On the Moments of Overflow and Freed Carried Traffic for the GI/M/C/0 System

In circuit-switched networks call streams are characterized by their mean and peakedness (two-moment method). The GI/M/C/0 system is used to model a single link, where the GI-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a GI/M/C/0 system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d. holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used. The main result of this paper is a numerically stable and efficient algorithm for computing the moments of freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.     

关于阶乘的Erds-Stewart猜想

摘要:设n是正整数;P_0=1,P_i(i=1,2,…)是第i个素数.本文证明了:方程 n!+1=P_k~aP_(k+1)~b,P_(k-1)0,b>0,仅有解(n,P_k,P_(k+1),a,b)=(1,1,2,1,0),(2,3,5,1,0),(3,5,7,0,1),(4,5,7,2,0),(5,7,11,0,2).上述结果证实了Erds和Stewart提出的一个猜想.     

A statistical model for the optimization of dsc performance in the evaluation of drugs for preformulation studies

Differential scanning calorimetry (DSC) is a thermal analytical tool for preformulation studies. Extrapolated melting temperature (T_P) and heat of fusion (ΔH_f) can be used as parameters for optimizing the DSC performance. Two model pharmaceuticals acetaminophen and nicotinamide are used in this study. Using a factorial design for the experimental model and matrix analysis the results, the effect of sample mass, heating rate and the nitrogen flow rate were evaluated on the ΔH_f values and T_P values. Two levels for each of the procedural variables were used as a balanced experimental design with two sample sizes, two heating rates and two nitrogen flow rates. It was found that the change in the heating rate caused significant changes in the ΔH_f values but not the T_p values for acetaminophen. However, no significant effect was found for the T_p value but ΔH_f value was affected to a certain extent for nicotinamide.     

Investigation of the limitations of saturated fractional factorial experimental designs,with confounding effects for an HPLC ruggedness test

Summary Recently much attention has been directed to the validation of analytical methods. The level of validation will depend on the method application. If a method is developed for general use, for instance by different analysts, instruments or laboratories, then the effect of these changes need evaluation. This is normally referred to as ruggedness testing, where the limitations of the method to changes in the specified conditions are examined.This paper examines the use of Plackett-Burman fractional factorial experiment designs for ruggedness testing in high performance liquid chromatography (HPLC). The ability of these designs to identify confounding effects is applied to the stability indicating analysis of Salbutamol and its major degradation product, AH4045. The results show that confounding effects, proving extremely pertinent to HPLC, can be identified.The assay proved rugged to most tested changes although not to the use of column packing material from different manufacturers.     

Application of a Factorial Design Method to Determine the Accuracy of a Solution to an Inverse Heat Conduction Problem

A numerical/experimental inverse procedure was employed to estimate the temperature-dependent thermal conductivity of a solid body in which 1D heat conduction in a top heated cylindrical sample is assumed. The emphasis is focused on the issue of sensitivity of results to selected assumptions made in inverse calculations. It has been found that the accuracy of heat capacity evaluation brings the largest contribution to final errors (up to 74%). Density accounts for one-fourth to one-third of the total error of determination. The failure to ensure unidirectional heat conduction in a sample during an experiment is important only at elevated temperatures.     

Effect of polymer and ion concentration on mechanical and drug release behavior of gellan hydrogels using factorial design

Developing optimized hydrogel products requires an in-depth understanding of the mechanisms that drive hydrogel tunability. Here, we performed a full 4 × 4 factorial design study investigating the impact of gellan, a naturally derived polysaccharide (1%, 2%, 3%, or 4% w/v) and CaCl₂ concentration (1, 3, 7, or 10 mM) on the viscoelastic, swelling, and drug release behavior of gellan hydrogels containing a model drug, vancomycin. These concentrations were chosen to specifically provide insight into gellan hydrogel behavior for formulations utilizing polymer and salt concentrations expanding beyond those commonly reported by previous studies exploring gellan. With increasing gellan and CaCl₂ concentration, the hydrogel storage moduli (0.1–100 kPa) followed a power-law relationship and on average these hydrogels had higher liquid absorption capability and greater total drug release over 6 days. We suggest that the effects of gellan and CaCl₂ concentration and their interactions on hydrogel properties can be explained by various phenomena that lead to increased swelling and increased resistance to network expansion.     

HPLC–PDA identification and resolution of rufinamide forced degradation impurities: A congregated chemometric expedite optimization coupled with factorials and desirability

Rufinamide is used presently to treat Lenaux–Gastaut syndrome. A full factorial design and desirability approach was investigated for the optimization of hydrolytic stress via response surface curves (RSCs). The degradation impurities were identified and resolved using reversed-phase high-performance liquid chromatography (RP-HPLC) on the Qualisil® BDS C₈ column. Acetonitrile–water (29:71, v/v) was optimized for the mobile phase and used at a flow rate of 1.0 ml/min with detection at a wavelength of 230 nm. Rufinamide showed appreciable susceptibility to hydrolysis under acidic and alkaline stress, and substantial degradation in the neutral condition. It degraded much less under oxidative stress. Exposure towards thermal and photolytic stress conditions indicated appreciable stability. The developed method was subjected to validation as per the recommendations of the International Conference on Harmonization. The proposed method showed no influence from the excipients and the degradation products. As well as good precision and accuracy in determination, the method showed a linear response between 2 and 12 μg ml⁻¹. The method was extended for determination in a human plasma sample, which resulted in excellent recovery without interference from matrix effects. The combined use of desirability and design for the optimization of acidic and alkaline hydrolytic stress led to simple and rapid analysis.     

Highly sensitive ion preconcentration method based on flow sorbent extraction using multiwall carbon nanotubes

In this work a solid phase on-line uranium ion preconcentration system coupled with spectrophotometry has been developed. The method is based on uranyl ion preconcentration at pH 3.75 onto multiwall carbon nanotubes treated with HNO₃. After preconcentration, the uranyl ions are eluted with 0.32?mol?L^?1HCl followed by reaction with 3,6-bis[(2-arsonophenyl)-azo]-4,5-dihydroxy-2,7-naphthalendisulfonic acid 0.08%[w/v] (Arsenazo III), which had maximum monitored absorbance of 650?nm. Effects of the pertinent experimental parameters on the system were investigated by means of 2^6?2 fractional factorial design, while optimization was carried out using the Doehlert matrix. Under optimized conditions, detection and quantification limits were found to be 0.21 and 0.7?µg?L^?1, respectively. The analytical curve ranged from 5 to 150?µg?L^?1 (r?=?0.998), while the relative standard deviations (RSD) were 3.27 and 2.56% for the respective uranium concentrations of 10 and 100?µg?L^?1 (n?=?10). The features obtained for the on-line preconcentration system were: preconcentration factor of 228, concentration efficiency of 57?min^?1, consumption index of 0.13?mL and sample throughput of 15?h^?1. In order to assess the accuracy of the proposed method, addition and recovery studies were carried out on spring water samples from different sources and synthetic seawater with satisfactory results ranging from 94.85 up to 103.65%.     

A Factorial Design Approach for Hydrothermal Synthesis of Phase‐Pure AgInO2: A Parametric Optimization Study

Owing to a wide range of industrial applications and fundamental importance, delafossite compounds have gathered tremendous interest in research community. In this study, the formation of hexagonal nanoplates of AgInO₂ mainly dominated by (00l) facets with no metallic Ag impurity, reported using a facile hydrothermal route at 180 °C using KOH as mineralizer by adopting a factorial design approach. Rietveld analysis of the powder XRD pattern and SAED confirms the rhombohedral system of AgInO₂. FE‐SEM image shows a uniform hexagonal plate‐like morphology with an average width of about 300 nm and thickness of 70 nm. XPS and EDX analysis confirm potassium ion free AgInO₂. A specific surface area of about 48.5 m² g^?1 is arrived from N₂ adsorption studies. Temperature‐dependent AC impedance measurements revealed an activation energy of 0.24 eV/f.u. Further, TG‐DTA studies found that the compound is stable in air up to 595 °C.