On the closure of the first Grigorchuk group

We consider the closure (in the natural topology) of the well-known periodic self-similar group. A finitely generated group that is not isomorphic to the Grigorchuk group and has the same closure is constructed.     

Calorimetric study of the cubic mesogen, ACBC(6)

The heat capacity of the cubic mesogen ACBC(16) was measured between 16 and 500 K by adiabatic calorimetry. As well as the known condensed phases, a new crystalline phase was found to undergo a glass transition at around 165 K. Phase transitions between crystal, SmC, cubic, and isotropic liquid phases took place at 399.16, 431.15, and 474.30 K, respectively. As in the case of ANBC, a broad hump was observed in the heat capacity of the isotropic liquid phase. The first order nature of the SmC-cubic phase transition was confirmed for the first time by the observation of supercooling of the cubic phase. The broad hump in the isotropic liquid phase was shown to extend to a low temperature side if the isotropic liquid was supercooled, suggesting that the event occurring at the hump is not directly related to the cubic-isotropic liquid phase transition.     

Microwave-resonance-induced resistivity: evidence of ultrahot surface-state electrons on liquid 3He

Measurements of the dc resistivity of surface-state electrons on liquid helium exposed to microwave radiation are reported. It is shown that the resonant microwave excitation of surface-state electrons is accompanied by a strong increase in their resistivity, which is opposite to the result expected from the previously used two-level model. We show that even a very small fraction of electrons excited to the first excited state and decaying back due to vapor-atom scattering strongly heat the electron system, causing a population of higher subbands. The calculated resistivity change is in good agreement with the observed data.     

Insights into the Pamamycin Biosynthesis

Pamamycins are macrodiolides of polyketide origin with antibacterial activities. Their biosynthesis has been proposed to utilize succinate as a building block. However, the mechanism of succinate incorporation into a polyketide was unclear. Here, we report identification of a pamamycin biosynthesis gene cluster by aligning genomes of two pamamycin‐producing strains. This unique cluster contains polyketide synthase (PKS) genes encoding seven discrete ketosynthase (KS) enzymes and one acyl‐carrier protein (ACP)‐encoding gene. A cosmid containing the entire set of genes required for pamamycin biosynthesis was successfully expressed in a heterologous host. Genetic and biochemical studies allowed complete delineation of pamamycin biosynthesis. The pathway proceeds through 3‐oxoadipyl‐CoA, a key intermediate in the primary metabolism of the degradation of aromatic compounds. 3‐Oxoadipyl‐CoA could be used as an extender unit in polyketide assembly to facilitate the incorporation of succinate.     

Unusually Strong Long‐Distance Metal–Metal Coupling in Bis(ferrocene)‐Containing BOPHY: An Introduction to Organometallic BOPHYs

The first organometallic BOPHY (BOPHY=bis(difluoroboron)‐1,2‐bis{(pyrrol‐2‐yl)methylene}hydrazine) containing two ferrocene substituents was prepared through a Knoevenagel condensation between tetramethyl substituted BOPHY and ferrocene carboxaldehyde. An unprecedentedly strong long‐range (≈17.2 Å) metal–metal coupling in this new complex was investigated using electrochemical, spectroelectrochemical, and chemical oxidation methods. Electrochemical data is indicative of a 200 mV separation between the first and the second ferrocene‐centered oxidation processes. Formation of the mixed‐valence states and appearance and disappearance of two NIR bands were observed during stepwise oxidation of the first organometallic BOPHY. The electronic structure and the nature of the excited states in this new chromophore were studied by DFT and TDDFT calculations.     

Intermediate carbene formation in the reaction of thioamides with phosphorus (III) derivatives: Quantum chemical investigation

The reactions of perfluoroalkyl thioamides with trimethyl phosphine, trimethyl phosphite, and tris(dimethylamino)phosphine have been analyzed by means of quantum chemical (DFT and MP2) calculations. The reaction seems to proceed via the nucleophilic attack of the electrophilic carbon atom by the phosphorus lone pair with the formation of cyclic or acyclic adducts. The latter releases the thiophosphate molecule forming perfluoroalkylaminocarbene as the short‐lived intermediate. The reaction of the carbene with the second molecule of trialkyl phosphite yields phosphorus ylide. The ylide undergoes a migration of fluorine from carbon to phosphorus. The reactions of perfluoroalkyl thioamides with phosphines and tris(dimethylamino)phosphine probably proceeds differently. Using alkyl thioamides or amides instead of perfluoroalkyl thioamides also makes the reaction less favorable. The only combination of perfluoroalkyl thioamides with trialkyl phosphite fulfills both the kinetic requirements (moderate activation energies and relative energies for intermediates) and the thermodynamic aspects (higher stabilities of the reaction products compared with the starting materials). © 2013 Wiley Periodicals, Inc.     

Numerical solution of multiple nonlinear Volterra integral equations

We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution.