Closer look at the operating definition of protein recovery in CE

Analyte recovery is an important figure to assess protein adsorption on fused‐silica capillaries. In 1991, Regnier et al. estimated recovery by assuming the loss of analyte from adsorption and thus the decrease in peak area measured by two detectors to be proportional to the length of the capillary section between them. In this report, we closely examine this concept and its adaptation to commercial CE instruments to determine protein recovery. We hypothesize that, once a steady‐state migration is reached, protein adsorption is a first‐order process with respect to protein concentration and surface density of adsorbing sites. This hypothesis is shown to be valid over a reasonably wide range of capillary effective length and, as a result, protein recovery decreases exponentially with the migrated distance. However, unlike the traditional recovery figure obtained through a conventional spike process, protein recovery measured by this approach does not have the same merit since it is strongly dependent from capillary dimensions and applied electric field. Nevertheless, protein recovery and the slope of the logarithmic protein peak area versus length plot are useful figures to compare protein adsorption on different capillary surfaces. Several literature reports dealing with the application of Regnier concept to calculate protein recovery are discussed.     

On the time‐dependent solutions of the Schrödinger's equation. II. The one‐mode field perturbed harmonic oscillator

The solution of the time‐dependent Schrödinger's equation for a perturbed harmonic oscillator is obtained using a solvable Lie algebra. We choose a harmonic oscillator interacting with a one‐mode field, where the perturbation happens to be periodic in time. This leads to one of the simplest Floquet problems. Using the Wei–Norman theorem, the Floquet wave function is obtained as well as the semiclassical Floquet shift in the energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The wave trace of the basic Laplacian of a Riemannian foliation near a non-zero period

Given a compact boundaryless Riemannian manifold that admits a Riemannian foliation, recall that the space of leaf closures is a singular stratified space. Associated to this space is an operator called the basic Laplacian defined on the space of smooth functions that are constant on the leaves (and, hence, the closures of the leaves of the foliation). The corresponding basic spectrum is, under certain assumptions, an infinite subset of the spectrum of the ordinary laplacian. If the metric is bundle-like with respect to the foliation, the trace of the basic wave operator can be analyzed, and invariants of the basic spectrum can be computed. These invariants include the lengths of certain geodesic arcs which are orthogonal to the leaf closures, and from them, basic wave trace asymptotic expansions are derived. Using the connection between Riemannian foliations and manifolds being acted upon by a compact Lie group of isometries, $G$ , the wave trace for the $G$ -invariant spectrum of a $G$ -manifold is sketched out as a related result.     

Wave Invariants of the Spectrum of the G-Invariant Laplacian and the Basic Spectrum of a Riemannian Foliation

Given a compact boundaryless Riemannian manifold upon which a compact Lie group G acts by isometries, recall that the G-invariant Laplacian is the restriction of the ordinary Laplacian on functions to the space of functions which are constant along the orbits of the action. By considering the wave trace of the invariant Laplacian and the connection between G manifolds and Riemannian foliations, invariants of the spectrum of the G-invariant Laplacian can be computed. These invariants include the lengths of certain geodesic arcs which are orthogonal to the principal orbits and contained in the open dense set of principal orbits are associated to the singularities of the wave trace of the G-invariant spectrum. If the action admits finite orbits, then the invariants also include the lengths of certain geodesics arcs connecting the finite orbit to itself. Under additional hypotheses, we obtain partial wave traces. As an application, a partial trace formula for Riemannian foliations with bundle-like metrics is also presented, as well as several special cases where better results are available.     

Development of a Continuous‐Flow System for Asymmetric Hydrogenation Using Self‐Supported Chiral Catalysts

Well‐designed, self‐assembled, metal–organic frameworks were constructed by simple mixing of multitopic MonoPhos‐based ligands ( 3 ; MonoPhos=chiral, monodentate phosphoramidites based on the 1,1′‐bi‐2‐naphthol platform) and [Rh(cod)₂]BF₄ (cod=cycloocta‐1,5‐diene). This self‐supporting strategy allowed for simple and efficient catalyst immobilization without the use of extra added support, giving well‐characterized, insoluble (in toluene) polymeric materials ( 4 ). The resulting self‐supported catalysts ( 4 ) showed outstanding catalytic performance for the asymmetric hydrogenation of a number of α‐dehydroamino acids ( 5 ) and 2‐aryl enamides ( 7 ) with enantiomeric excess (ee) ranges of 94–98 % and 90–98 %, respectively. The linker moiety in 4 influenced the reactivity significantly, albeit with slight impact on the enantioselectivity. Acquisition of reaction profiles under steady‐state conditions showed 4 h and 4 i to have the highest reactivity (turnover frequency (TOF)=95 and 97 h^?1 at 2 atm, respectively), whereas appropriate substrate/catalyst matching was needed for optimum chiral induction. The former was recycled 10 times without loss in ee (95–96 %), although a drop in TOF of approximately 20 % per cycle was observed. The estimation of effective catalytic sites in self‐supported catalyst 4 e was also carried out by isolation and hydrogenation of catalyst–substrate complex, showing about 37 % of the Rh^I centers in the self‐supported catalyst 4 e are accessible to substrate 5 c in the catalysis. A continuous flow reaction system using an activated C/ 4 h mixture as stationary‐phase catalyst for the asymmetric hydrogenation of 5 b was developed and run continuously for a total of 144 h with >99 % conversion and 96–97 % enantioselectivity. The total Rh leaching in the product solution is 1.7 % of that in original catalyst 4 h .     

Asymmetric hydrogenation of tert-alkyl ketones

A combined system of RuCl2(tolbinap)(pica) and an alkaline or organic phosphazene base catalyzes asymmetric hydrogenation of sterically congested tert-alkyl ketones (TolBINAP = 2,2'-bis(di-4-tolylphosphino)-1,1'-binaphthyl, PICA = alpha-picolylamine). Hydrogenation with RuH(eta1-BH4)(tolbinap)(pica) does not require any strong base. Alcoholic solvents strongly affect the catalytic efficiency. The reaction proceeds smoothly in ethanol under 1-20 atm of H2 and at room temperature with a substrate to catalyst molar ratio of up to 100 000. Various aliphatic, aromatic, heteroaromatic, and olefinic tert-alkyl ketones are convertible to the corresponding chiral carbinols in high enantiomeric purity. Olefinic and heteroaromatic functions are left intact. Certain cyclic ketones are also usable. The mode of enantioface selection is consistent and predictable.     

Flavor changing neutral currents from lepton and <Emphasis Type="Italic">B</Emphasis> decays in the two Higgs doublet model

Constraints on the whole spectrum of lepton flavor violating vertices are shown in the context of the standard two Higgs doublet model. The vertex involving the e- mixing is much more constrained than the others, and the decays proportional to such a vertex are usually very suppressed. On the other hand, bounds on the quark sector are obtained from leptonic decays of the B_d,s⁰ mesons and from . We emphasize that although the B_d⁰- mixing restricts severely the d-b mixing vertex, the upper bound for this vertex could still give a sizable contribution to the decay with respect to the standard model contribution, from which we see that such a vertex could still play a role in the phenomenology.Received: 16 September 2004, Published online: 26 April 2005PACS: 12.60.Fr, 12.15.Mm, 12.15.Ff, 11.30.Hv