Packing congruent hyperspheres into a hypersphere

The paper considers a problem of packing the maximal number of congruent nD hyperspheres of given radius into a larger nD hypersphere of given radius where n = 2, 3, . . . , 24. Solving the problem is reduced to solving a sequence of packing subproblems provided that radii of hyperspheres are variable. Mathematical models of the subproblems are constructed. Characteristics of the mathematical models are investigated. On the ground of the characteristics we offer a solution approach. For n ≤ 3 starting points are generated either in accordance with the lattice packing of circles and spheres or in a random way. For n > 3 starting points are generated in a random way. A procedure of perturbation of lattice packings is applied to improve convergence. We use the Zoutendijk feasible direction method to search for local maxima of the subproblems. To compute an approximation to a global maximum of the problem we realize a non-exhaustive search of local maxima. Our results are compared with the benchmark results for n = 2. A number of numerical results for 2 ≤ n ≤ 24 are given.     

Express Method for Determination of Low Value of Trans-membrane Potential of Living Cells with Fluorescence Probe: Application on Haemocytes at Immune Responses

The method for measurement of trans-membrane potential of cell membrane was evaluated for the case of low potential value using fluorescence probe 4-(4-dimethylaminostyryl)-1-methylpyridinium, DSM. The method is based on comparative titration of cells with probe in buffers containing Na(+) or K(+). The apparent trans-membrane potential obtained with this way is a result of K(+)-Na(+) pump activity. The presented approach allowed measuring the low value of potential with 1-2?mV of accuracy without additional calibration procedures. The method was applied for investigation of potential of cell membrane of haemocytes of Galleria mellonella larvae. The value of potential of intact insect's haemocytes was found in the range from -10 to -20?mV. The change of potential value of haemocytes was investigated under model immune response and natural envenomation and parasitizing. The obtained deviations of cell membrane potential were in good correlation with changes of activity of main immune reactions, described in literature and obtained by us earlier.     

Manipulation of Förster energy transfer of coupled fluorophores through biotransformation by Pseudomonas resinovorans CA10

An alkyne‐terminated anthracene and azide‐terminated carbazole were joined through a copper‐catalyzed cycloaddition to form a joined donor/acceptor pair. The photonic pair exhibited energy transfer when excited at the peak absorbance of carbazole and fluoresced with an anthracene spectral response. The fluorescent behavior was confirmed as Förster energy transfer (FRET). The lysate of Pseudomonas resinovorans CA10, a member of a predominant group of soil microorganisms that can metabolize a host of substrates, was employed to degrade the pair and alter the luminance spectral characteristics. The FRET was diminished and the corresponding, individual fluorescence of carbazole and anthracene returned. This general approach may find applications in single‐cell metabolic studies and bioactivity assays.     

Highly-controlled grafting of mono and dicationic 4,4'-bipyridine derivatives on SBA-15 for potential application as adsorbent of CuCl(2) from ethanol solution

Ultra-large-pore FDU-12 (ULP-FDU-12) silica with face-centered cubic structure (Fm3m type) of spherical mesopores was synthesized using Pluronic F127 triblock copolymer (EO(106)PO(70)EO(106)) and ethylbenzene as a new micelle expander at initial temperature of 14 °C. Ethylbenzene was identified on the basis of its reported extent of solubilization in poly(ethylene oxide)-poly(propylene oxide)-type surfactant micelles, which was similar to that of xylene, the latter having been shown earlier to afford ULP-FDU-12. The unit-cell parameter of as-synthesized ULP-FDU-12 was 55 nm, which is similar to the highest value reported when xylenes (mixture of isomers) were used and larger than that achieved with trimethylbenzene. The unit-cell parameter of calcined ULP-FDU-12 reached 52 nm. For the obtained materials, the nominal pore cage diameter calculated from nitrogen adsorption reached 32 nm, whereas the actual pore cage diameter calculated using the geometrical relation was 36 nm. The pore entrance size was below 5 nm before the acid treatment, but was greatly enlarged as a result of the treatment. The sample prepared without hydrothermal treatment was converted to ordered closed-pore silica at as low as 400-450 °C. Our study confirms the ability to select micelle expanders on the basis of data on solubilization of compounds in micelle solutions.     

Expedient one-pot organometallics-free synthesis of tris(2-pyridyl)phosphine from 2-bromopyridine and elemental phosphorus

2-Bromopyridine reacts with elemental phosphorus (red or white) in a superbasic KOH/DMSO(H₂O) suspension at 100 °C (for red phosphorus) and 75 °C (for white phosphorus) over 3 h to afford tris(2-pyridyl)phosphine in a 62% yield (from red phosphorus) and a 50% yield (from white phosphorus). Under microwave assistance, the reaction with red phosphorus takes just 20 min to produce tris(2-pyridyl)phosphine in 53% yield. A hitherto unknown complex, [Pd(PPy₃)₂Cl₂]·CH₂Cl₂, synthesized from tris(2-pyridyl)phosphine and PdCl₂, has the cis-configuration; this is unusual for bis(phosphino)palladium dichloride complexes.     

Diastereoselective Coupling of Chiral Acetonide Trisubstituted Radicals with Alkenes

The stereochemical outcome of reactions of chiral nucleophilic trisubstituted acetonide radicals with electron‐deficient alkenes is dictated by a delicate balance between destabilizing non‐bonding interactions and stabilizing hydrogen‐bonding between substituents on the α and β carbons.     

Rational design of methacrylate monomers containing oxadiazole moieties for single‐layer organic light emitting devices

Methacrylate derived monomers functionalized with pendant oxadiazole moieties were synthesized and copolymerized with carbazole containing monomers to form polymers with electron and hole transporting fragments in the same molecule. Substituents on the oxidazole moiety were varied with the purpose of bandgap tuning and performance optimization when employed in single‐layer organic light emitting devices (OLED). Quantum mechanical calculations of the HOMO‐LUMO levels of the oxidazole derivatives were used to down‐select promising candidates for chemical synthesis and testing in single‐layer OLEDs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1663–1673     

Koszul duality for extension algebras of standard modules

We define and investigate a class of Koszul quasi-hereditary algebras for which there is a natural equivalence between the bounded derived category of graded modules and the bounded derived category of graded modules over (a proper version of) the extension algebra of standard modules. Examples of such algebras include, in particular, the multiplicity free blocks of the BGG category O, and some quasi-hereditary algebras with Cartan decomposition in the sense of König.     

Time-dependent electrical properties of liquid crystal cells: unravelling the origin of ion generation

An understanding of possible sources of ion generation in liquid crystal materials is of utmost importance to ensure uncompromised performance of modern liquid crystal devices. In this paper, time-dependent electrical properties of filled liquid crystal cells are used to reveal important information about often overlooked source of ion generation in liquid crystals. This source of ions originates from the ionic contamination of substrates of the liquid crystal cell. Ionic contaminants can be inherently present in the alignment layers or can be induced by external factors such as mechanical rubbing or irradiation with light. The model of this ion generation process is presented and tested using existing experimental data.     

Aluminum phosphate dispersed on a cellulose acetate fiber surface: Preparation, characterization and application for Li, Na and K separation

Cellulose acetate fibers with supported highly dispersed aluminum phosphate were prepared by reacting aluminum-containing cellulose acetate (Al₂O₃=3.5 wt.%; 1.1 mmol g⁻¹ aluminum atom per gram of the material) with phosphoric acid. Solid-state NMR spectra (CPMAS ³¹P NMR) data indicated that HPO₄²⁻ is the species present on the fiber surface. The specific concentration of acidic centers, determined by ammonia gas adsorption, is 0.50 mmol g⁻¹. The ion exchange capacities for Li⁺, Na⁺ and K⁺ ions were determined from ion exchange isotherms at 298 K and showed the following values (in mmol g⁻¹): Li⁺=0.03, Na⁺=0.44 and K⁺=0.50. The H⁺/Li⁺ exchange corresponds to the model of the ideal ion exchange with a small value of the corresponding equilibrium constant K=1.1×10⁻². Due to the strong cooperative effect, the H⁺/Na⁺ and H⁺/K⁺ ion exchange is non-ideal. These ion exchange equilibria were treated with the use of models of fixed bi- or tridentate centers, which consider the surface of the sorbent as an assemblage of polyfunctional sorption centers. Both the observed ion exchange capacities with respect to the alkaline metal ions and the equilibrium constants were discussed by taking into consideration the sequence of the ionic hydration radii for Li⁺, Na⁺ and K⁺. The matrix affinity order for the ions decreases as the hydration radii of the cations increase, i.e. Li⁺>Na⁺>K⁺. The high values of the separation factors S_Na⁺/Li⁺ and S_K⁺/Li⁺ (up to several hundred) provide quantitative separation of Na⁺ and K⁺ from Li⁺ from a mixture containing these three ions.