Application of Nonlinear Fitting and Selection of the Most Fitted Equation by AIC in Stability Test of Pharmaceutical Ingredients

ABSTRACT

We proposed a method for objectively selecting the most fitted rate equation among candidate rate equations based on chemical kinetics by both nonlinear regression analysis and Akaike's information criterion (AIC), to express the decrease of pharmaceutical ingredient as an appropriate equation. Pseudo-zero, first, and second-order rate equations were prepared as candidates beforehand, and AIC was introduced for selecting the most fitted rate equation among the candidates. We compared the proposed method to the Weibull method that expressed any decrease patterns as a single equation.

We quantified the contents of thiamine nitrate (VB1) and taurine after storage for one, three, and six months under 40°C–75% relative humidity by high-pressure liquid chromatography. Decrease patterns of each sample were most fitted to one of the candidate rate equations, that is, pseudo-zero, first, and second-order rate equations, respectively, and the degree of fit in the most fitted equation was superior to that of the Weibull method, except for the pseudo-first-order rate equation.

Moreover, we confirmed that the proposed method was considerably precise for estimating the stability of pharmaceuticals by comparing estimated residual rates and confidence intervals to experimental data.     

Comparison of snow stability tests: Extended column test, rutschblock test and compression test

Several field tests have been proposed in the past for evaluating snow stability. However, few comparative studies have been performed so that presently the advantages and disadvantages of the various tests are partly unclear. During winter 2007–2008 we have collected a dataset of 146 snow profiles, consisting of snow stratigraphy, a rutschblock test (RB), one to two extended column tests (ECT) and in most of the cases also one to two compression tests (CT). Study slopes were classified in regard to stability as either rather stable or rather unstable, based on signs of instability or profile classification. We then studied whether the various tests were able to predict the slope stability class. The CT had an almost perfect probability of detection, but — as the structural stability index (threshold sum) — the CT largely overestimated instability (high proportion of false alarms). Of the small scale tests the ECT was best suited to differentiate between stable and unstable situations. By including the ECT score (number of taps), the number of false alarms was slightly reduced. The performance was similar to the RB which is, however, not independent of the stability classification we used. With two adjoining ECTs it was possible to classify 87% of our test slopes with an accuracy of about 90% into rather stable or rather unstable. Comparing two adjacent stability test results showed that only in about half of the pairs the same weak layer showed up as the most critical one. The snowpack properties (weak layer and slab) that favoured unstable test results for the ECT were associated with whole block releases in the rutschblock test. Thus, the two tests seem to provide similar information possibly related to fracture propagation propensity.     

The stability of long-term trends in the number of traffic fatalities in a sample of highly motorised countries

This paper examines the stability of long-term trends in the number of traffic fatalities in eight highly motorised countries: Norway, Sweden, Denmark, Finland, The Netherlands, Great Britain, Australia and The United States. In all these countries, the number of traffic fatalities reached a peak around 1970-1972 and has since declined. The decline has, however, been irregular and fairly long periods of stagnation or even increase in the number of fatalities have occurred in all countries. A stable trend is defined in this paper as a trend that remains unchanged and therefore can be used to successfully predict the future number of fatalities by means of extrapolation. It is concluded that the trends towards fewer fatalities in the countries selected have not been stable and that even trend lines that fit past trends very closely are usually worthless for predictive purposes. An attempt was made to identify factors influencing long-term trends by fitting negative binomial regression models to fatality data. Although some of the models fitted the data marginally better than simple trend lines, these models are not necessarily more useful for predicting future trends than simple trend lines, since using the models for prediction requires that future changes in all explanatory variables must be predicted. The chief lesson is that past trends do not provide a reliable basis for predicting future developments with respect to the number of traffic fatalities.     

Dynamic analysis of nonlinear membranes by the analog equation method: a boundary-only solution

 A boundary-only solution is presented for dynamic analysis of elastic membranes under large deflections. The solution procedure is based on the analog equation method (AEM). According to this method, the three coupled nonlinear second order hyperbolic partial differential equations in terms of displacements, which govern the response of the membrane, are replaced with three Poisson's quasi-static equations under fictitious time dependent sources. The fictitious sources are established using a BEM-based procedure and the displacements as well as the stress resultants at any point are evaluated from their integrals representations. Numerical examples are presented which illustrate the method. Received 16 December 2000 / Accepted 25 April 2002     

Exponentially fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation and related problems

Exponentially fitted Runge–Kutta methods for the numerical integration of the radial Schrödinger equation or systems of equations of the Schrödinger type and for the numerical solution of other related initial-value problems with periodic or oscillating solutions are developed in this paper. Numerical and theoretical results obtained for several well-known problems show the efficiency of the new methods.     

Structural, optical, and nonlinear optical absorption/refraction studies of the manganese nanoparticles prepared by laser ablation in ethanol

The structural, optical, and nonlinear optical properties of the manganese nanoparticles prepared by laser ablation in various liquids were investigated using the 532 and 1064 nm, 50 ps laser pulses. The TEM and spectral measurements showed temporal dynamics of size distribution of Mn nanoparticles in solutions. The nonlinear absorption (β = 2 × 10⁻¹⁰ and 4 × 10⁻¹¹ cm W⁻¹) and positive nonlinear refraction (γ = 8 × 10⁻¹⁵ and 2 × 10⁻¹⁴ cm² W⁻¹) of picosecond radiation were observed in the Mn colloidal suspensions using the 1064 and 532 nm radiation, respectively     

Application of nonlinear regression in the development of a wide range formulation for HCFC-22

An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based onP--T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Theoretical and numerical aspects of the material and spatial settings in nonlinear electro-elastostatics

The formulation of the spatial and material motion problem in nonlinear electro-elastostatics is revisited in this work. A finite element discretization is realized and a numerical example is presented to demonstrate possible application of the formulation in studying the closing process of cracks.     

Study on the stability and microstructural properties of barium sulfate nanoparticles produced by nanomilling

Barium sulfate nanoparticles were produced by nanomilling in stirred media mill using sodium salt of polyacrylic acid (PAA-Na) as a dispersant. The particles sizes of the ground product obtained in the grinding mill were determined by dynamic light scattering (DLS), Brunauer–Emmet–Teller (BET) nitrogen gas adsorption method, and transmission electron microscopy (TEM). The mean particle size calculated with various methods yielded different values due to the different characterization techniques. The stability of BaSO₄ nanoparticles produced was analyzed by zeta potential measurement and Turbiscan. The stability of barium sulfate nanoparticles was high in presence of dispersant PAA-Na and higher pH values. Further, the changes in microstructural properties, caused by wet grinding and adsorption of PAA-Na on BaSO₄ nanoparticles, were studied using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA). The surface activation and amorphization of BaSO₄ nanoparticles were observed due to increased stresses exerted on the particles during wet grinding.     

非线性滤波CRLB推导及在目标跟踪中的应用

针对可叠加零均值高斯白噪声的非线性滤波,利用无迹变换,推导出理论上的误差性能下界Cramét-Rao Low Bound(CRLB).在利用光电信号对目标进行纯方位角跟踪中,提出一种次优的非线性滤波算法--距离参数化无迹卡尔曼滤波(RPUKF).仿真中将其和距离参数化扩展卡尔曼滤波(RPEKF)的性能曲线以及理论性能下界做了比较.结果表明,两种次优算法的曲线逐渐逼近理论下界,且PRUKF性能更优.     

Study of the nonlinear optical properties and behavior in phenoxy-phthalocyanines liquid at nanosecond laser pulses

The nonlinear optical properties of 2,9,16,23-phenoxy-phthalocyanine (Pc1) and 2,9,16,23-phenoxy-phthalocyanine-zinc (Pc2) in solution were investigated under excitation with nanosecond laser pulses at 532 nm. Based on five-level model, the nonlinear absorption in nanosecond regime was theoretically analyzed. The A-OS and OL behavior of Pc1 and Pc2 were further investigated with the pump–probe technique and transmission measurement technique. The results show that the A-OS response time is determined by the lifetime of the first triplet excited state of molecule, and Pc1 and Pc2 exhibit strong optical limiting effect at nanosecond laser pulses. These studies make the samples a promising possibility for device realization.     

Concentration dependence of the optical limiting and nonlinear light scattering in aqueous suspensions of detonation nanodiamond clusters

Optical limiting (OL) is observed for detonation nanodiamond clusters (ND) suspended in water with mass concentrations of 3–0.01%. By using nanosecond Z-scan measurements at 1064 nm we demonstrate that the nonlinear light scattering strongly contributes to the OL in a wide range of ND concentrations. Moreover we show that the ratio of the nonlinear and linear extinction that can be seen as figure of merit for an optical limiter is a non-monotonous function of the ND concentration. Our analysis reveals that the concentration that corresponds to the optimum OL performance essentially depends on the incident intensity.     

An investigation on the influence of rotary bending and press fitting on stress intensity factors and fatigue crack growth in railway axles

The present paper summarizes the results of fatigue crack growth investigations on a hollow railway axle which were undertaken as a joint research project between the Politecnico di Milano, Italy, and the GKSS Research Centre Geesthacht, Germany, within an activity of ESIS-TC24 (Technical Committee on the Integrity of Railway Structures). Since no analytical stress intensity factor (SIF) solutions for semi-elliptical surface cracks in the S-transitions of railway axles were available, the first step in the research was to generate them for both reverse and rotary bending. The results were then used to investigate both the effects of rotary bending, and, of the press fits at the wheel and gear, on the fatigue crack growth and residual lifetime so as to provide essential input information for setting up inspection intervals. It was found that the effect of rotary bending, although existent, was rather moderate whereas the press fits had a large and detrimental effect.     

高压细水雾灭火系统在地铁车站公共区的应用研究

高压细水雾灭火系统作为扑救火灾的一项新技术,有污染小、安全等优点,但使用时受到火场气流速度的限制。为研究能否将该系统用于地铁车站公共区,本文以地铁车站站台发生火灾为场景,开启地铁车站防排烟系统,测量站台典型点处气流速度;测试结果显示站台内最大风速小于3m/s,在地铁车站公共区应用高压细水雾系统可以满足风速方面的要求;测试数据为进一步开展地铁车站火灾防护研究提供了基础。     

超声早期诊断深部组织损伤及预测压疮预后应用

目的:探究超声早期诊断深部组织损伤及预测压疮预后应用。方法:现将2018年8月至2019年8月来我院接受治疗的14例压疮患者(25处)作为调查对象,分析入组时超声影像学特征对压疮预后的影响,分析临床资料并得出相应的结论。结果:压疮第1次超声检查结果及预后情况25处压疮中,4周后13处(52.0%)压疮治愈,7处(28.0%)压疮分期不变,5处(20.0%)压疮进展。结论:运用超声早期诊断技术发现以及干预深部组织是预防压疮病情恶化最为重要的一步,并在临床实践中取得较为有效的效果,提高早期检出率,建议在临床护理当中积极推广。     

Estimation of the Fraction Defective in Curtailed Sampling Plans by Attributes

In this paper we have obtained the maximum likelihood estimate of the fraction defective (p) under three different sampling plans. Plan 1 considers complete inspection of the sample, Plan 2 considers curtailing of the inspection at the rejection stage and Plan 3 considers curtailing of the inspection at both the acceptance and rejection stages.     

Analysis and stability of the constituents of artichoke and St. John's wort tinctures by HPLC-DAD and HPLC-MS

In continuing our investigations on tinctures, which represent both herbal drug preparations and herbal medicinal products, 40% and 60% v/v tinctures of artichoke and St. John's wort were investigated. Artichoke is largely used in hepatic disorders, while St. John's wort is an anti-inflammatory, antidepressant, and healing agent.

Both herbal drugs contain various constituents, although the compounds responsible for the main effects have not yet been completely identified. However, caffeoylquinic acids and flavones seem to be of crucial importance for the activity of artichoke, as well as flavonoids, naphthodianthrones, and phloroglucinol derivatives for St. John's wort, and they are used as marker constituents. Thus, quantification of all these constituents was performed using high-performance liquid chromatography-diode array detection (HPLC-DAD) and HPLC-mass spectrometry (MS) analyses with rutin as external standard. In addition the stability of the constituents of these tinctures from accelerated and long-term testing was also evaluated. From the results it was evidenced that constituent content depends on the solvent used for the extraction. The stability was also shown to be very different and seems to be related to the water content of the tinctures.     

Comparing HPLC and UV spectrophotometric analysis methods for determining the stability of sorbic acid in nonionic creams containing lactic acid

This paper describes a comparison between ultraviolet (UV) spectrophotometric and high-performance liquid chromatographic (HPLC) methods of analysis for the determination of sorbic acid in nonionic creams containing lactic acid. Sorbic acid is an antimycotic agent and is used as a preservative in pharmaceuticals, cosmetics, and food products. UV spectrophotometric analysis was done by calculating the concentration of remaining sorbic acid from the absorbance values and the molar extinction coefficient E²⁵⁸_M = 24,080. A decrease in absorbance at 258 nm was accompanied by a simultaneous increase in total carbonyls and monoaldehyde content and the appearance of a very weak absorption maximum between 215 and 225 nm. HPLC analysis was done with a Hypersil BDS C₈ column with detection at 254 nm and employing a mobile phase consisting of a mixture of buffer and methanol (7:3 v/v) at a pH of 2.25. The buffer consisted of 0.85% H₂SO₄ in 17.5 mM KH₂PO₄. The validation results, together with statistical treatment of the data, demonstrated the reliability of both procedures. A drawback of the UV methods was, however, its lack of adequate measurement of sorbic acid stability at higher temperatures. For these assays, the HPLC method was found to be adequate, and it should therefore be used to obtain accurate stability data for sorbic acid in creams.     

Thermal post-buckling and the stability boundaries of structurally damped functionally graded panels in supersonic airflows

In this study, the thermal post-buckling behaviors and linear flutter analysis of structurally damped functionally graded (FG) panels under a supersonic airflow are investigated. The material properties are assumed to be temperature-dependent and vary in the thickness direction of the panel. First-order shear-deformation theory (FSDT) is applied to model the panel, and the von Karman strain–displacement relations are adopted to consider the geometric nonlinearity. In addition, the damping is modeled as the Rayleigh damping, and first-order piston theory is applied for the supersonic aerodynamic load. Results are obtained for the thermal post-buckling behavior, and linear flutter analysis of FG panels with a damping effect is performed to search for the origin of the flutter. The numerical data are validated through a comparison with the previous works, and the effects of structural damping are discussed in detail for various cases.     

面向C型货包的短距加速撞击试验装置及应用

目的 为C型货包90 m/s撞击试验提供新的试验方法和手段。方法 采用基于压缩空气驱动和反向牵引的短距加速技术,以及基于阻尼缓冲缸–迪尼玛绳的短距拦阻技术,建立新型高速重载撞击试验方法,并形成试验装置。结果 实现了负载大于5 t、速度大于90 m/s的大质量试件短距发射和撞击。结论 该试验装置与以往常用于C型货包撞击试验的火箭橇和高空缆绳相比,具有占地少、建设成本低、可调性和重复性好、测试方便、运行经济安全等特点,为C型货包的空运事故场景模拟与考核提供了一种新手段,同时也可为其他类型货包或装备的公路、铁路等运输事故场景模拟与考核提供试验技术支撑。