Laboratory soft-x-ray microscope for cryotomography of biological specimens

Soft-x-ray cryotomography allows quantitative and high-resolution three-dimensional imaging of intact unstained cells. To date, the method relies on synchrotron-radiation sources, which limits accessibility for researchers. Here we present a laboratory water-window microscope for cryotomography. It is based on a λ=2.48 nm liquid-jet laser-plasma source, a normal-incidence multilayer condenser, a 30 nm zone-plate objective, and a cryotilt sample holder. We demonstrate high-resolution imaging, as well as quantitative tomographic imaging, of frozen intact cells. The reconstructed tomogram of the intracellular local absorption coefficient shows details down to ～100 nm.     

First international comparison of femtosecond laser combs at the International Bureau of Weights and Measures

The first international comparison of femtosecond laser combs has been carried out at the International Bureau of Weights and Measures (BIPM). Three comb systems were involved: BIPM-C1 and BIPM-C2 from the BIPM and ECNU-C1 from the East China Normal University (ECNU). The agreement among the three combs was found to be on the subhertz level in the vicinity of 563 THz. A frequency difference measurement scheme was demonstrated that is suitable for general comb comparisons.     

Micellar induced regioselectivity in the two-step consecutive reaction of SO3(2-) with Br-(CH2CH2)n-Br (n=2-5)

High field (800 MHz) (1)H NMR was used to monitor the two-step consecutive reaction of excess SO(3)(2-) with symmetrical bifunctional alpha,omega-dibromoalkanes with butane (DBB), hexane (DBH), octane (DBO), and decane (DBD) chains in CTAB micelles at 25 degrees C. The first-order rate constant for the first substitution step for DBB and DBH is about 5 times faster than for the second, but the kinetics for DBO and DBD were not cleanly first-order. After 40 min, the solution contained about 80% of the intermediate bromoalkanesulfonate from DBB and DBH and the remainder is alkanedisulfonate and unreacted starting material. The same reactions were carried out in homogeneous MeOH/D(2)O solutions at 50 degrees C. The rate constants for all four alpha,omega-dibromoalkanes were first-order throughout the time course of the reaction and the same within +/-10%. However, because micellar solutions are organized on the nanoscale and bring together lipophilic and hydrophilic reactants into a small reaction volume at the micellar interface, they speed this substitution reaction considerably compared to reaction in MeOH/D(2)O. The CTAB micelles also induce a significant regioselectivity in product formation by speeding the first step of the consecutive reaction more than the second. The results are consistent with the bromoalkanesulfonate intermediates having a radial orientation within the micelles with the -CH(2)SO(3)(-) group in the interfacial region and the -CH(2)Br group directed into the micellar core such that the concentration of -CH(2)Br groups in the reactive zone, i.e., the micellar interface, is significantly reduced. These results provide the first example of self-assembled surfactant system altering the relative rates of the reaction steps of a consecutive reaction and, in doing so, enhancing monosubstitution of a symmetrically disubstituted species.     

Regularity of averages over hypersurfaces

Averages over smooth measures on smooth compact hypersurfaces inR ⁿ are studied. With assumptions on the decay of the Fourier transform of the measure we obtain mixed norm estimates for these means, for exampleL ^p estimates of multiparameter maximal functions over compact hypersurfaces.     

A class of infinitely divisible distributions connected to branching processes and random walks

A class of infinitely divisible distributions on {0,1,2,…} is defined by requiring the (discrete) Lévy function to be equal to the probability function except for a very simple factor. These distributions turn out to be special cases of the total offspring distributions in (sub)critical branching processes and can also be interpreted as first passage times in certain random walks. There are connections with Lambert's W function and generalized negative binomial convolutions.     

Ring-Opening 1-Amino-3-aminomethylation of Donor–Acceptor Cyclopropanes via 1,3-Diazepanes

The first ring-opening reaction of donor–acceptor cyclopropanes to give diamines is reported. For this reaction, a 1,3-bisfunctionalization was developed using cyclopropanes, triazinanes, and Sc(OTf)₃ as the catalyst, followed by treatment with acid. The reaction proceeds under very mild conditions and tolerates many functional groups. Moreover, a library of various 1,3-diazepanes, which arise as intermediates of the first formal aza-[4+3]-cycloaddition reaction with donor–acceptor cyclopropanes, was synthesized.     

The non-abelian self-dual string

Letters in Mathematical Physics - We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the...     

The Structure of a Lyotropic Liquid Crystalline Phase that Orients in a Magnetic Field

Abstract

The structure of a lyotropic liquid crystalline phase with positive diamagnetic anisotropy (type I), that spontaneously orients in a magnetic field has been studied by means of water NMR quadrupole splittings, NMR diffusion and polarized absorption spectroscopy. It is concluded that this phase is built up of long rodlike aggregates. A preliminary study of a sample with negative diamagnetic anisotropy (type II) shows that this phase probably consists of lamellar aggregates. It is suggested that these phases are suitable as orientation matrices for studies of chromophores with polarized light spectroscopy.