Spatial characterization of the transversal structure of rotationally symmetric pulsed beams

A simple analytical model is proposed to describe the transversal spatial structure of a tridimensional rotationally symmetric pulsed beam. The spatial behaviour of the pulse amplitude is shown to be linked to its (measurable) second- and higher-order intensity moments, namely, beam width, quality parameter and kurtosis. As an illustrative experimental example, this model has been applied to high-quality TEA CO2 laser pulses. This revised version was published online in November 2006 with corrections to the Cover Date.     

Differences Between Consecutive Primes

Let p_n be the nth prime. Then this paper is concerned with provingthe following result on the distribution of consecutive primes. The exponent of x in this theorem improves on the work of Heath-Brownwho proved (1) with exponent . Under the Riemann hypothesisone can prove (1) with exponent .The proof of the theorem startswith the Heath-Brown–Linnik identity which leads to aformula giving the number of primes in an interval in termsof coefficients of certain Dirichlet series. I then estimatethe coefficients by using, among other things, the informationwhich can be gained from Montgomery's mean value theorem andHuxley's version of the Hal' asz lemma. Furthermore, by usingfamiliar sieve arguments I am able to discard some of the coefficientsallowing us to gain an improvement over the previous resultof Heath-Brown. 1991 Mathematics Subject Classification: 11N05.     

A validated high-performance thin-layer chromatography method for the simultaneous estimation of berberine,berbamine, palmatine,magnoflorine and jatrorrhizine from Berberis aristata

JPC – Journal of Planar Chromatography – Modern TLC - Berberis aristata DC., well known as ‘Indian barberry’ or ‘tree turmeric’, (Berberidaceae) is a medicinal...     

Bioanalytical Method Development and Validation Study of Neuroprotective Extract of Kashmiri Saffron Using Ultra-Fast Liquid Chromatography-Tandem Mass Spectrometry (UFLC-MS/MS): In Vivo Pharmacokinetics of Apocarotenoids and Carotenoids

Kashmir saffron (Crocus sativus L.), also known as Indian saffron, is an important Asian medicinal plant with protective therapeutic applications in brain health. The main bioactive in Kashmir or Indian Saffron (KCS) and its extract (CSE) are apocarotenoids picrocrocin (PIC) and safranal (SAF) with carotenoids, crocetin esters (crocins), and crocetins. The ultra-fast liquid chromatography(UFLC)- photodiode array standardization confirmed the presence of biomarkers PIC, trans-4-GG-crocin (T4C), trans-3-Gg-crocin (T3C), cis-4-GG-crocin (C4C), trans-2-gg-crocin (T2C), trans-crocetin (TCT), and SAF in CSE. This study’s objectives were to develop and validate a sensitive and rapid UFLC-tandem mass spectrometry method for PIC and SAF along T4C and TCT in rat plasma with internal standards (IS). The calibration curves were linear (R² > 0.990), with the lower limit of quantification (LLOQ) as 10 ng/mL. The UFLC-MS/MS assay-based precision (RSD, <15%) and accuracy (RE, −11.03–9.96) on analytical quality control (QC) levels were well within the acceptance criteria with excellent recoveries (91.18–106.86%) in plasma samples. The method was applied to investigate the in vivo pharmacokinetic parameters after oral administration of 40 mg/kg CSE in the rats (n = 6). The active metabolite TCT and T4C, PIC, SAF were quantified for the first time with T3C, C4C, T2C by this validated bioanalytical method, which will be useful for preclinical/clinical trials of CSE as a potential neuroprotective dietary supplement.     

Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.