Development and Validation of Selective Spectrophotometric Methods for the Determination of Pregabalin in Pharmaceutical Preparation

Three simple, quick and sensitive methods are described for the spectrophotometric determination of pregabalin (Pgb) in pharmaceutical preparations. Among them, the first two methods are based on the reaction of Pgb as n-electron donors with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) and 7,7,8,8-tetracyanoquinodimethane (TCNQ) as π-acceptors to give highly colored complex species. The colored products were quantitated spectrophotometrically at 494 and 841 nm for DDQ and TCNQ, respectively. Optimization of the different experimental conditions was conducted. Beer’s law was obeyed in the concentration ranges 2.0—30.0 and 1.5—10 µg•mL－1 for DDQ and TCNQ methods, respectively. The third method is based on the interaction of ninhydrin (NN) with primary amine present in the pregabaline. This reaction produces a blue coloured product in N,N-dimethylformamide (DMF) medium, which absorbs maximally at 573 nm. Beer’s law was found in the concentration range 40.0—180.0 μg•mL－1. The methods were applied successfully to the determination of this drug in pharmaceutical dosage forms.     

No Gap Second-Order Optimality Conditions for Circular Conic Programs

In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.     

Global well-posedness of the velocity–vorticity-Voigt model of the 3D Navier–Stokes equations

The velocity–vorticity formulation of the 3D Navier–Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose a new regularization of the 3D Navier–Stokes equations, which we call the 3D velocity–vorticity-Voigt (VVV) model, with a Voigt regularization term added to momentum equation in velocity–vorticity form, but with no regularizing term in the vorticity equation. We prove global well-posedness and regularity of this model under periodic boundary conditions. We prove convergence of the model's velocity and vorticity to their counterparts in the 3D Navier–Stokes equations as the Voigt modeling parameter tends to zero. We prove that the curl of the model's velocity converges to the model vorticity (which is solved for directly), as the Voigt modeling parameter tends to zero. Finally, we provide a criterion for finite-time blow-up of the 3D Navier–Stokes equations based on this inviscid regularization.     

A posteriori error analysis of an augmented fully mixed formulation for the nonisothermal Oldroyd–Stokes problem

In this article, we consider an augmented fully mixed variational formulation that has been recently proposed for the nonisothermal Oldroyd–Stokes problem, and develop an a posteriori error analysis for the 2‐D and 3‐D versions of the associated mixed finite element scheme. More precisely, we derive two reliable and efficient residual‐based a posteriori error estimators for this problem on arbitrary (convex or nonconvex) polygonal and polyhedral regions. The reliability of the proposed estimators draws mainly upon the uniform ellipticity of the bilinear forms of the continuous formulation, suitable assumptions on the domain and the data, stable Helmholtz decompositions, and the local approximation properties of the Clément and Raviart–Thomas operators. On the other hand, inverse inequalities, the localization technique based on bubble functions, and known results from previous works are the main tools yielding the efficiency estimate. Finally, several numerical results confirming the properties of the a posteriori error estimators and illustrating the performance of the associated adaptive algorithms are reported.     

An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

Implicit Monte Carlo (IMC) and Implicit Monte Carlo Diffusion (IMD) are approaches to the numerical solution of the equations of radiative transfer. IMD was previously derived and numerically tested on grey, or frequency-integrated problems [1]. In this research, we extend Implicit Monte Carlo Diffusion (IMD) to account for frequency dependence, and we implement the difference formulation [2] as a source manipulation variance reduction technique. We derive the relevant probability distributions and present the frequency dependent IMD algorithm, with and without the difference formulation. The IMD code with and without the difference formulation was tested using both grey and frequency dependent benchmark problems. The Su and Olson semi-analytic Marshak wave benchmark was used to demonstrate the validity of the code for grey problems [3]. The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems [4]. The frequency dependent IMD algorithm reproduces the results of both Su and Olson benchmark problems. Frequency group refinement studies indicate that the computational cost of refining the group structure is likely less than that of group refinement in deterministic solutions of the radiation diffusion methods. Our results show that applying the difference formulation to the IMD algorithm can result in an overall increase in the figure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause significant numerical instabilities in regions of the problem with sharp spatial gradients in the solution. An adaptive implementation of the difference formulation may be necessary to focus its use in regions that are at or near thermal equilibrium.     

Optimal control for reinitialization in finite element level set methods

A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first‐order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE‐based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Simultaneous densitometric determination of anthelmintic drug albendazole and its metabolite albendazole sulfoxide by HPTLC in human plasma and pharmaceutical formulations

A new, simple, accurate and precise high‐performance thin‐layer chromatographic method has been developed and validated for simultaneous determination of an anthelmintic drug, albendazole, and its active metabolite albendazole, sulfoxide. Planar chromatographic separation was performed on aluminum‐backed layer of silica gel 60G F₂₅₄ using a mixture of toluene–acetonitrile–glacial acetic acid (7.0:2.9:0.1, v /v/v) as the mobile phase. For quantitation, the separated spots were scanned densitometrically at 225 nm. The retention factors (R _f) obtained under the established conditions were 0.76 ± 0.01 and 0.50 ± 0.01 and the regression plots were linear (r ² ≥ 0.9997) in the concentration ranges 50–350 and 100–700 ng/band for albendazole and albendazole sulfoxide, respectively. The method was validated for linearity, specificity, accuracy (recovery) and precision, repeatability, stability and robustness. The limit of detection and limit of quantitation found were 9.84 and 29.81 ng/band for albendazole and 21.60 and 65.45 ng/band for albendazole sulfoxide, respectively. For plasma samples, solid‐phase extraction of analytes yielded mean extraction recoveries of 87.59 and 87.13% for albendazole and albendazole sulfoxide, respectively. The method was successfully applied for the analysis of albendazole in pharmaceutical formulations with accuracy ≥99.32%.     

带凹性生产成本运输问题的新随机规划模型及其求解

提出了一种新的能反映决策者满意度的随机变量序关系,并据此研究了随机不等式的确定性等价类,方法被称为满意度方法.最后将其应用于带凹性生产成本运输问题的求解中,并将方法与常用的机会约束方法进行比较,说明满意度法不仅合理可行,而且当决策者对约束条件的要求越高时,它所得最优值越优于机会约束法所得最优值.     

Statistical stationary states for a two-layer quasi-geostrophic system

Existence of a family of locally invariant probability measures for large scale flows in enclosed temperate sea is proved. This model is extremely important for understanding the meso-scale phenomena in oceans. The techniques used are those developed by Albeverio and his collaborators.     

BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.