Porosity and the L p -conjecture

Recently, Abtahi, Nasr-Isfahani, and Rejali [1] have shown that if G is a locally compact but not compact topological group and p > 2, then there are two functions, f and g, such that the convolution f*g{f\star g} is equal to ∞ on some set of positive measure. In the paper we show the nonexistence of f*g{f\star g} on a set of positive measure for (f, g) from a complement of a σ-porous set.     

Epistemic irrelevance in credal nets: The case of imprecise Markov trees

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.     

Relaxation of signed integral functionals in BV

For integral functionals initially defined for ${u \in {\rm W}^{1,1}(\Omega; \mathbb{R}^m)}$ by $$\int_{\Omega} f(\nabla u) \, {\rm d}x$$ we establish strict continuity and relaxation results in ${{\rm BV}(\Omega; \mathbb{R}^m)}$ . The results cover the case of signed continuous integrands ${f : \mathbb{R}^{m \times d} \to \mathbb{R}}$ of linear growth at infinity. In particular, it is not excluded that the integrands are unbounded below.     

Anti-hydroxyl radical activity,redox potential and anti-AChE activity of Amanita strobiliformis polysaccharide extract

This study outlines antioxidant and anti-AChE activities of the polysaccharide (PSH) extract from the mushroom species Amanita strobiliformis. Both the presence of α and ß glucans within the aforementioned extract was recorded. PSH extract displayed a profound scavenging activity of OH radicals (IC₅₀ value, 11.86 ± 0.59 μg/mL) and high potential for reduction of Fe³⁺ ions (174.11 ± 8.70 mg eq. AA/g d.w.) being almost 48- and 5-fold more effective than mannitol and butylated hydroxytoluene used as a positive control, respectively. Compared with galanthamine (0.001 μg), the same extract exhibited a moderate anti-AChE activity (10 μg) in solid. Since purified PSH extract exhibited higher bioactivity (IC₅₀ value 7.27 ± 0.31 μg/mL, 197.68 ± 9.47 mg eq. AA/g d.w. and 0.1 μg, respectively), it can be predominantly ascribed to the polysaccharide compounds. A. strobiliformis PSH extract may be considered as a promising resource of potent bioactive polysaccharides of natural origin successfully addressing both oxidative stress and lack of acetylcholine.     

Monitoring membrane rafts in colorectal cancer cells by means of correlative fluorescence electron microscopy (CFEM)

Detergent-resistant membrane (DRM) rafts have been shown to play a pivotal role in regulating key cell biological processes, such as signal transduction, cellular transport and cell survival. The fine structure of membrane rafts are studied using various different imaging approaches and the outcomes are largely dependent on the detection methodology applied. All these microscopy techniques which employ light-, laser- and photon-optics, electrons as well as atomic force probing are characterized on their turn by their strengths and limitations for membrane raft identification. This explains in part the diversity of definitions available to describe these peculiar membrane structures. We present herewith an alternative and uncomplicated microscopy tool to study fluorescently labelled DRMs with information at the transmission electron microscopical level of the same cell, enabling us to obtain a snapshot of the morpho-functional relationships between the cell's interior and DRMs. The proposed approach of correlative fluorescence electron microscopy (CFEM) can therefore be considered as an additional alternative imaging approach to unravel DRM structure–function relationships from micro- to nanometre length scales, from the cell to the molecule.     

Self-Assembly of 1D Double-Chain and 3D Diamondoid Networks of Lanthanide Coordination Polymers through In Situ-Generated Ligands: High-Pressure CO2 Adsorption and Photoluminescence Properties

Two new lanthanide-based coordination polymers, [Sm₂(bzz)(ben)₆(H₂O)₃]·0.5H₂O (1) and [Eu(bbz)(ben)₃] (2), were synthesized and characterized. The described products were formed from in situ-generated benzoate (ben) and N’-benzoylbenzohydrazide (bbz) ligands, which were the products of transformation of originally added benzhydrazide (bzz) under hydrothermal conditions. Compound 1 exhibits a one-dimensional (1D) double-chain structure built up from the connection of the central Sm³⁺ ions with a mixture of bzz and ben ligands. On the other hand, 2 features a 3D network with a 4-connected (6⁶) dia topology constructed from dinuclear [Eu₂(ben)₆] secondary building units and bbz linkers. High-pressure CO₂ sorption studies of activated 1 show that maximum uptake increases to exceptionally high values of 376.7 cm³ g⁻¹ (42.5 wt%) under a pressure of 50 bar at 298 K with good recyclability. Meanwhile, 2 shows a typical red emission in the solid state at room temperature with the decay lifetime of 1.2 ms.     

Tailoring thermal development of gamma alumina sorbents material using combustion synthesis: the effect of amino acids (G,A, N) and equivalence ratio

Using a combustion synthesis, the range of achievable textures is broader than using conventional synthesis methods and can be controlled more successfully. As a tool allowing the achievement and control of desired textures, here we bring about wet chemistry synthesis using aluminium nitrate nonahydrate (ANN) precursor systematically combined with different fuels (amino acids). The amino acids; glycine (G), alanine (A) and asparagine (N) have been specifically selected in order to show the role of gradual increase in their: (1) molar mass, (2) enthalpy of combustion, (3) amine groups content and (4) ratio to ANN. Detailed (micro) structural and thermal characterisations confirm that the nanocrystalline character and thermomechanical stability were not diminished in the course of this synthesis. The conditions leading to development of different morphologies from gels to powders were found to be heavily under the influence of fuel/oxygen ratio, i.e. of the smouldering versus flaming mechanism of the combustion. Higher content of nitrates (predominately from amino-rich amino acids) strongly promoted auto-combustion behaviour. As-derived alumina precursors have been thermally treated at various temperatures (quenched and soaked), to monitor γ- and α-alumina crystallisation, with respect to the development of morphology. Different texture types have been observed, such as porous wormhole, porous and porous expanded flakes. Higher fuel levels promote specific surface increase. This combustion synthesis allows facile tailoring of nanocrystalline γ-alumina with different morphological features, whereas samples having optimal parameters were suitable for catalyst support application on behalf of rapid sorption performance.

     

Phenoxy herbicidal ammonium ionic liquids

Ammonium ionic liquids with the 4-chloro-2-methylphenoxyacetate anion were synthesized and characterized. Physicochemical properties, such as thermal stability, phase transition temperatures, viscosity, density, refractive index, as well as surface activity and herbicidal activity were determined. Improved physicochemical properties suggest a reduced environmental impact of newly formed group of herbicidal ionic liquids (HILs). HILs with a longer substituent can be characterized with better herbicidal activity in comparison with commercial products.