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We obtain the global well-posedness to the Cauchy problem of the Fokas-Lenells (FL) equation on the line without the small-norm assumption on initial data u 0 ∈ H 3 (R) ∩ H 2 , 1 (R). Our main technical tool is the inverse scattering transform method based on the representation of a Riemann-Hilbert (RH) problem associated with the above Cauchy problem. The existence and the uniqueness of the RH problem is shown via a general vanishing lemma. By representing the solutions of the RH problem via the Cauchy integral protection and the reflection coefficients, the reconstruction formula is used to obtain a unique local solution of the FL equation. Further, the eigenfunctions and the reflection coefficients are shown Lipschitz continuous with respect to initial data, which provides a prior estimate of the solution to the FL equation. Based on the local solution and the uniformly prior estimate, we construct a unique global solution in H 3 (R) ∩ H 2 , 1 (R) to the FL equation. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of global solutions in H 3 (R) ∩ H 2 , 1 (R) to the Fokas-Lenells (FL) equation on the line when the initial data includes solitons. A key tool in proving this result is a newly modified Darboux transformation, which adds or subtracts a soliton with given spectral and scattering parameters. In this way the inverse scattering transform technique is then applied to establish the global well-posedness of initial value problem with a finite number of solitons based on our previous results on the global well-posedness of the FL equation. [ABSTRACT FROM AUTHOR]

We study the long-time asymptotic behavior of the focusing Fokas-Lenells (FL) equation u x t + α β 2 u − 2 i α β u x − α u x x − i α β 2 | u | 2 u x = 0 with generic initial data in a Sobolev space which supports bright soliton solutions. The FL equation is an integrable generalization of the well-known Schrodinger equation, and also linked to the derivative Schrodinger model, but it exhibits several different characteristics from theirs. (i) The Lax pair of the FL equation involves an additional spectral singularity at k = 0. (ii) Four stationary phase points will appear during asymptotic analysis, which require a more detailed necessary description to obtain the long-time asymptotics of the focusing FL equation. Based on the Riemann-Hilbert problem for the initial value problem of the focusing FL equation, we show that inside any fixed time-spatial cone C (x 1 , x 2 , v 1 , v 2) = { (x , t) ∈ R 2 | x = x 0 + v t , x 0 ∈ [ x 1 , x 2 ] , v ∈ [ v 1 , v 2 ] } , the long-time asymptotic behavior of the solution u (x , t) for the focusing FL equation can be characterized with an N (I) -soliton on discrete spectrums and a leading order term O (t − 1 / 2) on continuous spectrum up to a residual error order O (t − 3 / 4). The main tool is a ∂ ‾ -generalization of the Deift-Zhou nonlinear steepest descent method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial value problem for the mixed Schrödinger equation. For the Schwartz initial data q 0 (x) ∈ S (R) , by defining a general analytical domain and two reflection coefficients, we ever found an unified long-time asymptotic formula via the Deift–Zhou nonlinear steepest descent method. In this paper, under essentially minimal regularity assumptions on initial data in a much weak weighted Sobolev space q 0 (x) ∈ H 2 , 2 (R) , we apply the ∂ ̄ steepest descent method to obtain long-time asymptotics for the mixed Schrödinger equation. In the asymptotic expression, the leading order term O ( t − 1 / 2 ) comes from the dispersive part qt + iqxx and the error order O ( t − 3 / 4 ) comes from a ∂ ̄ equation. [ABSTRACT FROM AUTHOR]

In this paper, an ultra-high-performance liquid chromatography coupled with linear ion trap quadrupole Orbitrap high resolution mass spectrometry (UHPLC-LTQ-Orbitrap HRMS) method was developed and validated for identification, confirmation and quantitation of illegal adulterated weight-loss drugs in plant dietary supplements. 13 wt-loss drugs were well separated by the gradient elution of 10 mmol/L ammonium acetate − 0.05% formic acid H 2 O and acetonitrile at a flow rate of 0.2 mL/min within 12 min. The MS analysis was operated under the positive ion and in full MS/dd-MS 2 (data-dependent MS 2 ) mode. The full MS scan with resolution at 60 000 FWHM and narrow mass windows at 5 ppm acquired data for identification and quantitation, and dd-MS 2 scan with resolution at 15 000 FWHM obtained product ions for confirmation. The method validation showed good linearity with coefficients of determination (r 2 ) higher than 0.9951 for all analytes. Meantime, all the LOD and LLOQ values were in the respective range of 0.3–2 and 1–9 ng/g. The accuracy, intra- and inter-day precision were in the ranges of −1.7 to 3.4%, 1.7–5.0% and 1.9–4.4%, respectively. The mean recoveries ranged from 85.4 to 107.1%, while the absolute and relative matrix effect were in the corresponding range of 98.2–108.6% and 2.6–8.7%. Among 120 batches of weight loss plant dietary supplements, sibutramine and fluoxertine or both were positive in 29 samples. In general, LTQ-Orbitrap HRMS technology was a powerful tool for the analysis of illegal ingredients in dietary supplements. [ABSTRACT FROM AUTHOR]

In this paper, we define a general analytical domain and two reflection coefficients to study the long-time asymptotics for a defocusing mixed nonlinear Schrödinger equation with the Schwartz initial data. It is shown that the solution of the initial value problem for the mixed Schrödinger equation can be expressed in terms of the solution associated with a Riemann-Hilbert problem. The long-time asymptotic of the mixed Schrödinger equation is further obtained via the Deift-Zhou nonlinear steepest descent method. The long-time asymptotic for the classical Schrödinger equation, derivative Schrödinger equation and modified Schrödinger equation are obtained directly from our results as special cases. [ABSTRACT FROM AUTHOR]

Abstract: In order to determine the contribution of intranasal (i.n.) administration to the uptake of large molecular weight (MW) substances into central nervous system (CNS), concentration in brain of the centrally acting polypeptide cobrotoxin (NT-I) versus time profiles were studied using dual-probe microdialysis in awake free-moving rats. NT-I, radiolabeled with sodium 125I-Iodide (125I-NT-I), was administered at the dose of 105μg/kg intravenously and intranasally in the same set of rat (n =15). The 125I-NT-Inasal preparations were formulated with borneol/menthol eutectic mixture (+BMEM) as an absorption enhancer and without (−BMEM). After application, the dialysates sampled simultaneously from olfactory bulb and cerebellar nuclei were measured in a gamma-counter for radioactivity. The real concentrations of NT-I were recalculated by in vivo recoveries of microdialysis probes. The results showed that the area under the curve (AUC) value in cerebellar nuclei (2283.51±34.54minng/ml) following i.n. administration (+BMEM) was significantly larger than those (AUColfactory =1141.92±26.42minng/ml; AUCcerebellar =1364.62±19.35minng/ml) after intravenous (i.v.) bolus, respectively. A prolonged time values to peak concentrations after i.n. application (+BMEM) were observed compared with those following i.v. administration. Also, following i.n. application (+BMEM) the measured time value to peak concentration in cerebellar nuclei (85min) was statistically longer than that in olfactory bulb (75min), which could be plausibly an indication for NT-I delivery into brain via nose–brain pathway in the presence of absorption enhancer. i.n. administration (−BMEM) had little or no ability of NT-I delivering into brain. In conclusion, i.n. administration (+BMEM) significantly enhanced brain transport of NT-I with uneven distribution in discrete regions of brain compared with i.v. administration. Additionally, multi-probe microdialysis technique should be considerably valuable in brain delivery studies. [Copyright &y& Elsevier]

The nanoscale Lycurgus cup arrays were hybrid structures of nanocups and nanoparticles with ultrasensitivity to refractive index change. In this study, an electrochemical localized surface plasmon resonance (LSPR) sensor was developed by coupling electrochemistry to LSPR spectroscopy measurement on the nanoscale cup arrays (nanoCA). Based on the combination of electrochemistry and LSPR measurement, the electrochemical LSPR on nanoCA was observed with significant resonance wavelength shifts in electrochemical modulation. The synchronous implementation of cyclic voltammetry and optical transmission spectrum can be used to obtain multiply sensing information and investigate the enhancement for LSPR from electrochemical scanning. The electrochemical enhanced LSPR was utilized as biosensor to detect biomolecules. The electrochemical LSPR biosensor with synchronous electrochemical and optical implement showed higher sensitivity than that of conventional optical LSPR measurement. Detecting with multi-transducer parameters and high sensitivity, the electrochemical LSPR provided a promising approach for chemical and biological detection. [ABSTRACT FROM AUTHOR]

A simple and sensitive method was developed for characterization of two impurities from commercial bendazac lysine eye drops, by using liquid chromatography combined with electrospray ionization and QTOF mass analyzer (LC–ESI-QTOF MS/MS). A known impurity was characterized rapidly by comparison with the retention time and MS/MS data of the reference standard. Based on high resolution mass spectrometry (HRMS) and the nuclear magnetic resonance (NMR), a new impurity, purified by preparative HPLC, was identified as 2-(1,5-dibenzyl-1 H -indazol-3-yloxy)acetic acid. In addition, a plausible mechanism for the formation of the impurities was also proposed. [ABSTRACT FROM AUTHOR]

• Based on UHPLC coupled with Q-TOF MS, a rapid and reliable method to analyze 31 anti-impotence compounds potentially illegally added to herbal-based dietary supplements was developed. • Sildenafil and/or tadalafil was founded illegally adulterated in two samples, while not very high concentration of icariin was detected in one sample. • The compound library including multiple adulteration of anti-impotence drugs with different mechanisms was established. In this paper, an ultra-high-performance liquid chromatography coupled with quadrupole time-of-flight mass spectrometry (UHPLC-Q-TOF HRMS) method was developed and validated for screening, confirmation and quantitation of 31 anti-impotence compounds potentially illegally added to herbal-based dietary supplements. The analytes were well separated by the mobile phase consisted of 0.1% formic acid solution and acetonitrile with gradient elution at a flow rate of 0.3 mL/min. The MS analysis was operated in positive mode and the mass error of the 31 compounds were below 2.9 ppm. The method validation showed good linearity with coefficients of determination (r2) higher than 0.9973 for all analytes. LODs and LLOQs ranged from 0.005 to 0.50 μg/g or μg /mL and from 0.02 to 1.24 μg /g or μg/mL, respectively. The accuracy was in the range of 86.6% to 113.7%, while the intra-and inter-day precision were in the ranges of 0.9–7.6% and 0.9–11.4%, respectively. The absolute and relative matrix effect were in the range of 65.8–115.6% and 0.6–13.3%. The mean recoveries were in the range of 80.5–116.9%. The stability ranged from 0.4% to 8.5%. Among 200 batches of herbal-based dietary supplements, sildenafil and/or tadalafil were found to be added illegally in two samples, while not very high concentration of icariin was detected in one sample. The Q-TOF mass spectrometry has been proved to be a very powerful and efficient tool for rapid screening of 31 anti-impotence compounds potentially illegally added to herbal-based dietary supplements, ensuring food safety and public health. [ABSTRACT FROM AUTHOR]