Chemometrics‐assisted chromatographic fingerprinting: An illicit methamphetamine case study

The volatile chemical constituents in complex mixtures can be analyzed using gas chromatography with mass spectrometry. This analysis allows the tentative identification of diverse impurities of an illicit methamphetamine sample. The acquired two‐dimensional data of liquid–liquid extraction was resolved by multivariate curve resolution alternating curve resolution to elucidate the embedded peaks effectively. This is the first report on the application of a curve resolution approach for chromatogram fingerprinting to identify particularly the embedded impurities of a drug of abuse. Indeed, the strong and broad peak of methamphetamine makes identifying the underlying peaks problematic and even impossible. Mathematical separation instead of conventional chromatographic approaches was performed in a way that trace components embedded in methamphetamine peak were successfully resolved. Comprehensive analysis of the chromatogram, using multivariate curve resolution, resulted in elution profiles and mass spectra for each pure compound. Impurities such as benzaldehyde, benzyl alcohol, benzene, propenyl methyl ketone, benzyl methyl ketone, amphetamine, N‐benzyl‐2‐methylaziridine, phenethylamine, N ,N ,α‐trimethylamine, phenethylamine, N ,α,α‐trimethylmethamphetamine, N‐acetylmethamphetamine, N‐formylmethamphetamine, and other chemicals were identified. A route‐specific impurity, N‐benzyl‐2‐methylaziridine, indicating a synthesis route based on ephedrine/pseudoephedrine was identified. Moreover, this is the first report on the detection of impurities such as phenethylamine, N ,α,α‐trimethylamine (a structurally related impurity), and clonitazene (as an adulterant) in an illicit methamphetamine sample.     

Existence and concentration of positive solutions for coupled Schrödinger equations

In this paper, we study the existence and concentration of positive solution of a class of coupled Schrödinger equations. We admit that the potentials may not be non-negative and suppose that the intersection of the sets has positive Lebesgue measure. By studying the modified functional of the associated functional carefully, we establish the existence of positive least energy solutions for the coupled Schrödinger system. Moreover, we prove the concentration phenomenon of the positive solution when the parameter goes to infinity.     

On Cartan's theorem for linear operators

In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights.     

On the global existence and time decay estimates in critical spaces for the Navier–Stokes–Poisson system

We are concerned with the study of the Cauchy problem for the Navier–Stokes–Poisson system in the critical regularity framework. In the case of a repulsive potential, we first establish the unique global solvability in any dimension for small perturbations of a linearly stable constant state. Next, under a suitable additional condition involving only the low frequencies of the data and in the L²‐critical framework (for simplicity), we exhibit optimal decay estimates for the constructed global solutions, which are similar to those of the barotropic compressible Navier–Stokes system. Our results rely on new a priori estimates for the linearized Navier–Stokes–Poisson system about a stable constant equilibrium, and on a refined time‐weighted energy functional.     

Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems

In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi e?ciency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, su?cient conditions for local (weak) quasi e?cient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.     

On the existence of positive least energy solutions for a coupled Schrödinger system with critical exponent

In this paper, we consider the following coupled Schrödinger system with critical exponent: where is a smooth bounded domain, λ > 0,μ≥0, and . Under certain conditions on λ and μ, we show that this problem has at least one positive least energy solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Pseudo‐spherical normal Darboux images of curves on a lightlike surface

We introduce the notions of the pseudospherical normal Darboux images for the curve on a lightlike surface in Minkowski 3‐space and study these Darboux images by using technics of the singularity theory. Furthermore, we give a relation between these Darboux images and Darboux frame from the viewpoint of Legendrian dualities.