Development,stability-indicating assessment,and evaluation of influential method conditions using a full factorial design for the determination of Nintedanib esylate-related impurities

The design of an appropriate analytical method for assessing the quality of pharmaceuticals requires a deep understanding of science, and risk evaluation approaches are appreciated. The current study discusses how a related substance method was developed for Nintedanib esylate. The best possible separation between the critical peak pairs was achieved using an X-Select charged surface hybrid Phenyl Hexyl (150 × 4.6) mm, 3.5 μm column. A mixture of water, acetonitrile, and methanol in mobile phase-A (70:20:10) and mobile phase-B (20:70:10), with 0.1% trifluoroacetic acid and 0.05% formic acid in both eluents. The set flow rate, wavelength, and injection volumes were 1.0 ml/min, 285 nm, and 5 μl, respectively, with gradient elution. The method conditions were validated as per regulatory requirements and United States Pharmacopeia general chapter < 1225 >. The correlation coefficient for all impurities from the linearity experiment was found to be > 0.999. The % relative standard deviation from the precision experiments ranged from 0.4 to 3.6. The mean %recovery from the accuracy study ranged from 92.5 to 106.5. Demonstrated the power of the stability-indicating method through degradation studies; the active drug component is more vulnerable to oxidation than other conditions. Final method conditions were further evaluated using a full-factorial design. The robust method conditions were identified using the graphical optimization from the design space.     

Application of a multivariate approach for analyte focusing by micelle collapse‐micellar electrokinetic chromatography for analyzing sunscreen agents in cosmetics

The operating parameters that affect the performance of the online preconcentration technique “analyte focusing by micelle collapse‐MEKC (AFMC‐MEKC)” were examined using a multivariate approach involving experimental design to determine the sunscreen agents in cosmetics. Compared to the single‐variable approach, the advantage of the multivariate approach was that many factors could be investigated simultaneously to obtain the best separation condition. A fractional factorial design was used to identify the fewest significant factors in the central composite design (cCD). The cCD was adopted for evaluating the location of the minimum or maximum response in this study. The influences of the experimental variables on the response were investigated by applying a chromatographic exponential function. The optimized condition and the relationship between the experimental variables were acquired using the JMP software. The ANOVA analysis indicated that the Tris pH value, SDS concentration, and ethanol percentage influenced the separation quality and significantly contributed to the model. The optimized condition of the running buffer was 10 mM Tris buffer (pH 9.5) containing 60 mM SDS, 7 mM γ‐CD, and 20% v/v ethanol. The sample was prepared in 100 mM Tris buffer (pH 9.0) containing 7.5 mM SDS and 20% v/v ethanol. The SDS concentration in the sample matrix was slightly greater than the CMC value that makes the micelle be easily collapsed and the analytes be accumulated in the capillary. In addition, sunscreen agents in cosmetics after 1000‐fold dilution were successfully determined by AFMC‐MEKC.     

The effect of transverse pressure on the stability of a plate

The stability problem of a centrally compressed infinite plate is solved with allowance for the transverse normal deformation caused by uniform load for various boundary conditions at the edges. The linearized nonlinear equations of elastic deformation of thin plates taking into account transverse shear and transverse normal deformation are used. The obtained critical loads are compared with existing solutions.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 170–178, March–April, 2005.     

任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法

采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。     

On the solution of plane boundary-value problems of elasticity in a rectangle

An algorithm for solving plane boundary-value problems of elasticity for a rectangular domain is expounded. The algorithm is based on a complex-valued representation of the general solution to the differential equations of the plane problem and on the use of Lagrange polynomials to satisfy the boundary conditions. The algorithm can quite easily be implemented in a computer program. This is probably the simplest way of solving boundary-value problems of this class __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 97–102, January 2006.     

Free vibration of non-uniform nanobeams using Rayleigh–Ritz method

In this article, boundary characteristic orthogonal polynomials have been implemented in the Rayleigh–Ritz method to investigate free vibration of non-uniform Euler–Bernoulli nanobeams based on nonlocal elasticity theory. Non-uniform cross section of nanobeams has been considered by taking linear as well as quadratic variations of Young's modulus and density along the space coordinate. Detailed analysis has been reported for all the possible cases of such variations. The objective of the present study is to analyze the effects of nonlocal parameter, boundary condition, length-to-diameter ratio and non-uniform parameter on the frequency parameters. It is found that clamped nanobeams are having highest frequency parameters than other types of boundary conditions for a particular set of parameters. It is also observed that frequency parameters decrease with increase in scaling effect parameter. First four deflection shapes of non-uniform nanobeams have also been incorporated. In this analysis, some of the new results in terms of boundary conditions have also been included.     

Reverse generalized Bessel matrix differential equation,polynomial solutions,and their properties

This paper is devoted to the study of reverse generalized Bessel matrix polynomials (RGBMPs) within complex analysis. This study is assumed to be a generalization and improvement of the scalar case into the matrix setting. We give a definition of the reverse generalized Bessel matrix polynomials Θ_n(A; B; z), , for parameter (square) matrices A and B, and provide a second‐order matrix differential equations satisfied by these polynomials. Subsequently, a Rodrigues‐type formula, a matrix recurrence relationship, and a pseudo‐generating function are then developed for RGBMPs. © 2013 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.