Measurement of the Λ→p μ− ¯v branching ratio

A sample of 1.2× 10⁶ Λ-hyperons was analyzed in order to detect the rare decay mode: Λ →pμ^?¯v. The Λ-hyperons were produced by stoppingK ^?-mesons in the 81 cm Saclay hydrogen bubble chamber at the CERN PS. We obtained for the branching ratio: $$\frac{{\Gamma {\text{(}}\Lambda \to p\mu ^ - \bar \nu )}}{{\Gamma {\text{(}}\Lambda \to {\text{all)}}}} = (1.4 \pm 0.5) \times 10^{ - 4} ,$$ based on 20 events, of which 6 have to be attributed to the background from the reaction $$\Lambda \to p\pi ^ - , \pi ^ - \to \mu ^ - \bar v.$$ The background was determined by a Monte Carlo calculation.     

A non-MRA C^r Frame Wavelet with Rapid Decay

A generalized filter construction is used to build an example of a non-MRA normalized tight frame wavelet for dilation by 2 in . This example has the same multiplicity function as the Journé wavelet, yet has a Fourier transform and can be made to be for any fixed postive integer . L. Baggett and P. Jorgensen were supported by a US–NSF Focused Research Group (FRG) grant.     

Profiling isoflavonoids found in legume root extracts using capillary electrophoresis

Legumes such as alfalfa (Medicago sativa L.), barrel medic (Medicago truncatula), white sweet clover (Melilotus alba) and fenugreek (Trigonella graecum), normally accumulate (-)-medicarpin and its malonated glucose conjugate as natural inhibitors of fungal pathogens. These plants also accumulate the biosynthetic precursor formononetin as well as the malonated glycoside. We were interested in developing a robust high-throughput method to quantitate the levels of these two isoflavonoids, both free and conjugated, in legume root extracts, for use in screening for mutant plants accumulating altered levels of these compounds. Capillary electrophoresis was examined as an alternative to current high-performance liquid chromatography (HPLC) methods to generate isoflavonoid profiles. The developed assay used micellar electrokinetic capillary chromatography (MEKC) to provide the required selectivity in complex root extracts. The addition of 1,2-hexanediol to the sodium dodecyl sulfate (SDS) electrolyte provided improved resolution of adjacent isoflavonoids. We examined the role of several factors including sample preparation, buffer composition, buffer pH, and organic component in the injected sample. The use of capillaries with longer path lengths were also examined to increase sensitivity. A comparison of results obtained using MEKC and HPLC showed good correlation in the relative amounts of the isoflavonoids studied.     

Innentitelbild: Regioregular Synthesis of Azaborine Oligomers and a Polymer with a syn Conformation Stabilized by N?H⋅⋅⋅π Interactions (Angew. Chem. 38/2015)

The regioregular synthesis of the first azaborine oligomers and a corresponding conjugated polymer was accomplished by Suzuki–Miyaura coupling methods. An almost perfectly coplanar syn arrangement of the heterocycles was deduced from an X‐ray crystal structure of the dimer, which also suggested that N H⋅⋅⋅π interactions play an important role. Computational studies further supported these experimental observations and indicated that the electronic structure of the longer azaborine oligomers and polymer resembles that of poly(cyclohexadiene) more than poly(p‐phenylene). A comparison of the absorption and emission properties of the polymer with those of the oligomers revealed dramatic bathochromic shifts upon chain elongation, thus suggesting highly effective extension of conjugation.     

Nonlinear femtosecond pulse compression at high average power levels by use of a large-mode-area holey fiber

We demonstrate that nonlinear fiber compression is possible at unprecedented average power levels by use of a large-mode-area holey (microstructured) fiber and a passively mode-locked thin disk Yb:YAG laser operating at 1030 nm. We broaden the optical spectrum of the 810-fs pump pulses by nonlinear propagation in the fiber and remove the resultant chirp with a dispersive prism pair to achieve 18 W of average power in 33-fs pulses with a peak power of 12 MW and a repetition rate of 34 MHz. The output beam is nearly diffraction limited and is linearly polarized.     

Operators arising from representations of nilpotent Lie groups

The following two results are obtained for an irreducible multiplier representation T of a connected nilpotent Lie group. First, T_f is a Hilbert-Schmidt operator if f is square-integrable with compact support. Second, T_f is of trace class if f has derivatives with sufficiently many moments. An application is made of the latter result to show that T_f can be of trace class even when f is not continuous.     

Comparative study of large-mode holey and conventional fibers

Little information exists regarding how large-mode holey fibers compare, in practical terms, with their conventional counterparts. We present what is to our knowledge the first experimental study of mode area and bend loss for a range of large-mode holey and conventional fibers. It is demonstrated here that large-mode holey fibers exhibit mode areas and bending losses that are comparable to those of conventional fibers at 1.55mu . However, the novel wavelength dependence of the numerical aperture in a holey fiber offers a significant advantage for broadband and short-wavelength applications in which single-mode operation is required.     

On functions that are trivial cocycles for a set of irrationals. II

Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non- cobounding function is constructed.