Dynamic stability of a class of fractional-order nonlinear systems via fixed point theory

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in $\left(\frac{1}{2},1\right)$. However, the case of the fractional-order belonging to $(0,\frac{1}{2})$ has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.     

An improved LC–MS/MS method for determination of docetaxel and its application to population pharmacokinetic study in Chinese cancer patients

Because of its unpredictable side effects and efficacy, the anticancer drug docetaxel (DTX) requires improved characterisation of its pharmacokinetic profiles through population pharmacokinetic studies. A sensitive and rugged LC–MS/MS method for the detection of DTX in human plasma was developed and optimised using paclitaxel as an internal standard (IS). The plasma samples underwent rapid extraction using hybrid solid-phase extraction-protein precipitation. The analyte and IS were separated with an isocratic system on a Zorbax Eclipse Plus C₁₈ column using water containing 0.05% acetic acid along with 20 μM of sodium acetate and methanol (30/70, v/v) as the mobile phase. Quantification was performed using a triple quadrupole mass spectrometer through multiple reaction monitoring in positive mode, using the m/z 830.3 → 548.8 and m/z 876.3 → 307.7 transitions for DTX and paclitaxel, respectively. The range of the calibration curve was 1–500 ng/mL for DTX, and the linear correlation coefficient was >0.99. The accuracies ranged from −4.6 to 4.2%, and the precision was no higher than 7.0% for the analytes. No significant matrix effect was observed. Both DTX and the IS showed considerable recovery. This method was finally applied to the establishment of a population pharmacokinetic model to optimise the clinical use of DTX.     

A sufficient condition for stability using slopes of isoclines in planar mappings

Coupled planar maps are often parameter dependent, with the stability of their fixed points depending on the values of the parameters chosen. As the magnitude of the eigenvalues is difficult to determine when the number of parameters is large, one commonly uses instead the Jury conditions for the Jacobian, but even this can present difficulties. In this paper, we will show a simpler sufficient criteria for local asymptotic stability that follows by comparing slopes of isoclines.     

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.     

Genetic diversity and haplotype structure of 21 Y‐STRs,including nine noncore loci,in South Tunisian Population: Forensic relevance

Y chromosome STRs (Y‐STRs) are being used frequently in forensic laboratories. Previous studies of Y‐STR polymorphisms in different groups of the Tunisian population identified low levels of diversity and discrimination capacity (DC) using various commercial marker sets. This definitely limits the use of such systems for Y‐STRs genotyping in Tunisia. In our investigation on South Tunisia, 200 unrelated males were typed for the 12 conventional Y‐STRs included in the PowerPlex® Y System. Additional set of nine noncore Y‐STRs including DYS446, DYS456, DYS458, DYS388, DYS444, DYS445, DYS449, DYS710, and DYS464 markers were genotyped and evaluated for their potential in improving DC. Allele frequency, gene diversity, haplotype diversity (HD), and DC calculation revealed that DYS464 was the most diverse marker followed by DYS710 and DYS449 markers. The standard panel of 12 Y‐STRs (DC = 80.5%) and the nine markers were combined to obtain DC of 99%. Among the 198 different haplotypes observed, 196 haplotypes were unique (HD = 99.999). Out of the nine noncore set, six Y‐STRs (DYS458, DYS456, DYS449, DYS710, DYS444, and DYS464) had the greatest impact on enhancing DC. Our data provided putative Y‐STRs combination to be used for genetic and forensic applications.     

重力场流分离系统用于聚苯乙烯颗粒的分离条件优化

重力场流分离是最简单的场流分离(gravitational flow-field fractionation,GrFFF)技术,常用于分离粒径几微米到几十微米的颗粒及生物样品。利用自组装加工的重力场流分离仪器分离3种不同粒径(3、6、20μm)的聚苯乙烯(PS)颗粒。自制了一种混合表面活性剂,并与商品化的表面活性剂FL-70进行了比较。通过均匀设计优化流速、混合表面活性剂中聚乙二醇辛基苯基醚(Triton X-100)的质量分数、载液黏度、停流时间等分离条件,以分离度(Rs)和保留比(R)为评价指标,发现FL-70的分离效能略优于自制的混合表面活性剂,可实现3种PS颗粒的完全分离(Rs1为1.771,Rs2为2.074)。结果表明该系统具有良好的分离性能。     

去甲万古霉素群体药代动力学与药效学优化研究

目的研究去甲万古霉素群体药代动力学指标差异,对患者进行药效学优化。方法选取2015年1月至2015年12月268例感染患者,将其按照年龄分为中青年组和老年组,每组各134例,采用群体药代动力学和药效学优化公式进行计算,分析患者上述指标差异。结果青年组与老年组的群体药代动力学各项指标差异明显具有统计学意义(P0.05)。结论感染患者通过去甲万古霉素药物治疗疗效确切,对革兰阳性菌的杀灭作用明显,采用群体药代动力学和药效学研究后发现,AUC24/MIC能够作为去甲万古霉素的应用指标,并以此指导临床用药效果显著,值得临床应用推广。     

A Hybrid Finite Volume Method for Advection Equations and Its Applications in Population Dynamics

We present in this article a very adapted finite volume numerical scheme for transport type‐equation. The scheme is an hybrid one combining an anti‐dissipative method with down‐winding approach for the flux (Després and Lagoutière, C R Acad Sci Paris Sér I Math 328(10) (1999), 939–944; Goudon, Lagoutière, and Tine, Math Method Appl Sci 23(7) (2013), 1177–1215) and an high accurate method as the WENO5 one (Jiang and Shu, J Comput Phys 126 (1996), 202–228). The main goal is to construct a scheme able to capture in exact way the numerical solution of transport type‐equation without artifact like numerical diffusion or without “stairs” like oscillations and this for any regular or discontinuous initial distribution. This kind of numerical hybrid scheme is very suitable when properties on the long term asymptotic behavior of the solution are of central importance in the modeling what is often the case in context of population dynamics where the final distribution of the considered population and its mass preservation relation are required for prediction. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1114–1142, 2017