On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations

In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone iterative technique together with upper and lower solutions, conditions for the existence and approximation of minimal and maximal solutions to the BVP under consideration are constructed. Some adequate results for different kinds of Ulam stability are investigated. Maximum error estimates for the corresponding solutions are given as well. Two examples are provided to illustrate the results.     

A correction method for finding lower bounds of eigenvalues of the second‐order elliptic and Stokes operators

In this paper, for the second‐order elliptic and Stokes eigenvalue problems with variable coefficients, we propose a correction method to nonconforming eigenvalue approximations and prove that the corrected eigenvalues converge to the exact ones asymptotically from below. In particular, the asymptotic lower bound property of corrected eigenvalues is always valid whether the eigenfunctions are smooth or singular. Finally, we prove that the convergence order of corrected eigenvalues is still the same as that of uncorrected eigenvalues.     

慢增长的Laplace-Stieltjes变换的逼近

主要研究了全平面内收敛的Laplace-Stieltjes变换所表示的有限对数级整函数的增长性与逼近问题,得到了涉及对数级、对数型、Laplace-Stieltjes变换的系数与误差算子的若干定理,推广了罗茜,孔荫莹,Singhal和Srivastava等人的结果.     

图的区间边着色的收缩图方法

图G的一个用了颜色1,2,…,t的边着色称为区间t-着色,如果所有t种颜色都被用到,并且关联于G的同一个顶点的边上的颜色是各不相同的,且这些颜色构成了一个连续的整数区间.G称作是可区间着色的,如果对某个正整数t,G有一个区间t-着色.所有可区间着色的图构成的集合记作■.对图G∈■,使得G有一个区间t-着色的t的最小值和最大值分别记作ω(G)和W(G).现给出了图的区间着色的收缩图方法.利用此方法,我们对双圈图G∈■,证明了ω(G)=△(G)或△(G)+1,并且完全确定了ω(G)=△(G)及ω(G)=△(G)+1的双圈图类.     

下肢静脉曲张腔内激光治疗与传统剥脱手术治疗的远期疗效对比研究

目的 比较静脉腔内激光治疗（EVLT）和传统剥脱手术治疗下肢静脉曲张（VVLE）的远期疗效。方法 选取VVLE患者120例,随机分为EVLT 组与对照组,每组各60例。EVLT组采用EVLT治疗,对照组采用传统剥脱手术治疗。分别对两组患者手术并发症、术后1、2、3 年复发率以及术后生活质量进行对比评价。结果 术后3 个月EVLT 组患者生活质量调查表（CIVIQ）评分显著高于对照组（P＜0.05）,术后6 个月两组患者CIVIQ 评分比较则无统计学差异（P＞0.05）。EVLT 组患者术后皮下瘀血、感觉麻木、硬结、皮下脂肪液化感染的发生率均显著低于对照组（均P＜0.01）,皮肤灼伤的发生率则高于对照组（P＜0.05）,两组患者静脉炎的发生率无统计学差异（P＞0.05）;两组患者术后1、2、3年复发率比较均无统计学差异（均P＞0.05）。结论 应用EVLT治疗VVLE 手术并发症少,患者术后恢复较快,远期疗效理想,值得临床推广应用。     

On the number of cusps on cuspidal curves on Hirzebruch surfaces

In this article we give an upper bound for the number of cusps on a cuspidal curve on a Hirzebruch surface. We adapt the results that have been found for a similar question asked for cuspidal curves on the projective plane, and restate the results in this new setting.     

Lower bounds of eigenvalues of the biharmonic operators by the rectangular Morley element methods

In this article, we analyze the lower bound property of the discrete eigenvalues by the rectangular Morley elements of the biharmonic operators in both two dimension (2D) and three dimension (3D). The analysis relies on an identity for the errors of eigenvalues. We explore a refined property of the canonical interpolation operators and use it to analyze the key term in this identity. In particular, we show that such a term is of higher order for 2D, and is negative and of second order for 3D, which causes a main difficulty. To overcome it, we propose a novel decomposition of the first term in the aforementioned identity. Finally, we establish a saturation condition to show that the discrete eigenvalues are smaller than the exact ones. We present some numerical results to demonstrate the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1623–1644, 2015     

Highly sensitive capillary electrophoresis-mass spectrometry for rapid screening and accurate quantitation of drugs of abuse in urine

The combination of capillary electrophoresis (CE) and mass spectrometry (MS) is particularly well adapted to bioanalysis due to its high separation efficiency, selectivity, and sensitivity; its short analytical time; and its low solvent and sample consumption. For clinical and forensic toxicology, a two-step analysis is usually performed: first, a screening step for compound identification, and second, confirmation and/or accurate quantitation in cases of presumed positive results. In this study, a fast and sensitive CE-MS workflow was developed for the screening and quantitation of drugs of abuse in urine samples. A CE with a time-of-flight MS (CE-TOF/MS) screening method was developed using a simple urine dilution and on-line sample preconcentration with pH-mediated stacking. The sample stacking allowed for a high loading capacity (20.5% of the capillary length), leading to limits of detection as low as 2 ng mL⁻¹ for drugs of abuse. Compound quantitation of positive samples was performed by CE-MS/MS with a triple quadrupole MS equipped with an adapted triple-tube sprayer and an electrospray ionization (ESI) source. The CE-ESI-MS/MS method was validated for two model compounds, cocaine (COC) and methadone (MTD), according to the Guidance of the Food and Drug Administration. The quantitative performance was evaluated for selectivity, response function, the lower limit of quantitation, trueness, precision, and accuracy. COC and MTD detection in urine samples was determined to be accurate over the range of 10–1000 ng mL⁻¹ and 21–1000 ng mL⁻¹, respectively.     

A Novel Nanocomposite Hydrogel with Precisely Tunable UCST and LCST

Novel thermosensitive nanocomposite (NC) hydrogels consisting of organic/inorganic networks are prepared via in situ free radical polymerization of 2‐(2‐methoxyethoxy) ethyl methacrylate (MEO₂MA) and oligo(ethylene glycol) methacrylate (OEGMA) in the presence of inorganic cross‐linker clay in aqueous solution. The obtained clay/P(MEO₂MA‐co‐OEGMA) hydrogels exhibit double volume phase transition temperatures, an upper critical solution temperature (UCST), and a lower critical solution temperature (LCST), which can be controlled between 5 and 85 °C by varying the fraction of OEGMA units and the weight percentage of cross‐linker clay. These new types of NC hydrogels with excellent reversible thermosensitivity are promising for temperature‐sensitive applications such as smart optical switches.

     

Banach空间中—类四阶常微分方程两点边值问题的最大解和最小解存在性

通过建立比较定理，利用半序与上下解方法，在Banach空间研究了源弹性梁的—类四阶常微分方程两点边值问题的最大解与最小解的存在性．