Tight closure, plus closure and Frobenius closure in cubical cones

We consider tight closure, plus closure and Frobenius closure in the rings , where is a field of characteristic and . We use a -grading of these rings to reduce questions about ideals in the quotient rings to questions about ideals in the regular ring . We show that Frobenius closure is the same as tight closure in certain classes of ideals when . Since , we conclude that for these ideals. Using injective modules over the ring , the union of all th roots of elements of , we reduce the question of whether for -graded ideals to the case of -graded irreducible modules. We classify the irreducible -primary -graded ideals. We then show that for most irreducible -primary -graded ideals in , where is a field of characteristic and . Hence for these ideals.

     

Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout

We have detected coherent quantum oscillations between Josephson phase qubits and critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. These results reveal a new aspect of the quantum behavior of Josephson junctions, and they demonstrate the means to measure two-qubit interactions in the time domain. The junction-fluctuator interaction also points to a possible mechanism for decoherence and reduced fidelity in superconducting qubits.     

Laser-polarized (129)Xe NMR and MRI at ultralow magnetic fields

Laser-polarized (129)Xe and a high-T(c)superconducting quantum interference device (SQUID) are used to obtain magnetic resonance images in porous materials at a magnetic field of 2.3 mT, corresponding to a Larmor frequency of 27 kHz. Image resolution of 1 mm is obtained with gradients of only 1 mT/m. The resolution of xenon chemical shifts in different physicochemical environments at ultralow fields is also demonstrated. Details of the circulating flow optical pumping apparatus and the SQUID spectrometer are presented.     

Biological soft X‐ray tomography on beamline 2.1 at the Advanced Light Source

Beamline 2.1 (XM‐2) is a transmission soft X‐ray microscope in sector 2 of the Advanced Light Source at Lawrence Berkeley National Laboratory. XM‐2 was designed, built and is now operated by the National Center for X‐ray Tomography as a National Institutes of Health Biomedical Technology Research Resource. XM‐2 is equipped with a cryogenic rotation stage to enable tomographic data collection from cryo‐preserved cells, including large mammalian cells. During data collection the specimen is illuminated with `water window' X‐rays (284–543 eV). Illuminating photons are attenuated an order of magnitude more strongly by biomolecules than by water. Consequently, differences in molecular composition generate quantitative contrast in images of the specimen. Soft X‐ray tomography is an information‐rich three‐dimensional imaging method that can be applied either as a standalone technique or as a component modality in correlative imaging studies.     

Screening for antioxidants in complex matrices using high performance liquid chromatography with acidic potassium permanganate chemiluminescence detection

The use of high performance liquid chromatography with acidic potassium permanganate chemiluminescence detection to screen for antioxidants in complex plant-derived samples was evaluated in comparison with two conventional post-column radical scavenging assays (2,2-diphenyl-1-picrylhydrazyl radical (DPPH) and 2,2'-azinobis-(3-ethylbenzothiazoline-6-sulfonic acid) radical cation (ABTS(+))). In this approach, acidic potassium permanganate can react with readily oxidisable compounds (potential antioxidants), post-column, to produce chemiluminescence. Using flow injection analysis, experimental parameters that afforded the most suitable permanganate chemiluminescence signal for a range of known antioxidants were studied in a univariate approach. Optimum conditions were found to be: 1×10(-3)M potassium permanganate solution containing 1% (w/v) sodium polyphosphates adjusted to pH 2 with sulphuric acid, delivered at a flow rate of 2.5 mL min(-1) per line. Further investigations showed some differences in detection selectivity between HPLC with the optimised post-column permanganate chemiluminescence detection and DPPH and ABTS(+) assays towards antioxidant standards. However, permanganate chemiluminescence detection was more sensitive. Moreover, screening for antioxidants in green tea, cranberry juice and thyme using potassium permanganate chemiluminescence offers several advantages over the traditional DPPH and ABTS(+) assays, such as faster reagent preparation and superior stability; simpler post-column reaction manifold; and greater compatibility with fast chromatographic separations using monolithic columns.     

Nonlinear analysis of high-harmonic slotted gyro-TWT amplifier

A nonlinear self-consistent simulation code is employed to investigate the behavior of the slotted gyrotron traveling-wave amplifier (gyro-TWT), in which an axis-encircling electron beam synchronously interacts with a high-order azimuthal mode in a magnetron-type waveguide. The efficiency of a fourth-harmonic device with an ideal 60 kV, 5 A beam is shown to reach 30% for α≡ν_⊥/ν_z=2. The growth rate for the π mode is roughly 25% larger than for the 2π mode. The efficiency increases for lower voltage and the device is found to be moderately sensitive to the radial spread of the beam's guiding center position and extremely sensitive to the axial velocity spread. For an ideal 60 kV, 5 A beam with α=1.5, the efficiency of a second-harmonic gyro-TWT is 42% and falls to 10% for an eighth-harmonic device. The design of a 35 GHz, 60 kV, 5A, α=1.5, eight-vane, fourth-harmonic gyro-TWT with 7% axial velocity spread is presented. It is predicted that this design will yield a peak output power of 90 kW, a peak efficiency of 30%, and 6.3% saturated bandwidth     

Improvement of resolution in solid state NMR spectra with J-decoupling: an analysis of lineshape contributions in uniformly C-enriched amino acids and proteins

In magic angle spinning (MAS) NMR spectra of highly and uniformly 13C,15N-enriched amino acids and proteins, homo-nuclear coupling interactions contribute significantly to the 13C linewidths, particularly for moderate applied magnetic field strengths and sample spinning frequencies. In this work, we attempted to dissect, analyze, and control the contributions of J-coupling and residual homo-nuclear dipolar coupling interactions to the linewidths of uniformly 13C,15N-enriched crystalline alanine; these studies were carried out at 9.4 T using a range of spinning frequencies from 5 to 15 kHz. The anisotropic second-order dipolar shifts and the J-splittings are comparable in their contribution to the linewidths, but behave very differently in terms of experimental protocols for line narrowing. In contrast to the J-coupling interactions, the second-order dipolar broadening cannot be refocused using selective pulses on the passively coupled spin. We carried out experiments to remove or refocus the 13C J-coupling interactions (omega1 J-decoupling) using a selective DANTE pulse in the center of the indirect evolution period. Inversion profiles and bandwidths of selective DANTE pulses acting on transverse magnetization, in the regime of moderate spinning frequencies, were characterized computationally and experimentally. A dramatic improvement in the resolution of the 2D spectrum was achieved when this decoupling protocol was employed.     

Peptides—XXXII: The use of phenyl esters in peptide synthesis

Phenyl esters of N-terminal amino-protected peptides are valuable intermediates in synthesis of polypeptides. The phenyl ester function is stable during the customary manipulations of chain extension, and it can be removed selectively by treatment with one equivalent of hydrogen peroxide at pH 10.5 in a variety of solvents such as 80% acetone, dimethylfonnamide, hexamethylphosphoramide or trifluoroethanol. The method has always been satisfactory providing that dimethylsulphide is used as a scavenger.