A New Validated Potentiometric Method for Batch and Continuous Quality Control Monitoring of Oseltamivir Phosphate (Taminil) in Drug Formulations and Biological Fluids

A new validated potentiometric method is described for batch and continuous quality control monitoring of the drug oseltamivir phosphate (Taminil) (OST). The method involves the development of a potentiometric sensor responsive to the drug based on the use of the ion‐association complex of (OST⁺) cation with phosphomolybdate anion (PMA^?) as an electroactive material in a poly(vinyl chloride) matrix membrane plasticized with o‐nitrophenyloctyl ether (o‐NPOE). Optimization of the performance characteristics of the sensor is described. A membrane incorporating the OST‐PMA‐NPOE complex in a tubular flow through detector is used in a two channel flow injection set up for continuous monitoring of the drug at a frequency of ～30 samples h^?1. The sensor shows fast near‐Nernstian response for OST over the concentration range 5.2×10^?5–0.8×10^?2 M (21.34 µg mL^?1–3.23 mg mL^?1) with a detection limit of 9.1×10^?6 M (3.73 µg mL^?1) over the pH range 4.6–6.1. The sensor displays good selectivity for OST drug over some basic drugs, inorganic cations, excipients and diluents commonly used in the drug formulations. Validation of the assay method is tested by measuring the lower detection limit, range, linearity, bias, trueness, accuracy, precision, and between‐day‐variability, within day reproducibility, selectivity and ruggedness (robustness). The results reveal good potentiometric performance of the proposed sensor for determination of OST in pharmaceutical capsules and in biological fluid matrices as well as for testing the dissolution profile of the drug and drug homogeneity.     

New developments in frequency domain optical tomography. Part I: Forward model and gradient computation

This two part study introduces new developments in frequency domain optical tomography to take into account the collimated source direction in the computation of both the forward and the adjoint models. The solution method is based on the least square finite element method associated to the discrete ordinates method where no empirical stabilization is needed. In this first part of the study, the solution method of the forward model is highlighted with an easy handling of complex boundary condition through a penalization method. Gradient computation from an adjoint method is developed rigorously in a continuous manner through a lagrangian formalism for the deduction of the adjoint equation and the gradient of the objective function. The proposed formulation can be easily generalized to stationary and time domain optical tomography by keeping the same expressions.     

Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free‐space fundamental solution. The other is a typical boundary value problem (BVP) with specified boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null‐field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier densities, the second‐part solution is easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

Primal-Dual Interior-Point Method for an Optimization Problem Related to the Modeling of Atmospheric Organic Aerosols

A mathematical model for the computation of the phase equilibrium related to atmospheric organic aerosols is presented. The phase equilibrium is given by the global minimum of the Gibbs free energy for a system that involves water and organic components. This minimization problem is equivalent to the determination of the convex hull of the corresponding molar Gibbs free energy function. A geometrical notion of phase simplex related to the convex hull is introduced to characterize mathematically the phases at equilibrium. A primal-dual interior-point algorithm for the efficient solution of the phase equilibrium problem is presented. A novel initialization of the algorithm, based on the properties of the phase simplex, is proposed to ensure the convergence to a global minimum of the Gibbs free energy. For a finite termination of the interior-point method, an active phase identification procedure is incorporated. Numerical results show the robustness and efficiency of the approach for the prediction of liquid-liquid equilibrium in multicomponent mixtures.Communicated by R. GlowinskiThis work was supported by US Environmental Protection Grant X-83234201. The second author was partially supported by Swiss National Science Foundation Grant PBEL2-103152.     

Kinetic decomposition for kinetic models of BGK type

In this paper, we consider kinetic models of BGK type which describe the scalar conservation law at the microscopic scale. We use new technique developed in Comm. Partial Differential Equations 27 (2002) 1229 in order to get the convergence. First, we obtain the approximate transport equation for the given kinetic models of BGK type. Then using the averaging lemma, we obtain the convergence. This paper shows how to relate the given kinetic model with the averaging lemma to get the convergence.     

Multisymplectic Geometry,Local Conservation Laws and a Multisymplectic Integrator for the Zakharov–Kuznetsov Equation

The multisymplectic geometry for the Zakharov–Kuznetsov equation is presented in this Letter. The multisymplectic form and the local energy and momentum conservation laws are derived directly from the variational principle. Based on the multisymplectic Hamiltonian formulation, we derive a 36-point multisymplectic integrator.     

On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal‐order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid‐based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions. Copyright © 2008 John Wiley & Sons, Ltd.     

Vaidya Space-Time in Black-Hole Evaporation

We take a boundary-value approach to quantum amplitudes arising in gravitational collapse to a black hole. Pose boundary data on initial and final space-like hypersurfaces Σ _F,I , separated at spatial infinity by a Lorentzian proper-time interval T. Quantum amplitudes are calculated following Feynman's approach; rotate: T→|T|exp (−iθ) into the complex, where 0< θ≤π/2, and solve the corresponding well-posed complex classical boundary-value problem. We compute the classical Lorentzian action S _class and corresponding semi-classical quantum amplitude, proportional to exp (iS _class). To recover the Lorentzian amplitude, take the limit θ→ 0₊ of the semi-classical amplitude. For the classical boundary-value problem with given perturbative boundary data, we compute an effective spherically-symmetric energy-momentum tensor 〉 T ^μν〈 _EFF , averaged over several wavelengths of the radiation, describing the averaged extra energy-momentum contribution in the Einstein field equations, due to the perturbations. This takes the form of a null fluid, describing the radiation (of quantum origin) streaming radially outwards. The classical space-time metric, in this region of the space time, is of Vaidya form, justifying the adiabatic radial mode equations, for spins s = 0 and s = 2.     

Stokes问题在各向异性网格下的Bernadi-Raugel有限元逼近

在各向异性网格下,得到了Stokes问题著名的Bernadi-Raugel混合有限元格式的超逼近性质,而且通过构造插值后处理算子得到了关于速度的超收敛结果.     

Two-Sided Symmetric Condition in the Analysis of Magnetic Fields with Permanent Magnets

Mathematical treatment of a planar magnetic field excited by permanent magnets is presented. A special two-sided condition for differential magnetic reluctivity is introduced to prove the unique existence of both the weak and the approximate solutions and also a certain error estimate. Notes to numerical algorithm and practical applications are given.This work was supported by the project MSM 262200022.