Supercritical carbon dioxide extraction and gas chromatography–mass spectrometry analysis of Gymnema sylvestre R.Br. roots

Supercritical fluid extraction (SFE) achieves a wide range of applications since the past decade as a sustainable green technology. The present study investigates the process for producing high yield by supercritical carbon dioxide (Sc-CO₂) extraction form Gymnema sylvestre R.Br. roots. The effect of temperature and pressure on the percentage of accumulative yield is demonstrated. It is found that the highest yield is obtained at the temperature of 60°C and the pressure of 10?MPa. A proper review showed that there is a lack in the study of Sc-CO₂ extraction of this plant especially for optimization of SFE process which makes this study useful and valuable. For more benefit, the extract which achieves highest percentage is subjected to gas chromatography–mass spectrometry to study its chemical composition and detect the active principle compounds which present with high concentration and expected to be responsible of the pharmaceutical properties of the extract.     

Evaluation of the effect of Ramadan fasting on fat-soluble antioxidants and markers of oxidative stress in healthy Pakistani subjects

The aim of this study is to evaluate the effect of Ramadan fasting on the fat-soluble antioxidants [all-trans-retinol (vitamin A) and α-tocopherol (vitamin E)] in healthy Pakistani subjects. Thirty (30) healthy male volunteers (aged 30–50 years) with Ramadan fasting have participated in the study. Blood sampling from these subjects was conducted 1 day before and on 15th and 28th days of Ramadan. The serum levels of vitamin A and vitamin E were measured using liquid chromatography linked with UV–visible (HPLC–UV). The comparison between the samples taken at different times was made by Minitab software applying two samples and paired t-test at (p?<?0.05) as significant. No significant changes have been found in the levels of all-trans-retinol before and during Ramadan values. The levels of α-tocopherol on 28th Ramadan have been decreased significantly when compared with its values before Ramadan (p?<?0.0001). It is concluded that there is nonsignificant change in the levels of vitamin A during the month of Ramadan while the levels of α-tocopherol have been decreased significantly on the 28th day of Ramadan. It is therefore suggested that the fasting of Ramadan has effect on the levels of α-tocopherol and food-based interventions might be necessary to modify the diet during Ramadan.     

Efficient and selective analytical method for the quantification of a β-adrenoceptor agonist,isoproterenol, by LC–MS/MS and its application to pharmacokinetics studies

Isoproterenol (ISO) is a synthetic catecholamine with a powerful cardiac stimulate, bronchial smooth and skeletal muscle relaxation, coronary artery and peripheral vasodilator effects. In this study, a simple, rapid, and selective liquid chromatography–tandem mass spectrometry has been developed for the determination of ISO in rat plasma. Proteins were precipitated in plasma samples with 0.1?g?mL^?1 trichloroacetic acid and the ISO/internal standard (IS) were separated on a C₈ column. The ISO was detected by a triple-quadrupole mass spectrometer with electrospray ionization source. The transitions of m/z 212.1?→?193.9 for ISO and m/z 285.2?→?193.2 for IS were conducted through multiple reaction monitoring mode. This method was linear over the range of 2–500?n?g?mL^?1. The intra- and inter-day assay precision were observed between 3 and 10%. The accuracy was within ±11%. Stability study results demonstrated that ISO was stable in the autosampler at 4°C for 24?hr, and for 8?hr at room temperature. Only one freeze–thaw cycle at ?80°C for 24?hr was found to be stable. The validated method was successfully applied to a pharmacokinetic study of ISO in rats following subcutaneous administration.     

Integrated quality by design (QbD) and design of experiments (DoE) approach for UFLC determination of telaprevir in rat serum

An ultrafast liquid chromatographic bioanalytical method was developed and validated for the determination of telaprevir in Wistar albino rat serum. Principles of quality by design (QbD) were implemented for enhancing the bioanalytical liquid–liquid extraction of telaprevir from rat serum. A Box–Behnken design was utilized in the studies by selecting extraction time, centrifugation speed, and vortex time as the critical method variables for evaluating their effect on the critical analytical attribute, i.e., %recovery of telaprevir. Chromatographic separation was achieved within a run time of 10?min using a C-18 column and mobile phase comprising of methanol:borate buffer of pH 9 (90:10 v/v) flowing at 1.2?mL/min. Photodiode array detection was performed at 270?nm. Results of validation studies were satisfactory. The method was linear over a concentration of 25–10,000?ng/mL. Limit of detection for the developed method was 10?ng/mL. Further, design of experiments (DoE) used for inter-day accuracy and precision study suggested superior method reliability. This integrated QbD- and DoE-based approach ensured the development of a validated and reliable analytical method for optimum bioanalysis of telaprevir in biological matrix.     

Divided-difference equation and three-term recurrence relations of some systems of bivariate q-orthogonal polynomials

Partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial divided (or q)-difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials.     

Non-synchronous oscillations in four-dimensional nonlinear semelparous Leslie matrix models

In a certain class of semelparous Leslie matrix models, either a positive equilibrium is stable and an invariant set on the boundary of the nonnegative cone is unstable or vice versa generically if the model dimension is two or three. This dynamic dichotomy is expected to be failed in the four-dimensional case. Our study focuses on a semelparous Leslie matrix model with specific nonlinearities and rigorously proves that the dynamic dichotomy does not hold in the four-dimensional case. This result is derived by showing that the four-dimensional semelparous Leslie matrix model can be uniformly persistent with respect to the boundary of the nonnegative cone even if there exists an unstable positive equilibrium. In such a situation, there are no missing age-classes but population oscillation occurs.     

Complex dynamics of a discrete predator–prey model with the prey subject to the Allee effect

In this paper, complex dynamics of the discrete predator–prey model with the prey subject to the Allee effect are investigated in detail. Firstly, when the prey intrinsic growth rate is not large, the basins of attraction of the equilibrium points of the single population model are given. Secondly, rigorous results on the existence and stability of the equilibrium points of the model are derived, especially, by analyzing the higher order terms, we obtain that the non-hyperbolic extinction equilibrium point is locally asymptotically stable. The existences and bifurcation directions for the flip bifurcation, the Neimark–Sacker bifurcation and codimension-two bifurcations with 1:2 resonance are derived by using the center manifold theorem and the bifurcation theory. We derive that the model only exhibits a supercritical flip bifurcation and it is possible for the model to exhibit a supercritical or subcritical Neimark–Sacker bifurcation at the larger positive equilibrium point. Chaos in the sense of Marotto is proved by analytical methods. Finally, numerical simulations including bifurcation diagrams, phase portraits, sensitivity dependence on the initial values, Lyapunov exponents display new and rich dynamical behaviour. The analytic results and numerical simulations demonstrate that the Allee effect plays a very important role for dynamical behaviour.     

Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems

In this paper we introduce the theory of dominant solutions at infinity for nonoscillatory discrete symplectic systems without any controllability assumption. Such solutions represent an opposite concept to recessive solutions at infinity, which were recently developed for such systems by the authors. Our main results include: (i) the existence of dominant solutions at infinity for all ranks in a given range depending on the order of abnormality of the system, (ii) construction of dominant solutions at infinity with eventually the same image, (iii) classification of dominant and recessive solutions at infinity with eventually the same image, (iv) limit characterization of recessive solutions at infinity in terms of dominant solutions at infinity and vice versa, and (v) Reid’s construction of the minimal recessive solution at infinity. These results are based on a new theory of genera of conjoined bases for symplectic systems developed for this purpose in this paper.     

Efficient Computation of the Joint Sample Frequency Spectra for Multiple Populations

A wide range of studies in population genetics have employed the sample frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation of the expected joint SFS for thousands of individuals sampled from hundreds of populations related by a complex demographic model with arbitrary population size histories (including piecewise-exponential growth). Our results are implemented in a new software package called momi (MOran Models for Inference). Through an empirical study, we demonstrate our improvements to numerical stability and computational complexity.