The Simultaneous Coupling Scheme for SU(3)

We present a simple method for calculating the Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations of SU(3). The calculation given here is an application and extension of the simultaneous coupling scheme proposed in 2010 for the rotation group SU(2).     

Backward heat equation with time dependent variable coefficient

Backward heat equation with time dependent variable coefficient is severely ill‐posed in the sense of Hadamard, so we need regularization. In this paper, we consider Backward heat equation with time dependent variable coefficient, and by small perturbing, we obtain an approximation problem. We show this approximation problem is well‐posed with small parameter. Also, we show this approximation system converges to the original problem when parameter goes to zero. Here, we use modified‐quasi boundary value method to regularize this problem. Copyright © 2016 John Wiley & Sons, Ltd.     

The time reversal operator for semigroup evolutions

A quantum theory combining an irreversible time evolution semigroup with a time reversal operator is presented.     

Perturbations of unitary representations of the Galilei group: Mass operators with continuous spectra

We present a systematic procedure for constructing mass operators with continuous spectra for a system of particles in a manner consistent with Galilean relativity. These mass operators can be used to construct what may be called point-form Galilean dynamics. As in the relativistic case introduced by Dirac, the point-form dynamics for the Galilean case is characterized by both the Hamiltonian and momenta being altered by interactions. An interesting property of such perturbative terms to the Hamiltonian and momentum operators is that, while having well-defined transformation properties under the Galilei group, they also satisfy Maxwell’s equations. This result is an alternative to the well-known Feynman-Dyson derivation of Maxwell’s equations from non-relativistic quantum physics.     

Synthesis of Boc-protected bicycloproline

The synthesis of a highly constrained quaternary carbocyclic α-amino acid, (+)-N-Boc-bicycloproline, has been achieved starting from sodium cyclopentadienylide. Key steps include a rhodium-catalyzed nitrenoid C-H insertion to install the tert-alkylamine and a ring-closing metathesis reaction to form the pyrrolidine ring.     

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.     

A high-efficiency sample introduction system for capillary electrophoresis analysis of amino acids from dynamic samples and static dialyzed human vitreous samples

A low-volume automated injection system for the analysis of chemically complex, amino acid samples is presented. This system utilizes submicroliter sample volumes stored on a 75-μm inner diameter capillary. A pulse of positive pressure (82 kPa) is used to load nanoliter sample volumes into an in-house fabricated interface and onto a separation capillary. Residual sample solution in the interface is immediately washed away by a continuous transverse flow through the injection interface, yielding a sharp and reproducible sample plug. By performing multiple injections of a static sample, one may average the signals to yield a signal-to-noise ratio improvement of up to 4.07-fold for 20 injections compared with a theoretical maximum of a 4.47-fold improvement. Without interruption of the applied voltage, injections performed every 150 s were used to monitor the progress of the reaction of multiple amino acids with the fluorogenic dye 3-(4-carboxybenzoyl)quinoline-2-carboxaldehyde. Analysis of dialyzed clinical vitreous samples demonstrates the resolution and quantitation of arginine, lysine, leucine, glutamine, and glutamate. Observed levels are comparable with those of nonautomated injection methods and reports by others. Figure Multiple injections of fluorescently labeled human vitreous with a detailed view of a single injection (above) and with all injections segmented and averaged for signal-to-noise ratio improvement (right)     

Natural dissolved organic matter affects electrospray ionization during analysis of emerging contaminants by mass spectrometry

Dissolved organic matter (DOM), present in many forms in water, can interfere with analysis of organic contaminants by atmospheric pressure ionization–mass spectrometry. A quantitative analysis of this interference, or matrix effect, on organic contaminant target analyte measurements was carried out using un-fractionated and fractionated dissolved natural organic matter from the Suwannee River, GA (SROM), a standard reference material, that was directly infused into the tandem mass spectrometer during multiple reaction monitoring (MRM) of a suite of endocrine disrupting compounds–pharmaceuticals and personal care products (EDC/PPCPs). Most target analytes suffered signal suppression in the presence of both fractionated and un-fractionated SROM, however greater interferences were measured with fractionated relative to bulk SROM. This finding is consistent with the view of organic matter as a supramolecular association of low molecular mass components having separate charged and structural features revealed only after dissociation.     

Analysis of deprotonated acids with silicon nanoparticle-assisted laser desorption/ ionization mass spectrometry

Chemically modified silicon nanoparticles were applied for the laser desorption/negative ionization of small acids. A series of substituted sulfonic acids and fatty acids was studied. Compared to desorption ionization on porous silicon (DIOS) and other matrix-less laser desorption/ionization techniques, silicon nanoparticle-assisted laser desorption/ionization (SPALDI) mass spectrometry allows for the analysis of acids in the negative ion mode without the observation of multimers or cation adducts. Using SPALDI, detection limits of many acids reached levels down to 50 pmol/μl. SPALDI of fatty acids with unmodified silicon nanoparticles was compared to SPALDI using the fluoroalkyl silylated silicon powder, with the unmodified particles showing better sensitivity for fatty acids, but with more low-mass background due to impurities and surfactants in the untreated silicon powder. The fatty acids exhibited a size-dependent response in both SPALDI and unmodified SPALDI, showing a signal intensity increase with the chain length of the fatty acids (C12-C18), leveling off at chain lengths of C18-C22. The size effect may be due to the crystallization of long chain fatty acids on the silicon. This hypothesis was further explored and supported by SPALDI of several, similar sized, unsaturated fatty acids with various crystallinities. Fatty acids in milk lipids and tick nymph samples were directly detected and their concentration ratios were determined by SPALDI mass spectrometry without complicated and time-consuming purification and esterification required in the traditional analysis of fatty acids by gas chromatography (GC). These results suggest that SPALDI mass spectrometry has the potential application in fast screening for small acids in crude samples with minimal sample preparation.