Operator equivalents without the use of Clebsch-Gordan coefficients

The operator equivalent O^k_q is expressed as the qth difference of O^k_o for which a two-term recurrence relation is derived. The differences contain simple products of Stirling numbers and binomial coefficients.     

The homomorphismM*⊗N → Hom (M,N)

In this note we prove two theorems. In theorem 1 we prove that if M andN are two non-zero reflexive modules of finite projective dimensions over a Gorenstein local ring, such that Hom (M, N) is a third module of syzygies, then the natural homomorphismM* ⊗N → Hom (M, N) is an isomorphism. This extends the result in [7]. In theorem 2, we prove that projective dimension of a moduleM over a regular local ringR is less than or equal ton if and only if Ext_R ⁿ (M, R) ⊗M → Ext_R ⁿ (M, M) is surjective; in which case it is actually bijective. This extends the usual criterion for the projectivity of a module.     

Rapid identification of primary constituents in parotoid gland secretions of the Australian cane toad using HPLC/MS‐Q‐TOF

Toad parotoid gland secretion or toad venom has in recent years been increasingly shown to possess potentially beneficial pharmacological effects; this speculation has drawn much interest centred on elucidating the chemical basis of its multimodal effects. For this purpose, we explored the use of a rapid and accurate analysis method for systemic investigation of the parotoid gland chemistry, when extracted from Australian cane toads. Full‐scan data of cane toad venom extract was acquired using high‐performance liquid chromatography coupled with a hybrid quadrupole–time of flight mass spectrometry system (HPLC/MS‐Q‐TOF), with multiple ionization sources (ESI and APCI) in positive and negative mixed modes. By measuring the exact mass differences between the theoretical and measured mass of each assumed compound, we confirmed the presence of 12 key constituents. The present results demonstrate that the use of HPLC/MS‐Q‐TOF with multiple ionization sources delivers exemplary selectivity and sensitivity, allowing for the rapid and accurate identification of constituents within cane toad venom. This paves the way for this technique to be used in future routine screening of components within the genus Bufo and for key analytes too, then reliably assessed for any purported beneficial (clinic) properties. Copyright © 2013 John Wiley & Sons, Ltd.     

Polymerized hemin as an electrocatalytic platform for peroxynitrite's oxidation and detection

Peroxynitrite (ONOO⁻) constitutes a major cytotoxic agent, implicated in a host of pathophysiological conditions, thereby stimulating a tremendous interest in evaluating its role as an oxidant in vivo. Some of the detection methods for peroxynitrite include oxidation of fluorescent probes, EPR spectroscopy, chemiluminescence, immunohistochemistry, and probe nitration; however, these are more difficult to apply for real-time quantification due to their inherent complexity. The electrochemical detection of peroxynitrite is a simpler and more convenient technique, but the best of our knowledge there are only few papers to date studying its electrochemical signature, or reporting amperometric microsensors for peroxynitrite. Recently, we have reported the use of layered composite films of poly(3,4-ethylenedioxythiophene) (PEDOT) and hemin (iron protoporphyrin IX) as a platform for amperometric measurement of peroxynitrite. The main goal herein is to investigate the intrinsic catalytic role of hemin electropolymerized thin films on carbon electrodes in oxidative detection of peroxynitrite. The electrocatalytic oxidation of peroxynitrite is characterized by cyclic voltammetry. The catalytic current increased as a function of peroxynitrite's concentration, with a peak potential shifting positively with peroxynitrite's concentration. The catalytic efficiency decreased as the scan rate increased, and the peak potential of the catalytic oxidation was found to depend on pH. We show that optimized hemin-functionalized carbon electrodes can be used as simple platforms for peroxinitrite detection and quantification. We report dose–response amperometry as an electroanalytical determination of this analyte on hemin films and we contrast the intrinsic hemin catalytic role with its performance in the case of the PEDOT–hemin as a composite matrix. Finally, we include some work extending the use of simple hemin films for peroxynitrite determination on carbon microfiber electrodes in a flow system.     

Unbiased sequential estimation of1/p: Settlement of a conjecture

Summary We present a complete characterization of the class of (unbounded) sampling plans providing unbiased (sequential) estimation of the reciprocal of the Bernoulli parameterp. This settles a conjecture set forth by Sinha and Sinha (1975,Ann. Inst. Statist. Math.,27, 245–258) regarding the nature of such plans as sought out by Gupta (1967,Ann. Inst. Statist. Math.,19, 413–416). Incidentally, a special type of sampling plans (termed ‘infinite-step generalizations of the inverse binomial plans’), studied by Sinha and Bhattacharyya (1982, Institute of Statistics Mimeo Series, Raleigh), are seen to play a central role in this study.     

Two-dimensional solid state NMR characterization of physisorbed siloxane polymer (OV-225) on silica

Physisorbed cyanopropyl-methyl-phenyl-methyl-siloxane polymer on a silica surface was characterized by one- and two-dimensional solid state NMR techniques including heteronuclear proton-silicon correlation spectroscopy. Spin-lattice relaxations of protons of the siloxane polymer exhibited only small changes upon anchoring to the silica surface indicating somewhat altered molecular dynamics of proton moieties that contribute to the relaxation process. However, the same relaxation rates of the siloxane polymer’s silica atoms were reduced due to restricted mobility of the polymer. Proton-silicon heteronuclear correlation spectroscopy (HETCOR) revealed strong correlations of silanol protons with both Q³ and Q⁴ sites of the silica surface. In addition, a correlation between methyl protons and the Q³ site of the silica surface was observed when HETCOR experiments with very small mixing time (5 ms) were performed. The presence of these correlations is indicative of the coherent magnetization transfer mainly through dipolar mechanisms. Since magnetization transfer through the dipolar mechanism is 1/r³ dependent, methyl protons must lie in close proximity to the silica surface. Hydrogen bonding of the silica surface’s hydroxyl protons with the bridging oxygen of the siloxane polymer is most likely responsible for positioning the methyl protons closer to the surface. Additional correlations between ²⁹Si nuclei and methylene protons next to cyano group was also observed with mixing time indicating the closer proximity of these protons to the silica surface as well. This juxtaposition of methylene protons is most likely due to hydrogen bonding of the siloxane polymer through the cyano moiety. Furthermore, the hydrogen bonding through the cyano group is most likely to be in parallel orientation to the surface. Finally, the aromatic protons exhibited weak correlations only with Q³ sites, indicating that these protons must also lie in close proximity of the silica surface.     

Shear-induced alignment and nanowire silica synthesis in a rigid crystalline surfactant mesophase

Highly aligned stringlike silica nanostructures are obtained through templated synthesis in the columnar hexagonal structure of a rigid crystalline surfactant mesophase. A two-step procedure is used to first shear-align the surfactant mesophase and then conduct synthesis under quiescent conditions in the mesophase. The mesophase retains its alignment for extended periods, allowing materials synthesis to be decoupled from the application of shear. The observations have significant implications in the control of ceramic microstructure morphology and transitions from nonaligned to aligned nanowire type structures.     

Structural evolution in cationic micelles upon incorporation of a polar organic dopant

Micelles of cetyltrimethylammonium bromide (CTAB), when doped with increasing levels of 4-ethylphenol, show microstructural transitions from spherical micelles to elongated wormlike micelles, disks, and subsequently to globular and then to tubular vesicles. Wormlike micelles are observed at a dopant-to-CTAB molar ratio of 1:3. At higher dopant ratios (1:1), globular vesicles are observed which transition to tubular vesicles when the dopant becomes the predominant species at a ratio of 3:1. These transitions are reflected in small-angle neutron scattering analysis and, interestingly, can be directly observed through cryo-transmission electron microscopy. The para-substituted phenol is interfacially active and modulates interfacial curvature of the micelles. The observations of microstructure modifications have relevance to the synthesis of mesoporous materials using CTAB as the template.     

One-dimensional analysis of the wall region for a multiple-temperature argon plasma

The present analysis is restricted to the wall region for a confined gas plasma and applied specifically to an argon plasma. The wall may be either positive or negative in potential with respect to the plasma, and the electric current may flow either parallel or normal to the wall. Estimates of the Debye shielding distance and the mean free path of various components are made to obtain the range of validity of the analysis, in addition to the situation where the wall acts like a cathode, an anode, or an electrical insulation. Analysis is for a one-dimensional case with an outer boundary, where the plasma temperature is specified. The computational domain is split into a continuum region, where both equilibrium compositions for a two-temperature plasma and a chemically reacting plasma are studied, and a free-fall region. The results allow a quantitative assessment of temperature nonequilibrium and electrical potential distribution in the free-fall region.