The Weak and Strong Lefschetz Properties for Artinian K-Algebras

Let A = bigoplus_{i >= 0} A_i be a standard graded Artinian K-algebra, where char K = 0. Then A has the Weak Lefschetz property if there is an element ell of degree 1 such that the multiplication times ell : A_i --> A_{i+1} has maximal rank, for every i, and A has the Strong Lefschetz property if times ell^d : A_i --> A_{i+d} has maximal rank for every i and d. The main results obtained in this paper are the following. 1) EVERY height three complete intersection has the Weak Lefschetz property. (Our method, surprisingly, uses rank two vector bundles on P^2 and the Grauert-Mulich theorem.) 2) We give a complete characterization (including a concrete construction) of the Hilbert functions that can occur for K-algebras with the Weak or Strong Lefschetz property (and the characterization is the same one). 3) We give a sharp bound on the graded Betti numbers (achieved by our construction) of Artinian K-algebras with the Weak or Strong Lefschetz property and fixed Hilbert function. This bound is again the same for both properties. Some Hilbert functions in fact FORCE the algebra to have the maximal Betti numbers. 4) EVERY Artinian ideal in K[x,y] possesses the Strong Lefschetz property. This is false in higher codimension.Comment: To appear in J. Algebr

Siegert pseudostate perturbation theory: one- and two-threshold cases

Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relationship of the Siegert Pseudostates. We apply the theory to a 2-channel model problem, and find the rate of convergence of the perturbation expansion should be examined with the aide of the variance $D= ||E-\sum_{n}\lambda^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually

Evidence for defect-mediated tunneling in hexagonal boron nitride-based junctions

We investigate tunneling in metal-insulator-metal junctions employing few atomic layers of hexagonal boron nitride (hBN) as the insulating barrier. While the low-bias tunnel resistance increases nearly exponentially with barrier thickness, subtle features are seen in the current-voltage curves, indicating marked influence of the intrinsic defects present in the hBN insulator on the tunneling transport. In particular, single electron charging events are observed, which are more evident in thicker-barrier devices where direct tunneling is substantially low. Furthermore, we find that annealing the devices modifies the defect states and hence the tunneling signatures.Comment: 5 pages, 5 figure

Quantum Effects in Small-Capacitance Single Josephson Junctions

We have measured the current-voltage (I-V) characteristics of small-capacitance single Josephson junctions at low temperatures (T=0.02-0.6 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. The single-junction I-V curve is sensitive to the impedance of the environment, which can be tuned IN SITU. We have observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance R_0' of the SQUID arrays is much higher than the quantum resistance R_K = h/e^2 = 26 kohm. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling within the theory of current-biased single Josephson junctions. Based on the theory, we have calculated the I-V curves numerically in order to compare with the experimental ones at R_0' >> R_K. The numerical calculation agrees with the experiments qualitatively. We also discuss the R_0' dependence of the single-Josephson-junction I-V curve in terms of the superconductor-insulator transition driven by changing the coupling to the environment.Comment: 11 pages with 14 embedded figures, RevTeX4, final versio

Structural Elucidation of Metabolites of Synthetic Cannabinoid UR-144 by Cunninghamella elegans Using Nuclear Magnetic Resonance (NMR) Spectroscopy

© 2018, American Association of Pharmaceutical Scientists. The number of new psychoactive substances keeps on rising despite the controlling efforts by law enforcement. Although metabolism of the newly emerging drugs is continuously studied to keep up with the new additions, the exact structures of the metabolites are often not identified due to the insufficient sample quantities for techniques such as nuclear magnetic resonance (NMR) spectroscopy. The aim of the study was to characterise several metabolites of the synthetic cannabinoid (1-pentyl-1H-indol-3-yl) (2,2,3,3-tetramethylcyclopropyl) methanone (UR-144) by NMR spectroscopy after the incubation with the fungus Cunninghamella elegans. UR-144 was incubated with C. elegans for 72 h, and the resulting metabolites were chromatographically separated. Six fractions were collected and analysed by NMR spectroscopy. UR-144 was also incubated with human liver microsomes (HLM), and the liquid chromatography-high resolution mass spectrometry analysis was performed on the HLM metabolites with the characterised fungal metabolites as reference standards. Ten metabolites were characterised by NMR analysis including dihydroxy metabolites, carboxy and hydroxy metabolites, a hydroxy and ketone metabolite, and a carboxy and ketone metabolite. Of these metabolites, dihydroxy metabolite, carboxy and hydroxy metabolites, and a hydroxy and ketone metabolite were identified in HLM incubation. The results indicate that the fungus is capable of producing human-relevant metabolites including the exact isomers. The capacity of the fungus C. elegans to allow for NMR structural characterisation by enabling production of large amounts of metabolites makes it an ideal model to complement metabolism studies

In vitro metabolism of synthetic cannabinoid AM1220 by human liver microsomes and Cunninghamella elegans using liquid chromatography coupled with high resolution mass spectrometry

© 2018, The Author(s). Purpose: Identifying intake of synthetic cannabinoids generally requires the metabolism data of the drugs so that appropriate metabolite markers can be targeted in urine testing. However, the continuous appearance of new cannabinoids during the last decade has made it difficult to keep up with all the compounds including {1-[(1-methylpiperidin-2-yl)methyl]-1H-indol-3-yl}(naphthalen-1-yl)methanone (AM1220). In this study, metabolism of AM1220 was investigated with human liver microsomes and the fungus Cunninghamella elegans. Methods: Metabolic stability of AM1220 was analysed by liquid chromatography–tandem mass spectrometry in multiple reaction monitoring mode after 1 µM incubation in human liver microsomes for 30 min. Tentative structure elucidation of metabolites was performed on both human liver microsome and fungal incubation samples using liquid chromatography–high-resolution mass spectrometry. Results: Half-life of AM1220 was estimated to be 3.7 min, indicating a high clearance drug. Nine metabolites were detected after incubating human liver microsomes while seven were found after incubating Cunninghamella elegans, leading to 11 metabolites in total (five metabolites were common to both systems). Demethylation, dihydrodiol formation, combination of the two, hydroxylation and dihydroxylation were the observed biotransformations. Conclusions: Three most abundant metabolites in both human liver microsomes and Cunninghamella elegans were desmethyl, dihydrodiol and hydroxy metabolites, despite different isomers of dihydrodiol and hydroxy metabolites in each model. These abundant metabolites can potentially be useful markers in urinalysis for AM1220 intake

Data on individual metabolites of synthetic cannabinoids JWH-018, JWH-073 and AM2201 by Cunninghamella elegans

© 2016 The Authors. Synthetic cannabinoids JWH-018, JWH-073 and AM2201 were metabolised by the fungus Cunninghamella elegans. In this article, data on individual metabolites of their retention times, mass accuracies, major product ions and structures indicated by product ions are presented. The data in this article is related to "Biotransformation of synthetic cannabinoids JWH-018, JWH-073 and AM2201 by Cunninghamella elegans" [1]

Biotransformation of synthetic cannabinoids JWH-018, JWH-073 and AM2201 by Cunninghamella elegans

© 2015 Elsevier Ireland Ltd. Being marketed as "legal" smoking blends or mixtures, synthetic cannabinoids are abused widely owing to its cannabis-like effect. Due to the rapid introduction of new generation analogues of synthetic cannabinoids to escape from legislative/judicial control, the investigation of the metabolic pathways of these substances is of particular importance for drug control, abstinence and forensic toxicology purposes. In this study, the in vitro metabolism of JWH-018, JWH-073 and AM2201 by the fungus Cunninghamella elagans has been investigated with the purpose of validating its potential as a complementary model for investigating synthetic cannabinoid metabolism. JWH-018, JWH-073 and AM2201 were incubated for 72 h with C. elegans. Detection of metabolites was based on liquid chromatography-tandem mass spectrometry and high resolution mass spectrometry analysis. C. elegans was found capable of producing the majority of the phase I metabolites observed in earlier in vitro and in vivo mammalian studies as a result of monohydroxylation, dihydroxylation, carboxylation, dehydrogenation, ketone formation, dihydrodiol formation, dihydrodiol formation with N-dealkylation and combinations thereof. C. elegans can thus be a useful and economic model for studying synthetic cannabinoid metabolism

Disorder-sensitive superconductivity in the iron silicide Lu2_2Fe3_3Si5_5 studied by the Lu-site substitutions

We studied effect of non-magnetic and magnetic impurities on superconductivity in Lu$_2$Fe$_3$Si$_5$ by small amount substitution of the Lu site, which investigated structural, magnetic, and electrical properties of non-magnetic (Lu$_{1-x}$Sc$_x$)$_2$Fe$_3$Si$_5$, (Lu$_{1-x}$Y$_x$)$_2$Fe$_3$Si$_5$, and magnetic (Lu$_{1-x}$Dy$_x$)$_2$Fe$_3$Si$_5$. The rapid depression of $T_c$ by non-magnetic impurities in accordance with the increase of residual resistivity reveals the strong pair breaking dominated by disorder. We provide compelling evidence for the sign reversal of the superconducting order parameter in Lu$_2$Fe$_3$Si$_5$.Comment: 4 pages, 5 figure