Framework for three-dimensional coherent diffraction imaging by focused beam x-ray Bragg ptychography

We present the framework for convergent beam Bragg ptychography, and, using simulations, we demonstrate that nanocrystals can be ptychographically reconstructed from highly convergent x-ray Bragg diffraction. The ptychographic iterative engine is extended to three dimensions and shown to successfully reconstruct a simulated nanocrystal using overlapping raster scans with a defocused curved beam, the diameter of which matches the crystal size. This object reconstruction strategy can serve as the basis for coherent diffraction imaging experiments at coherent scanning nanoprobe x-ray sources.     

Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)

Algorithms are presented which find a basis of the vector space of cuspidal cohomology of certain congruence subgroups of SL(3, $\text{Z}$) and which determine the action of the Hecke operators on this space. These algorithms were implemented on a computer. Four pairs of cuspidal classes were found with prime level less than 100. Tables are given of the eigenvalues of the first few Hecke operators on these classes.     

A Conjecture Concerning the Spectrum of a Sentence

We give a plausible-sounding conjecture involving the number of n-equivalence classes of structures of size m which would imply that the complement of a spectrum is also a spectrum. Mathematics Subject Classification : 03B10, 03D15, 68Q15.     

Separating chemical shift and quadrupolar anisotropies via multiple-quantum NMR spectroscopy

Chemical shift anisotropy (CSA) has been an invaluable probe of structure and dynamics for a variety of systems in NMR spectroscopy. Unfortunately, the presence of strong quadrupolar couplings has severely limited the ability to measure CSA in nuclei with spins I > 1/2. Here we show that these two interactions can be refocused at different times in a 2D multiple-quantum NMR experiment on polycrystalline samples. Combining this experiment with appropriate affine transformations allows these interactions to be cleanly separated into orthogonal dimensions. The 1D projection onto each axis can be fit to extract the respective principal tensor components. These components can then be used to fit the 2D spectrum for the relative orientation between the CSA and quadrupolar-coupling tensors. The necessary affine transformation parameters are given for all possible I values. Illustrative examples of spectra and analyses are given for 63Cu in K3[Cu(CN)4], 59Co in K3[Co(CN)6], and 87Rb in RbCrO4.     

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.

     

Phage display-derived inhibitor of the essential cell wall biosynthesis enzyme MurF

Background  

To develop antibacterial agents having novel modes of action against bacterial cell wall biosynthesis, we targeted the essential MurF enzyme of the antibiotic resistant pathogen Pseudomonas aeruginosa. MurF catalyzes the formation of a peptide bond between D-Alanyl-D-Alanine (D-Ala-D-Ala) and the cell wall precursor uridine 5'-diphosphoryl N-acetylmuramoyl-L-alanyl-D-glutamyl-meso-diaminopimelic acid (UDP-MurNAc-Ala-Glu-meso-A2pm) with the concomitant hydrolysis of ATP to ADP and inorganic phosphate, yielding UDP-N-acetylmuramyl-pentapeptide. As MurF acts on a dipeptide, we exploited a phage display approach to identify peptide ligands having high binding affinities for the enzyme.     

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.     

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.