Quantum symmetric derivatives

For , a one-parameter family of symmetric quantum derivatives is defined for each order of differentiation as are two families of Riemann symmetric quantum derivatives. For , symmetrization holds, that is, whenever the th Peano derivative exists at a point, all of these derivatives of order also exist at that point. The main result, desymmetrization, is that conversely, for , each symmetric quantum derivative is a.e. equivalent to the Peano derivative of the same order. For and , each th symmetric quantum derivative coincides with both corresponding th Riemann symmetric quantum derivatives, so, in particular, for and , both th Riemann symmetric quantum derivatives are a.e. equivalent to the Peano derivative.

     

Mass spectral behavior of the hydrolysis products of sesqui- and oxy-mustard type chemical warfare agents in atmospheric pressure chemical ionization

Bis(2-hydroxyethylthio)alkanes and bis(2-hydroxyethylthioalkyl)ethers are important biological and environmental degradation products of sulfur mustard analogs known as sesqui- and oxy-mustards. We used atmospheric pressure chemical ionization mass spectrometry (APCI MS) to acquire characteristic spectra of these compounds in positive and negative ionization modes. Positive APCI mass spectra exhibited [M + H](+); negative APCI MS generated [M + O(2)](-), [M - H](-), and [M - 3H](-); and both positive and negative APCI mass spectra contained fragment ions due to in-source collision-induced dissociation. Product ion scans confirmed the origin of fragment ions observed in single-stage MS. Although the spectra of these compounds were very similar, positive and negative APCI mass spectra of the oxy-mustard hydrolysis product, bis(2-hydroxyethylthiomethyl)ether, differed from the spectra of the other compounds in a manner that suggested a rearrangement to the sesqui-mustard hydrolysis product, bis(2-hydroxyethylthio)methane. We evaluated the [M + O(2)](-) adduct ion for quantification via liquid chromatography-MS/MS in the multiple-reaction monitoring (MRM) mode by constructing calibration curves from three precursor/product ion transitions for all the analytes. Analytical figures of merit generated from the calibration curves indicated the stability and suitability of these transitions for quantification at concentrations in the low ng/mL range. Thus, we are the first to propose a quantitative method predicated on the measurement of product ions generated from the superoxide adduct anion of the sesqui-and oxy-mustard hydrolysis products.     

Periodic behaviour for the evolutionary dam problem and related free boundary problems Evolutionary dam problem

The time dependent dam problem describing the seepage of a compressible or incompressible fluid in a porous dam is studied. We prove existence of solutions in a suitable weak sense, and uniqueness for rectangular dams. Existence or periodic solutions is established and questions ofstability and periodic behavior for large time are studied.     

Direct Sums of Mod p Characters of Gal and the Homology of GL(n, ℤ)

The paper classifies multilincnr algebras, known as comlrans algebras, that are determined by pairs of matrices and have dimensions which are less than or equal to two. The comtrans algebras are isomophic if and only if the corresponding pairs of matrices arc multiplicatively cogredient by a matrix M.     

Exploring the low-Z shore of the island of inversion at n=19

The technique of invariant mass spectroscopy has been used to measure, for the first time, the ground state energy of neutron-unbound (28)F, determined to be a resonance in the (27)F+n continuum at 220(50) keV. States in (28)F were populated by the reactions of a 62 MeV/u (29)Ne beam impinging on a 288 mg/cm(2) beryllium target. The measured (28)F ground state energy is in good agreement with USDA/USDB shell model predictions, indicating that pf shell intruder configurations play only a small role in the ground state structure of (28)F and establishing a low-Z boundary of the island of inversion for N=19 isotones.     

Drawing with Iron on a Gel Containing a Supramolecular Siderophore

Guanosine‐5′‐hydroxamic acid ( 3 ) forms hydrogels when mixed with guanosine ( 1 ) and KCl. The 5′‐hydroxamic acid (HA) unit is pH‐responsive and also chelates Fe³⁺. When gels are prepared under basic conditions, the 5′‐HA groups are deprotonated and the anionic hydrogel binds cationic thiazole orange (TO), signaled by enhanced fluorescence. The HA nucleoside 3 , when immobilized in the G‐quartet gel, acts as a supramolecular siderophore to form red complexes with Fe³⁺. We patterned the hydrogel's surface with FeCl₃, by hand and by using a 3D printer. Patterns form instantly, are visible by eye, and can be erased using vitamin C. This hydrogel, combining self‐assembled G‐quartet and siderophore–Fe³⁺ motifs, is strong, can be molded into different shapes, and is stable on the bench or under salt water.     

The crystalline state as a dynamic system: IR microspectroscopy under electrochemical control for a [NiFe] hydrogenase

Controlled formation of catalytically-relevant states within crystals of complex metalloenzymes represents a significant challenge to structure–function studies. Here we show how electrochemical control over single crystals of [NiFe] hydrogenase 1 (Hyd1) from Escherichia coli makes it possible to navigate through the full array of active site states previously observed in solution. Electrochemical control is combined with synchrotron infrared microspectroscopy, which enables us to measure high signal-to-noise IR spectra in situ from a small area of crystal. The output reports on active site speciation via the vibrational stretching band positions of the endogenous CO and CN⁻ ligands at the hydrogenase active site. Variation of pH further demonstrates how equilibria between catalytically-relevant protonation states can be deliberately perturbed in the crystals, generating a map of electrochemical potential and pH conditions which lead to enrichment of specific states. Comparison of in crystallo redox titrations with measurements in solution or of electrode-immobilised Hyd1 confirms the integrity of the proton transfer and redox environment around the active site of the enzyme in crystals. Slowed proton-transfer equilibria in the hydrogenase in crystallo reveals transitions which are only usually observable by ultrafast methods in solution. This study therefore demonstrates the possibilities of electrochemical control over single metalloenzyme crystals in stabilising specific states for further study, and extends mechanistic understanding of proton transfer during the [NiFe] hydrogenase catalytic cycle.

Electrochemically-coupled IR microspectroscopy of single crystals provides insight into proton-coupled electron transfer in [NiFe] hydrogenase.