Infinite covering systems of congruences which don't exist

We prove there is no infinite set of congruences with: every integer satisfying exactly one congruence, distinct moduli, the sum of the reciprocals of the moduli equal to 1, the lcm of the moduli divisible by only finitely many primes, and a prime greater than 3 dividing any of the moduli.

     

Room temperature crystallization of amorphous polysiloxane using photodimerization

Bulk crystallization in flexible polymeric systems is difficult to control due to the random orientation of the chains. Here we report a photo cross-linking strategy that results in simultaneous cross-linking and crystallization of polysiloxane chains into millimeter sized leaf-like polycrystalline structures. Polymers containing pendant anthracene groups are prepared and undergo [4+4] photocycloaddition under 365 nm irradiation at room temperature. The growth and morphology of the crystalline structures is studied using polarized optical microscopy (POM) and atomic force microscopy and is found to progress through three unique stages of nucleation, growth, and constriction. The mobility of the individual chains is probed using pulsed-field gradient (PFG) NMR to provide insights into the diffusion processes that may govern chain transport to the growing crystal fronts. The room temperature crystallization of this conventionally amorphous polymer system may allow for a new level of morphological control for silicone materials.

Millimeter sized polymer crystallites grow rapidly when anthracene-containing siloxanes are photocrosslinked using UV light.     

Inside Cover: Biomimetic Chiral Pyridoxal and Pyridoxamine Catalysts (Chin. J. Chem. 2/2019)

The inside cover picture shows the development of chiral pyridoxal and pyridoxamine catalysts by mimicking vitamin B₆‐dependent enzymes. These chiral pyridoxals and pyridoxamines displayed extraordinary catalytic performances in asymmetric biomimetic transamination and Mannich reaction, to give various chiral α‐amino acids and α,β‐diamino acid esters in good yields with excellent diastero‐ and/or enantioselectivities. The research has provided some useful information for further applications of the catalytic power of vitamin B6 in the area of asymmetric cayalysis. More details are discussed in the article by Zhao et al. on page 103–112.

     

Transformation diagrams for the collapse of a phospholipid monolayer

The kinetics of phase transitions in three-dimensional bulk materials are commonly presented in transformation diagrams. Time-temperature transformation (TTT) and continuous-cooling-transformation (CCT) diagrams plot the time required to transform specific fractions of the material to the new phase by cooling below a transition temperature. Transformation occurs isothermally for the TTT diagrams and during continuous cooling through a range of temperatures for CCT curves. Here we present analogous transformation diagrams for two-dimensional monolayers, which collapse at the equilibrium spreading pressure (pi e) to form a three-dimensional bulk phase. Time-surface pressure-transformation (TpiT) diagrams give the time required for specific fractions of the film to collapse when surface pressure is constant, and continuous-compression-transformation diagrams give the same information when surface pressure varies continuously. The diagrams, constructed here from previously reported data for 1-palmitoyl-2-oleoyl phosphatidylcholine, provide insights into the behavior of the films. The TpiT diagrams successfully predict the existence and approximate magnitude of a threshold rate for compressing the films to high surface pressures above pi e and the approximate shape of isotherms obtained with different rates of interfacial compression. The diagrams also caution that the behavior of mixed monolayers, explained previously in terms of compositional changes, can instead result from collapse that varies with surface pressure. Finally, the similarity between the shapes of the TTT and TpiT diagrams, with the time for transformation passing through a minimum and then increasing as the systems deviate further from equilibrium, suggests that analogous mechanisms determine the behavior of both systems.     

Separation of porphyrin-based photosensitizer isomers by laser-induced fluorescence capillary electrophoresis

Methods for the separation of photosensitizer isomers, such as benzoporphyrin derivative monoacid, benzoporphyrin ethyl monoacid, 2-[1-hexyloxyethyl]-2-devinylpyropheophorbide-a, diethyleneglycol diester benzoporphyrin derivative, tin ethyl etiopurpurin, and phthalocyanine tetrasulfonate, have been systematically developed by CE. Detection was accomplished by UV absorption at 214 nm or by LIF with excitation at 442/488 nm and emission at 690 nm. The effects of three major experimental parameters of buffer types, organic solvents, and surfactant additives are described. The optimized separation conditions were determined so as to provide satisfactory separation efficiency and analysis time. The methods are shown to be suitable for the separation and determination of porphyrin and phthalocyanines regioisomers, diastereoisomers, and enantiomers.     

Kinetics for the collapse of trilayer liquid-crystalline disks from a monolayer at an air-water interface

Unlike surfactants considered in previous studies, when phosphatidylcholine (PC) monolayers collapse at constant surface tension to form a 3D bulk phase, surface area decreases at rates that slow. The different kinetics could result from collapse by a distinct mechanism. Rather than the transfer of molecules all along the interface between the monolayer and bulk phase, PC films can collapse by the folding and subsequent sliding of a bilayer over the monolayer. By this mechanism, molecules can transfer to collapsed trilayers through a locus of constant size. In this article, we use the theory of nucleation and growth to show analytically that during collapse, the area can decrease at rates that decelerate when each individual structure grows through a region of fixed dimensions. We also show that binary films of 30% dihydrocholesterol (dchol) and dipalmitoyl phosphatidylcholine (DPPC), which have previously been shown to form a homogeneous monolayer from which trilayer disks grow through a point, collapse with rates of area decay that slow, in agreement with our analytical expressions.     

Trapping an Unexpected/Unprecedented Hexanuclear Ce(III) Hydrolysis Product with Neutral 4-Amino-1,2,4-triazole

Using Ce(III) as both a representative lanthanide and actinide analog, the ability of mixtures of acidic and basic azoles to allow direct access to homoleptic N-donor f-element complexes in one pot reactions from hydrated salts as starting materials was examined by reacting mixtures of 4-amino-1,2,4-triazole (4-NH₂-1,2,4-Triaz), 5-amino-tetrazole (5-NH₂-HTetaz), and 1,2,3-triazole (1,2,3-HTriaz) in 1 : 1 and 1 : 3 ratios with CeCl₃ ⋅ 7H₂O, [C₂mim]₃[CeCl₆] ([C₂mim]⁺=1-ethyl-2-methylimidazolium), and Ce(NO₃)₃ ⋅ 6H₂O. Although unsuccessful in our goal, structural analysis revealed that neutral 4-NH₂-1,2,4-Triaz is structure directing via η²μ₂κ² bridging, with the formation of the dinuclear complexes [Ce₂Cl₂(μ₂-4-NH₂-1,2,4-Triaz)₄(H₂O)₈]Cl₄ ⋅ 4H₂O, [Ce₂(μ₂-4-NH₂-1,2,4-Triaz)₄(4-NH₂-1,2,4-Triaz)₂(Cl)₆], and [4-NH₂-1,2,4-HTriaz][Ce₂(μ₂-4-NH₂-1,2,4-Triaz)₂(μ₂-NO₃)(NO₃)₆(H₂O)₂]. When the synthetic conditions favored hydrolysis, the hexanuclear Ce(III) complex [Ce₆(μ₃-O)₄(μ₃-OH)₂(μ₃-Cl)₂(Cl)₆(μ₂-4-NH₂-1,2,4-Triaz)₁₂] ⋅ 7H₂O was isolated. This unexpected hydrolysis product represents the first example of a high nuclearity lanthanide complex where all Ln atoms are pairwise connected through 12 N-donor ligands or 12 neutral bridging ligands of any type, a rare example of incorporation of non-oxo coordinating anions in the M₆X₈ core, and the first reported Ce(III) hexanuclear complex of this type.     

Cross-metathesis of the vinyl group on tetrapyrrolic macrocycles: reactivity, selectivity, and mechanism

To find a general strategy for modifying the peripheral structure of vinylchlorin and porphyrin substrates, cross-metathesis on the vinyl group of these tetrapyrrolic macrocycles was investigated. The N-heterocyclic carbene-containing ruthenium complex 3 efficiently catalyzed the cross-metathesis (CM) of vinylchlorins and vinylporphyrins with a variety of olefins in high E-stereoselectivity. Different substituents on the olefin dramatically influenced the reaction. While the chlorins were more reactive than the porphyrins (as free bases), the corresponding zinc complexes showed higher activity. The reaction mechanism was investigated, and an empirical model for selective CM was applied to our studies to direct further reactions.     

A Lyndon-Hochschild-Serre spectral sequence for certain homotopy fixed point spectra

Let and be closed subgroups of the extended Morava stabilizer group and suppose that is normal in . We construct a strongly convergent spectral sequence

where and are the continuous homotopy fixed point spectra of Devinatz and Hopkins. This spectral sequence turns out to be an Adams spectral sequence in the category of -local -modules.