The phase φ+− of CP violation in the K0 → π+π− decay

The phase φ_+? is evaluated on the basis of measurements of the K_S-K_L interference in the π⁺π^? decay mode and the mass difference Δm, both reported previously by this group. The result is: φ_{+? = 45.9° ± 1.6°}. This, together with previous results on $\text{|η}{}_{\mathrm{+?}}\text{|, |}\text{η}{}_{00}\text{η}{}_{\mathrm{+?}}\text{|}$ and the charge asymmetry δ in leptonic decay, is compared with the prediction of the superweak model, with good agreement.Finally the result is used to find, on the basis of unitarity, a new upper limit on CP violation in the decay K⁰ → 3π⁰. This limit is |η₀₀₀|^2? 0.21.     

On the Swan subgroup of certain periodic groups

Ohne Zusammenfassung     

A geometric approach to divergent points of higher dimensional Collatz mappings

We define generalized Collatz mappings on free abelian groups of finite rank and study their iteration trajectories. Using geometric arguments we describe cones of points having a divergent trajectory and we deduce lower bounds for the density of the set of divergent points. As an application we give examples which show that the iteration of generalized Collatz mappings on rings of algebraic integers can behave quite differently from the conjectured behavior in \(\mathbb {Z}\).     

Design and characterization of two-dye and three-dye binary fluorescent probes for mRNA detection

We report the design, synthesis, and characterization of binary oligonucleotide probes for mRNA detection. The probes were designed to avoid common problems found in standard binary probes such as direct excitation of the acceptor fluorophore and overlap between the donor and acceptor emission spectra. Two different probes were constructed that contained an array of either two or three dyes and were characterized using steady-state fluorescence spectroscopy, time-resolved fluorescence spectroscopy, and fluorescence depolarization measurements. The three-dye binary probe (BP-3d) consists of a Fam fluorophore which acts as a donor, collecting light and transferring it as energy to Tamra, which subsequently transfers energy to Cy5 when the two probes are hybridized to mRNA. This design allows the use of 488 nm excitation, which avoids the direct excitation of Cy5 and at the same time provides a good fluorescence resonance energy transfer (FRET) efficiency. The two-dye binary probe system (BP-2d) was constructed with Alexa488 and Cy5 fluorophores. Although the overlap between the fluorescence of Alexa488 and the absorption of Cy5 is relatively low, FRET still occurs due to their close physical proximity when the probes are hybridized to mRNA. This framework also decreases the direct excitation of Cy5 and reduces the fluorescence overlap between the donor and the acceptor. Picosecond time-resolved spectroscopy showed a reduction in the fluorescence lifetime of donor fluorophores after the formation of the hybrid between the probes and target mRNA. Interestingly, BP-2d in the presence of mRNA shows a slow rise in the fluorescence decay of Cy5 due to a relatively slow FRET rate, which together with the reduction in the Alexa488 lifetime provides a way to improve the signal to background ratio using time-resolved fluorescence spectra (TRES). In addition, fluorescence depolarization measurements showed complete depolarization of the acceptor dyes (Cy5) for both BP-3d (due to sequential FRET steps) and BP-2d (due to the relatively low FRET rate) in the presence of the mRNA target.