Charge qubit purification by an electronic feedback loop

We propose the manipulation of an isolated qubit by a simple instantaneous closed-loop feedback scheme in which a time-dependent electronic detector current is directly back-coupled into qubit parameters. As a specific detector model, we employ a capacitively coupled single-electron transistor. We demonstrate the stabilization of pure delocalized qubit states above a critical detector-qubit coupling. This electronic purification is independent of the initial qubit state and is accomplished after few electron jumps through the detector. Our simple scheme can be used for the efficient and robust initialization of solid-state qubits in quantum computational algorithms at arbitrary temperatures.     

On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results

A result by Elton⁽⁶⁾ states that an iterated function system

Separation of andrographolide and neoandrographolide from the leaves of Andrographis paniculata using high-speed counter-current chromatography

The bioactive diterpenes andrographolide and neoandrographolide from the leaves of Andrographis paniculata NEES (Acanthaceae) were successfully separated by counter-current chromatography. A single 280-min separation yielded 189 mg of 99.9% andrographolide and 9.5 mg of 98.5% neoandrographolide applying water-methanol-ethyl acetate-n-hexane (2.5:2.5:4:1) solvent system. Structure confirmation was done by electrospray MS, one-dimensional NMR experiments, circular dichroism, optical rotation dispersion, and specific optical rotation [alpha]D.     

The Minimal Subgroup of a Random Walk

It is proved that for each random walk (S _n ) _n0 on ^d there exists a smallest measurable subgroup of ^d , called minimal subgroup of (S _n ) _n0, such that P(S _n )=1 for all n1. can be defined as the set of all x ^d for which the difference of the time averages n ^{–1 n} _k=1 P(S _k ) and n ^{–1 n} _k=1 P(S _k +x) converges to 0 in total variation norm as n. The related subgroup * consisting of all x ^d for which lim _n P(S _n )–P(S _n +x)=0 is also considered and shown to be the minimal subgroup of the symmetrization of (S _n ) _n0. In the final section we consider quasi-invariance and admissible shifts of probability measures on ^d . The main result shows that, up to regular linear transformations, the only subgroups of ^d admitting a quasi-invariant measure are those of the form ₁×...× _k × ^l–k ×{0} ^d–l , 0kld, with ₁,..., _k being countable subgroups of . The proof is based on a result recently proved by Kharazishvili⁽³⁾ which states no uncountable proper subgroup of admits a quasi-invariant measure.     

Blackwell's renewal theorem for certain linear submartingales and coupling

The present work surveys some extensions of Blackwell's renewal theorem for a certain class of linear submartingalesS which have been recently obtained by the author. The basic assumption onS is that their conditional increment distribution functions with respect to some filtration are bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell-type renewal theorems. The latter are derived by employing a coupling argument similar to that which has been used in the i.i.d. case by Lindvallet al. A number of applications are also presented.     

Synthesis and structure of novel 1lambda4,2,6-thiadiazines

S,S-Disubstituted sulfodiimines 9 are known to be versatile building blocks for the synthesis of various sulfur-nitrogen-containing heterocycles. Addition-condensation reactions of 9 with three different activated carbonylsubstrates 14-16 lead to several new 1lambda(6),2,6-thiadiazine-3-ones 17-20. S-Debenzylation via a novel synthetic approach utilizing different electrophiles such as TMSCl, Alk(3)O(+)BF(4)(-), Tos(2)O, and Mes(2)O gives rise to a variety of so far hardly known 1lambda(4),2,6-thiadiazine-3-ones 25 and 26. Structure elucidation reveals NH/CH tautomers in solution as well as a tetrahedral asymmetric sulfur attached to the conjugated planar N/C skeleton. The structural features of the 1lambda(4),2,6-thiadiazines 25 and 26 as well as their reactivity toward certain electrophiles will be discussed in detail. Alkylation with Alk(3)O(+)BF(4)(-) preferably results in formation of the 3-alkoxy-1lambda(4)-2,6-thiadiazines 29. In the presence of acid or base, also the N-2-alkyl isomers 30 are formed. Mesylation of 26 with methanesulfonic acid anhydride followed by aminolysis furnishes a variety of the desired heterocycles 5 in moderate overall yield.     

Note on irregularities of distribution

Letf be a periodic function on with period 1, piecewise continuously differentiable, satisfying . For an arbitrary sequence = ( _i ) in [0,1) put and . If then _n (f,) >c· logn holds for some positive constantc (depending onf only) and almost alln. In a certain sense the converse is also true: there is a class of functionsf with such that _n (f,) =o (logn).Support has been received from Netherlands Organization for the Advancement of Pure Research (Z. W. O.).     

Isolation of N-Ethyl-2-pyrrolidinone-Substituted Flavanols from White Tea Using Centrifugal Countercurrent Chromatography Off-Line ESI-MS Profiling and Semi-Preparative Liquid Chromatography

N-Ethyl-2-pyrrolidinone-substituted flavanols (EPSF) are marker compounds for long-term stored white teas. However, due to their low contents and diasteromeric configuration, EPSF compounds are challenging to isolate. In this study, two representative epimeric EPSF compounds, 5′′′R- and 5′′′S-epigallocatechin gallate-8-C N-ethyl-2-pyrrolidinone (R-EGCG-cThea and S-EGCG-cThea), were isolated from white tea using centrifugal partition chromatography (CPC). Two different biphasic solvent systems composed of 1. N-hexane-ethyl acetate-methanol-water (1:5:1:5, v/v/v/v) and 2. N-hexane-ethyl acetate-acetonitrile-water (0.7:3.0:1.3:5.0, v/v/v/v) were used for independent pre-fractionation experiments; 500 mg in each separation of white tea ethyl acetate partition were fractionated. The suitability of the two solvent systems was pre-evaluated by electrospray mass-spectrometry (ESI-MS/MS) analysis for metabolite distribution and compared to the results of the CPC experimental data using specific metabolite partition ratio K_D values, selectivity factors α, and resolution factors R_S. After size-exclusion and semi-preparative reversed-phase liquid chromatography, 6.4 mg of R-EGCG-cThea and 2.9 mg of S-EGCG-cThea were recovered with purities over 95%. Further bioactivity evaluation showed that R- and S-EGCG-cThea possessed in vitro inhibition effects on α-glucosidase with IC₅₀ of 70.3 and 161.7 μM, respectively.