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.     

A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

Stable isotope dilution assay for the accurate determination of tricaine in fish samples by HPLC–MS–MS

Tricaine methanesulfonate is one of most commonly used anesthetics in fish during blood sampling, artificial propagation and long‐distance transportation. In this study, an accurate method for the quantitative determination of tricaine in fish samples by a stable isotope dilution assay coupled with high‐performance liquid chromatography–triple quadrupole mass spectrometry was developed. Tricaine‐D₅ was synthesized and used as an isotopically labeled internal standard for the determination of tricaine. The analytical performance of the method was validated for tricaine determination in marine fish and freshwater fish. The determination of tricaine was linear in the range of 2.0–200.0 μg L^?1. The limit of detection and limit of quantitation for fish muscle tissues were 1.0 and 4.0 μg kg^?1, respectively. Good recoveries were obtained in the range of 92.08–97.50%. The inter‐ and intra‐assay relative standard deviations (RSD values) were investigated, and the values were 0.39–3.01 and 0.85–2.77%, respectively. The values of CCα and CCβ were 10.21–10.43 and 10.42–10.87 μg kg^?1, respectively. The clearance of MS‐222 from grass carp was further studied using our method. The results demonstrate that MS‐222 could be well absorbed and rapidly eliminated after bath administration.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Thermally Stable and Organo-soluble Polyamides Containing Triazine Rings and Ether Linkages in the Main Chain: Synthesis and Characterization

In order to synthesize new polyamide(PA) 5 and copolyamides(Co PA) 7a-7d, a new-type of dicarboxylic acid containing triazine ring was successfully synthesized from 2,4-dichloro-6-methoxy-s-triazine 1 and 4-aminobenzoic acid. New polyamide 5 containing triazine moiety was prepared from 4,4'-(6-methoxy-1,3,5-triazine-2,4-diyl)bis(azanediyl)dibenzoic acid 3 and 4,4′-diaminodiphenylether by direct polycondensation reaction. Then new series thermally stable copolyamides 7a-7d with high solubility in common organic solvents were synthesized from the direct polycondensation reaction of diacid 3 as a first monomer, aliphatic-aromatic diacids 6a-6d as second diacids and 4,4′-diaminodiphenylether. All of the above polymers were fully characterized by 1H-NMR and FTIR spectroscopy, elemental analysis(CHN), inherent viscosity, solubility tests, gel permeation chromatography(GPC), differential scanning calorimetry(DSC) and thermogravimetric analysis(TGA). The resulted Co PAs 7a-7d have shown good inherent viscosities, solubility and thermal properties.     

Establishment and validation of an SIL-IS LC–MS/MS method for the determination of ibuprofen in human plasma and its pharmacokinetic study

In this work, we developed and validated a highly sensitive, rapid and stable LC–MS/MS method for the determination of ibuprofen in human plasma with ibuprofen-d3 as a stable isotopically labeled internal standard (SIL-IS). Human plasma samples were prepared by one-step protein precipitation. The chromatographic separation was achieved on a Poroshell 120 EC-C₁₈ (2.1 × 50 mm, 2.7 μm). Aqueous solution (containing 0.05% acetic acid and 5 mm NH₄Ac) and methanol were selected as the mobile phase with gradient elution. An electrospray ionization source was applied and operated in negative ion mode. Multiple reaction monitoring mode was used for quantification using target fragment ions m/z 205.0 → 161.1 for ibuprofen and m/z 208.0 → 164.0 for SIL-IS, respectively. This method exhibited a linear range of 0.05–36 μg/ml for ibuprofen with correlation coefficient >0.99. Mean recoveries of ibuprofen in human plasma ranged from 78.4 to 80.9%. The RSD of intra- and inter-day precision were both < 5%. The accuracy was between 88.2 and 103.67%. The matrix effect was negligible in human plasma, including lipidemia and hemolytic plasma. A simple, efficient and accurate LC–MS/MS method was successfully established and applied to a pharmacokinetic study in healthy Chinese volunteers after a single oral administration of ibuprofen granules.