A convenient synthesis of 2-C-methyl-d-erythritol 4-phosphate and isotopomers of its precursor

A new synthetic approach toward 2-C-methyl-d-erythritol 4-phosphate (MEP), a key intermediate in the mevalonate-independent biosynthetic pathway for isoprenoids, and deuterated analogues of its precursor, 2-C-methyl-d-erythritol acetonide, is described. This procedure uses 2-C-methyl-d-erythrose acetonide as starting material and delivers, through a mono-protection strategy, the target compounds in a short way and in high yield.     

Feebly associativeP-hypergroupoids

In this paper we study the hyperstructures, saidP-hypergroupoids, (H, P*) in whichH is a set andP* is one of the hyperoperations defined as follows: ?(x, y) εH ²,xP*y=xyP orxP*y=Pxy whereP is a subset ofH. In particular we give a general formula for to express the simple hyperproducts ofn elements and then we consider some cases in which (H, P*) is feebly associative. We study, in such cases theβ-relations.     

Validation of a novel, fully automated high throughput high-performance liquid chromatographic/tandem mass Spectrometric method for quantification of pantoprazole in human plasma

An automated high-throughput HPLC/MS/MS method was developed for the quantitative determination of pantoprazole in human plasma. Only 100 microL plasma was placed in 2.2 mL 96 deep-well plates, and both pantoprazole and omeprazole (IS) were extracted from human plasma by liquid-liquid extraction, using diethyl ether-dichloromethane (70:30, v/v) as the organic solvent. Robotic liquid-handling workstations were used for all liquid transfer and solution preparation steps and resulted in a short sample preparation time. After vortexing, centrifugation, and freezing, the supernatant organic solvent was evaporated and reconstituted in a small volume of reconstitution solution. Sample analysis was performed by utilizing the combination of RP-HPLC/MS/MS, with positive-ion electrospray ionization and multiple reaction monitoring detection. The chromatographic run time was set at 1.8 min with a flow rate of 0.6 mL/min on a Nucleosil octylsilyl (C8) analytical column. The method was proven to be sensitive, specific, accurate, and precise for the determination of pantoprazole in human plasma. The method was applied to a bioequivalence study after per os administration of a 40 mg pantoprazole gastric retentive tablet.     

Dielectric breakdown and avalanches at nonequilibrium metal-insulator transitions

Motivated by recent experiments on the finite temperature Mott transition in VO(2) films, we propose a classical coarse-grained dielectric breakdown model where each degree of freedom represents a nanograin which transitions from insulator to metal with increasing temperature and voltage at random thresholds due to quenched disorder. We describe the properties of the resulting nonequilibrium metal-insulator transition and explain the universal characteristics of the resistance jump distribution. We predict that by tuning voltage, another critical point is approached, which separates a phase of boltlike avalanches from percolationlike ones.     

Disposable pipette extraction for gas chromatographic determination of codeine, morphine, and 6-monoacetylmorphine in vitreous humor

The availability of a sensitive and rapid analytical method for the determination of opiates, and other substances of forensic interest, in a variety of biological specimens is of utmost importance to forensic laboratories. Solid-phase extraction is very popular in the pre-treatment of forensic samples. Nevertheless, a new approach, disposable pipette extraction (DPX), is gaining increasing interest in sample preparation. DPX has already been applied to the analysis of drugs of abuse in common biological matrices, such as urine and blood, but has not yet been evaluated on alternative biological samples, such as vitreous humor. The objective of this study was to evaluate the applicability of DPX on the analysis of opiates in vitreous humor. The currently developed method is fast, reliable, and easy to perform. The sensitivity, precision, and accuracy are satisfactory. Recoveries obtained are within the range of 72-91%, whereas the sample volume of vitreous humor required is only 100 μL.     

Spectral Exterior Calculus

A spectral approach to building the exterior calculus in manifold learning problems is developed. The spectral approach is shown to converge to the true exterior calculus in the limit of large data. Simultaneously, the spectral approach decouples the memory requirements from the amount of data points and ambient space dimension. To achieve this, the exterior calculus is reformulated entirely in terms of the eigenvalues and eigenfunctions of the Laplacian operator on functions. The exterior derivatives of these eigenfunctions (and their wedge products) are shown to form a frame (a type of spanning set) for appropriate L² spaces of k -forms, as well as higher-order Sobolev spaces. Formulas are derived to express the Laplace-de Rham operators on forms in terms of the eigenfunctions and eigenvalues of the Laplacian on functions. By representing the Laplace-de Rham operators in this frame, spectral convergence results are obtained via Galerkin approximation techniques. Numerical examples demonstrate accurate recovery of eigenvalues and eigenforms of the Laplace-de Rham operator on 1-forms. The correct Betti numbers are obtained from the kernel of this operator approximated from data sampled on several orientable and non-orientable manifolds, and the eigenforms are visualized via their corresponding vector fields. These vector fields form a natural orthonormal basis for the space of square-integrable vector fields, and are ordered by a Dirichlet energy functional which measures oscillatory behavior. The spectral framework also shows promising results on a non-smooth example (the Lorenz 63 attractor), suggesting that a spectral formulation of exterior calculus may be feasible in spaces with no differentiable structure. © 2020 Wiley Periodicals, Inc.     

Large subgroups in finite groups

Following Isaacs (see [6, p. 94]), we call a normal subgroup N of a finite group Glarge, if ${\mathbf{C}}_G(N)\le N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing large subgroups in finite groups (see Theorem A, Theorem C). We also consider the more specialised problems of finding large (non-abelian) nilpotent as well as abelian subgroups in soluble groups.     

An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters

We derive a new algorithm for calculating an exact confidence interval for a parameter of location or scale family, based on a two-sided hypothesis test on the parameter of interest, using some pivotal quantities. We use this algorithm to calculate approximate confidence intervals for the parameter or a function of the parameter of one-parameter continuous distributions. After appropriate heuristic modifications of the algorithm we use it to obtain approximate confidence intervals for a parameter or a function of parameters for multi-parameter continuous distributions. The advantage of the algorithm is that it is general and gives a fast approximation of an exact confidence interval. Some asymptotic (analytical) results are shown which validate the use of the method under certain regularity conditions. In addition, numerical results of the method compare well with those obtained by other known methods of the literature on the exponential, the normal, the gamma and the Weibull distribution.