Let f(z) be a function analytic in the complex domain C+∪C−∪(−1,+∞), real for real z and such that f(z), f2(z) are anti-Herglotz functions. In this paper we show that f(z) possesses simple upper and lower bounds given by rational functions. Our main tool is the analytic theory of continued fractions. An application to the theory of solutions of the Feigenbaum-Cvitanović equation is given.

We present a simple protocol for two-player secure circuit evaluation. The protocol enables players C and D to cooperate in the computation of f(x) while D conceals her data x from C and C conceals his circuit for f from D. The protocol is based on the technique of hiding information from an oracle [Abadi, Feigenbaum, Kilian, J. Comput. System Sci. 39(1):21{50, August, 1989].

In this paper, we develop a new approach to the construction of solutions of the Feigenbaum-Cvitanović equation whose existence was shown by H. Epstein. Our main tool is the analytic theory of continued fractions.

The 1-hydroxy-1-methyl-6,6-diphenyl-5-hexenyl radical (4a) and the 1-hydroxy-1-methyl-7,7-diphenyl-6-heptenyl radical (4b) were prepared from the corresponding PTOC esters (anhydrides of a carboxylic acid and N-hydroxypyridine-2-thione). The key step in the synthetic method for the precursors was a coupling reaction of the respective carboxylic acids with the thiohydroxamic acid, which was cond...

OH radicals play a key role as an intermediate in the water formation chemistry of the interstellar medium. For example the reaction of OH radicals with H2 molecules is among the final steps in the astrochemical reaction network starting from O, O2, and O3. Experimentally it was shown that even at 10 K this reaction occurs on ice surfaces. As the reaction has a high activation energy only atom ...

We have calculated the form-factors F and G in K → ππℓν decays (K ℓ4) to two-loop order in Chiral Perturbation Theory (ChPT). Combining this together with earlier two-loop calculations an updated set of values for the L r i , the ChPT constants at O(p 4), is obtained. We discuss the uncertainties in the determination and the changes compared to previous estimates. 1. The theoretical study of K ...

Let k[X] be the algebra of polynomials in n variables over a field k of characteristic zero, and let f ∈ k[X] r k. We present a construction of a derivation d of k[X] whose ring of constants is equal to the integral closure of k[f ] in k[X]. A similar construction for fields of rational functions is also given.

Advancements in self-assembly and nanotechnology will require multiple assembly “codes” to be executed simultaneously. At the molecular level this will require fidelity or orthogonality in molecular recognition events. To explore the limits of orthogonal assembly, association constants (K assoc ) and dimerization constants (K dimer ) were measured with a known series of matched and mismatched r...

The nuclear K–shell electron–capture (EC) and positron (β) decay constants, λEC and λβ+ of H–like Pr and He–like Pr ions, measured recently in the ESR ion storage ring at GSI, were calculated using standard weak interaction theory. The calculated ratios R = λEC/λβ+ of the decay constants agree with the experimental values within an accuracy better than 3%. The anomalous experimental value of th...