Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B   decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ$B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3)$\mathrm{SU}(3)$ sum rule for pairs of B→Kπ$B\to K\pi$ and B→Kη₈$B\to K{\eta }_8$, generalized to pairs of B→Kπ$B\to K\pi$, B→Kη$B\to K\eta$ and B→Kη^′$B\to K{\eta }^{\prime }$.     

Nonproteolytic cleavage of aspartyl proline bonds in the cellulosomal scaffoldin subunit from Clostridium thermocellum

Previous work from our group [Morag (Morgenstern), E., Bayer, E. A., and Lamed, R. (1991), Appl. Biochem. Biotechnol. 30, 129–136] has demonstrated an anomalous electrophoretic mobility pattern for scaffoldin, the 210-kDa cellulosome-integrating subunit of Clostridium thermocellum. Subsequent evidence [Morag, E., Bayer, E. A., and Lamed, R. (1992), Appl. Biochem. Biotechnol. 33, 205–217] indicated that the effect could be attributed to a nonproteolytic fragmentation of the subunit into a defined series of lowermolecular-weight bands. In the present work, a recombinant segment of the scaffoldin subunit was employed to determine the site(s) of bond breakage. An Asp-Pro sequence within the cohesin domain was identified to be the sensitive peptide bond. This sequence appears quite frequently in the large cellulosomal proteins, and the labile bond may be related to an as yet undescribed physiological role in the hydrolysis of cellulose by cellulosomes.     

A Macrocyclic Furan with Accessible Oxidation States: Switching Between Aromatic and Antiaromatic Global Ring Currents

Macrocyclic furans are predicted to switch between global aromaticity and antiaromaticity, depending on their oxidation states. However, the macrocyclic furans reported to date are stabilized by electron withdrawing groups, which result in inaccessible oxidation states. To circumvent this problem, a post-macrocyclization approach was applied to introduce methylene-substituted macrocyclic furans, which display an extremely low oxidation potential of −0.23 vs. Fc/Fc⁺, and are partially oxidized in ambient conditions. Additional oxidation to the dication results in aromaticity switching to a global 30πe⁻ aromatic state, as indicated by the formation of a strong diatropic current observed in the ¹H NMR spectrum. NICS and ACID calculations support this trend and provide evidence for a different pathway for the global current in the neutral and dicationic states. According to these findings, macrocyclic furans can be rendered as promising p-type materials with stable oxidation states.     

Practical anodes for Li-ion batteries comprising metallurgical silicon particles and multiwall carbon nanotubes

Journal of Solid State Electrochemistry - Silicon is considered to be a very attractive anode material for next-generation lithium-ion batteries due to its high theoretical capacity...     

On the symmetric square: unstable local transfer

Summary We prove the fundamental lemma for spherical functions with respect to the natural (induction) lifting fromPGL(2) toPGL(3) which appears as the unstable counterpart of the stable symmetric-square lifting fromSL(2) toPGL(3) (see [IV] for an introduction to this project, and [VI] for the final results). Thus spherical functions onPGL(2) andPGL(3) which correspond to each other by satisfying an elementary representation theoretic relation are shown to have matching orbital integrals. The proof of this local statement is based on an application of the global trace formula.Partially supported by NSF grants     

Motivic torsors

The torsorP _δ=Hom^⊗ (H _DR,H _σ) under the motivic Galois groupG _σ=Aut^⊗ H _δ of the Tannakian category generated by one-motives related by absolute Hodge cycles over a field κ with an embedding σ:k↪ℂ is shown to be determined by its projectionP _σ→P _σ/G _σ ⁰ to a Gal( )-torsor, and by its localizationsP _σ⊕_k k _ξ at a dense subset of orderings ϕ of the field κ, provided κ has virtual cohomological dimension (vcd) one. This result is an application of a recent local-global principle for connected linear algebraic groups over a field κ of vcd ≤1.     

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω _d is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r ^α ) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with n = πr ² particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and Redig. Yuval Peres is partially supported by NSF grant DMS-0605166.     

The threshold for random -SAT is

Let be a random -CNF formula formed by selecting uniformly and independently out of all possible -clauses on variables. It is well known that if , then is unsatisfiable with probability that tends to 1 as . We prove that if , where , then is satisfiable with probability that tends to 1 as .

Our technique, in fact, yields an explicit lower bound for the random -SAT threshold for every . For our bounds improve all previously known such bounds.

     

Excited-state intermolecular proton transfer of firefly luciferin III. Proton transfer to a mild base

Steady-state and time-resolved techniques were employed to study the excited-state proton transfer (ESPT) from d-luciferin, the natural substrate of the firefly luciferase, to the mild acetate base in aqueous solutions. We found that in 1 M aqueous solutions of acetate or higher, a proton transfer (PT) process to the acetate takes place within 30 ps in both H(2)O and D(2)O solutions. The time-resolved emission signal is composed of three components. We found that the short-time component decay time is 300 and 600 fs in H(2)O and D(2)O, respectively. This component is attributed either to a PT process via the shortest water bridged complex available, ROH··H(2)O··Ac(-), or to PT taking place within a contact ion pair. The second time component of 2000 and 3000 fs for H(2)O and D(2)O, respectively, is attributed to ROH* acetate complex, whose proton wire is longer by one water molecule. The decay rate of the third, long-time component is proportional to the acetate concentration. We attribute it to the diffusion-assisted reaction as well as to PT process to the solvent.