi-norm c being a norm given by an inner product on E*. We show that if X and Y are independent, pseudo-isotropic and such that X+Y is also pseudo-isotropic, then either X and Y are both symmetric -stable, for some (0, 2], or they define the same quasi-norm c on E*. The result seems to be especially natural when restricted to elliptically contoured random vectors, namely: if X and Y are symmetric, elliptically contoured and such that X+Y is also elliptically contoured, then either X and Y are both symmetric Gaussian, or their densities have the same level curves. However, even in this simpler form, this theorem has not been proven earlier. Our proof is based upon investigation of the following functional equation:

Polyphenolic Compounds of Crataegus Berry,Leaf, and Flower Extracts Affect Viability and Invasive Potential of Human Glioblastoma Cells

Crataegus contains numerous health-promoting compounds that are also proposed to have anti-cancer properties. Herein, we aimed at a contemporaneous evaluation of the effects of polyphenol-rich extracts of berries, leaves, and flowers of six Crataegus species on the viability and invasive potential on the highly aggressive human glioblastoma U87MG cell line. The treatment with the extracts evoked cytotoxic effects, with the strongest in the berry extracts. All extracts not only promoted the apoptosis-related cleavage of poly (ADP-ribose) polymerase 1 (PARP1) but also substantially inhibited the activity of pro-survival kinases, focal adhesion kinase (FAK), and protein kinase B (PKB; also known as Akt), thus indicating the suppression of proliferative and invasive potentials of the examined glioblastoma cells. The qualitative and quantitative characterization of the extracts’ content was also performed and revealed that amongst 37 polyphenolic compounds identified in the examined Crataegus extracts, the majority (29) was detected in berries; the leaf and flower extracts, exerting milder cytotoxic effects, contained only 14 and 13 compounds, respectively. The highest polyphenol content was found in the berries of C. laevigata x rhipidophylla x monogyna, in which flavan-3-ols and phenolic acids predominated. Our results demonstrated that a high content of polyphenolic compounds correlated with the extract cytotoxicity, and especially berries were a valuable source of compounds with anti-cancer potential. This might be a promising option for the development of an effective therapeutic strategy against highly malignant glioblastomas in the future.     

Phase Transitions and Structural Changes in DPPC Liposomes Induced by a 1-Carba-Alpha-Tocopherol Analogue

Steady-state emission spectroscopy of 1-anilino-8- naphthalene sulfonate (ANS) and 1,6-diphenyl-1,3,5-hexatriene (DPH), fluorescence anisotropy, and DSC methods were used to characterize the interactions of the newly synthesized 1-carba-alpha-tocopherol (CT) with a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) membrane. The DSC results showed significant perturbations in the DPPC structure for CT concentrations as low as 2 mol%. The main phase transition peak was broadened and shifted to lower temperatures in a concentration-dependent manner, and pretransition was abolished. Increasing CT concentrations induced the formation of new phases in the DPPC structure, leading to melting at lower temperatures and, finally, disruption of the ordered DPPC structure. Hydration and structural changes of the DPPC liposomes using ANS and DPH fluorescent probes, which are selectively located at different places in the bilayer, were studied. With the increased concentration of CT molecules in the DPPC liposomes, structural changes with the simultaneous formation of different phases of such mixture were observed. Temperature studies of such mixtures revealed a decrease in the temperature of the main phase transition and fluidization at decreasing temperatures related to increasing hydration in the bilayer. Contour plots obtained from concentration–temperature data with fluorescent probes allowed for identification of different phases, such as gel, ordered liquid, disordered liquid, and liquid crystalline phases. The CT molecule with a modified chromanol ring embedded in the bilayer led to H-bonding interactions, expelling water molecules from the interphase, thus introducing disorder and structural changes to the highly ordered gel phase.     

Neutron scattering study of the structural change induced by photopolymerization of AOT/D2O/dodecyl acrylate inverse microemulsions

Small-angle and ultrasmall-angle neutron scattering (SANS/USANS) measurements were used to determine the structural changes induced by photopolymerization of AOT/D2O/(dodecyl acrylate) inverse microemulsion systems. Scattering profiles were collected for the initial microemulsions and the films resulting from photopolymerization of the oil phase. The SANS data for the microemulsions were modeled as spherical, core-shell droplets. Upon polymerization, the clear mircoemulsions formed opaque films. From the SANS/USANS data of the films, it was apparent that this morphology was not preserved upon polymerization; however, it was clearly observed that the formulation of the microemulsion had a large impact on the structure within the films. The Guinier region in the USANS data (2.5 x 10(-5) A(-1) < or = Q < or = 5.3 x 10(-3) A(-1)) from the films indicates that very large structures are formed. Simultaneously, a well-defined peak (0.15 A(-1) < or = Q < or = 0.25 A(-1)) in the SANS data indicates that there are also much smaller structures formed. It is proposed that the low-Q scattering arises from aggregation of the nanometer-size water droplets in the microemulsion to form droplets large enough to scatter visible light, while the peak in the high-Q region results from bilayered structures formed by the surfactant.     

The role of the histidine residue in the coordination abilities of peptides with a multi-histidine sequence towards copper(II) ions

Cu²⁺ complexes with peptides containing three histidine residues have very specific metal binding abilities and can mimic the structures of various multi-histidine metal binding sites in proteins. The main goal of the work concerns the investigations of coordination abilities of the group of N-terminally protected Ac-His-Arg-His-Gly-His-Gly, Ac-His-Gly-His-Arg-His-Gly, Ac-Gly-His-His-Arg-His-Gly and Ac-His-His-Gly-His-Arg-Gly, and their unprotected analogs His-Arg-His-Gly-His-Gly, His-Gly-His-Arg-His-Gly, Gly-His-His-Arg-His-Gly and His-His-Gly-His-Arg-Gly towards Cu²⁺ ions. Detailed spectroscopic (UV/Vis, CD and EPR) and potentiometric studies have been made. The stoichiometry and binding mode for each ligand–Cu²⁺ system were determined.     

Influence of inorganic mobile phase additives on the retention and separation efficiency of selected amino acids in thin-layer chromatography on cellulose layers

Selected amino acid standards are investigated on cellulose layers using organic-aqueous eluent systems modified with neutral and chaotropic salts: chlorides, iodides, nitrates, thiocyanates, perchlorates, and hexafluorophosphates at low concentrations ranging from 10 up to 80mM in whole mobile phase. The effect of salts used as the mobile phase modifier is analyzed by the comparison of densitograms, peak symmetry coefficient, and theoretical plate number. The efficiency of chromatographic systems modified with inorganic salts additives depends primarily on the kind of salt and organic solvent in the mobile phase. The best efficiency is obtained through the addition of ammonium thiocyanate to the mobile phase containing acetonitrile as an organic modifier.     

“Cap-Pair” Effect as the Reason of the Catalytic Properties of Nicotinic Acid: Experimental and Theoretical Studies

The influence of nicotinic acid (NC) on the kinetics and the mechanism of electroreduction of Zn²⁺ ions in the acetate buffer (pH=6.0) was investigated using electrochemical methods (EIS, CV, SWV and DC). It was shown that the anions of NC catalyze the electrode reaction (cap-pair effect) by adsorbing on the surface of the mercury electrode. The catalytic activity of NC is due to its ability to form active NC−Zn²⁺ complexes on the electrode surface, facilitating the electron transfer process. However, no evidence of the formation of such complexes in the solution was found using classical molecular dynamics. Moreover, it was proved that the electroreduction of Zn²⁺ ions in the presence of NC is a two-stage process. The first stage involves the transfer of the first electron, preceded by the partial loss of the hydration shell by the Zn²⁺ ions and formation of the active complex. Moreover, it was shown that in the range of lower concentrations, c≤1.10⁻² mol.dm⁻³, the nicotinic acid shows weaker catalytic abilities than another form of vitamin B3 – nicotinamide. In the range of its higher concentrations, the nicotinic acid is a more effective catalyst for the electroreduction of Zn²⁺ ions.     

A Symplectic Generalization of the Peradzyński Helicity Theorem and Some Applications

Symplectic and symmetry analysis for studying MHD superfluid flows is devised, a new version of the Z. Peradzyński (Int. J. Theor. Phys. 29(11):1277–1284, [1990]) helicity theorem based on differential-geometric and group-theoretical methods is derived. Having reanalyzed the Peradzyński helicity theorem within the modern symplectic theory of differential-geometric structures on manifolds, a new unified proof and a new generalization of this theorem for the case of compressible MHD superfluid flow are proposed. As a by-product, a sequence of nontrivial helicity type local and global conservation laws for the case of incompressible superfluid flow, playing a crucial role for studying the stability problem under suitable boundary conditions, is constructed.